Electromagnetic modeling of noise interactions in packaged electronics using the partial element equivalent circuit formulation

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ELECTROMAGNETIC MODELING OF NOISE INTERAC­ TIONS IN PACKAGED ELECTRONICS USING THE PAR­ TIAL ELEMENT EQUIVALENT CIRCUIT FORMULATION

by William Patrick Pinello

A Dissertation Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY

In the Graduate College THE UNIVERSITY OF ARIZONA 199 7 DMI NTjmber; 9817341

Copyright 1998 by Pinello, William Patrick

All rights reserved.

UMI Microform 9817341 Copyright 1998, by UMI Company. All rights reserved.

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UMI 300 North Zeeb Road Ann Arbor, MI 48103 THE UNIVERSITY OF ARIZONA » GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have

read the dissertation prepared by William Patrick Pinello

entitled Electromagnetic Modeling of Noise Interactions In Packaged

Electronics Using The Partial Element Equivalent Circuit

Formulation

and recommend that it be accepted as fulfilling the dissertation

requirement for the Degree of Doctor of Philosophy

la/io/qy Andreas/^C. I±ati6 , . Date izjiilQi Kathleen L. Virga ^ J Date

iteven L. Dvorak Date

Date

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

l.a/io/M7 DissertatiDTr"D5r^crttfr Date Andreas C. Cangellaris 3

STATEMENT BY AUTHOR

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TABLE OF CONTENTS

LIST OF FIGURES 6

LIST OF TABLES 8

ABSTRACT 9

1. INTRODUCTION 10

2. THE PARTIAL ELEMENT EQUIVALENT CIRCUIT METHOD 16 2.1. Development of the Electric Field Integral Equation 21 2.2. Derivation of the Partial Element Equivalent Circuit Model 25 2.2.1. Discrete Models used to Approximate Current Flow 27 2.2.2. Discretization of the Electric Field Integral Equation 33 2.3. Modified Nodal Analysis 43 2.3.1. Semi-Condensed Modified Nodal Analysis 46 2.3.2. Condensed Modified Nodal Analysis 48 2.3.3. Modified Loop Analysis 50 2.3.4. Comparison of Reduced Modified Nodal Analysis Schemes 53 2.4. Partial Inductances 56 2.4.1. Partial Self Inductance of a Filament 57 2.4.2. Partial Mutual Inductance Between Two Filaments 60 2.4.3. Calculation of Partial Inductances 61 2.5. Partial Coefficients of Potential 62 2.6. Equivalent Circuits for Skin-Effect Models 66

3. EXTENSIONS AND REDUCED FORMS OF PEEC MODELS 73 3.1. Incident Fields 74 3.2. Dielectric Modeis 75 3.3. Image Problem 78 3.4. Far-Field Calculation 83 3.5. Hierarchical Electromagnetic Modeling 85

4. TRANSIENT ANALYSIS 100 4.1. Numerical Integration Methods 101 4.1.1. The Backward Euler Method 102 4.1.2. The Theta Method 106 4.2. Numerical Stability 108 4.2.1. The Phase Grid Approach 109 4.2.2. The Alternating Green's Function Approach 113 4.2.3. Evaluation of Stability Improvement Using PGA and AGFA 114 4.3. Waveform Relaxation 120

5. NUMERICAL RESULTS 123 5.1. High Frequency Effects Associated with Modeling Split and Solid Ground Planes 124 5.2. Characterization of Noise in Printed Circuit Boards 127 5.3. Imbalances Encountered in Single Chip Packages 132

6. CONCLUSIONS AND FUTURE WORK 137

A. CIRCUIT STAMPS FOR MODIFIED NODAL ANALYSIS 141

REFERENCES 151 5

LIST OF FIGURES

2.1. rV'Cs and CSCs for ID model 29 2.2. rVCs and CSCs for ID model taking into account skin-effect along width 29 2.3. rVCs and CSCs for ID model taking into account skin-effect along width and thick­ ness 29 2.4. rVCs and CSCs for 2D model with L-directed current taking into account skin-effect along thickness 30 2.5. rVCs and CSCs for 2D model with W-directed current taking into account skin-effect along thickness 30 2.6. rVCs and CSCs for 2D model with L-directed current 31 2.7. IVCs and CSCs for 2D model with W-directed current 31 2.8. rVCs and CSCs for 3D model with L-directed current 31 2.9. IVCs and CSCs for 3D model with W-directed current 32 2.10. IVCs and CSCs for 3D model with T-directed current 32 2.11. Placement of CVCs surrounding an IVC 37 2.12. Equivalent circuit for PEEC model in Fig. 2.13 40 2.13. Simple PEEC model with two IVCs and three CVCs 40 2.14. Equivalent circuit for PEEC model in Fig. 2.13 (including capacitive coupling mod­ el) 43 2.15. Equivalent circuit used for MNA solution 45 2.16. Equivalent circuit used for cMNA solution 49 2.17. Norton equivalent circuit used in MLA 51 2.18. Equivalent circuit used for MLA solution 52 2.19. CVC and adjacent inductors for PEEC model with 3D current 55 2.20. Partial self-inductance for rectangular conductors 59 2.21. Partitioning of conductors and 60 2.22. Cells oriented in parallel 63 2.23. Cells oriented perpendicular to each other 64 2.24. Discrete model for 2D current flow 67 2.25. Equivalent circuit for PEEC model in Fig. 2.24 68 2.26. First order 2D PEEC skin-effect model 69 2.27. Second order 2D PEEC skin-effect model 70 2.28. Third order 2D PEEC skin-effect model 71 3.1. Transformation to image currents and voltages 78 3.2. PEEC model before applying image theory 80 3.3. PEEC model after applying image theory 81 /

3.4. Hierarchy for PEEC conductor models 86 3.5. Short-circuited coplanar waveguide 88 3.6. SPICE transmission-line model for coplanar waveguide 89 3.7. PEEC model for coplanar waveguide 89 3.8. Comparison of PEEC and SPICE transmission-line responses 90 3.9. Far-field response for coplanar waveguide 91 3.10. Coplanar waveguide with a right-angle bend 92 3.11. Source currents (PEEC) for coplanar waveguide with right-angle bend 92 3.12. Hybrid PEEC/SPICE transmission-line model of a coplanar waveguide with right- angle bend 93 3.13. Source currents (Hybrid/PEEC) for coplanar waveguide with right-angle bend .94 3.14. Effect of changing the length of the SPICE transmission-line 95 3.15. Far-field response for coplanar waveguide with a right-angle bend 96 3.16. Generic mixed analog/digital system 97 3.17. Voltage across capacitor on left end for lines driven simultaneously 98 3.18. Voltage across input to antenna 99 4.1. Example of instability observed when using () PEEC 108 4.2. Stabilization of 0.9 x 1.0 cm patch using PGA 112 4.3. Effect of time-step on stability for 0 PEEC 116 4.4. Resistors in parallel with partial mutual inductors 117 4.5. Stability enhancement of PGA vs. time-step 118 4.6. Stability enhancement of AGFA vs. coupling radius 119 5.1. Interconnect above a solid ground plane 125 5.2. Input impedance for active line above a solid ground plane 126 5.3. Interconnect above a split ground plane 126 5.4. Input impedance for active line above a split ground plane 128 5.5. Geometry for example 2 128 5.6. Voltage across the load resistor of the antenna in Fig. 5.5 calculated without the short­ ing pin 130 5.7. Voltage across the load resistor of the antenna in Fig. 5.5 calculated with the shorting pin 131 5.8. Current distribution on the conductors of the structure in Fig. 5.5 at f=1.67GHz. .132 5.9. Geometry for example 3 (Case I) 132 5.10. Geometry for example 3 (Case 2) 133 5.11. Common mode currents 134 5.12. Current flowing through ground path 135 8

LIST OF TABLES

2.1. Overhead compared to MLA associated with solving large PEEC models 54 4.1. Comparison of convergence with and without retardation 121 9

ABSTRACT

The Partial Element Equivalent Circuit method is used to develop a flexible, hierarchical electromagnetic modeling and simulation environment for the analysis of noise generation and signal degradation mechanisms in packaged electronic components and systems. The circuit-oriented approach used by the method for the development of the numerical approximation of the electric field integral equation is used to develop a SPICE-compati- ble. yet fully dynamic, discrete approximation of the electromagnetic problem. Contrary to other full-wave formulations, the proposed method has the important attribute of lend­ ing itself to a very systematic and physical model complexity reduction on the basis of the electrical size of the various portions of the system. Thus, a hybrid electromagnetic model­ ing and simulation environment is established for the analysis of complex structures, which exhibit large variation in electrical size over their volume, using a combination of lumped circuit elements, transmission lines, as well as three-dimensional distributed elec­ tromagnetic models which may or may not account for retardation, depending on the elec­ trical size of the part of the structure that is being modeled. These special attributes of the proposed electromagnetic simulation environment are demonstrated through several examples from its application to the modeling of noise interactions in generic interconnect and package geometries. 10

CHAPTER 1

INTRODUCTION

Transient electromagnetic field solvers have had a significant impact on our ability to

model package- and interconnect-induced noise interactions in high-speed digital elec­ tronic systems. Contrary to transmission-line based simulation, the electromagnetic effects associated with the three-dimensional character of the structures can be modeled accu­ rately by such simulators. Consequently, in addition to crosstalk, propagation delay, and reflections, the impact of radiation losses due to unbalanced interconnects or other discon­ tinuities in the interconnect and power/ground plane structures on signal distortion and internal and external electromagnetic compatibility of the component can be predicted and analyzed. Transient electromagnetic simulators, in particular, can be used for nonlinear electromagnetic analysis. Such simulation capability is important for accurate radiated emissions prediction from high-speed digital electronic systems, and for electromagnetic noise analysis of mixed digital/analog/RP integrated circuits. Both the Finite-Difference

Time-Domain (FDTD) method and the Transmission Line Matrix (TLM) method have been used successfully for such nonlinear electromagnetic simulations [l]-[5].

Time-domain mtegral equation-based formulations are also suitable for nonlinear elec­ tromagnetic analysis. However, the numerical, late-time instability exhibited by such for­ 11

mulations has prevented their extensive application to transient simulation of electromagnetic systems. Following several years of research activity, the reasons for the numerical instability are now fairly well understood, and several approaches have been proposed for its prevention (e.g. [6]-[10]).

Of particular interest to RF/microwave and high-frequency, high-speed, mixed-signal circuit electrical analysis is the Partial Element Equivalent Circuit (PEEC) formulation of the time-domain electric field integral equation [11]. The reason for this is that this formu­ lation results in a circuit model for the electromagnetic problem under study which includes all retardation effects and is compatible with nonlinear circuit simulators such as

SPICE. Consequently, full-wave electromagnetic modeling within a SPICE-like, nonlin­ ear, circuit simulation environment can be effected in a straightforward manner. Further­ more, once the PEEC model for an electromagnetic system has been developed, a systematic procedure can be used to reduce its complexity, taking into account the charac­ teristic times over which the system response is sought, or, equivalently, the electrical size of the structure under study. To elaborate further, consider the case where the characteris­ tic time of the excitation (i.e. the rise time of a pulsed excitation or the period of a time- harmonic excitation) is such that useful wavelengths are much larger than the spatial extent of the system. Under such conditions, all retardation effects can be neglected.

Moreover, such model complexity reduction can be effected in a selective fashion over those parts of the structure where the aforementioned electrical size constraints are valid.

This attribute of the PEEC formulation is extremely useful when the size or complexity of 12

the structure is such that the number of degrees of freedom used in the numerical approxi­

mation is much larger than the one required for acceptable engineering accuracy of the

simulation results. Clearly, this is the case for packaged electronics. These systems are

very representative cases of multi-scale electromagnetic structures in the sense that they exhibit large variability in the electrical size of their various components and subsystems.

In addition, finite difference techniques such as FDTD require oversampling in space in die sense that the grid size should be chosen fine enough to resolve the smallest of the fea­ tures relevant to the proper description of the structure. This usually results in extremely large computational burden. On the other hand, integral equation techniques such as PEEC involve the discretization of only the conducting bodies. This results in a huge savings when compared to FDTD.

In the following chapters, a framework will be presented for the development of com­ puter aided design (CAD) of high-speed electronics for the 21^' century. Typically, when systems are designed, the analysis is performed using network or full-wave analysis. How­ ever, the recent increase in hybridized systems necessitated a merger between these two levels of analysis. There have been many successful attempts, however all seem to fall short when both efficiency and accuracy are considered. PEEC offers an alternate solution to this problem by allowing for the seamless integration of the elements used for network analysis in a full-wave simulation environment. This seamless integration is accomplished through the generation of equivalent circuit elements corresponding to the conducting bodies and the subsequent insertion of the results into the network topology description. 13

This way, portions of the system attributing to the full-wave characteristics can be inter­

faced with portions of the system consistent with basic circuit theory. Thus PEEC ulti­

mately provides a mechanism through which no additional approximations is required and

no loss in efficiency is expected.

The background and formulation of the PEEC method is discussed in Chapter 2. This

discussion details the development of the PEEC model starting with Maxwell's equations

and ending with an equivalent circuit model and methods for its solution. In addition,

guidelines are given for the calculation of the equivalent inductances, resistances, and

potential coefficients all of which make up a PEEC model. The methods of solution dis­

cussed include the one used in most variants of SPICE as well as more sophisticated and

complex, yet computationally efficient, approaches. Finally, details are given for the mod­

eling of conducting traces when skin-effect has to be considered.

Chapter 3 gives an overview of extensions to the basic PEEC formulation which consid­

ers lossy conductor in homogeneous space. The first extension discussed is the modifica­

tion to the PEEC model when it is in the presence of an applied external electric field.

Second, the formulation of dielectrics is provided for the characterization of inhomoge-

neous systems. It is shown that a dielectric PEEC model is very similar to a conducting

PEEC model. Intuitively, this is appeasing since conductors allow for conduction current

and dielectrics allow for displacement current. Third, the solution of PEEC models is dis­ cussed when an image plane is introduced. This is very appealing since image theory

allows for the elimination of planes which inherently cause a tremendous computational 14

burden. Fourth, the formulation is included for the calculation of the electric field when

using the far-field approximation. Lastly, a framework is discussed for the selective reduc­

tion in complexity of systems which include PEEC models. This idea is key for the rapid

solution of complex integrated designs. Moreover, this ability for reduction in complexity,

coupled with the seamless integration of network and full-wave designs, make PEEC the

clear choice for the next generation of electronic CAD tools. Definitely, this hybrid or

EM-SPICE approach provides a powerful solution to electromagnetic designs ranging

from antenna to board-level to package-level to ic-Ievel design.

Chapter 4 details the solution of PEEC models in the time-domain. An overview is given of two simple methods for the numerical integration of the resulting system of ordinary differential equations. Next, the issue of stability is discussed for PEEC solutions which are consistent with a full-wave approximation to Maxwell's equations. Methods for the elimination of instability as well as insight into its behavior are given. Lastly, waveform

relaxation is introduced. This techniques allows for the partitioning of PEEC, or any cir­ cuit model for that matter, for an iterative solution. Waveform relaxation is especially use­ ful for the reduction of a large problem into a set of smaller problems thus allowing for an efficient solution on a distributed computing environment.

In Chapter 5, numerical results are given. The examples in this section provide insight into the versatility of PEEC solutions. The emphasis of this chapter is to give general ideas on how solutions are affected when model complexity changes.

Lastly, conclusions and future work are discussed. The contribution of this work is assessed and unresolved issues are examined. 16

CHAPTER 2

THE PARTIAL ELEMENT EQUIVALENT CIRCUIT

METHOD

Within the discipline of computational electromagnetics, there exist two distinct avenues through which solutions are developed. These are differential equation and integral equa­ tion based formulations. Differential equation methods are formulated through the numer­ ical approximation of the differential form of Maxwell's equations. This results in a sparse system of equations which are constructed in a very straightforward manner. In fact, the ease at which solutions are constructed has been a contributing factor for die popularity of these methods. Examples of differential equation based techniques include the Finite-Dif­ ference Time-Domain Method (FDTD) [13] and the Transmission Line Matrix Method

(TLM) [14]. With these methods, the solution is developed by discretizing those regions of space where electromagnetic phenomena is of interest. This causes a problem with geom­ etries which radiate into unbounded space because the computational domain has to be truncated at some point using absorbing or truncation boundary conditions. These absorb­ ing boundary conditions not only increase computation time, but also introduce artificial reflections back into the solution space if not carefully implemented. 17

On the other hand, integral equation techniques are formulated using electric scalar and

magnetic vector potential functions, which are defined using the assumption of radiation

into homogeneous space. This is a great advantage for problems involving radiation and

scattering, but is a disadvantage for problems whose boundaries are enclosed by perfect

electric or magnetic conductors. For example, if it is desired to calculate the response of a

two conductor transmission line system in homogeneous space, then the unknowns are

assigned only over the extent of the transmission lines. On the other hand, if it is desired to

calculate the response of a two conductor transmission line in an enclosed box with per­

fectly conducting walls, then state variables are assigned to not only the transmission line,

but also to the enclosure. For those geometries which include dielectrics, additional state

variables are used to describe the resulting polarization currents. Examples of integral equati'^n based techniques include the Method of Moments (MoM) [15] and the Partial

Element Equivalent Circuit Method (PEEC) [11][12]. The steps by which solutions are developed using MoM and PEEC are similar. For PEEC, starting with the expression for the electric field in terms of the integral form of the electric scalar and magnetic vector potential functions, the solution is developed by first expanding the unknowns inside the integral in terms of interpolation functions and then testing the resulting equations using the same interpolation functions. This process is known as Galerkin's method. For the electromagnetic problem, the resulting state variables are more or less coupled to all other state variables. Thus, the corresponding matrix is generally dense, and sparse matrix solu­ tion techniques cannot be employed. The key differences between MoM and PEEC are 18

that: a) PEEC does not make use of the continuity equation at the beginning stages of the solutions; b) PEEC relates the coefficients in the solution matrix to circuit elements of an

"equivalent" model. This is an important attribute for PEEC since the "equivalent" model is compatible with non-linear circuit simulators. This "equivalent" model is composed of a lumped network of inductors, capacitors, and resistors, not to mention coupling between the capacitors and coupling between all the inductors which are directed along the same axis. Although the model is lumped, the number of elements in the resulting circuit is determined by considering the smallest wavelength of interest and then using 10 to 40 ele­ ments per wavelength. Furthermore, all couplings are properly delayed in consistency with the retardation character of the electromagnetic Green's function. In this way, distrib­ uted effects such as wave propagation and attenuation can be accounted for using lumped circuit models. It is also important to note that although elementary circuit models are employed, the resulting system is consistent with Maxwell's equations, thus allowing for a full-wave representation using circuit elements that have been up to this point only used for low-frequency solutions. After the values of the circuit elements have been calculated, then the solution is effected using standard circuit techniques such as Modified Nodal

Analysis (MNA) [16].

At this point, it is important to note three key features of PEEC which make it one of the most interesting methods when considering the solution of problems involving high-speed electronic design. First, imbedded within the formulation of PEEC, there exists a hierar­ chical structure for adjusting model complexity. This allows designers to choose for each 19

portion of the system the most efficient model which properly takes into account the elec­ tromagnetic interactions. For example, it may be the case that one portion of a system requires a model which takes into account high frequency effects. This section may be characterized by a full-wave PEEC model, i.e. a model where retardation effects are taken into account. On die hand, other portions of the system may not require such a detailed representation of the electromagnetic phenomena for accurate solutions. These sections can use reduced PEEC models such as resistive/inductive, resistive/capacitive, or resistive networks. The three most common applications for reduced models include the calculation of package inductance, package resonance, and delay of short on-chip interconnects using

RL, RLC, and RC PEEC models, respectively.

Second, since the non-retarded or non-delayed formulation of the PEEC model results in a circuit which can be solved in a circuit simulator such as SPICE [17], connection of external circuit elements such as drivers and terminations to the PEEC model is as simple as just adding them to the resulting network topology description. This seamless connec­ tion to circuit elements does not exist in finite difference techniques. For FDTD, there needs to be a conversion between electric and magnetic fields and voltages and currents so that the equations governing the corresponding circuit element may be properly character­ ized. If the circuit elements are non-linear, then there is an added complication in FDTD since the time-step used in FDTD may be orders of magnitude different than the time-step required to properly represent the non-linear devices.

Third, solutions corresponding to integral equation representations are typified by a high 20

degree of coupling. This results in an exceedingly large computation time for the matrix inversion routines as the problem size increases. Fortunately, PEEC allows for matrix sparsification by elimination of some of the capacitive and inductive coupling terms. For example, if there exists coupling between two inductors or capacitors which are shielded by a power or ground plane, then the coupling may simply be removed. Coupling terms between elements which are not shielded from one another require additional insight before those terms may be neglected. Modem electronic CAD frameworks take advantage of "model development rules" that facilitate such physical complexity reduction, and the interpretation of EM interactions in terms of L, C coupling is extremely useful for such purposes. Up to this point, most simulation tools neglect individual capacitive/inductive coupling terms if the coefficients are sufficiently small or if the capacitors/inductors are separated by a prescribed distance. However, for the case of inductive coupling, there is an additional constraint that those couplings which are removed cannot be contained in the same current path [18].

In this chapter, the PEEC formulation will be presented in much detail. Starting with

Maxwell's equation, the model is developed in such a way as to preserve the full-wave nature of the solution. This discussion is driven by the objective to establish a mathemati­ cal model that is entirely compatible with SPICE while allowing for electromagnetic anal­ ysis with the aforementioned physical model reduction capability in place. One can view this as an enhancement need in SPICE-like simulators to deal with the electromagnetic modeling needs of the next generation of information processing and communication sys- 21

terns. In essence, this development provides the backbone for the "21^ Century SPICE".

2.1 Development of the Electric Field Integral Equation

We begin with the time-harmonic form of Maxwell's equations in linear, homogeneous,

isotropic media

Vx£(r) = -jco^ffCr) (2.1) VxH(r) = jaiEE(r) + aE(r) = yO)££(r) +/(r) (2.2) V • eE(r) = q(r) (2.3) V • iiHCr) = 0 (2.4) where cy is the conductivity, q is electric charge density, J is the electric current density.

fi and e are the permeability and permittivity, respectively. From (2.4), it is evident that

the magnetic flux, B = \iH, is divergenceless and can therefore be represented by the cur!

of a vector which we shall identify as the magnetic vector potential,

VxA(r) = fl(r) = \lH{r). (2.5) Substituting (2.5) into (2.1), we obtain

Vx£(r) = -ya)VxA(r) (2.6) or equivalently

Vx[E(r)+yCi)A(r)] = 0. (2.7) From the vector identity, Vx(-V(j)) = 0, where

the identification that the bracketed term in (2.7) can be rewritten as

E{r) + j(aA{r) = -V0(r) (2.8) or E{r) = - V({>(r)-yQ)A(r). (2.9) Thus, instead of relating the curl of the electric field, E, in terms of the time rate of change

of the magnetic field, as in (2.1), the electric field is now given in terms of scalar and

vector quantities designated as the electric scalar potential and magnetic vector potential.

respectively.

Now that the electric field has been expressed in terms of the potential functions. 0 and

A . what remains is to obtain expressions for their solution. The first step towards a solu­

tion involves taking the curl of (2.5)

VxVxA(r) = Vx|i^(r). (2.10) Upon use of the vector identity, VxVxA = V( V • A) - V-A, (2.10) can be expressed as

V(V •A(r))-V2A(f) = Vxn^(r). (2.11) Assuming that the permeability, (i, is not a function of position, then it may be moved to

the left of the curl operator in (2.11). In addition, (2.2) is substituted into (2.11) giving

V(V • A(r)) - V-A(r) = ycO|l££(r) + |iy(r). (2.12) Furthermore, upon using (2.9) which relates the electric field in terms of the electric scalar

and magnetic vector potential functions, (2.12) can be expressed as

V(V • A(r)) - V-A(r) = ycop.e(-V{|)(r)-y(0A(r)) + |iy(r) (2.13) or upon rearranging terms,

V-A(r) + co"p.eA(r) = - |iy(r) + V[V • A(r)+ycop.e(j)(r)]. (2.14) We now have an expression for the magnetic vector potential, A, in terms of the electric scalar potential. 0. and source term given by the electric current density. J. This is still an 23

undesirable expression since both A and 0 are unknowns. Fortunately, this problem may be prevented by making use of the fact that the definition of A through (2.5) is incomplete since its divergence has not been defined. Therefore, in an attempt to simplify (2.14) so that the unknown quantity A be expressed solely in terms of the known source 7, the fol- lowmg choice is made for V • A,

<{)(0 = -T-^—V-A(r). (2.15) yco|i£ This is the familiar Lorentz gauge.

Finally, we recover the desired relation for A given by

W^A{r)(Si~\ieA{r) = -fl/Cr) (2.16) also known as the inhomogeneous vector Helmholtz equation. The solution of this equa­ tion is the well known magnetic vector potential integral equation.

M-r) = if -I 4nJv \r — r\ where the wave number K is defined as (BA/jli, f represents the point at which the poten­ tial is evaluated, and r' represents a point over which the source is evaluated. Given this expression, the solution for (}) may be obtained by simply taking the divergence and sub­ stituting (}) for A as defined by the Lorentz condition (2.15),

V A(r) = = V . f f 4KJv v—r] 7/-'\ -j<\r-f'\ J / - JLf V ~ 47cJv \r-r'\ or expanding the integral. 24

-yQ)^£(t)(r) = [V /(ni^ |, 4- (2.19) 47tJvL

Since the operator, V, is with respect the unprimed coordinate system, the first term in the integral is identically zero, giving

,2.20,

From symmetry, the gradient may be written in terms of the primed coordinate system,

,2.21,

Again, using a vector identity, the integral may be expanded,

I- /• -yKlr-r'l . -/'ic|r-r'| . -J„) = (2.22,

The first term in the integral of (2.22) may be interpreted as a surface integral and evalu­ ated at a surface at infinity. The contribution of this term is zero and thus leaves only the second term in the integral,

-/•Q)^ie(()(r) = if (2.23) 4nJv I'' - ^ I At this point, it is necessary to make an additional definition before (2.18) can be simpli­ fied. The continuity equation or conservation of charge is introduced. This equation is obtained by simply taking the divergence or Faraday's Law and making use of Gauss'

Law. Thus, after taking the divergence of Faraday's Law (2.2), we obtain V Vx£'(r) = V • (/coe£(r)+y(f)) = 0 (2.24) since the divergence of the curl of any vector is zero. Now, upon use of Gauss' Law to

eliminate the electric field term.

-joaqir) = V • J{r) (2.25) we recover an expression for the electric charge density, q, in terms of the gradient of the electric current density, J. After inspection of (2.18), we can see that upon application of

the continuity equation, the solution for the electric scalar potential,

form involving only the electric charge density, q. The solution for 0 is now given by

j_ r q{r )e dv (2.26)

This completes the development of the electric field integral equation (2.9) in terms of the unknown magnetic vector potential (2.17) and the electric scalar potential (2.26) func­ tions. The corresponding relations for the electric field integral equation in time-domain form are obtained by simply Fourier transforming (2.9), (2.17), and (2.26), which results in replacing all occurrences of yoi and /(r')exp(-jK|r-r'l) with d/dt and

/(r', t') = f{r', t-\f- r'\/v) , respectively, where the retardation time t' is used to indi­ cate that the interaction between the charge or current density at f' with the charge or cur­ rent density at r is delayed in accordance widi the finite speed v of electromagnetic wave propagation in the medium.

2.2 Derivation of the Partial Element Equivalent Circuit Model

As discussed in detail in [11], the development of the PEEC approximation of an elec­ 26

tromagnetic boundary value problem is based on the proper electromagnetic interpretation of the various terms in the electric field integral equation (2.9) subject to the conservation of charge equation (2.15). Consider a system composed of K conductors in a homoge­

neous, linear, isotropic medium; the potential functions may be recast in the following form,

^ ~ry-/\ -/flr-r'l , ,

k=\ ^ , /-'A -j<\r-r'\ J /

it = 1 where denotes the volume of the conductor.

In this analysis, the solution will be developed using the frequency domain form of the equations. As mentioned above, the time-domain result may be recovered via Fourier transformation. Even though the development here is restricted to homogeneous media with constant permeability \l and permittivity £, the generalization of the model for the case of inhomogeneous dielectrics is possible and is effected through the use of polariza­ tion currents [19]-[20]. This generalization will be discussed later in section 3.2. This way. for the case of conductors of finite extent, homogeneous-medium Green's functions are used in the integral representations of the potentials, as shown in the equations above.

With these assumptions, inserting (2.27) and (2.28) into (2.9), enforcing (2.9) at a point inside one of the conductors and making use of Ohm's law 7 = gE , we obtain an integral expression involving the unknown quantities 7 and q, 27

y(£) y r y(r')g _!_ y ^rr ,?(r-)g'^'"'-"'rfv'-[

K = 1 it = 1

2.2.1 Discrete Models used to Approximate Current Flow

In order to solve the system of equations in (2.29), the current and charge densities on the conducting bodies are discretized using piecewise constant expansion functions. For reasons which will become apparent later in the development of the PEEC model, the cur­ rent density is described in terms of inductive volume cells (IVC). The charge density, on the other hand, is described in terms of capacitive surface cells (CSC) which are located over the periphery of their corresponding capacitive volume cells (CVC). It is important to note that the IVCs and the CVCs do not occupy the same positions in space. In fact, the rVCs and CVCs are constructed in an overlapping manner depending upon the order of complexity required for the calculation of the current flow over the conductor.

The simplest model is one which approximates current flow directed along the length of a thin wire. In this and all other levels of model complexity, use of the piecewise constant expansion functions dictates that the current density is constant throughout each IVC and the potential or charge density is constant over the surface of each CVC. Attached to each

CVC is a node which identifies the location of CVC for the purpose of delay calculation.

Figures 2.1-2.3 illustrate the manner in which the IVCs are CSCs are defined for one- dimensional current flow where the local coordinate system L, V/, and 7", denotes the length, width, and thickness axes, respectively. The IVCs and CSCs are identified by the solid and dashed lines, respectively. The volume which defines each CVC is made up of 28

those groupings of CSCs with the same fill pattern. The arrows shown in these figures denote the direction of current flow along each FVC. Figure 2.1 is the model for a wire whose cross-section (W-T plane) is small compared to skin depth. In this case, it is assumed that the current is distributed evenly across the cross-section and the charge resides on the surface. Figure 2.2 is the model for a wire whose width is comparable to skin depth, and thus requires multiple IVCs, but only one CVC along the W axis. For the skin-effect model, as the dimension of interest becomes large compared to skin depth, the current and charge densities concentrate more and more along the edges, thus requiring more cells to properly describe this non-uniform effect. Figure 2.3 is the model for a wire whose width and thickness are both comparable to skin depth. It should be noted that since skin depth is a function of frequency, the choice of discretization depends upon the fre­ quency at which the simulation is performed. In general, as the operating frequency increases for a given system, more cells are required to represent the distribution of current and charge. More importantly, it may be the case that the sensitivity of the desired output characteristic is such that a simplified model will suffice. For example, for delay calcula­ tions, it may not be necessary to calculate the response with a high degree of accuracy.

However, variations in overshoot may be more sensitive to the level of discretization. For the models with one dimensional current flow, the nodal positions using the L, W, T coor­ dinate system are given by

0

V At

Fig. 2.2 IVCs and CSCs for ID model taking into account skin-effect along width. At

Fig. 2.3 rvCs and CSCs for ID model taking into account skin-effect along width and thickness. 30

At

Fig. 2.4 rVCs and CSCs for 2D model with L-directed current taking into account skin-effect along thickness. At

Fig. 2.5 IVCs and CSCs for 2D model with W-directed current taking into account skin-effect along thickness.

th for the i node of a conductor of length with I CSCs and where and are equal to one-half the width and thickness, respectively. The exposed nodal positions are shown in the figures by solid black circles.

On the other, if the width of the conductor is about the same size as the length, then it is Fig. 2.6 rVCs and CSCs for 2D model with L-directed current. At

^ I ~ -x "

'„r_~ 33L^ • "IT'^

Fig. 2-7 rVCs and CSCs for 2D model with W-directed current.

At

Fig. 2.8 rvCs and CSCs for 3D model with L-directed current. Fig. 2.9 rVCs and CSCs for 3D model with W-directed current.

V ' ,.M r_v r„v 512:.. i_ LiJ i~T-| -- - I • I —h •

'^§E::'"'iiiSi rn

Fig. 2.10 rVCs and CSCs for 3D model with T-directed current. necessary to use a model which is capable of quantifying two-dimensional current distri­ butions. Figures 2.6-2.7 show the discretization scheme used to model this situation. As can be seen, the IVCs used to describe Z,-directed current flow (Fig. 2.6) are different than those used to describe IV-directed current flow (Fig. 2.7). However, in both cases, the

CSCs and the nodal positions are identical. This model is appropriate when the thickness of the conducting plate is small compared to skin depth. But, when the thickness is large enough to warrant using a skin-effect model, then the appropriate discretization scheme is shown in Figs. 2.4-2.5. For both discretization schemes, the nodal positions are given by 33

(/, 0 = («„„/(/- 1 1), (2.31)

th th for the i ,j node of a conductor of length and width ^ ^ CSCs, and

where is equal to one-half the thickness.

Lastly, when the length, width, and thickness are all of comparable size, then it is neces­

sary to use a model which accurately describes three-dimensional current flow. Figures

2.8-2.10 show the discretization scheme used to model this situation. As can be seen, the

IVCs used to describe L-directed current flow (Fig. 2.8), -directed current flow (Fig.

2.9), and T-directed current flow (Fig. 2.10) are different. However, in all three cases, the

CSCs and the nodal positions are identical and are given by

0 < / < / (/, vv, f) = (//^^/(/- I),yw^,y(y- 1)). 0

2.2.2 Discretization of the Electric Field Integral Equation

Mathematically, the discretization of the conductors as described in section 2.2.1 is achieved by defining the following rectangular pulse functions

p _ f I inside the nk'^' IVC ^ ^3) lo elsewhere for the current density where y = x,y,z indicates the component of the current in the n''

th rVC of the k conductor and 34

J1 on the CSCs of the mk"" CVC , Pmk = \^ (2.34) LO elsewhere th tfx for the charge density over the m CVC of the k conductor.

Given the definition of the pulse functions in (2.28) and (2.29), the current and charge densities both multiplied by the exponential factor which accounts for the retardation are approximated over each of the K conductors by

n = 1 and

M, -yic|r-r'| 1ei^ = 2- PmkHmk^ (2-36) m = I where represents the position vector for the n of Nyi^ IVCs of the k conductor for (h Y directed current. Similarly, represents the position vector of the m of CVCs of the k''^ conductor. Additionally, denotes the number of volume cells for conductor k with Y directed current and denotes the number of surface cells for conductor k.

Substituting (2.30) into (2.24), we get for a point inside the p IVC of the / conductor describing y directed current.

r . K J,, 'ypt ycon Y Y p J f I (-) 37) jfc= In = 1

1 Y ^ = 0. 4ne ^dy k=\ IV-r'l 35

This step is followed by the testing of the resulting equation in the Galerkin approximation sense (i.e. the aforementioned pulse functions used for the expansion of the current and charge densities are also used for testing) utilizing an inner product over the volume of a cell defined as follows

— f /(r)Jv = —f [ f{r)dadl (2.38) where is the volume of cell m, is the cross-section of the cell, is the length, and

th f{r) is the integrand. Thus the inner product for the first term in (2.37) over the p IVC of the / th conductor describing y directed current gives

_L_ f — _!_r_^j!2L a I = — I R P 39i a Jv a f''' a , aa , , 'wi^ypi (-39) fpl yp' "Yp/L^"Yp/-i Yp' where and denote the length and cross-section, respectively for that [VC. The term represents the resistance for this IVC. Thus, the final expression in (2.39) is interpreted as the voltage drop over the ypl''' IVC due to loss in the conductor.

Next, taking the inner product of the second term in (2.37) and rearranging terms gives

, 4- riif-"'!''"-'"!,M-e ' " ' ' f ,f dy^,dv lynk = (2-40) 4na. r. 1/1 = 1 yml"^ynkj'fii ^ynkjrt^ ly* "Vft r"* !• II'-yp/j ^ VMjfji / 'inl\_jnt K ^ ^ ^Pypiynk^ynk^ 4=1/1=1 where the position vectors r- for the IVC in the exponential term are approximated by the distance to the center of its volume by ?• and 36

has the units of inductance. Thus, the term on the right-hand side of (2.40) represents the

th inductive voltage drop across the ypl IVC. When p = n and I = k, then Lp- • is the partial self inductance. In all other cases, Lp- j is the partial mutual inductance. The par­ tial mutual inductances serve to take into account all of the couplings between the induc­ tors when the equivalent circuit is constructed.

For the last term in (2.37), application of (2.36) and taking the inner product over the

ypl'^ IVC gives

K Mt . J (2.42) J-.* Vypl - Wl J with the volume integration changed to a surface integration since the charge only exist on the surface of the volume. This expression can be reduced further by using the approxima­ tion

(2.43) to eliminate the derivative and one of the integral terms.

f ds^,^ _ rJ j. ds^,^ e :! f "•'mk _ -JWtpl -''mk\ f (2.44) /(:= Im^ = 1 4rte 7. \ ^ Js, where r* is one-half cell past the ypl'^ IVC and r' is one-half cell preceding the ypl'^ rVC. This may seem to create a problem, but after closely inspecting how the IVCs and

CVCs are partitioned across the conductors, it is apparent that tlie volumes which are one- 37

half cell proceeding and past the yplth FVC are really CVCs. For example, consider the

top view of the ypl'*^ FVC shown in Fig. 2.11. The size of the CVCs are the same as die

rVC and are displaced by one-half cell. The position vectors r- for the CVC in the expo-

cvc" rvc cvc^

Jy

Fig. 2.11 Placement of CVCs surrounding an IVC.

nential term are approximated by the distance to its corresponding node by ?•. Next, using

the definition for total charge = q^k^mk where is the total surface area of the

mk th CSC. (2.44) may be rewritten as

k = \ m = \ where ypl+ and ypl'* are the CVCs to right and left, respectively, of the ypl th IVC and

I r PPi j = [ rr—-71- (2.46) 47C£aJ.Jr.-rj The pp^ J terms in (2.45) are called partial coefficients of potential. These terms contrib­ ute to calculation of the potential at a point through

= I.PPi.jQ/'''''''"'- (2-47) j 38

Thus, after inserting (2.47) into (2.45), we observe that (2.45) is actually the capacitive th voltage drop across the ypl IVC,

^ -O (2.48) 7/7/ Ypf At this point, if important to note that there is an added complexity when considering con­ ductors which allow three-dimensional current flow. Careful inspection of Figs. 2.8-2.10 reveals the existence of CVCs in the interior of the volume of the conductor. These interior

CVCs need to be treated differently than the CVCs which are on the exterior of the con­ ductor since, as will be described later, the calculation of the partial coefficients of poten­ tial only involve those CSCs of the CVC which are on the surface of the conductor.

However, since the operating frequencies encountered in high-speed design result in relax­ ation times which are negligible, it is sufficient to consider only those CVCs with CSCs located on the exterior of the conductors.

Although the potential coefficients may be thought of as inverse capacitances, it is not valid to make such an assertion when retardation is considered. Thus, treatment of capaci­ tive coupling via potential coefficients ultimately results in an equivalent circuit which does not employ capacitors and mutual capacitors. The capacitive effects are taken into account through capacitors and current controlled sources. The derivation is as follows.

Substinjting the equation which relates the current to the total charge i = dQ/dt into the time derivative of (2.47), we get 39

''' <2.49) J ' j '

What results is an expression relating the value of the time derivative of the potential at die

th i CVC to its partial self coefficient of potential pp- • multiplied by the current flowing

through the CVC, . and the sum total of all the partial mutual coefficients of poten­

tial multiplied by the corresponding CVC current . This is more appealing than (2.47) in

the sense that it is an expression relating voltage to current, whereas in (2.47) the voltage

was related to total charge, which is incompatible with circuit formulations.

In summary, the preceding development has shown how to interpret each term of the

electric field equation (2.9) in terms of equivalent resistors, inductors, and capacitors in such a way as to maintain the full-wave nature of the solution. In other words, the PEEC

approximation provides a discrete approximation to

£(r) + j(0ACr) + V(l)(r) = 0 (2.50) ih applied at the ypZ IVC where each of the resulting terms are associated with voltage drops across equivalent circuit elements,

K ^ (2.51) i= In = I

K . I- - I I S = 0. i = 1 m = 1 By inspection of the various terms in (2.51), it is apparent that the equivalent circuit solu- th tion defined over the ypl IVC is composed of a resistor in series with an inductor and capacitors on either end. Therefore, the equivalent circuit for the entire system may be 40

constructed by identifying the equivalent circuit elements which result from the applica­ tion of (2.51) at each FVC and noting the overlapping nature in which the circuit is con­ structed. For example, consider the conductor with two FVCs and three CVCs as shown in

Fig. 2.13. Upon application of (2.51) to each of the IVCs, the equivalent circuit in Fig.

2.12 may be constructed by inspection. Note that there is one CVC which is common to both rVCs. Also, it is satisfying to note that the layout of the circuit elements is totally consistent with a lumped representation of the transmission-line or telegraphers equations.

However, although the PEEC and transmission-line representations are similar in appear­ ance, the actual circuit elements required to construct a PEEC circuit are different than those in Fig. 2.12. This difference is due to the fact that PEEC models which are consistent with full-wave solutions require couplings between all the capacitors and ail of the induc­ tors directed along the same axis. These couplings are not included in the circuit model

loop 1 loop 2

Fig. 2.12 Equivalent circuit for PEEC model in Fig. 2.13.

• • •

Fig. 2.13 Simple PEEC model with two FVCs and three CVCs. 41

shown in Fig. 2.12 for clarity. In order to illustrate how a complete solution is constructed,

the example in Figs. 2.13-2.12 will be used to facilitate this discussion. The first step

towards a solution involves applying (2.51) at each of the two IVCs. This is equivalent to

enforcing Kirchoff's Voltage Law (KVL) around the two loops shown in Fig. 2.12. result­

ing in the following loop equations,

2 •^>"2 iPl..'/p.<2.52) n = I

I -pp,- ^e J = 0 m = I

2 +y<» i; + <2") 3 = I

-PPy.n,' J = 0 m = 1 where several of subscripts were omitted due to the simplicity of the circuit. Next. Kir­ choff's Current Law (KCL) is applied at each of the three nodes shown in Fig. 2.12.

Enforcement of KCL is to circuit theory what the continuity equation (2.25) is to Max­

well's equations. In fact, since there is no charge accumulation at the nodal positions and

through the definition of the pulse functions in (2.33), discretization of the continuity equation gives

£/,- = 0 (2.54) i where I- represents each of the currents flowing into the node around which the continuity equation is applied. As it turns out, this discrete form of the continuity equation is identi­ cal to KCL. For the circuit shown in Fig. 2.12, enforcement of KCL at each of the three nodes gives

= -hp,, 12-55) 'c, = I2-56) 'c, = (2-57) where the currents i are given by a rearrangement of the terms in (2.49) and change in ^ I notation for die potential coefficients,

i, =—,-(2.58) p ^p- '^1 ^ U I j I

In circuit terms, the first quantity to the right of die equal sign in (2.58) is interpreted as the equation for the current flowing through a capacitor of value l/p^ ,. This capacitance is known as the self capacitance. The second term to the right of the equal sign in (2.58) is interpreted as a sum of current-controlled current sources with coefficients j/p- , and controlling currents i evaluated at all other CVCs. These controlled sources provide a / mechanism by which the capacitive couplings may be included. With this in mind, a more representative model may now be constructed which properly accounts for the capacitive coupling. Figure 2.14 shows such a circuit. In this diagram, die currents in the current-con­ trolled current sources are defined as

'F = (2.59) ' ^p- • ' i^J 43

and the inductors which represent the mutual couplings are not shown. The independent

R. ^Pu R, MAAKinp—MAV^

clyV- c2tV- '».e

'u-y Oi 4^®^' ^ O2

Fig. 2.14 Equivalent circuit for PEEC model in Fig. 2.13 (including capacitive coupling model).

voltage sources attached to the capacitive branches are of value OV and act as ammeters

which monitor the currents flowing into the corresponding CVCs.

This finalizes the solution for the simple PEEC model shown in Fig. 2.13. Starting with

five unknowns (O,, 4>2, O3, ), the two KVL equations (2.52)-(2.53) and die

three KCL equations (2.55)-(2.57) completes the solution. The auxiliary equation

i = dQ/dt is necessary to relate the total charge in terms of the current. In addition, the definitions in (2.5S) and (2.59) are also needed.

2.3 Modified Nodal Analysis

Although the process of applying KVL and KCL as detailed in the previous section pro­

vides a rigorous solution to problems involving PEEC models, it has the disadvantage of being very difficult to manage as the problem size increases. There is an alternative 44

approach called Modified Nodal Analysis (MNA) [16] which provides for a much more intuitive and straight-forward procedure for the solution of circuit equations. The MNA process involves forming the solution through enforcement of KCL at each node, in addi­ tion to construction of auxiliary or branch constitutive equations (BCEs) for circuit ele­ ments such as inductors which do not have an admittance representation, i.e. those circuit elements which cannot be described by the following terminal characteristics,

I = YV (2.60) where I is the branch current, Y is the admittance, and V is the terminal voltage.

The first step towards a solution using MNA is to enumerate the total number of voltages and currents required to form the resulting matrix. Appendix A lists the voltages and cur­ rents which are needed for each elementary circuit type. Next, a square mauix is formed such that the rows and columns correspond with the unknown voltages and currents. Typi­ cally, the matrix is formed by first specifying the node voltages followed by the branch currents. Next, values for each circuit element are "stamped" or added to the matrix according to format given in Appendix A.

In order io illustrate the power and simplicity of the MNA approach, the PEEC circuit from the previous section will be formulated using MNA. The circuit is shown again in

Fig. 2.15 with the series resistance values omitted for simplicity. The solution is con­ structed by adding the circuit stamp associated with each element one-by-one to the solu­ tion matrix. The resulting matrix is given by 45

Fig. 2.15 Equivalent circuit used for MNA solution.

0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 -I I 0 I 0 0 0 0 ^2 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 ^3 0 0 0 0 0 0 0 -1 0 0 -I 0 0 ^C, 0 0 0 0 0^2, 2 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 «3,3 0 0 0 0 -1 0 0 -1 1 -1 0 0 0 0 -pl, 2 0 0 0 0 0 0 -Pi, I ''Pl. 1 (2.61) 0 I -1 0 0 0 -P2,1 —P2, 2 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 C2 0 0 1 0 0 -I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -"^1,2 -Y1.3 1 0 0 0 0 0 0 0 0 0 0 -Y2.1 0 -^2, 3 0 1 0 0 0 0 0 0 0 0 0 -Y3.1 -Y3. 2 0 0 0 I where the following notation is used.

aij = '— (2.62) ' Pi.i -ymXi P/.y = jcoLp-je (2.63) 46

Pi i lij = -^e (2.64) Pi, i with the substitution of and for the time delay of the inductive and capacitive

terms, respectively.

As an alternative to merely interpreting MNA as the method used to solve circuit equa­

tions through the use of "stamping" in values to solution matrix, a more intuitive interpre­

tation may be used instead. Upon close inspection of the rows involving the node voltages

in (2.61), it is apparent that those rows may be simply formed by enforcing KCL at those

nodes. For example, the current equation for v-, in (2.61) is given by

" = 0- (2.65)

In addition, the rows corresponding to the branch currents represent the additional equa­

tions required by those circuit elements without an admittance representation. For exam­

ple, the BCE for _ in (2.61) is given by

-ycOTt V,I'/p,,-yC0^/?l.2e = 0- ^-66) This analysis shows that MNA provides a mechanism for the solution of circuit equations through the enforcement of KCL at every node voltage in addition to the selective enforce­ ment of KVL through certain branches.

2.3.1 Semi-Condensed Modified Nodal Analysis

Although MNA provides an intuitive approach for the solution of FEEC models, there is a significant computational overhead involved in forming such a solution. This is due to 47

the fact that the MNA process generates an excess number of unknowns, i.e. more unknowns than are absolutely necessary to completely model the system. Upon inspection of the equivalent circuit in Fig. 2.15, it is desirable in most cases to eliminate the unknowns representing the currents through the current-controlled current sources ip since these values are generally not of interest.

The process of reducing the size of the MNA solution through the elimination of the cur­ rents through the current-controlled current sources is called semi-condensed MNA

(scMNA). This reduction in computational effort is accomplished by first noting the form of the BCEs for the rows corresponding to the ic variables. In (2.61), those relations are given by

ip = e t- + e I. (2.67) ' P\.i • Pi.\ Ip = e I. + —^e I. (2.68)

- Pi,! " Pzi ip = —=-e I. + —^e I.. (2.69) P3,3 Pi, 3 Since the expressions for ip are not dependent upon one another, these variables may by eliminated by simply substituting for each occurrence of ip , its corresponding definition as given in (2.67), (2.68), or (2.69). Given this development, the scMNA reduced matrix corresponding to (2.61) is given by 48

0 0 0 0 0 0 1 0 1 0 0 ^1 0 0 0 0 0 0 -1 1 0 1 0 ^2 0 0 0 0 0 0 0 -I 0 0 1 ^3 0 0 0 ®1,1 0 0 0 0 -1 -YI.2-YI,. 0 0 0 0 ^^2, 2 0 0 0 -Y2.1 -Y2,: 0 0 0 0 0 "3,3 0 0 -Y3.1 •Y3.2 -1 (2.70) 0 1 -I 0 0 0 -P..1 ~PL. 2 0 0 0 ''Pl. 1 0 1 -1 0 0 0 "^2. 1 "1^2. 2 0 0 0 ^Ipz. 2 1 0 0 -I 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 C; 0 0 1 0 0 -1 0 0 0 0 0 - - whose solution is mathematically equivalent to the one using (2.61). It is important to note that scMNA, not to mention any other method which reduces the computational effort of

MNA, results in a matrix which is not compatible or consistent with the SPICE algo­ rithms. In other words, to effect a solution using anything other than MNA requires the development of a special purpose circuit simulator with that variation of MNA built-in. To complicate matters further, the exponential factor which accounts for the delay in the cou­ pling terms may only be implemented in such a special purpose circuit simulator since non-linear factors are not allowed for mutual inductors or current-controlled current sources in SPICE.

2.3.2 Condensed Modified Nodal Analysis

The technique which results in the fewest number of unknowns which works in both fre­ quency and time-domain solutions is called Condensed Modified Nodal Analysis (cMNA) 49

[27]. cMNA allows the system to be characterized with only one unknown for each IVC and CVC. More specifically, a branch current is assigned to each IVC and a node voltage is assigned to each CVC.

^Pl,l

cl, c2. c3,

:t>vi ^ 1,1 2^T 3J

Fig. 2.16 Equivalent circuit used for cMNA solution.

Starting with the circuit shown in Fig. 2.15, cMNA is developed through the elimination of the independent voltage sources or ammeters which were responsible for the additional unknowns and . This results in a system of equations involving only v- and .

Figure 2.16 shows the equivalent circuit used in this formulation. The cMNA approach can be interpreted as a modification to scMNA which eliminates both v. and r as unknowns. This is achieved by utilizing the expressions at the rows corresponding to and from (2.70),

'c, = (2.71)

'c, = "2, 2^C; ~ Y2, I 'c, ~ Y2, 3'c3 (2.72)

'c, = a3.3Vc3-Y3.l'c -Y3.2^c, (2.73) V, = (2.74) 50

Vj = (2.75) V-,J = V Cj (2.76) where (2.74)-(2.76) are substituted into (2.71)-(2.73) and is eliminated from the right- hand-side of (2.7l)-(2.73) by

'c, - -'/pi.. (2.77) 'c; '/pi. I 'ipi.: (2.78) LCj = '/r,'P:.: • (2.79) This development results in the following expressions for solely in terms of the cMNA unknowns v, and i,

'c, - ^1. 1^1 (2.80) 'c, = "2. 2^2 Y2, 1 '/p, , ~ "Yl. , (2.81) 'cj = "3.3*^3 "*"^3. I'/p,, ~Y3.2('/p,, (2.82) which upon substituted into (2.70) gives 1 1 «i.i 0 0 I-Y1.2 yi.2-Yi. 0 a2 2 0 - ^ + Y2.1 J - Y2,: 0 0 aj ^3 (2.83) 1 -1 0 -Pi.i -P1.2 ''Pi. 1 0 1 -1 "^2, 1 "^2. 2 ''Pi 1

2.3.3 Modified Loop Analysis

The last and most reduced form of MNA is a method specific to the frequency-domain called Modified Loop Analysis (MLA) [26], This scheme is similar to MoM in that the unknowns are all currents. More specifically, for PEEC these currents are the branch cur­ rents through the FVCs or inductors. The main idea behind MLA is to replace the parallel 51

combination of capacitor and current-controlled current source which represents each

CVC with its Norton equivalent circuit or series combination of capacitor and current-con­ trolled voltage source.

Fig. 2.17 Norton equivalent circuit used in MLA.

Figure 2.17 demonstrates the transformation which takes place for the circuit elements representing each CVC. For the Norton equivalent circuit, the complex impedance for the capacitor p, /s and the current-controlled current source of value (taken from (2.59))

<2.84. are multiplied and result in the current-controlled voltage source value.

"• <2-85) j '"y This analysis is not applicable in the time-domain since the l/s term in (2.85) corre­ sponds to an integration in the time-domain and would therefore be inconsistent with a

MNA-type solution. Fig. 2.18 Equivalent circuit used for MLA solution.

Using this idea, the MLA formulation results in the circuit shown in Fig. 2.18 for the 2- cell PEEC model shown in the previous sections. This circuit has two unknowns . iip^ therefore all that is required is to perform KVL around the two loops.

Pi \ ', + + P-, (2.86)

Pt •> . r 1 Pi 3 + " +% + ^'c3- (2.87)

The expressions above are simplified further through the use of (2.85) and (2.77)-(2.79) to obtain equations involving only the unknown current through the inductors.

[ T .P\,l,P2,2 Pl.2 PZI •'"Vi]. (2.88)

r r P2,2 , Pl,2 . P%2 ^sLp^2^ + -p^^e +—e J'/p,: = ^

r , P2,2 . Px\ P3A . P3,2 + (2.89)

[ T . P2,l , Pl.h P2,3 Ph. 2 "'"V:"!- n 2.3.4 Comparison of Reduced Modified Nodal Analysis

Schemes

In sections 2.3.1-2.3.3, three variations to MNA were introduced. scMNA and cMNA represented alternate formulations which can be used in both the time and frequency domains while MLA is specific to only frequency domain. These methods serve to reduce the computational effort involved in effecting a circuit-oriented solution containing PEEC models via the strategic elimination of those unknowns in the system which are not required to solve the problem. Although these schemes serve as a straightforward approach for reducing the size of the system, simulators such as SPICE are only capable of using MNA. Therefore, it is necessary to either modify SPICE or create a special purpose simulator if these methods are to be exploited.

In the development of these alternative schemes, the solution for a 2-cell PEEC model was generated in each case. The number of unknowns required to solve the equivalent cir­ cuit for MNA, scMNA, cMNA, and MLA were 14, II, 5, and 2, respectively. Extrapolat­ ing from this result. Table 2.1 summarizes the overhead compared to MLA in the number of unknowns as the circuit size increases with or without the series resistor. It is evident that there is a lot to gain in efficiency by using any one of these variations. However, as the overhead is reduced, the complexity and generality of the resulting system is compro­ mised. For example, MLA requires the fewest number of unknowns, but upon inspection of the matrix coefficients (see (2.88)-(2.89)), it is evident that the formulation can become 54

Overhead Overhead Scheme (without Resistor) (with Resistor)

cMNA 2x 3x

scMNA 4x 5x

MNA 5x 6x

Table 2.1 Overhead compared to MLA associated with solving large PEEC models. quite tedious and prone to error as the problem size increases. Moreover, MLA has the unique distinction in that the only allowable external connections to the PEEC models are independent voltage sources. On the other hand, MNA requires the largest number of unknowns, but is the easiest to formulate and can accommodate any circuit element.

In addition to the added complexity in formulating the reduced schemes, there is added overhead in computation time associated with the overwhelming number of entries into the matrix as the dimensionality of current flow is increased. Figure 2.19 shows the equiv­ alent circuit for a CVC and its adjacent inductors for the case of 3D current flow. As explained in Section 2.2.2, the current acts as an ammeter and monitors the sum total of all the currents flowing in that CVC. For the case shown in Fig. 2.19, if the currents sur­ rounding the CVC are named through , then the CVC current is given by

6 V = I <2-90) n = 1 The consequence of this seemingly minor detail is that instead of being able to reference the CVC current using one variable, it is now necessary to use six variables. Hence the 55

Fig. 2.19 CVC and adjacent inductors for PEEC model with 3D current. number of entries into tiie matrix invariably increases. In addition, ttiere is added complex­ ity in identifying which currents flow into the CVCs.

The factors which ultimately dictate the method of solution are the reduction of matrix size and the ability to include any external circuit. This can be accomplished by using

MLA and cMNA for frequency- and time-domain, respectively, on those portions of the

PEEC model which do not contain external connections and using scMNA on those por­ tions with external connections. Such a combined technique seems to be the best compro­ mise between functionality and efficiency. Nevertheless it may very difficult to implement in a general-purpose simulator. 56

2.4 Partial Inductances

up to this point, it has been assumed that the term on the right-hand-side of (2.40) is the partial inductance which is given by (2.41). However, in general, this value is classified in two categories: the particil self inductance and the partial mutual inductance. The partial self inductance represents the inductance of a conductor due to a current induced on that conductor while the partial mutual inductance represents the mutual inductance between two conductors due to a current induced on one of the conductors. For linear, reciprocal systems, the partial mutual inductance between conductors A and B is equal to the partial mutual inductance between conductors B and A .

As a first step towards the calculation of the partial inductances, it is beneficial to recast

(2.41) into the following form.

(2.91) where the notation = [r- - ry| is used and the volume integrations are expanded with the dl term designating the direction of current flow for the corresponding conductors.

The dot product, dl- • dlj, states mathematically that the partial mutual inductance is zero if the conductors are orthogonal. For the special case where the conductor cross-sections are small compared to their lengths, (2.91) reduces to the expression suitable for filamen­ tary current elements,

(2.92) 57

Upon substitution of (2.92) into (2.91),

represents the partial inductance resulting from the integration of Lf over the cross-sec- J 1.1 tions of both conductors. Numerically, (2.93) is calculated by subdividing the cross-sec­ tions of the conductors into smaller and smaller pieces until the subdivided cross-sections are small compared to the lengths of the conductors. Assuming that the cross-sections of conductors i and j are segmented into K and M sections of equal cross-sectional area, respectively, the discrete form of (2.93) is given by

K M

« = ly = 1 Thus, the partial inductance can be calculated numerically by a discrete summation of par­ tial inductances of filamentary current elements. The calculation of die partial induc­ tances, Lpj , has been performed in [2l]-[24] and closed-form expressions exist for many different conductor shapes. In what follows, a summary will be given detailing the computation of the partial self inductance (/ = j) and the partial mutual inductance

These two cases need to be treated separately since the term r-j in the integrand of the integral for the partial self inductance is singular.

2.4.1 Partial Self Inductance of a Filament

In this section, formulas will be given for the calculation of partial self inductance for rectangular geometries with length /, width W, and thickness T. For the case of a conduc­ 58

tor with appreciable thickness, the partial self inductance of a filament with u = l/W and

w = T/W is given by

3) (2.951

u' ^ -if (a \ u . -if u \ ^7 1 -ifuoi - —tan —— + 7—Ag - -tan —— + — - —tan — 6Q) \uAJ 4Q) ° 6 yaAj 4 6© VA4

H ^[In(M + Aj) - Ay] H ^(A[ - A^) + I - A2) 24Q)~ 20co" 60CO"H

where

A J — /JI + u'

At = Vl +C0" I 2 2 A 3 = a/ CO + u

A4 = 7l +co^ + «~

A5 = In

/(» +A, As = ln( ^

fu+A^ '^1 = ln(^ Ai For case of thin conductors or w 0, Lp^ // is given by 59

= ^|31n[M + Ju~ + l] + u~ + u ' (2.96)

As can be seen in Fig. 2.20, (2.95) and (2.96) yield practically the same result for values of

vv less than 0.01.

T/W=1

a.

0.1

0.01 0.1 1 10 100 1000 l/W

Fig. 2.20 Partial self-inductance for rectangular conductors.

In the calculation of partial self inductance (K = M), (2.95) and (2.96) represent M of

the necessary M2 calculations, assuming the conductor is segmented into M pieces along the width and thickness. The other M(M- 1) values are given through the formulas for

partial mutual inductance as explained in the next section. This may seem misleading 60

since (2.95) and (2.96) are formulas for the partial self inductance. But, it is important to

remember that (2.95) and (2.96) represent the partial self inductance of a filament. Thus,

since a single conductor is split into several smaller filaments, (2.95) and (2.96) are appro­

priate only for those filaments which overlap.

2.4.2 Partial Mutual Inductance Between Two Filaments

For filaments which do not totally overlap one another, it is necessary to use yet another

• X 4 ^ j

D. y D.

Fig. 2.21 Partitioning of conductors i and j.

formula for calculation of partial inductance. This quantity is called the partial mutual inductance. Referring to conductors i and j in Fig. 2.21, the partial mutual inductance between the filament with cross-sectional area a, on conductor i and the filament with 61

cross-sectional area on conductor j is given by

S |(-U''^'gfelog[gfe + 7gi^l-A^i^} (2.97) ' i= 1 I- 1 where

^1 = I +P g2 = 1 +p-V ^3 = P-v 8A = P with the normalizations v= lj/l. , p = Dyii , and r= + Dyi^ .This formula is also applicable for the calculation of partial mutual inductance between different filaments on the same conductor.

2.4.3 Calculation of Partial Inductances

Given the formulas for the partial self (2.95)-(2.96) and mutual (2.96) inductances of fil­ aments in the previous section, the partial self and mutual inductance for the conductors may be calculated by summing up the contributions of the filaments which make up the conductor. For example, the partial mutual inductance between two conductors is given approximately by the discrete summation in (2.94). It is important to note that Lp^ j approaches the exact value as the number of filaments approaches infinity. However, in most cases, the partial inductance may be accurately calculated with only a few filaments for each conductor. For those cases where the aspect ratio is large between the width and length, it may be necessary to employ thin tape-tape algorithm [23] to speed up conver- 62

gence of the summation in (2.94).

On the other hand, for a conductor segmented into K divisions along the width and

thickness, the partial self inductance is given by expanding (2.94),

K K K '•Pu = is 'L'-Pf,., = 73 S I S ^Pf... <2-98) ^ i=lj= I fr t = 1 y = 1 £ = 1 y where the first term in the brackets denotes the mutual contribution between the filaments and the second term in the brackets denotes the self contribution for the filaments.

2.5 Partial Coefficients of Potential

As identified in section 2.2.2, the partial coefficient of potential is given by

I <• dS; PPli = (2.99) 4iiea.}Js, "n |r I - r,|";i This expression involves an integration over each surface of CVC y. However, this may be stated in an alternate way by using the notation

M J = £ J (2.100, ' m=l - to signify that the surface area may be decomposed into each of its M contiguous sur­ faces; i.e. the contribution from the surface area of some volume may described by sepa­ rately summing up the effects from each of its six faces. Upon substitution of (2.100) into

(2.99), we get 63

Af ds^ (2.101)

m = 1 with 5^ denoting the total surface area of all M sides of the jJh CVC. Taking the inner product (2.38) of (2.101) with respect to i•th. CVC and applying (2.100), we get

L M L M ds,ds. 1 p I 4;te5 5 S Z where the potential coefficient is now referred to as p instead of pp for the purpose of emphasizing the fact that some operations were needed to transform pp from its original form in (2.99) although its interpretation has not changed. The quantity 5^ represents the total surface area of all L sides of the CVC.

Fig. 2.22 Cells oriented in parallel. 64

Fig. 2.23 Cells oriented perpendicular to each other.

The integral ipsi^) in (2.102) is very difficult to evaluate for general shaped conduc­

tors. However, the solution to this integral exists in closed-form for a limited number of

geometric arrangements [12],[25]. Two of the most common arrangements include con­

ducting surfaces which conform to the cartesian coordinate systems and are either parallel or perpendicular to each other. Figures 2.22 and 2.23 show these two arrangements. The exact value of the potential coefficient for the parallel cell arrangement in Fig. 2.22 is given by

4 4 2 ^2 a, -C f + V -—a,ln(a,-I-p) +—b^\n{b^ + p) (2.103) := lw= I

-g(Z>2-2C2 + af)p-fc^Ca,tan where 65

P = M + K + (r and

a, = a,; - fa— - — 1 V 2 2

"2 = "0*1-J

= a,; + ^faja ^

<24 = a;;~-Efa.ia + -~ •'J '2 2

b, = V 2 2

b, = fc. J±JA - 'J 2 2 b, = A, J± + i' y 2 2 h - h fb

The exact value of the potential coefficietit for the perpendicular cell arrangement in Fig 2.23 is given by

P^im = III (_l)^ + f + v+i (2.104) i = I f = 1 V = I

.17 '6"+ P' + ( Y - f + p)

+ a,b,c,\n(c, + P) - ^ - ^tan-'f—'] 3 6

with 66

p = and additionally.

bz: y 2

br. 2

^ij ^2 Js ""ij 2' This completes the derivation of the partial coefficients of potential. It is important to note that the equations for in (2.103)-(2.104) are appropriate for the calculation of the pjutial mutual as well as partial self coefficients. These expressions may be further reduced if cells / and m are identical. However, it is equally valid to adjust the namral logarithm and inverse tangent terms in (2.103)-(2.104) such that a small number. e = 10-12 , is added to the denominators of their arguments. This minor adjustment insures that these operations will not result in overflow while preserving the numerical accuracy of the algorithms.

2.6 Equivalent Circuits for Skin-Effect Models

Starting with Maxwell's equations, the main focus of this chapter was to outline the steps necessary in deriving equivalent circuit models via the PEEC methodology. During the development of these equivalent circuit models, approximations were made and justi­ fied where appropriate. However, in section 2.2.1, there was no explanation or justification 67

for the choice of discretization for the skin-effect models. This discussion was intention­ ally absent from the section since it involved an understanding of the sections proceeding it. The phenomenon of skin-effect is related to how the field penetrates along the cross-

AT

Fig. 2.24 Discrete model for 2D current flow.

section of conductors, thus changing the distribution of current. Typically, these effects are captured through the use of parallel combinations of inductors/resistors along the direction of current flow. In the following, only one of the cross-sectional dimensions is used in the discussion of skin-effect. This simplification is solely for the purpose of reducing the com­ plexity of the examples to aid readability.

Consider the discrete model for 2D current flow shown in Fig. 2.24. This model is con­ sistent with the one in Figs. 2.6-2.7 and shows how the IVCs and CVCs are partitioned for

L- and W-directed current flow. The equivalent circuit for this choice of discretization is shown in Fig. 2.25. It is evident in this circuit model how the two discrete models in Fig.

2.24 are combined to form a truly 2D representation for current flow. In particular, the four

CVCs shown by the alternating fill patterns in Fig. 2.24 are represented by the four combi­ nations of capacitor and current-dependent current source. Also, the two FVCs for L- and

W-directed current flow result in two equivalent inductors directed along the L- and W- 68

4,4

Fig. 2.25 Equivalent circuit for PEEC model in Fig. 2.24. axes, respectively. The purpose of using such a 2D model is to characterize the current flow throughout finite size ground planes or wide traces with negligible thickness. How­ ever, for the case that the width is relatively small compared to the length, the 2D model becomes less and less important since the current which flows along the width is almost zero. In this case, although the current directed along the width is small, the fact that there may be charge accumulation on the ends of the conductor necessitates using the same arrangement of L-directed inductors. This reduced model is realized by simply replacing the W-directed inductors with short circuits. This simplification to the circuit may not seem to bring about much change in the overall system, but is important to note that the 69

removal of the two circuit elements greatly reduce computation time since, as for the case

of the inductors, they are coupled to every other inductor directed along the same axis. In

other words, through the removal of one coupled element from a system of N + \ coupled

elements, that element as well asN coupling elements are reduced. Therefore, through the

use of this simple reduction, there comes significant savings in computation time at the

expense of a small reduction in accuracy. The equivalent circuit for this reduced circuit is

shown in Fig 2.26. Through careful inception of this circuit, it is apparent that the "amme-

Fig. 2.26 First order 2D PEEC skin-effect model.

ters" or OV voltage sources are still present. In terms of the PEEC approximation, the 70

unknowns attnbuted to the currents actually represent the unknown charges on the

CVCs. This gives the model the ability to account for charge accumulation on the CVCs or capacitive plates.

LPii

Fig. 2.27 Second order 2D PEEC skin-effect model.

For the next level of approximation, the shorted voltage sources are connected together to form one voltage source. As a result the capacitors representing the partial self potential coefficients which were in separate branches are now connected in parallel while the par­ tial mutual interactions for the potential coefficients are now combined. This model is capable of accounting for the charge distribution along the CVCs for the partial self contri­ bution, but neglects the charge distribution for the partial mutual contribution. When cal­ culating the mutual interactions, the capacitive subdivisions are formed by connecting those CVCs which are now in parallel. The equivalent circuit for this configuration is shown in Fig. 2.27.

The simplest yet least accurate model is constructed by joining all parallel combinations of partial self potential coefficients into one value from the second order skin-effect model. This choice of discretization is consistent with the one shown in the layout of the

CVCs and FVCs from section 2.2.1. From the figures in that section, it can be seen that the discretization of the CVCs is that of a one-dim.ensional model. This gives a clue as to how the equivalent circuits are formed. Figure 2.28 shows the equivalent circuit when this approximation is applied to the 2D PEEC model.

Fig. 2.28 Third order 2D PEEC skin-effect model.

In this section, three approximate models were presented for the characterization of skin-effect PEEC models. The skin-effect models serve to decrease the computational requirements at the expense of overall accuracy. For the three models presented, the trade­ 72

off of accuracy for efficiency increased with each level. The determination of the optimum level to model skin-effect depends on model complexity as well as the sensitivity of skin- effect to the desired output. Model complexity affects the accuracy of the skin-effect model because as the system becomes more complex, the charge distributions along the edges of the conductors become more irregular due to non-uniformities in the geometry and ultimately contribute to the proximity effect. The proximity effect can only be accounted for when the currents flowing through the CVCs are retained as unknowns in die system. These currents correspond to the charges on the surface of the CVCs and are properly accounted on the level one skin-effect and full PEEC models. Ultimately, sensi­ tivity of the system output to skin-effect is the means by which the proper skin-effect model may be selected. There are no steadfast rules by which this process may be expe­ dited. It is only through numerical simulations that the designer may arrive at the most appropriate skin-effect model. On the other hand, if fast solutions and memory require­ ments are not a priority, the full PEEC model may be used. 73

CHAPTER 3

EXTENSIONS AND REDUCED FORMS OF PEEC

MODELS

A common misconception among those who are not very familiar with PEEC is that it is merely a way to interpret MoM-type solutions in terms of equivalent circuit elements. On the contrary, there has been extensive progress in the past few years which show how this method may be extended to include incident fields, dielectric models, images, and calcula­ tion of field quantities. Even more important is the fact that the model complexity of the resulting PEEC model may be reduced after the discrete model has be formulated. This last characteristic is totally unique to the PEEC method and may ultimately serve to propel the PEEC methodology well into the next generation of EM CAD tools for high-speed electronic systems. In fact, there are many new commercially-available electronic design tools which use the PEEC method for the noise characterization of systems ranging from relatively low frequency board-level designs to high frequency design of package- and IC- level interconnects. 74

3.1 Incident Fields

A recent advancement to the PEEC methodology allows for the solution of systems in the presence of external electromagnetic fields [26]-[27]. This extension is known as

SPEEC since it results in a scattered field formulation. The SPEEC model is developed via recasting the electric tield integral equation in terms of its scattered field equivalent, or

'^{f) = (3.1) where Ef, Ef, and denote the scattered, total, and incident electric fields, respectively. and the total electric field is given by

E'er) = ^ + V

^(f) = + V(j)(r)+ycoA(r). (3.3) G The presence of the ^ term in (3.3) represents a source term since the incident field is known over the domain. Since this expression may be interpreted as the full-wave analog to KVL, the incident electric field can be accounted for through the introduction of an additional voltage drop across the loop in which this expression is evaluated. In particular, since (3.3) is applied at each FVC, the voltage sources which ultimately account for the incident field are placed in series with the partial self inductances. The values of the addi­ tional voltage sources obviously depend on the form of incident electric field and are quantified through forming an inner product at each rVC,

— [ £'(r)

3.2 Dielectric Models

One of the inherent problems involving integral equation formulations like PEEC and

MoM is that their basic formulations do not support the direct incorporation of materials whose dielectric constant is different than that of the background medium unless, of course, an appropriate Green's function is available for the geometry resulting from the combination of the background medium with the added materials (e.g. case of layered substrates). In the PEEC formulation, and especially in view of our interest in maintaining a SPICE-compatible time-domain formulation, this problem is dealt with through the addition of polarization currents [19]-[20] which appear as additional terms in Ampere's

Law

Vx//(r) = jtiiZoEif)+T{r)+J^{f) (3.5) = + cE{f) +yQ)eo(e^- l)£(r) where ^ and 7^ represent the conduction and polarization currents, respectively. If the contribution from both of these currents are identified as the total current or 76

f{f) = y{f)+i^{f), (3.6) then (3.5) may be rewritten as

Vx^(r) = y(oeo£(r)+y'(r). (3.7) The concept of splitting the total current in terms of its individual contributions allows for the development of a equivalent circuit model for dielectric media which parallels that of conducting media. Recall that for a conductor, the electric field is related to the current through

E{f) = T(r)/

ECr) = T—7^ r/Cr) (3.9) 7Coeo(e^- 1) where is the dielectric constant. Substitution of (3.9) into the expression relating the electric field to the magnetic vector and electric scalar potentials (2.9) yields

-/(r) + V^r) +y(0A(r) = 0 (3.10) yO)£o(e;.- 1) where the current density (r) is associated with the magnetic vector potential and the bound charge residing on the surface of the dielectric volume q''(.r) is associated with the electric scalar potential. Upon substitution of (2.27)-(2.28) into (3.10) for a system with K dielectric/conducting bodies, the electric field integral equation now becomes r I

77

k=I which is very similar to the statement involving only conducting geometries in (2.29).

Through this observation, it is correct to assume that the equivalent circuit model for

dielectrics is of the same general form as the conductors except for the circuit element

which represents the first term in (3.11). The circuit element which corresponds to this

first term can be obtained by taking its inner product as in (3.10),

L L,, a = _z_ ,3,,, aJv7COEo(e^-1) aL/a)eo(er-l)aj 7CoeQ(e^-l)a ycoC^^ where v, a, and / are the volume, cross-sectional area, and length of the FVC over which

the inner product is performed. The equivalent circuit represented by this term is an excess

capacitance whose value is given by the familiar parallel plate equation ta/l with

permittivity e = £0(2^" ^ • Thus, the equivalent circuit model for dielectrics is the same

as for conductors except that the resistors are replaced by capacitors.

Upon discretization of (3.11), the unknown quantities associated with the dielectric bod­

ies are the dielectric current Y{f) throughout the volume and the bound charge {r)

over the surface. However, the second and third terms of (3.11) involve integration over

the total current and charge. This means that the dielectric currents, or equivalently partial

inductances, couple to both dielectric and conductor currents. Also, the bound charges, or

equivalently potential coefficients, couple to both dielectric and conductor potential coef­ 78

ficients. Thus, the model for the dielectric is very much like that for a conductor except

that polarization current is modeled instead of conduction current. The existence of such dielectrics in PEEC models attribute to added complexity since the dielectrics are gener­ ally described by models using three-dimensional current flow.

3.3 Image Problem

Fig. 3.1 Transformation to image currents and voltages.

For geometries containing one or more conducting planes, there is a tremendous require­ ment computationally due to the fact that these planes are generally discretized using large two-dimensional PEEC models. These problems not only create a large number of unknowns, but the number of coupling terms added to the system becomes prohibitive. To circumvent this problem, if it appropriate to assume that the planes are lossless and infinite in extent, then a Green's function taking into account these planes may be used to elimi­ nate the unknowns representing the planes. Alternatively, it is appropriate to solve this problem using the image concept. Both the image concept and construction of an altema- tive Green's function result in the same solution. The image concept involves the elimina­ tion of the conducting planes with "imaged" coupling terms. 79

Figure 3.1 shows the transformation of a geometry with one ground plane to one replaced by the branch currents and node voltages plus their images located equidistant from the ground plane. Note that the images of the branch currents oriented parallel to the axis of the ground plane incur a change of sign. The imaged node voltages also have a sign change.

For the image problem, the value of the image currents and voltages are identically equal to those currents and voltages from which they are obtained. This means that when solving the image problem, there is not an increase in the number of unknowns. However, there will be an increase in the number of coupling terms, A/^/' number of coupling terms in the absence of the ground plane, . Fortunately, the number of coupling terms in the presence of the ground plane, N^q, is much greater than Therefore, when solving the image problem, in addition to saving in the number of unknowns, there also is a significant reduction in the number of coupling terms. So, for those cases where the edge effects associated with the finite size of the ground plane are negligible, it is very favorable to solve the image problem.

What remains for the solution of the image problem is the calculation of the coupling terms associated with the image currents and voltages. For simplicity, assume that there is one ground plane. For currents situated parallel to the image plane, an image current will be created which is opposite in direction to the current in which it is referenced from.

Therefore, any coupling of this type associated with a current and any image is simply 80

~^pij where is the partial mutual associated with the non-image case. For currents situated perpendicular to the ground plane, there is no change of sign when referring to their images. Lastly, the coefficients of potential associated with any voltage and image voltage are given by -p-j where p-j is the coefficient of potential associated with the non- image case.

As an example, consider the CMNA solution of the two cell PEEC model in Fig. 3.2.

This circuit has a vertical as well as horizontal cell situated above a perfectly conducting ground plane of infinite extent. The inductor Lp, , represents the vertical element and the inductor Lp2 2 represents the horizontal element. Using the notation from (2.62)-(2.64),

V. V. 2 OF 3

Fig. 3.2 PEEC tncxlel before applying image theory.

the solution to this circuit in the absence of the ground plane is given in (2.83). However, when the ground plane is present, it is beneficial to solve the image problem. The trans­ formed circuit is shown in Fig. 3.3. Notice that the orientation of the imaged inductor cur- 81

• i.i

Vi tsr •=<*jt

4iP- "Jf

"ij. V. V3

Pia-T ^ ^ PJJ-T Ci>^

c3 •\y/- •ipzj

- Vi

cl

Fig. 3.3 PEEC model after applying image theory. rents are consistent with image theory. The solution is constructed by first identifying the unknowns in the system. For this problem, they are identical to the case where the ground plane is absent. In particular, the unknown node voltages are v,, v,, V3 and the unknown inductor currents are i/p^ ^^. The equations governing current flow through the three

CVCs above the image plane are given by 82

'c. = ("i. I+Tri)^i+(Yr2-Yi.2)'c,+(Yr3-Ti.3)'c3 (3.13)

'c, = 2 + Yr2)^2 + (yr1 - Y2, I )'c, + (7^3 - Y2. 3)'C3 (3.14) = («3, 3 + Yr3)^3 + (rr 1 - Y3. 1 )'c, + (7^2 " ^3. 2)'c, (3.15) where y-j denotes the capacitive coupling between the /''' CVC and the image CVC where the appropriate delays are taken into account between the imaged and non-imaged

CVCs. Substituting for with the equivalent inductive currents from (2.77)-(2.79),

(3.13)-(3.15) become

'c, = («I,1 +Yri)^i+(Yi'"2-Yi.2)('/p,,-V,) + (Yr3-Yi.3)V: (3.16)

'c, = ("2.2 +Yr2)^2 + (Y2. 1 -Yri)'/p, , +(Yr3 -Y2.3)V: (3-17)

'C3 = («3.3+Yr3)^3+(Y3.1-Yfi)'/p,,+(Yr2-Y3.2)(V,-'//':.:^- The corresponding CMNA matrix is

^ r\ . im im im «i.i 0 0 I+Y1.2-Y1.2 Y1.3-Y1.3+Y1.2-Y1.2 M

0 a; 2 0 - 1 + Y2.1 -Y^I Y2,3 ^2 (3.19) 0 0 ab Y3.i-Yri+Yr2-Y3,2 "1 + Yb.Z-Y'S^ ^3 1 -I 0 -Pu-Pti 0 ''Pi.i

0 1-1 0 where a,', = a, , + and (3 •"! denotes the inductive coupling between the FVC and th j image IVC. For this matrix, the inductive couplings R. , and Pj j are zero since the inductors are perpendicular to each other. In comparison to the matrix solution in the absence of the ground plane (2.83), (3.19) represents the solution to the image problem where only a few additional coupling terms are needed to effect a solution which takes 83

into account an infinitely large ground plane. Thus, image theory serves as a very powerful tool for the reduction of problem size and computation time. Image theory can also be applied for the case of multiple ground planes. In this case, the solution requires the trun­ cation of the infinite number of imaged coupling terms which result.

3.4 Far-Field Calculation

Given the far-field assumption, the calculation of the field quantities from the known branch currents and node voltages is fairly straightforward. We begin with the time har­ monic form of the electric field.

E{r) = -ycoA(r) - V(r) (3.20) where A and are the magnetic vector and electric scalar potentials, respectively, and E is the electric field vector at some point in space and frequency, co. The potentials are defined in a AT conductor system by (2.27)-(2.28). The extension to include dielectrics is straightforward and will be discussed at the end of this section. If the source point or primed coordinates conform to the cartesian coordinate system and if the observation point or unprimed coordinates conform to the spherical coordinate system, the far-field expressions for (2.27) and (2.28) become

-y'Kr (3.21) 84

= i - i • ''• '"2' fc = 1 k = { * where a' = (x'cos0 +>-'sin

-jKr ^ S I <3.23, i = 1 n = I for y = X, y, z with d = (xcoscj) + ysin(t))sin9 + zcosG and Y from (3.22) extends between the limits Y±Ay/2 for the n IVC of the k conductor describing current flow in the y direction with cross sectional area, , perpendicular to current flow. In a similar manner, discretization of (3.22) gives

. -jKr fc o,

fc= lo = 1 th th where is the sum of all branch currents flowing out of the o CVC of the k conduc­ tor.

Now that the vector and scalar potential functions have been approximated and evalu­ ated numerically, all that remains is to insert both expressions into (3.20). In the far-field, the r components of E and H are negligible compared to the (j) and 9 components.

Therefore, after performing the gradient of the scalar potential in spherical coordinates, the non-zero components of the electric field can be written as

£0(r, 9, 0) = -yCi)[A^cos0cos0 + AyCos9sin(l) - A^sin9] (3.25) yfc[(.rcos(t) + _vsin(j))cos9 - jsinGl^ 85

E^(r, 9, 0) = -yco[-A_jSin(() + A^cos0] ycos0)^ (3.26) where Ay and O are given by (3.23) and (3.24), respectively. Given the solution for E in

(3.25) and (3.26), the presence of image currents and voltages are taken into account by simply included them into to calculation of Ay and while preserving the proper signs for those terms.

There are no modifications necessary for the far-field calculation of a system with con­ ducting as well as dielectric bodies. The expressions for the potential functions in (3.23)-

(3.24) are applicable for both cases. In other words, the far-field is calculated by applying

(3.23) and (3.24) at each IVC and CVC, respectively in the entire system. The next section will discuss the simplification of the problem via the systematic removal of partial induc­ tances and potential coefficients. For these cases, removal of partial inductances from the problem results in the calculation of the far-field with A = 0. Similarly, removal of potential coefficients from the problem results in the calculation of the far-field with

= 0.

3.5 Hierarchical Electromagnetic Modeling

Two key attributes of the PEEC formulation are its ability to model heterogeneous sys­ tems (i.e. systems involving lumped circuit elements as well as distributed electromag­ netic components) and its suitability for hierarchical electromagnetic modeling. This second attribute is closely related to model complexity (or model order) reduction, and it is of critical importance to the efficiency with which electromagnetic analysis of intercon- 86

General Full-Wave PEEC Model (R, Lp, P, T)

Electrically Small (R, Lp, P)

RL Dominance I RC Dominance I (R, Lp) I (R, P) I

Fig. 3.4 Hierarchy for PEEC conductor models. nect and packaging structures associated with high-speed digital and high-frequency ana­ log electronics can be effected. For example. Fig. 3.4 depicts the hierarchical complexity which evolves from the PEEC model of a lossy conductor where the particular simplifica­ tions are identified by the symbols R, Lp, P, and T for resistors, partial inductances, potential coefficients, and delays, respectively.

A review of the applications of PEEC to electromagnetic simulation reveals that the most popular model complexity reduction has been the elimination of the delays in PEEC models. Clearly, this approximation is acceptable when the size of the structures under investigation is small compared to the minimum wavelength of interest. As an example, we mention the application of PEEC for the electrical modeling of single-chip package interconnects in terms of a network of resistors, partial inductances, and potential coeffi­ cients. Furthermore, if only the inductive behavior of the package is of interest, the PEEC model reduces to the so-called (/?, L^) PEEC model, which is essentially a discrete 87

approximation of the magnetic diffusion equation, and has been used extensively for pacic- age inductance modeling [22]-[23].

The implementation of the PEEC formulation in a SPICE-compatible simulator provides for a more versatile application of the aforementioned quasi-static reduced PEEC models.

More specifically, different levels of interconnect and different parts in the package and board of a system can be modeled for the purpose of signal integrity prediction by imple­ menting different types of electrical models as appropriate. For example, an (/?, P)

PEEC model can still be used to model the interconnects and associated ground and power planes within a single-chip package, with SPICE models for the driver electronics and

SPICE-compatible transmission line models for the coupled interconnects on the integrat­ ing substrate, card or board. This way, very complex interconnect/packaging structures can be modeled efficiently using a single modeling/simulation environment.

In the aforementioned example it is assumed that the emphasis of the simulation is on the prediction of signal degradation due to crosstalk, interconnect delay, reflection, and simultaneous switching noise. If, in addition, the prediction of electromagnetic radiation from the interconnect and package structure is of interest, the aforementioned model becomes inadequate, and retardation effects need be taken into account. Furthermore, if it is possible to identify the dominant sources of radiation, the delays can be incorporated selectively and in a limited fashion where appropriate. For example, selected interconnects on printed circuit boards, which exhibit imbalances due to discontinuities or layout con­ straints. can be modeled using a rigorous electromagnetic PEEC model, while the remain­ 88

ing of the well-balanced interconnects can be modeled using SPICE-compatible transmission line models. To illustrate this concept, consider the 1.8 cm short-circuited coplanar waveguide shown in Fig. 3.5. Each of the three zero-thickness conductors are

1.8cm

1.0mm 0.5inm

Fig. 3.5 Short-circuited coplanar waveguide.

1.0 mm wide and are separated by 1.0 mm. The current sources attached to the near end of the waveguide are of equal magnitude for this balanced system. For the analysis of this waveguide, two methods shall be employed. First, a method of characteristics or SPICE transmission-line model is used as shown in Fig. 3.6. For this model, the characteristic impedance is Zq = 134.0 Q and the equations for the voltages are given by

VV = V2{t-TD)-k-ZQ-n{t-TD) (3.27) Vr = V\{t-TD)+ZQ - I\\t-TD) (3.28) where the line delay \s TD = 0.06 ns. Second, a (/?, P) PEEC model is employed to characterize the same waveguide. The equivalent circuit for this model is constructed through lumped inductor/capacitor combinations as shown in Fig. 3.7. In this figure, the rectangles and circles denote the inductors and capacitors, respectively. Note that the mutual interactions are accounted for in this model, but are not shown for clarity. For this 89

II 12

ZO Z1 VI V2

VI' V2

Fig. 3.6 SPICE transmission-line model for coplanar waveguide.

PEEC model, the number of inductive/capacitive cells was determined by using 20 sec­ tions/A, at 12.5 GHz. For a 1.8 cm line in free-space, this results in 3/4 wavelength or equivalently 15 sections. In order to compare the accuracy of both approaches, consider

Fig. 3.7 PEEC model for coplanar waveguide.

the input impedance of the transmission-line vs. frequency. For this simple arrangement of conductors, transmission-line theory predicts an input impedance of the form,

^in = y2otan(/:/) = yZotan( 1.5;r). (3.29) The result for both the SPICE tranmission-line and (/?, Lp, P) PEEC models is shown in

Fig. 3.8. As can be seen, the predicted impedances are in close agreement even at very high frequencies. This suggests that for well-balanced systems, simple transmission-line 90

10 SPICE TL

FEEC

(0 E

(D O J aC •a Q.

^ -5

-10 3 5 7 9 11 13 15 Freq (GHz)

Fig. 3.8 Comparison of PEEC and SPICE transmission-line responses.

models will suffice. Moreover, there is no noticeable difference in the (/?, P) and

(/?, L^, P, X) PEEC responses. This is demonstrated through the plot of the electric field at

3 m in Fig. 3.9 using far-field expressions. In this plot, the magnitude of the electric field is calculated at the first resonance, 4.1 GHz, for (() = 0 and 0 < 0 < 27C where 9 = 0 corresponds to the y-axis. This plot shows that both retarded and non-retarded PEEC results in the same elecuic field. Thus, this simple study shows that for balanced intercon­ nect geometries, the SPICE tranmission-line, (/?, L^, P), and (/?, L^, P, T) PEEC models result in indistinguishable solutions.

As the previous example showed, well-behaved balanced systems are very simple to model. However, in most practical cases, such simplifications are not possible due to the 91

0.5

-1.5 -1.0 -0.5 0.5

-0.5

RLPT PEEC 3K-*RLP PEEC

Fig. 3.9 Far-field response for coplanar waveguide. complex arrangement of conductors found in high-speed electronic designs. As a slight modification to the previous example, consider the same coplanar waveguide now with a right-angle bend. This geometry is shown in Fig. 3.10 where L + L^ = 2.3 cm. In this case, the waveguide is driven with voltage sources instead of current sources. For the first study, consider the magnitude of the current flowing at the input of the top conductor vs. frequency for both {R,Lp,P) and (/?, P, t) PEEC models. Figure 3.11 shows the resulting waveforms. As can be seen, the two responses are fairly consistent with each other for frequencies less than about 10 GHz. Beyond that point, differences become noticeable between the two waveforms. The differences in the peak values are attributed to the fact that (R, L^, P) and (/?, L^, P, T) PEEC models have different loss mechanisms. Fig. 3.10 Coplanar waveguide with a right-angle bend.

RLPT TOP ^LPfOP

1 1. i

. . . J j , 1 6 8 10 12 14 16 Freq (GHz) Fig. 3.11 Source currents (PEEC) for coplanar waveguide with right-angle bend,

Thus, for reasonable frequencies, both retarded and non-retarded PEEC give similar 93

results. As an alternative to strictly using either a SPICE transmission-line model or PEEC

model to represent the conductors, a hybrid model may be used instead. This hybrid model

consists of both SPICE transmission-line and retarded PEEC models. As shown in Fig.

Fig. 3.12 Hybrid PEEC/SPICE transmission-line model of acoplaneir waveguide with right-angle bend.

3.12, the SPICE transmission-line model is used at the source and load ends of the

waveguide since these sections are considered to behave in a manner consistent with trans­

mission-line theory. On the other hand, the bend is modeled using a retarded PEEC model.

With this hybrid model, the magnitude of the current flowing at the input of the top and

bottom conductors vs. frequency is shown in Fig. 3.13 where L = 1.6 cm and

= 0.7 cm. Close inspection of this plot reveals that the hybrid model tends to average

the resonances which develop on the top and bottom conductors when modeling the

waveguide entirely with a retarded PEEC model. If the length of line which is represented

by the SPICE transmission-line is reduced in favor of increasing (i.e. moving away

from the discontinuity before transmission line modeling is used), a better correspondence

is expected between the hybrid and PEEC models. Figure 3.14 shows this case as L is decreased from 1.6 cm to 1.4 cm and is increased from 0.7 cm to 0.9 cm. Again, the 94

800 RLPT TOP 700 RLPTBOf RLP~f/SPTCE~tL 600 < E •

Figure 3.15 shows magnitude of the electric field calculated at the first resonance. 95

450 RLPT TOP 400 RLPTBOf FrLPT/SP7cl"tL 350 < £ 300 o 3 250 o> CO ! E 200 c0) w 150 O ii 100 .• JJ? ,1 • • II 11It 1 u 1 u 50 y ,1 . t 0 'J i .''3 J 0 6 8 10 12 14 16 Freq (GHz)

Fig. 3.14 Effect of changing the length of the SPICE transmission-line.

3.4 GHz, for ({> = 0 and 0 < 0 < 27t. The field is evaluated at r = 3 m using far-field expressions. This figure shows that the addition of the bend to the waveguide results in an electric field which varies between the retarded and non-retarded cases.

Finally, it is mentioned that this hierarchical capability of the proposed simulator is very suitable for efficient electromagnetic analysis of mixed-signal electronics, where interac­ tions between the interconnect and power/ground distribution networks for the high-speed digital and the analog/RP blocks need to be taken into account for proper electrical design.

As an example, we mention the case where noise generated in the digital block of a porta­ ble computing device is radiated out and eventually received by an antenna used for pro­ viding a wireless data link for the device. A generic example of such an interaction is 96

1.0

0.5

-1.5 -0.5 0.5 1/0

-0.5

-1.0 RLPT PEEC - - - RLP PEEC

Fig. 3.15 Far-field response for coplanar waveguide with a right-angle bend. illustrated in Fig. 3.16. This system consists of blocks which represent package intercon­ nects, board interconnects, and an antenna located 20 p.m, 200 ^m, and 1 mm, respec­ tively, above a perfectly conducting ground plane which extends to infinity. The package interconnect block consists of a group of four 50x50 p.m driven signal traces with ground traces on either side. The source for these lines is composed of a 75 Q resistor in series with a periodic pulse train with 50 ps rise and fall times, 0.4 ns pulse width, and 1 ns period. The board interconnects are comprised of four 0.5x0.5 mm lines each terminated by a I pF capacitor. The antenna consists of a 1x5 cm loop connected to a band-pass fil­ ter with cut-off frequency 3 GHz and terminated by twice the odd-mode impedance.

200 Q, of the difFerential-mode line with conductors of 1 mm width, 0.1 mm thickness. 97

Antenna

Son

Package Board Interconnects Interconnects 1.5cm Son fc=3GHz

Son

I I I I T T T X

Fig. 3.16 Generic mixed analog/digital system. and 0.4 mm separation.

The motivation for investigating this particular mixed analog/digital system is to deter­ mine when retardation effects become important. First, consider the voltage across the left-most load capacitor of the board interconnect on the left-most end. Figure 3.17 shows the waveforms when using retarded and non-retarded PEEC models. These waveforms are typically investigated in signal integrity analysis where the delay, overshoot, undershoot, etc. is of interest. As can be seen by the close agreement between the waveforms, the incorporation of delays is not absolutely necessary in such a system even when consider- 98

RLPT ^LP

0.8

> 0.6 oO) CO 3 0.4 >

0.2

-0.2 0 1 2 3 4 5 Time (ns)

Fig. 3.17 Voltage across capacitor on left end for lines driven simultaneously. ing a relatively fast rise-time of 50 ps. On the contrary, examination of the voltage across the input to the antenna as shown in Fig. 3.18 shows that there is a big difference in the resulting waveforms for the retarded and non-retarded cases. This analysis shows that whether the full-wave model should be incorporated depends no only on the geometry and the spectrum of the excitation, but also on the what output is desired from the system. In this mixed analog/digital system, it was observed that the output across the loads of the interconnects was mainly due to the propagation of the signal along the length of the line.

This phenomenon was simulated with reasonable accuracy without the addition of retarda­ tion. However, in the case of the antenna, the only source of energy to this component is due to radiative coupling. As it turns out, coupling through radiation is a very sensitive to 99

5e-05 RLPT 4e-05 ^LP 3e-05 2e-05 ^ 1e-05 ®O) r\U i5 V ' > -1e-05 -2e-05 -3e-05 -4e-05 -5e-05 0 1 2 3 4 5 Time (ns)

Fig. 3.18 Voltage across input to antenna. the level of approximation used and thus requires a fiill-wave or retarded PEEC model to accurately recover the correct response. (

100

CHAPTER 4

TRANSIENT ANALYSIS

One of the most appealing features of PEEC is that its formulation is not specific to the

time- or frequency-domain. All that is necessary to change the formulation from the fre­

quency to time-domain is to replace all occurrences of yco and /(R')exp(-YK|R-R'|)

with d/dt and f{r', t') = f{f\ t-\r-r'\/v) , respectively, where r' is used to indicate

that the interaction between the charge or current density at r' with die charge or current

density at r is delayed in accordance with the finite speed of electromagnetic wave propa­

gation in the medium with propagation speed v. After the necessary changes have been

made to the matrix, all that remains is to employ a numerical integration scheme like

Backward-Euler or Theta to solve the system of equations. This ability to switch from fre­

quency to time-domain and vice versa after the problem has been formulated is a very

desirable characteristic of PEEC.

There are however issues concerning stability with the (/?, Lp, P, x) PEEC formulation.

This instability has been observed for many years in this as well as other time-domain

methods which involve the solution of an electric field integral equation. Many methods

have been proposed for the solution of the problem and some attempts have succeeded to

provide solutions to cases which were previously unstable. However, there remains to be 101

one method which rigorously solves the problem of stability in all cases. In the mean time,

there are many situations which result in stable solutions using the (R, L^, P, x) PEEC for­

mulation, and for those cases which result in instability, the always stable {R,Lp,P)

PEEC formulation can be used, provided that the elimination of delays is a reasonable

approximation for the problem under study.

Aside from the potential instability in the time-domain version of (/?, Lp, P, T) PEEC.

the ability to perform transient analysis using PEEC is of great interest to those who are concerned with electromagnetic noise interactions and signal integrity analysis. More spe­ cifically, the incorporation of non-linear devices is only possible in time-domain solutions.

This fact drives researchers towards the goal of devising stable solutions in the time- domain.

Another appealing feature of the time-domain formulation is that waveform relaxation may be employed. Waveform relaxation is an iterative technique which serves to reduce the memory and computation requirements for large problems and is ideally suited for dis­ tributed computing.

4.1 Numerical Integration Methods

As stated above, the time-domain solution of a system involving PEEC models is effected by first replacing the jco terms in the matrix with d/dt as well as interpreting the

/(r')exp(-yKlr-r'l) terms as functions in the time-domain whose value is delayed by

= fir', t-\f -f'\/v) . Once these changes have been made, the time-domain 102

solution is accomplished through the application of a numerical integration scheme. In this section, two implicit schemes will be employed, namely Backward Euler (BE) and Theta

(0). In order to illustrate these methods, the cMNA formulation in Section 2.3.2 will be considered.

4.1.1 The Backward Euler Method

In the BE [28] method serves to provide a numerical solution to the time derivative of an arbitrary function x at time is approximated

where Ar = - tp_^. In addition to the choice of numerical integration scheme, time- domain PEEC solutions require two additional definitions. First, a numerical approxima­ tion is required for the delayed functions, x(tp-X), where .r is evaluated at the present time tp minus the delay T . Assuming that the function is evaluated at integral multiples of the time-step At, these delayed functions need to be interpolated between these point in such a way that the order of approximation is not greater than that of the numerical inte­ gration scheme. If we choose to linearly interpolate between the past values, that corre­ sponds to a first order scheme as is of the same order as the numerical integration scheme.

Therefore, if it is required to approximate the function x{tp - 1.25Af), linear interpolation results in the following relationship,

x(tp- l.25At) =0.75x(tp- At) +0.25xitp-2At) (4.2) = 0.75.r(fp_,) + 0.25.r(rp_2). 103

Second, a numerical approximation is required for the delayed derivative terms which appear. These terms are of the form x(tp-x) where the dot denotes a time derivative.

Again, these values need to be approximated in such a way that the order of approximation used is not greater than that used for the numerical integration scheme. Linear interpola­ tion of the derivative meets this requirement also for this case. As an example, consider the numerical solution to 1.25Ar). The approximation of the delayed derivative is given by

At 1 = ^[0.75x(fp_i) -0.50j:(rp_2) -0.25.r(/p_3)].

Now, all that remains for a time-domain PEEC solution is to apply these approximations to the corresponding matrix elements. As an example, consider the cMNA formulation in

(2.83). The time-domain form of this matrix is given by

0 0 Pi.i Pi I P..: p, I <>'•> 1 d 0 0 P-LV Pi, 1^^ P2,2 Pi, 1 I d ^3,1. . ^3,2, . P% "> (4.4) 0 0 p^^dt P3 3 P33 P'--

-1 0 -L — PxAdt ^lP\.\

-1 -L 0 1 'P2.2dt 104

where the notation (T ) represents the variable evaluated at r = r- T„ and —(T, ) y-i p Pt.] di represents the time derivative of the variable evaluated at F = - T, . For this example. P J assume that the delays are as follows.

= T = 0.5 Ar (4.5) PI.2 Pz.1 T_ = x_ = 1.25Ar (4.6) Pi. 3 Pi. I x„ = T„ = 2.0Ar (4.7) P:.} P3.2 t,Ltf 1 2 = Xr { = l.5Ar. (4.8) The approximation of the currents delayed by T_ in (4.5)-(4.7) and the derivatives of the Pt.j currents delayed by x, in (4.8) are given by

(4.9) iitp -0.5At) = Q.5Ktp) + O.Siitp _ ,) (4.10) i(tp- 1.25At) ^0.75iitp_i) +0.25iitp_,) (4.11) i(tp-2.0At)='i{tp_2) (4.12) and

diit -l.SAt) 0 5 0 5

where the result in (4.13) for the delayed derivative is the second order approximation known as the central difference. Even though this second order result seems to violate the requirement of first order accuracy, it is only second order accurate at one point along the interval At and thus should not be considered to a problem. All that remains in the time- domain solution is for the substitution of the corresponding terms in (4.9)-(4.13) to the matrix in (4.4). Assuming that the solution is computed at r = , all of the terms in (4.9)- 105

(4.13) which are delayed by more than one time-step will be moved to the right-hand-side

vector. After making the necessary substitutions, (4.13) becomes

0 0 1-0.5^ 0.5^ Pi.\^ P\,i Pi.I Px 1 0 0 -1+0.5 1 Pi,i^ Pi, 2 1 0 0 0 -1 = a (4.14) P3,2^ L Pi. 1 1 -1 0 0 h

L„Pz. 0 1 -I 0 h hp.J^p) where h = At and

2r . P\.3. ^V, ('p - I) + 0-5^['(p,,(V - I) - "(p,:(V - I > I 2

a = (4.15) P3.3^ ^" ' ^^3.3 ""* P3.3

P:.:.- 9L2h ['/Pl 1) U ^lp2.z^^p-0 where

Y/,/ = 0J5iipJtp_^) + 0.25iip{tp_2). (4.16) 106

This completes the formulation of the matrix for the time domain solution using the

implicit method, BE. The solution is effected in a time-marching manner through the use of the inverse of (4.14).

4.1.2 The Theta Method

In contrast to the implicit method BE, the Forward Euler (FE) [28] method is totally explicit since it approximates a numerical solution to the time derivative of an arbitrary function x at time by

Explicit methods such as this one have not been used for the solution of differential equa­ tions resulting from MNA-type formulations. The reason is that explicit methods such as this one imposes great restrictions on the allowable time-step for stable solutions. BE on the other hand is an implicit formulation and imposes no restriction on allowable time- step.

An alternative to these methods is the theta method. The theta method is defined as a weighted average of both BE and FE. Mathematically, it is given by

(4.18)

Upon close inspection of (4.18), it can be seen that choosing 0 = I results in BE while choosing 0 = 0 results in Ft. Also, for the case that 0 = 0.5, (4.18) reduces to the sec­ ond order accurate trapezoidal method. Thus, through the adjustment of the parameter 9 . 107

this method is capable of functioning like three different integration schemes. Moreover, values of 0 between the intervals 0.0-0.5 or 0.5-1.0 allow for adjusting the desired response. For example, the trapezoidal method has very little numerical damping while

BE causes significant numerical damping which helps enhance stability. If 9 is chosen to be 0.52, then the response will be nearly identical to the trapezoidal solution except for the addition of a little numerical damping which helps enhance stability. This choice of 0 may be desirable in those cases where the absence of loss in the circuit results in an potentially unstable solution.

With this scheme, the numerical approximation of the time derivative at t = requires the value of the derivative at r = . In other words, this scheme requires saving the past derivative. For example, consider the evaluation of Cdv/dt at r = . The first step in the solution process involves using (4.18) for the approximation to the time derivative.

(4.19) where the last term on the right-hand-side is the past derivative. At the first time-step, it is assumed that the past derivative is zero. Therefore, the first term on the right-hand-side of

(4.19) is the only non-zero quantity at the first time-step. For all subsequent time-steps, the past derivative is computed from (4.18) as

(4.20) where dv(tp_^)/dt is the previously computed past derivative. Therefore, as far as the computation of the time derivative in (4.19) is concerned, theta and BE are similar in form 108

except now there is an extra term and there is additional overhead required through the

storage of a past derivative.

Finally, the computation of the delayed values amd delayed derivatives can be accom­

plished in exactly the same way as for BE. Given this description of the theta method, all

that is required is to make minimal changes to the solution developed in Section 4.1.1.

4.2 Numerical Stability

0.5

0.25

> ®C3) Un ffl o >

-0.25

-0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (ns)

Fig. 4.1 Example of instability obsen/ed whea using (R, Lp, P, T) PEEC.

The mechanisms which influence stability in (/?, L^, P, x) PEEC as well as other time- domain electric field integration equation formulations has been investigated for many 109

years [6]-[I0]. Unstable solutions such as the one shown in Fig. 4.1 are sometimes observed. These solutions are actually quite accurate until the onset of the oscillations

which grow to infinity. These oscillations may either be present at the beginning of the response or during late times after the transients have died out. One of the reasons which makes analysis of stability so difficult is that the observed instabilities are very difficult to predict. Slight perturbations of a PEEC model may result in a stable model going unstable or vice versa. Sometimes, if the adjustment of a parameter in the model makes the solution unstable, further adjustment may lead to stable results again. In the following, two tech­ niques for improving stability will be discussed. The aim of this development is to not only introduce methods for which reduce the occurrence of instability, but also to reveal the mechanisms which bring about the instabilities.

4.2.1 The Phase Grid Approach

The main idea behind the Phase Grid Approach (PGA) [10] is to reduce the error intro­ duced through the approximation of the exponential terms contained within the potential coefficient and partial inductance calculations in (2.40). For the term in (2.40) represent­ ing the partial inductances, the approximation of the exponential term in

(4.21) is appropriate for those cases when the quantity K^r^pi - is essentially constant over the limits of volumes and . This corresponds to low frequencies since the factor 110

K is directly proportional to frequency. One way to maintain accuracy at high frequency is

to discretize finer or reduce the size of the volumes and . However, this is not

practical since this leads to an increase in the number of unknowns. As a result, the expo­

nential terms are not resolved with a high degree of accuracy at frequencies well beyond

those of interest. This may not seem to be a concern, but for time domain solutions, the

numerical integration scheme allows such frequencies to influence the solution. In fact, the trapezoidal scheme has infinite frequency content. Methods like BE do not have an infinite frequency response, however it does allow into the solution frequencies which are well above the desired frequency range. This leaves two possibilities if we are to leave the

PEEC model unchanged. We can either choose a numerical integration scheme which has a high roll off with frequency or we can do a better job with the approximation of the exponential function. The former seems to be undesirable since such schemes are complex and require much more overhead; but the latter seems appealing if an efficient and accu­ rate solution can be achieved.

As stated above, extremely high frequencies are brought into the solution upon applica­ tion of the numerical integration scheme. These frequencies may be on the order of 50 times higher than the highest frequency resolved through discretization. Therefore, instead of discretizing 50 times finer, which would create an enormous number of unknowns, we can resolve the exponential terms 50 times finer while retaining the same discretization.

Consider again the term representing the inductance in (4.21). Instead of evaluating

\^ypi~^ynk\ between volumes and by \rypi-ry„;,\ where r denotes the average of the spatial extent of r, each volume v may be subdivided into P sub-volumes where the averaging is now taken place over the sub-volumes. Mathematically, this process can be described as the refinement of error introduced through the approximation of the phase in

by the subdivision of IVCs yml and ynk into P^'"' and sub-volumes, respectively, giving

pimi ptnk -jK\r, -r,\

where s and t denote the subdivided cells of the IVCs yml and ynk. Therefore, each par­ tial self and partial mutual inductance is now interpreted as a double sum of partial induc­ tances multiplied by their corresponding exponential delay factors. This subdivision process is also required for the potential coefficients, but does not need to be explained since the steps are identical to that of the partial inductances.

Although stability is only a concern in the time-domain, PGA was developed using fre­ quency-domain concepts. The idea of resolving the phase more accurately is to the fre- quency-domain what resolving the time delay is to the time-domain. Therefore, it was hoped that through a finer resolution of the phase in the frequency-domain, the overall sta­ bility of the system in the time-domain would be improved enough to resolve the high fre­ quencies allowed by the numerical integration scheme. This method was tested and 112

perfected entirely in the frequency-domain through the measurement of input impedances

several test circuits using retarded PEEC. Assuming that for a particular test case, the fre­

quency was resolved at 20 nodes per wavelength at 20 GHz, the frequency response would

then be measured up to 1000 GHz. Examination of the real and imaginary part of the input

impedance over this large frequency gave information on the relative stability of the cir­

cuit. More specifically, stability is compromised for those frequencies in which the real

0.3

0.25

0.2 > §, 0.15 o > 0.1

0.05

0 0 10 20 30 40 50 60 70 80 90 100 Freq (GHz) Fig. 4.2 Stabilization of 0.9 x 1.0 cm patch using PGA.

part of the input impedance is negative. Before application of PGA on a retarded PEEC

model, Lhe frequency response at high frequencies reveals this unwanted behavior. How­ ever, the response becomes much more well-behaved after applying PGA. As shown in 113

Fig. 4.2, the real part of the input impedance looking into the comer of a 0.9 by 1.0 cm

plate discretized at 20 elements per wavelength at 15 GHz becomes well-behaved after

using PGA (dashed line).

4.2.2 The Alternating Green's Function Approach

Based upon the insight gained from studying the effect of time-step on stability, the

Alternating Green's Function Approach (AGFA) provides stability enhancement to

{R, Lp, P,x) PEEC solutions in a very straightforward manner. The objective of this approach is to provide a solution which has the stability characteristics of (R,Lp,P)

PEEC while maintaining the full-wave accuracy of {R, L^, P,x) PEEC. Although this ideal situation has not been achieved in a rigorous manner with AGFA, it can provide solu­ tions for systems which were previously unstable with accuracy better than that of

(/?, Z.p,/>)PEEC.

Through many simulations, it has been observed that the delayed couplings between those elements which are near one another play a major role on stability. AGFA entails replacing those delayed couplings with non-delayed couplings. Therefore, for each capac- itive and inductive coupling term, a radius r is defined such that any coupling inside that radius is not delayed and any coupling outside that radius is delayed. Mathematically, this method can be interpreted as using the Green's Function, I 14

for those couplings separated by a distance greater than r, and

for those coupling separated by a distance less than r.

This very simple idea is capable of good stability enhancement at the expense of some loss in accuracy. However, the major loss in accuracy is only observed in the fast transient portion of the response. The steady-state solution does not seem to be affected very much.

Also, there is an adjustable parameter r which needs to be specified prior to performing the analysis. This value is dependent on the geometric complexity and electrical size of the problem. The optimum value can be arrived at through numerical simulations whereby the overall accuracy of the solution is compromised by ever increasing r.

4.2.3 Evaluation of Stabilify Improvement Using PGA and AGFA

Of those integration methods derived from the 0 -method, BE is by far the most stable while FE is the most unstable. When using BE to solve problems involving circuit ele­ ments derived from (/?, L^, P, x) PEEC, there is a limit for the minimum time-step allow­ able. On the other hand, FE only results in stable solutions for a narrow window of time- steps. Lastly, trapezoidal method (0 = 0.5) also imposes a minimum limit on time-step and is less diffusive and less stable than BE. The trapezoidal method is a second-order method while all other values of theta result in first order solutions. In this study, values of 1 15

0 ranging from 0.5 to 1.0 will be used to study accuracy. The range 0 < 0 < 0.5 results in

very unstable solutions and will not be considered for that reason.

Consider a zero-thickness conducting plate of size 0.9 by 1.0 cm. A trapezoidal pulse of current with rise-time, roof-time, and fall-time of 0.1, 0.3, and 0.1 ns, respectively is used as the source which is fed into one comer. The stability of the (R, L^, P, T ) PEEC circuit is observed over a 10.0 ns period while changing the time-step, integration method, and sta­ bilization scheme. For the sake of simplicity, only three values of 0 will be used in this study: 0.5,0.75, and 1.0. In this analysis the plate is segmented into square cells of side 0. i cm. Thus the approximate model describes a two-dimensional current flow. A two-dimen­ sional case is used for this study since it has been observed through simulation that it is much more unstable than one-dimensional cases. Figure 4.3 shows the length of time in which a stable solution is maintained as a function of time-step for different integration methods and using no stability enhancements. The point at which each of the lines ends corresponds to the point at which that corresponding integration method has achieved sta­ bility for at least 10 ns. As can be seen, the range of stability does not vary linearly with time-step. In fact, the dependence of stability on time-step is so erratic that it makes the process of predicting stability quite difficult. The only thing one may conclude from such an analysis is that after a certain time-step, stability is achieved. Time-steps lower than that may cr may not result in stability. In fact, the BE curve in Fig. 4.3 shows a stable simula­ tion time of 10 ns for a time-step of 1.4 ps. However, if the time-step is made a little larger or smaller, then the solution goes unstable. Another thing which can been seen from this 1 16

10 BE 9 THEfA^.ZS 8 THETA^.SO

7 cCO 0 6 / \ 1 c [ 1 1 1 I 4 /' 1 E / CO 3 fI 1 1 \ J / / / / • \ / 0 L. 1 1 J 1 1 1 I i 1 1 1 1—1—1—1 1 0.0001 0.001 0.01 Time-steo (ns)

Fig. 4.3 Effect of time-step on stability for (R, L^, P, t) PEEC. figure is that the trapezoidal method is the least stable of all three schemes. This method is even unstable for time-step values up to 0.01 ns. A surprising, but not conclusive result from this study is the observation that 9 = 0.75 is more stable than BE. More specifi­ cally, stability is achieved for 0 = 0.75 and BE at 2.0 and 3.0 ps, respectively.

Next, stability is analyzed for PGA where each full-sized IVC and CVC is subdivided into 4 smaller sections. For the FVCs and CVCs on the edge of the boundaries, the half- cells are subdivided into 2 smaller sections and the quarter-cells are not subdivided at all.

This choice of subdivision may or may not be optimal for any general geometry, but it does give a general indication on how this stabilization scheme performs. In [ 10], PGA not only entails subdividing the FVCs and CVCs, but it also includes connecting a resistor in 117

-AMr *

V V, AAA r?nn "2 A A A NNN 3

cl, .X

Fig. 4.4 Resistors in parallel with partial mutual inductors.

parallel with each partial self inductance as shown in Fig. 4.4. The idea behind this modi­ fication is that if there is a resistor in parallel with each partial self inductance and the value of the resistor is large enough to not destroy the low frequency response, then hope­ fully this resistor will represent a lower impedance path than the inductor at high frequen­ cies and thus improve stability by making the effect of the inductor negligible at high frequency. However, in the test cases performed in this study, the addition of the parallel resistor did not make an appreciable affect. This is not to say that the addition of such a resistor does not affect stability, it is the case that stability was not affecting in this analy­ sis. Figure 4.5 shows the stability of PGA vs. time-step for three different integration schemes. This figure shows that stability is definitely improved for such a choice of cell subdivision. This study shows how an arbitrary choice of subdivision affects stability.

Again, it is the case that 0 = 0.75 is the most stable followed by BE and then the trape­ zoidal rule. For each value of theta, there may be different values chosen for sub-cell size 118

8

7

6

5

4

3

2

1

01= 0.0001 0.001 0.01 Simulation Time (ns)

Fig. 4.5 Stability enhancement of PGA vs. time-step. which result in even more stable solutions. Also, this study involved choosing the FVC and

CVC sub-cell size to be identical. However, the sub-cell size may be different for the IVCs and CVCs.

Next, the effect of AGFA on stability is investigated. The same geometry is considered in this case as for PGA. In this study, the time-step is fixed at I ps and the radius r is increased from 0 until stability is achieved. Figure 4.6 demonstrates how stability is affected by varying r. For small values of r, the results are identical to that of the PEEC without using a stabilization scheme. When the value of r is comparable to the cell size, then the stability is affected. Initially, stability is worse but then steadily increases until stable solutions are achieved. Again, the three integration schemes demonstrate stability in 119

7

6

5

4

3

2

1 ./"N

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 radius (cm)

Fig. 4.6 Stability enhancement of AGFA vs. coupling radius. a manner similar to the above. For this approach, the trapezoidal rule is especially ineffec­ tive and stability is only achieved for values of r comparable to the size of the entire struc- oire. In this case, the stable solution is identical to that of non-retarded PEEC.

Although the above discussions involved the study of simple cases, the general trends observed are fairly representative of more complex geometries. More specifically, the phe­ nomenon of numerical instability can be predicted for simple two-dimensional and com­ plex one-dimensional problems; yet it is difficult to determine a priori the exact transition to instability. To complicate matters, the generation of dependencies on stabilization fac­ tors on overall stability as in Figs. 4.5-4.6 require a tremendous amount of time to gener­ ate. Therefore, the insight necessary to fully understand the mechanisms which influence 120

stability is compromised by the overwhelming amount of simulation time required. How­ ever, it is hoped that these studies will provide the preliminary information needed to per­ form such studies or even better develop more rigorous solutions for the elimination of instability.

4.3 Waveform Relaxation

The waveform relaxation (WR) method is well known for the solution of partitioned sys­ tems of circuits or differential equations in the time-domain. The method has been suc­ cessfully applied for the solution of very large circuits on both scalar as well as parallel computer, e.g. [33]. In addition, the range of problems solved with the WR method may be extended to include circuit based EM formulations such as PEEC. The PEEC solution cor­ responds to an electric field integral equation (EPTE) which in the time-domain leads to a neutral delay differential equation formulation.

The fundamental idea of the WR method is to decouple the problem into subproblems.

The subsystems are chosen in such a way that the coupling is moderate at least in one direction. Then, the subsystems are solved for a window in time rather than a point in time as is usually the case. The size of the time window depends on several aspects like the delays in the system and the strength of the coupling between the subsystems. Finally, the solution is iterated between the subsystems using the very efficient Gauss Seidel method so that the new solutions are utilized as soon as they are available. For parallel processing, it is also desirable to use the latest answer as soon as it is available. However, this may not 121

be possible for all variables, and a Gauss Jacobi update is employed for some of the vari­ ables. This process is called mostly Seidel. For the results given, it is possible to use the latest updated waveform for each subsystem solution since only a single processor is used.

In order to illustrate the technique, a simple two conductor system is chosen. The sub­ system corresponding to each patch is solved independently and the iterative process is performed according to a basic schedule where the subsystems associated with each con­ ductor are solved in a serial manner. For large systems of equations, there is a tremendous decrease in computation time due to the efficient manner in which the smaller matrices can be inverted. For small problems, a slight loss in speed is observed since the multiple solution over the time windows counteracts the relatively small gain in the matrix solution time.

Separation Iterations to Convergence Between Cond. Delays Window I Window 2 Window 3 Window 4 0.5 Yes 4 4 3 2 0.5 No 6 6 5 5 5.0 Yes 3 2 2 2 5.0 No 4 4 4 3

Table 4.1 Comparison of convergence with and without retardation.

In any case, the WR method is highly parallizable. For the numerical example, consider two conductors with length 2 cm and width 0.5 cm. A piecewise linear current source with rise, roof, and fall times of 50 ps drives the far end of one conductor. WR is applied to this system where the iterations to convergence is determined as a function of the separation 122

between conductors. This analysis is performed with and without the use of retardation.

Table 4.1 shows the results of this analysis. Clearly, incorporation of the appropriate delays into the system dramatically speeds up convergence, especially for the large cou­ pling case where the conductors are only separated by 0.5 cm. In this example, there are 4 time windows of length 0.5 ns. 123

CHAPTER 5

NUMERICAL RESULTS

For a hierarchical electromagnetic analysis of interconnect and packaging structures, a special purpose PEEC simulator has been developed capable of handling linear elements.

This simulator includes parameter extraction modules for the calculation of equivalent

partial inductances and potential coefficients of the geometry under study as well as a new

version of a circuit simulator, which mimics SPICE [17], with all the necessary enhance­ ments to accommodate electromagnetic retardation. The following numerical examples illustrate some of the capabilities of the simulator.

In order to effect an accurate and efficient solution for a system constructed from the

PEEC formulation, it is necessary to discretize the conductors in such a way as to limit the number of unknowns without compromising the accuracy of the solution. As a first step, conductors representing pins, vias, and traces are usually discretized along their length with 20 elements per wavelength corresponding to the highest frequency of interest.

Ground and power planes are discretized in a similar fashion, except that two dimensional current flow is accounted for. In all cases, for simplicity, effects from skin-effect are neglected. Once the geometry is discretized, then the corresponding partial inductances and potential coefficients are calculated according to the PEEC formulation, thus resulting 124

in an equivalent circuit model consistent with Maxwell's equations.

After the equivalent circuit elements are computed, then the system is solved in the time-

or frequency-domain using modified nodal analysis. For the time-domain solution where

retardation is present, late time instability is still a concern and ultimately dictates the min­

imum time-step allowed. As discussed in the previous chapter, recent progress in this area

has led to better understanding of the sources of instability, as well as new methodologies

for its suppression. For the simulator used to obtain results for this analysis, the procedure

for the selection of the optimum time-step was an ad-hoc one and was based on conver­

gence studies for the specific problem at hand. The issue of convergence is related to the

fact that the numerical integration used for this study, Backward-Euler, is dissipative, a

property which enhances numerical stability but may result in unacceptable anificial damping of the solution. Thus, it is important to choose the time-step carefully so that enhanced stability is achieved without unacceptable numerical damping. Since numerical damping is controlled by using small time-steps, the ad-hoc procedure for the selection of the time-step is as follows. The initial value for the time-step is taken to be in the order of

10% of the rise time of the excitation pulse. Then it is decreased until convergence is reached or the solution becomes unstable. The following numerical examples illustrate some of the capabilities of this approach for obtaining PEEC solutions.

5.1 High Frequency Effects Associated with Modeling Split and Solid Ground Planes f I

125

Fig. 5.1 Interconnect above a solid ground plane.

The first example for the geometry shown in Fig. 5.1 consists of an interconnect above a

finite ground plane and is used for code validation purposes. The line is driven by a volt­

age source and terminated by S6Q, resistors at each end. The ground plane is 2.0cm long

by 1.0cm wide and divided into 20 cells along the length and 6 cells along the width. The

line, placed 0.5mm above the ground plane, is 2.0cm long with a width of 1mm. It is

divided into 20 cells along the length. For this example, two-dimensional current flow is

only accounted for on the ground plane.

Since the layout of the conductors in this example models quite closely the effects of a

sim.ple two-conductor transmission line, the current distribution along the line and the

return ground path are expected to exhibit the differential mode character of transmission

line currents. As a result, the solution from a full-wave electromagnetic analysis should be

almost identical with the one predicted using a method of characteristics model with the

appropriate transmission line impedance and delay. The PEEC model without retardation

is somewhat like the method of characteristics model, except that the longitudinal cou­ 126

plings are also included. Figure 5.2 depicts the variation of the input impedance of the line vs. frequency calculated using the PEEC formulation with and without delays.

0.1

c; ^ 0.0 (U o c o •D Re(Zin) No delays S. -0.1 E No delays Re(Zj Deloys -0.2 lm(Z;J Delays

1 10 Frequency (GHz)

Fig. 5.2 Input impedance for active line above a solid ground plane.

Fig. 5.3 Interconnect above a split ground plane. 127

Alternatively, if the arrangement of conductors results in a response which cannot be accurately described by the method of characteristics models due to the presence of dis­ continuities and other interconnect features that give rise to electromagnetic radiation, then it is imperative to include the retardation in the simulation. The geometry shown in

Fig. 5.3 depicts an interconnect crossing a gap between two conducting plates. These types of structures occur frequently in packages for mixed signal electronics where sepa­ rate ground planes are used for the digital and analog blocks. The presence of the slot in the ground plane results in slot-line modes which eventually lead to energy loss through radiation. To illustrate this phenomenon, the structure of Fig. 5.3 was simulated. The dimensions and discretization for this geometry are the same as the previous example, except that the ground plane is now split into two equal halves with 1mm separation. Fig.

5.4 shows the input impedance of the line for this case. It is clear that the calculated impedances with and without retardation are very different for the higher frequencies where the resonant properties of the structure and radiation effects dominate the response.

This is due to the fact that the energy which is radiated from the slot can only be accounted for accurately when retardation effects are included.

5.2 Characterization of Noise in Printed Circuit Boards

The second example deals with the modeling of electromagnetic radiation caused by the presence of parasitic high frequency current flowing in the attached cables of printed cir­ cuit boards [31]. This source of noise is modeled with a generic structure as shown in Fig. 128

0.10

a js: -0.00 r (U o c o -0.10 "O(D Q. Re(Z;n) No delays E lm(Z;n) No delays -0.20 r / Re(Zj Delays lm(Z;n) Delays -0.30 1 10 Frequency (GHz)

Fig. 5.4 Input impedance for active line above a split ground plane.

cable

antenna

shorting pin

3mm—»•8mm^

Fig. 5.5 Geometry for example 2.

5.5. The high frequency digital noise flowing through the cable is modeled by a current source which generates a periodic sequence of trapezoidal shaped pulses. The rise, roof. 129

and fall times are O.lns and the period of the signal is 0.6ns. The current amplitude is

10mA. The length of the cable is 15cm. It is modeled as an infinitesimally thin strip of

width 1.0mm. The cable runs parallel to a finite ground plate of width 0.8cm and length

3.Gem. It is positioned 0.5mm above the plate. The receiving element for the radiation

caused by the protruding cable is a wire monopole connected at the other end of the

ground plate with a terminating resistance of 35i2. The antenna length is 8.0cm and it is

modeled as an infinitesimally thin strip of with 1.0mm. Three possible arrangements of the

antenna will be compared as shown in Fig. 5.5. The PEEC model for this structure is

developed assuming one-dimensional current for the wires and two-dimensional current

for the ground plate. Figure 5.6 shows the voltage across the load resistor for the three

arrangements of the receiving antenna in the absence of the shorting pin. As expected, the coupled noise voltage exhibits a time harmonic variation of frequency consistent with the effective length of the structure formed by the antenna and the ground plate. In particular,

the frequency of the time harmonic variation of the voltage for the x-directed antenna is approximately 1.67GHz which corresponds to a wavelength of 18.0cm. The combined length of the antenna with the ground plate is S.Ocra which is approximately half-wave­ length at the aforementioned frequency. The visualization of the current flow along the wires and the magnitude of the current density at f=1.67GHz is shown in Fig. 5.8.

Figure 5.7 shows the voltage across the load resistor of the receiving antenna when a pin is used to short the cable to the ground plate. Since the presence of the pin allows for a very low impedance path for die noise current back to its source, the radiated emissions 130

are minimized. In practice, this noise suppression is often effected using ferrite beads.

(U CP o o > -0.1

X Directed Antenna Y Directed Antenna -0-2 r z Directed Antenna

0 1 2 Time (ns)

Fig. 5.6 Voltage across the load resistor of the antenna in Fig. 5 J calculated without the shorting pin. 131

0.0020

0.0010

r 0.0000 (U 2 -0.0010 >o -0.0020 X Directed Antenna Y Directed Antenna -0.0030 Z Directed Antenna

0 12 3 Time (ns)

Fig. 5.7 Voltage across the load resistor of the antenna in Fig. 5.5 calculated with the shorting pin. V32

OA >•

0 2 4 6 8 AO 12 A*

.,1.6'ionz- 5.5 at' \tvP'^S-^ stni

wuo" 5 8Curte^^ FiS ioSVoS^® MOteved Eoc® ,Va»c®® imba

{or 5 9Gcofnc*^ F'vg- f I

133

0.5cm

3cni

Fig. 5.10 Geometry for example 3 (Case 2).

The last example deals with an interconnect configuration diat is often encountered in

single chip packages without a ground plane. In such packages, ground is brought to the

die through conducting traces in the package. These ground traces are then connected to a

ground ring or some other ground pad at the periphery of the package. These types of con­

nections result in unbalanced interconnects which, as is well known, give rise to radiation.

Even though this radiation is part of the overall electromagnetic behavior of the resulting

interconnect strucmre, it is customary to quantify the amount of this radiation in terms of

the so-called common mode component in the current flowing through the interconnect

[32]. Figures 12 and 13 depict two cases of such interconnects. In Case 1, the ground trace

is connected to the ground pad at a distance of 2.5cm from the signal trace, while in Case

2 the ground pin is placed right next to the signal trace. In both cases, the traces are 1mm

wide with a 1mm separation between them. Their distance from the ground pad is 0.5mm.

The length of the signal trace is 2.0cm in both cases. The length of the ground trace for

Case 2 is 1.5cm while for Case 1, an extra length of 2.5cm is contributed by the portion 134

that runs parallel to the edge of the ground pad until it reaches the ground pin. The charac­

teristic impedance of the differential line formed by the signal and ground trace is 22SQ.

and is used as the input source impedance. The signal trace is terminated with a 2pF

capacitor for both cases.

0.05

-0.00

-0.05 0) V. 3W. o -0.10

-0.15 0.5 1.0 1.5 2.02. Freq (GHz)

Fig. 5.11 Common mode currents.

Figure 5.11 compares the common-mode currents at the input of the interconnect for the two cases of ground pin placement. Clearly, Case 2 results in a more "balanced" configu­ ration, and thus the common-mode component of the current is smaller for this case. For the more "unbalanced" Case, the magnitude of the common-mode current starts increasing fast for frequencies higher than 1 GHz. 135

0.14

Case 2 c; Case 1 <5- 0.08

^ 0.06 E 0.04

0.02 0.00 0.0 0.2 0.4 0.6 0.8 1.0 Frequency (GHz)

Fig. 5.12 Current flowing through ground path.

It is often the case that the ground-path inductance is sought for purposes of simulta­ neous switching noise studies. This quantity can be calculated easily from the results gen­ erated by PEEC. To demonstrate this, consider the geometry of Fig. 5.10. For the frequency range over which the current through the source and the current through the capacitor are almost equal, the impedance of the return path can be calculated as the ratio of the difference between the voltages at nodes A and B and the current through the source. For those frequencies, radiation should be negligible, and the impedance should exhibit an almost inductive behavior. This is confirmed by the curves in Fig. 5.12 for the 136

imaginary part of the impedance of the ground path for Cases I and 2. The slopes of the curves (at the lower frequencies) are the effective inductances for the ground paths. As expected. Case I exhibits a higher value of ground inductance. Furthermore, it departs faster from the linear behavior due to the greater imbalance in the system. 137

CHAPTER 6

CONCLUSIONS AND FUTURE WORK

The Partial Element Equivalent Circuit (PEEC) formulation is an electric field integral

equation method which provides a full-wave electromagnetic solution using circuit ele­

ments such as inductors, capacitors, and resistors. This method differs from most other

techniques in that a systematic and localized reduction in model complexity can be

effected after the solution has been constructed. This reduction in complexity can be

accomplished through the removal of delays, elimination of unnecessary couplings, or the

removal of unneeded circuit elements.

The full-wave, retarded, or (/?, L^, P, x) PEEC model results in the most general and complex solution. The variables R, L^, P, T stand for resistor, partial inductance, potential coefficient, and delay. When combined in a ladder network similar to that of a lumped rep­

resentation of a transmission-line model, a full-wave solution is made possible in the cir­ cuit domain. This means that the incorporation of non-linear drivers and terminations is as easy as connecting those elements to the terminal of the PEEC model using familiar

SPICE notation. In other words, since PEEC results in a circuit representation of the sys­ tem, those circuit elements can thus be inserted into a SPICE file and connected to other linear and non-linear circuit elements. This almost seamless incorporation of PEEC ele­ 138

ments is one of the characteristics which distinguish it from other methods. Besides the

apparent ease at which circuit elements can be attached to PEEC models, another impor­

tant benefit is that since PEEC is solved in the circuit domain, there is no additional reduc­

tion in accuracy involved with adding external circuit elements. Methods such as Finite-

Difference Time-Domain and Method of Moments suffer from the fact that such incorpo­

ration of circuit elements add complexity and inaccuracy. Also, for methods involving time integration using fixed time-steps, the addition of non-linear circuit elements creates additional challenges due to the different requirements placed upon the limits of the time- steps.

Another important attribute of PEEC entails model complexity reduction. This concept involves the systematic reduction of circuit elements in the PEEC solution which have minimal affect on the total solution. The first level of reduction in complexity is achieved by simply removing the delays between the couplings. This form is called (/?, Lp, P)

PEEC and is the most accurate model that can be used in most commercial circuit simula­ tors. The reason for this is full-wave PEEC requires delayed couplings which necessitate the existence of delayed mutual inductances and delayed current-controlled current- sources in the circuit simulator. In those cases where the return path is clearly defined in a design, the simplified or (/?, L^, P) PEEC method is appropriate. The effect of removing delays from the system results in a solution which cannot account for loss due to radiation.

It is well known that systems which are dominated by differential mode effects radiate less and thus allow for such a reduction in complexity. The next level of simplification involves 139

removal of either the potential coefficients or the partial inductances. The situation where the system is modeled using resistors and potential coefficients is called (/?, P) PEEC.

This simplified model is ideally suited for the characterization of on-chip interconnects and semiconductor substrate coupling. Alternatively, the situation where the system is modeled using resistors and partial inductances result in a model appropriate for applica­ tions such as package inductance modeling.

Upon construction of either a (/?, L^, P, x), (/?, L^, P), (/?, L^), or (i?, P) PEEC model, the resulting matrix is generally dense assuming condense formulations such as MLA and

CMNA are used. This results in an enormous burden placed on the matrix inversion rou­ tine as the system size is increased. One way to expediate the solution of such system is through the systematic removal of unnecessary inductive and capacitive coupling. For the removal of capacitive coupling terms, it is sufficient to discard those coupling coefficients less than a certain threshold. However, that is not the case for inductive coupling. Removal of partial mutual inductances can only be performed for those coefficients which are less than a certain threshold and whose corresponding partial inductances are not contained within the same current loop.

Given these key attributes, it is easy to see how the PEEC formulation provides the ideal framework for the development of computer aided design (CAD) of high-speed electron­ ics for the 21®' century. The seamless integration of full-wave models in a SPICE-like sim­ ulator is very appealing to designers who up to this point have strictly dealt with SPICE.

Moreover, such a methodology is ideally suited as the backbone for the design of the next 140

generation of circuit simulators in tliat minimal changes are necessary in existing imple­ mentations to effect such full-wave solutions.

As for future work, there is an ever growing need for more efficient, stable, and accurate solution of circuits involving PEEC networks. Stability remains to be the most difficult hurdle for the solution of full-wave PEEC formulations in the time-domain. Achieving sta­ bility in a rigorous manner for the analysis of systems using non-linear components will be the most challenging problem. It is hoped that the ideas presented in this work can be adopted in such a way as to provide the impetus for achieving such a goal. In addition to the problem of stability, as designs become more and more complex, there is an ever increasing need for the reduction of such large systems in a way that is efficient while pre­ serving acceptable accuracy. 141

Appendix A

CIRCUIT STAMPS FOR MODIFIED NODAL ANALYSIS

The following gives a summarized listing of the matrix entries used for circuit ele­

ments according to the guidelines of Modified Nodal Analysis[16]. For each circuit ele­

ment. there is an entry showing the variables added to the system as a result of including

that particular element. Also, if applicable, the a branch constitutive equation is given.

This equation represents the additional information needed by MNA to form a solution

with that particular element. Lastly, the required additions to the solution matrix are shown for each element. Resistor

Rval

'--AAAr'"-

Unknowns;

Branch Constitutive Equation: None

1 -1 Rval Rval

-1 1 Rval Rval » ^ !

143

Inductor

Lval

iL

Unknowns: v„.,

di. Branch Constitutive Equation: • —

1 VI1+ 0

-1 Vn- 0

• 1 -1 0 dt

) 144

Capacitor

Cval n+. n-

Unknowns:

Branch Constitutive Equation: None

V*n+ VCo­

eval -Cval 0 at at n+

-Cval Cval 0 at (ft n- Independent Voltage Source

Vval

Unknowns: v^_, if. Branch Constitutive Equation: - v^_ = V^.^i

1 Vn+ 0

-1 Vn- 0

1 -1 Vval 1 1 Independent Current Source

Ival n+.

Unknowns: v^_ Branch Constitutive Equation: None

n+ -Ival

Ival Voltage Controlled Voltage Source

Eval

Unknowns: Branch Constitutive Equation; ^C-)

V^^ V^. Ij^

1 Vn+ 0

-1 Vn- 0

1 -1 -Eval Eval iK 0 148

Current Controlled Current Source

Fval

Unknowns: if^ Branch Constitutive Equation; = ^vai 'h

1 0

-1 Vn- 0

• Fvai 1 1L 0 149

Voltage Controlled Current Source

Gval n+ n-

Unicnowns: Branch Constitutive Equation: None

V*c+ V'^c-

Gval -Gval n+ 0

-Gval Gval n- 0 150

Current Controlled Voltage Source

Hval n+ n-

'K

Unknowns: v„., if^ Branch Constitutive Equation: - v^ )

^n+ ^n-

n+ 0

-1 n- 0

-1 -Hval 0 151

REFERENCES

[1] Y.-S. Tsuei, A. C. Cangellaris and J. L. Prince, "Rigorous electromagnetic modeling of chip-to-package (first-level) interconnections," IEEE Trans. Components Hybrids & Manuf. Tech., vol. 16, pp. 876-883, 1993. [2] B. Toland, J. Lin, B. Houhmand and T. Itoh, "FDTD analysis of an active antenna." IEEE Microwave and Guided wave Letters, vol. 3, pp. 423-425, 1993. [3] M. J. Picket-May, A. Taflove and J. Baron, "FD-TD modeling of digital signal prop­ agation in 3-D circuits with passive and active loads," IEEE Trans. Microwave The­ ory Tech., vol. 42, pp. 1514-1523, 1994. [4] P. Mezzanotte, M. Mongiardo, L. Roselli, R. Sorrentino and W. Heinrich, "Analysis of packaged microwave integrated circuits by FDTD," IEEE Trans. Microwave The­ ory Tech., vol. 42, pp. 1796-1801, 1994. [5] W. J. R. Hoefer, "Transmission line matrix (TLM) models of electromagnetic fields in space and time," Proceeding Int. Zurich Symp. on EMC, vol. 11, Zurich, Switzer­ land, Feb. 1997. [6] B. P. Rynne, "Comments on a stable procedure in calculating the transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propag.. vol. 41. pp. 517-520, April 1993. [7] A. Sadigh and E. Arvas, "Treating the instabilities in marching-on-in-time methods from a different perspective," IEEE Trans. Antennas Propag., vol. 41, pp. 1695- 1702, Dec. 1993. [8] A. Ruehli, U. Miekkala, A. Bellen and H. Heeb, "Stable time domain solutions of EMC problems using PEEC circuit models," Proc. of the International Symposium on Electromagnetic Compatibility, pp. 371-376, Chicago, IL, Aug. 1994. [9] W. Linger and A. Ruehli, 'Time domain integration methods for electric field inte­ gral equations," Proc. of the 1995 International Symposium on EMC. Zurich, Swit­ zerland, March 1995. [10] J. Garrett, A. E. Ruehli, C. R. Paul, "Stability improvement of integral equation models," Proc. IEEE Antennas Prop. Society International Symposium, Montreal. CA, July, 1997. 152

[11] A. E. Ruehli, "Equivalent circuit models for three dimensional multiconductor sys­ tems," IEEE Trans. Microw. Theory and Techn., vol. 22, no. 3, pp. 216-221, 1974. [12] A. E. Ruehli, "An integral equation equivalent circuit solution to a large class of interconnection systems," PhD Dissertation, University of Vermont, 1972. [13] K. S. Yee, "Numerical solution of initial boundary value problems involving Max­ well's equations in isotropic media," IEEE Trans. Antennas Propag., vol. 14. no. 3, pp. 302-307, 1966. [14] P. B. Johns and R. L. Beurle, " Numerical solution of two-dimensional scattering problems using transmission-line matrix," Proc. lEE, vol. 59, pp. 1203-1208, 1971. [15] R. F. Harrington, Field Compulation by Moment Methods, Macmillan, 1968. [16] C. W. Ho, A. E. Ruehli, and P. A. Brennan, "The modified nodal approach to net­ work analysis," IEEE Trans. Circuits Syst I & II, vol. 22, no. 6. pp. 504-509, 1975. [17] L. W. Nagel, "SPICE2: A Computer Program to Simulate Semiconductor Circuits," Electronic Research Laboratory Rep. No. ERL-M520, University of California, Ber­ keley, 1975. [18] Zhijiang He, M. Celik, and L. T. Pileggi, "SPIE: Sparse Partial Inductance Extrac­ tion", Design Automation Conference, Anaheim, CA, 1997. [19] A. E. Ruehli and H. Heeb, "Circuit models for three-dimensional geometries includ­ ing dielectrics," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1507-1516, 1992. [20] H. Heeb and A. E. Ruehli, "Three-dimensional interconnect analysis using partial element equivalent circuits," IEEE Trans. Circuits Syst., vol. 39, no. 11, pp. 974-982, 1992. [21] A. E. Ruehli, "Inductance calculations in a complex integrated circuit environment," IBM J. of Res. and Develop., vol.16, no.5, pp. 470-481, 1972. [22] P. A. Brennan, N. Raver and A. E. Ruehli, "Three-dimensional inductance computa­ tions with partial element equivalent circuits," IBM J. Res. Develop., vol. 23, no. 6. pp. 661-668, 1979. [23] P. K. Wolff and A. E. Ruehli, "Inductance computations for complex three dimen­ sional geometries," Proc. of the International Symposium on Circuits and Systems., Chicago, IL, 1981. [24] F. Grover, Inductance Calculations: Working Formulas and Tables, Dover, New York, 1962. [25] A. E. Ruehli and P. A. Brennan, "Efficient capacitance calculations for three-dimen­ sional multiconductor systems," IEEE Trans. Microwave Theory Tech., vol. 21, pp. 76-82,1973. 153

[26] J. Garrett, A. E. Ruehli, C. R. Paul, "Efficient frequency domain solutions for sPEEC EFIE for Modeling 3D Geometries," Proc. of the 1995 International Symposium on EMC, Zurich, Switzerland, March 1995. [27] A. E. Ruehli, J. Garrett, C. R. Paul, "Circuit Models for 3D Structures with Incident Fields," Proc. of the 1993 International Symposium on EMC, Dallas, TX, 1993. [28] W. Liniger, F. Odeh. A. Ruehli. Circuit analysis, simulation, and design, Elsevier Science Publishers, 1986. [29] L. Peterson and S. Mattisson, "The design and implementation of a concurrent cir­ cuit simulation program for multicomputers", IEEE Trans, on Computer-Aided Dp sign, pp. 1004-1014, July, 1993. [30] A. Lumsdaine and J. K. White, "Accelerating waveform relaxation methods with application to parallel semiconductor device simulation", Numer. Funct. and Opti- miz., no. 16(3«&;4), pp. 395-414, 1995. [31] J. L. Drewniak, T. H. Hubing, and T. P. Van Doren, "Investigation of fundamental mechanisms of common-mode radiation from printed circuit boards with attached cables", Proc. of the 1994 IEEE International Symposium on Electromagnetic Com- patability, pp. 110-115, Aug. 1994. [32] C. R. Paul, Introduction to Electromagnetic Compatibility, John Wiley & Sons, New York, 1992. [33] E. Lelarasmee, A. E. Ruehli, and A. L. Sangiovanni-Vincintelli, 'The waveform relaxation method for time-domain analysis of large-scale integrated circuits", IEEE Trans, on Computer-Aided Design, pp. 131-145, July, 1982. 148 Volcanic Component

The major physical factors of the volcanic component include the porosity, permeability, and hydraulic conductivity of the volcanic rocks

(table 25) and their initial boron contents. The hydraulic conductivity, K, of a rock is a function of the interaction of the properties of the rock with the properties of the fluid and gravity (Fetter, 1994). K = pgk/^i, where p is the density of the water, p. is the dynamic viscosity of the water in the rock matrix, g is the acceleration due to gravity, and k is the intrinsic permeability of the rock. Hydraulic conductivity is usually expressed in units of meters per day. Data on the permeability and hydraulic conductivity of volcanic rocks are rare. Most published permeability's for volcanic rocks can be traced to original work by Keller (1960) and Schoeller (1962). However, more recent work characterizing the geology of potential radioactive waste sites has made information on hydraulic conductivity of volcanic rocks available (Bedinger and others, 1985, 1989a,b,c,d). In 1985, Bedinger and others determined that hydraulic conductivity for given rock types had either lognormal or normal distributions (figure 13). Specifically, for many rock types having granular and fracture permeability, hydraulic conductivity is described by a lognormal distribution. Porosity for other rock types can commonly can be described using a normal distribution, except for fractured, unweathered crystalline rocks whose porosity is an exponential function when the fracture density and geometry are uniform. They also found that intrinsic permeability Table 25. Porosity, permeability, and hydraulic conductivity of volcanic rocks.

Porosity (7o) 'ermeability lydraulic Conductivity (m/day) Rock Type Range Median (darcys) lange Median Source basalt, dense 0.8 Davis, 1969 basalt, porous 11.4 Davis, 1969 basalt 7.7 1.4x10-'' Davis, 1969 obsidian 0.52 Davis, 1969 phonolite 1.98 Davis, 1969 pumice 87.3 Davis, 1969 tuff 31 Davis, 1969 tuff, zeolitized 39 4.0x10 S Keller, 1960 tuff, pumiceous 40 1.15x10-2 Keller, 1960 tuff, friable 36 1.40x10-^ Keller, 1960 tuff, welded 14 3.3x10 •»3 Keller, 1960 basalt 0.1 - 5 lxI0-> - IxlO S AGI Data Sheet, 1989 rhyoandesite 4-15 1x10 2- 1x10-8 AGl Data Sheet, 1989

undif vole rocks 1x10-1 DedinRer and others, 1989a lava flows 3x10" Bedingcr and others, 1989a ash-flow tuff 1x10-' Bedinger and others, 1989a ash-flow tuff 4xUH fiedinger and others, 1989a undif vole rocks 4XHH nedinger and others, 1989a undif vole rocks 4x10-3 Hedinger ami others, 1989a lava flows SxlO-'' Hedinger and others, 1989n lava flows 5x10-1 Hedinger and others, 198'>a lava", fractured and <2x10 2 - >1x10-1 5x10-1 Bedingerand others, 1989b cavernous lava*, moderately dense <5xlO-S->4xl0-'' 4x10-4 Bedingerand others, 1989b to dense tuff"*, welded and <.3x10-1 - >5x10" 1x10" Bedinger and others, 1989b fractured tuff", welded and <3x10 >4x10 1 4x10 •« Bedinger and others, 1989b t

1 1 i ! pumice 87.3 Davis, 1969

tuff 31 IJavis, 1969

tuff, zeolitized 39 4.0x10 S Keller, 1960

tuff, puiniceous 40 1.15x10-2 Keller, 1960

tuff, friable 36 1.40x10-^ Keller, 1960

tuff, welded 14 3.3x10-'3 Keller, 1960

basalt 0.1 - 5 1x10-1 - 1x10-5 AGl Data Sheet, 1989

rhyoandesitc 4 - 15 ixlfl 2- 1x10« AGl Data Sheet, 1989

undif vole rocks 1x10-1 Bedinger and others, 1989a

lava flows 3x10-" Bedinger nnd otiiers, 1989a

ash-flow tuff IxlO-l Bedinger and others, 1989a

ash-flow tuff 4x10-4 Bedinger nnd others, 1989a

undif vole rocks 4x10-4 Bedinger and others, 1989a

undif vole rocks 4x10-3 Bedinger nnd others, 1989n

, lava flows 5x10-4 Bedinger nnd others, 1989a

lava flows 5x10 1 Bedinger rtnd oll)ers, 1989.1

lava*, fractured and <2x10-2->1x10-' 5x10-1 Bedinger nnd others, 1989b cavernous

lava*, moderately dense <5x10-5 - >4x10 -'' 4x10-4 Bedinger nnd others, 1989b to dense

tuff**, welded and <3x10-1 - >5x10" 1x10" Bedinger and others, 1989b fractured

tuff**, welded and <3x10 >4x10 1 4x10 4 Bedinger nnd others, 1989b moderately fractured or dense

tuff**, nonwelded, <2x10-''->5x10-3 4x10--'' Bedinger and others, 1989b friable, zeolitized zeolitized luff 19.8 - 48.3 ,38.8 2.04xl0-<'-2.xl0-2 2.45x10-4 Winograd and Thordnrson, 1975

clayey tuff 1.8-21.6 10.4 8.16x10"- 1.6.1x10-2 2.45x10'"' Winograd and Thordarson, 197S

nonwelded tuff 2.45x10-^' - 2.4.5x10 4 Winograd nnd Thordnrson, 1975

r

-Ll: rti

V . t H-i VI is

)0» lO' J0> I0-' 10' 10°

HYDRAULIC CONDUCTIVITY, K, IN METERS PER DAY

EXPLANATION

BASALT METAMORPHIC ROCKS 1-Modatilaly danta to dansa lava llowi 1-Unwaathaiad matamorphic and intrusiva rockt 2-Fracturad cavarnoui basalt with fracture parmaability, graatar than 300 matats balow land tutfaca BASIN FILL 2-Unwaaiheiad matamorptiic and intiusiva rocks l-Flna-oialnad basin fill wilh Itactura paimeability, lass than 300 maiats balow land suifaca 2'Coarta-grainad basin (ill 3-WeBthaiad matamoiptiic and intiusiva rocks

CARBONATE ROCKS 1-Danta to modufataly danta catbonata locka TUFF 2-Fractuiad, karstic caibonata rocka 1-Nonwaldad to partially waldad, baddad tuft 2-Weldad, modatataly fracturad to dansa tuff CLASTIC ROCKS 3-Fractu(ad, waldad tuff I Fina-gtainad clastic locks 2-Coataa-grainad clastic tockt Figure 13. Hydraulic conductivity, K distributions for a variety of lithologies (from Bedinger and others, 1985).

U1 o 151 decreases with depth, especially with depths up to 300 m. It should be noted that the relative hydraulic conductivity of materials may vary with soil/surface moisture conditions; i.e., the unsaturated hydraulic conductivity of a clay may be greater than that of a sand at these lower moisture contents (Fetter, 1994). Bedinger and others (1985, 1989b) classified the hydraulic conductivity of volcanic rocks as belonging to lavas or tuffs (table 25). The lava group included compositions ranging from rhyolite to basalt and was subdivided into fractured and cavernous lavas and dense lavas. The tuff group also included a full range of compositions and was subdivided into 1) welded and fractured tuffs, 2) welded and slightly fractured or dense tuffs, and 3) nonwelded, bedded, and friable tuffs. Although the hydraulic conductivity of volcanic rocks can vary from none to very high, most have low to moderate hydraulic conductivity. It is also recognized that permeability varies with thickness of volcanic flows, with the highest permeability's in the flow tops and bases and along its contacts with other flows and rocks.

Commonly, the vertical permeability is very small in volcanic rocks compared with the horizontal permeability (Davis and DeWiest, 1966). The permeability characteristics of volcanic rocks, may encourage relatively shallow throughflow or interflow over deeper groundwater flow. The relatively low hydraulic conductivity of many volcanic rocks may contribute to the leaching of boron due to longer water/rock interaction times as a result of slow throughflow and (or) interflow.

Volcanic rocks, on average, contain approximately 17 ppm B (Barker and Lefond, 1985). Basalt contains only about 5 ppm B, while andesite 152 averages 20 ppm, rhyolite 30 ppm, and volcanic glass 13 ppm (table 5). Figure 14 shows the distribution of B content in volcanic rocks; most of the

data area from the Bolivian Altiplano, but the data set also includes analyses

from Nevada and Europe. These data show that the B content in volcanic rocks varies from 0 (zero) to 1500 ppm; the median of this data set is 20 ppm B which is very similar to the average value reported by Barker and Lefond (1985).

Factors Not Explicitly Considered

There are several factors that negatively affect the quantity of boron in a

basin. Little or no vegetation can survive at the surface of Quaternary salars due to the salinity of the soils and salts; in fact, boron itself when present in

large quantities is a natural herbicide. As a result of this, and depending o n the precise composition and dryness of the salar, large amounts of minerals

may be lost from the salar surface due to wind erosion. Wind erosion may generate clouds of debris that extend hundreds of meters vertically and several kilometers downwind (Orris and others, 1992). On a very windy day, several tons of material may be lost from the surface of a salar.

Other factors that may have a large negative effect on borate mineralization include the adsorption of boron onto clay surfaces and the substitution of boron for silicon or aluminum in micas and clay minerals

(Barker and Lefond, 1985). Illite in saline environments may contain from

100 ppm to more than 2000 ppm B (Harder, 1959). Boron is not easily

removed from clays despite its generally high mobility. An additional 153

n = 164

0.8 -

0.6 u>» c o C3 o £ 0.4

0.2 » O

0

0 20 40 60 80 100 120 140 160 180 200

B (ppm)

Figure 14. Distribution of the B content in volcanic rocks. Data largely from the Bolivian Altiplano (U.S. Geological Survey and Servicio Geologico de Bolivia, 1992) and Europe and Nevada (MacDonald and Bailey, 1973) 154 negative factor that is not explicitly considered in this model is the likelihood of boron loss from the basin during basin overflow.

Factors that may contribute positively to boron deposits and not addressed in this model include contributions to spring waters from magmatic fluids, boron scavenged from older sedimentary rocks, and boron mobilized from older, buried deposits. In addition, contributions of boron due to overflow from upstream basins, as in the case of Searles Lake, were not explicitly considered.

Determination of B Endowment

There has been very little work done on the rate of solubility of boron i n volcanic rocks, but experimental results of Ellis and Mahon (1967) showed that 50 to 80% of the initial boron in volcanic glass was removed by hot- water leaching before their samples exhibited visible evidence of alteration.

They further concluded that boron concentrations in the associated fluids could reach 20-30 ppm without any magmatic contribution. These values are within the measured values of B in inflow streams, rivers and most springs associated with known borate deposits (figure 15; Barker and Barker,

1985). The data compiled for figure 15 shows that the distribution of B in springs and B in rivers are similar for much of their distributions, but that relatively rare, very high values are restricted to thermal springs. Using a

Mann-Whitney rank-sum test of the two populations, the null hypothesis that the populations are identical cannot be rejected at the a = 0.01 level of significance. 155

Distribution of B in springs and rivers

1.2

o Spg Frequency 4 River Frequency

0.8

0.6 o*

0.4-

0.2-

0.0 0 1 0 20 30 40 50 60

B content (ppm)

Figure 15. Distributior\ of B in springs and rivers. 156 The total boron deposited in the basin can be calculated by adding B values of the inflow waters over time in a manner similar to G.I. Smith's calculation of thermal spring input of B to Searles Lake (G. Smith, 1966). Estimates of total boron in each analogue basin calculated in this maimer are shown in table 26. Alternatively, known B levels for inflows into three B- bearing analogue areas with perennial lakes was used to back-calculate the rate of boron extraction from the volcanic rocks in the drainage basin (table 26). The selected basins for this calculation contained only volcanic rocks at the surface, were considered to be Holocene in age, and contained no known springs. It was assumed that only the surficial Quaternary volcanics contributed significantly to the B levels in the inflow waters. The relatively low hydraulic conductivity of volcanic rocks could result in a significant lag time in supplying boron to a newly created closed basin (table 13) from throughflow, interflow, or shallow groundwater flow. This time lag allows more time for the water to react with the host rocks to release B into solution. The volume of volcanic rock was estimated using a maximum thickness of 250 m which is an approximate depth limit for water that remains part of the active hydrologic cycle.

Boron enrichment of the study basins over periods of 5000, 10,000, cind

20,000 years calculated in both these manners produce estimates that vary highly from the boron contents known to be present in the mineralized analogue basins. The 10,000 year estimates from inflow waters commonly exceed the known borate contents even for basins that are substantially older

(30,000 to 50,000 years), previously were part of a larger drainage basin, or that have received boron from overflow of upstream lakes. Estimates of B Table 26. Estimates of B endowment. [ROCK estimate is based on volume of volcanic rock and back-calculated rate of extraction (see text); Waterl estimate is based on average B inflow value and total basin inflow; Water2 estimate is based on average B inflow value from volcanics and proportion of basin inflow originating in volcanics.]

KNOWN B B(Mt) B(Mt) B(Mt) RESOURCES ROCK Waterl Water2 BASIN NAME (Mt) lOKyrs lOKyrs lOK

Busch o Kalina, 0.00500 0.00141 0.23824 0.06326 Laguna Cachi, Laguna 0.00010 0.00255 0.01725 0.00601 Capina, Laguna 0.34210 0.00798 0.01815 0.00736 Challviri, Salar de 0.32550 0.01836 0.81497 0.36486 Chojllas, Laguna 0.00002 0.00204 0.05351 0.02581 Colorada, Laguna 0.00600 0.01992 1.94775 0.88887 Coruto, Laguna 0.00300 0.00738 0.15919 0.11975 Mama Khumu 0.00200 0.00102 0.06200 0.03833 Pastos Grandes, 0.96350 0.00582 0.27342 0.08098 Lagunas Uyuni, Salar de 10.20000 0.31479 13.93643 2.56760

China Lake 0.00010 0.000012 0.09919 0.01394 Koehn Lake 0.00078 0.00977 0.00015 Saline Valley 0.00100 0 0.00977 0.00171 Searles Lake 8.57260 0.00135 0.06113 0.00056 Clayton Valley/Silver 0.00600 0.0042 0.01473 0.00166 Peak Marsii Columbus Marsh 0.00250 0.00063 0.01011 0.00059 Fish Lake Marsh 0.00120 0.00402 0.03419 0.00318 Rhodes Marsh 0.00300 0 0.00536 0.00029 Teels Marsh 0.00830 0.00078 0.00859 0.00001 158 endowment based on calculated average B extraction rates from volcanics are typically closer to known B resources when adjusted for the ages of the basins, but still commonly overestimate the endowment. 159 DISCUSSION AND CONCLUSIONS

This study was undertaken to devise and test quantitative alternatives to assessment utilizing subjective quantitative estimation of numbers ot deposits. Borate deposits in Quaternary salar and lacustrine settings were selected for study because the deposits occur at or near the surface, the young age precludes major deposit deformation or alteration, and many of the processes involved in their formation were believed to be fairly well understood in a geologic sense. Of the two approaches devised in this study to assess and predict boron mineralization, the statistical estimation of borate contents using a sequence of discriminant and regression analyses produced results that hold more promise in the short term as an assessment tool than did the results of the process-based approach. The statistical methodology is a two-step process. Forward stepwise discriminant analysis of the areas and logged areas of basinal lithologies proved to be an effective tool for distinguishing B-mineralized versus non- B-mineralized basins. Stepwise regression of lithologic and other related variables on known boron endowment was shown to be an effective method for predicting the known amount of B in a basin. Used together, the discriminant and regression relationships can quantitatively estimate the probability for B mineralization in a basin. One problem associated with this methodology includes sensitivity of the regression model to the size of variance (over 5 orders of magnitude) of some variables. A second concern is the dependence of the regression model on good initial estimates of B endowments of the analogue basins. Without question, the estimated 160 endowment of several of the basins is a minimum due to the lack of data at

depth. Additionally, the methodology is unappealing in a geologic sense,

because process/genesis is not explicitly considered.. The more geologic process-based approach produced highly variable

results that highlighted the lack of understanding in any quantitative sense of many of the processes involved in the concentration of boron in salar and

lacustrine systems, especially those processes that remove boron from the sequence of mineralizing processes. Boron endowment calculated from the simple process-based model commonly exceeds known mineralization

levels. Boron could be "lost" from the proposed mineralizing sequence

through several mechanisms, including;

• adsorption of B to clay surfaces; • loss of B through basin leakage;

• loss of B through post-mineral wind or water erosion. Boron has a high affinity for clays, especially at low temperatures

(<150°C) and can be adsorbed unto clay surfaces or incorporated into clay structures and become unavailable to form borate minerals (Leeman and Sisson, 1996). While various studies have looked at how and in what form boron is incorporated with clays and at the distribution coefficient between boron in sediments and solution, they have not addressed what happens

with different proportions of clay sediments and solutions or with different

mixes of clay minerals. Additionally, the parameters under which clay adsorption of boron is easily reversed are not well known.

The amount of boron lost through subsurface basinal leakage into adjacent basins or regional aquifers has also not been studied. Due to its 161 extreme mobility, boron and its minerals are extremely susceptible to hydrologic transport out of the mineralizing system at practically any point in the process. Lastly, wind erosion can play a major role in loss of minerals in a salar system; tons of surficial minerals and materials can be removed,

but these amounts can only be guessed at.

At this point, it should be noted that the overestimation of B in some basins could be due to other factors. Lack of strong geologic age constraints on some basins may mean that B endowment was calculated for a period that exceeded the basins actual age; of course, the contrary, that the basin is significantly older and therefore the estimate of B would be even larger is also true. The hydrologic relationships in this study, although consistently computed, have an unknown relationship to reality and the B-estimate could be affected by the overestimation of inflow rates to the basins or changes over time in the B content of the inflow waters. Additionally, the calculated average boron concentrations of inflow waters may be too high, although cutting the concentrations in half (an amount believed to exceed the potential error in the original estimates) does not universally solve the problem of overestimation of B endowment. Lastly, failure to properly specify the model is always an option to be considered. In this case, the model was known to be incomplete due to the lack of data on loss of boron from the system. Only in the youngest and geologically-simplest of these systems does the simple process model predict a boron-endowment as close to known endowment as the statistical methodology.

Despite its many drawbacks, there is some knowledge to be gained from the attempt to predict B-endowment from the process-based model: 162 • The availability of adequate B from inflow waters is not an issue for

any of the basins that were studied;

• The permeability's and hydraulic conductivity's of the volcanic

rocks must be toward their high ends of range in Bolivia to

maintain some of the perennial shallow lakes that receive little or no snow melt from higher elevations. Values at the low end of

the range may, along with higher temperatures and accompanying

elevated evaporation, help account for the lack of perennial lakes in the US, despite similar precipitation rates.

In the long run, many of the uncertainties in the boron process model

might be addressed by the application of boron isotope and other geochemical studies, such as that by Palmer and Sturchio (1990), to specific mineral endowment process questions. Already these types of studies have helped to describe the process and conditions of boron adsorption by clays. These studies also offer potential insights into the source rocks and (or) fluids of the borates in specific deposits; the degree, conditions, and rate of remobilization of adsorbed boron; and the conditions and rates of B extraction by water from volcanic rocks.

In summary, the methodologies developed here offer two different perspectives for estimating B endowment. The statistical methodology produces an estimate based on observable geologic features and analogue basin estimated endowments. Although the simple process model produces highly variable results, it does establish the availability of boron for mineralization even though the method cannot currently account for boron losses within the process. At the very least, the methods can be used to 163 establish whether a basin is likely to contain boron mineralization (from the discriminant step of the statistical methodology), calculate a minimal endowment level (regression step of the statistical methodology) and the

probability of that level of endowment (statistical methodology), and a maximum level of endowment given no boron losses (process model).

Additional data on the distribution of deposits and their sizes and grades within single basins could then be used to recast endowment estimates to estimates of numbers of deposits. Such results could be used in isolation or to constrain a subjective assessment. 164 APPENDIX A: BORATE MINES AND OCCURRENCES OF THE WORLD Table 1 Bofata deposlls. I iotSTRICT oeposfT 1 ASSOCIATED MINERALS MM DEPOSrTNAME lor SITE? LATTTUDE LONCnUDE TYPE(S» 1 BORATE MMERALS [('•dominant ntlnaialiitilon) AG£ ( 1 1 Argentina ! 1 Acaioque 's 24I7-30S P66-2P-30W P i borax, ulexlte, brine .sodium sullala, iiavenino OUAT? t ' ..... Alejandra Occurrence 's 25 09-56S 066 S9-25W 0 Alex Prospect i® 2&-U-S2S 067-02-13W 0 Archibarca Ravine area !o ,ulexl|e, borax clay, travenine, onyx, irona AAjana y js 23-37- S 067 05- W iulexite 15!« OUAT Lart S 23 30- S 067-pp- W s> julexlje, borax ^travertine ^AT Los Bayos S 23-3^ S 067 ps- W s> ^ulexlte OUAT Tropa Pete Is ?3-35- S P67-0S- W s> |ulexiie |lraverline| onyx, trona PUAT Baria Prospect s 2S-t5-16S 0a7-04-03w 0 Blanca Ula Mine is p uiexlie ) LQUAT Boratera da Aniuco S i24-10-19S 066-40-16W SP ulexlte jcalclle, manganese. Iravertine. onyx PLIO-HaO? Cell! Occurrence ;S 2310-3aS P66-36-4SW p julexite lhaljle CoyaQuaima ulexlte. minor borax halite, calcite. travertine, tula, aragonlle 22-4e-35S 066-33-30W 3^ LQUAT E) Toro 's 3» iulexite OUAT La Mucar ;S 23-22-36S 067 04-59W P ,ulexlte OUAT? Quachalayle IS 23 05-S1S 0e6-57 39W P ulexlte Lagurta Ouayalayqc D 23-15*. S Ms-sg- W P ulexlte halite, clay QUAT7 Baraloyoc Mine !s 23-20-17S 065-52-14W P ulexlte halite OUAT? Orupo Cordoba s 23-2S-S2S 065-51 ^GW P ulexlte hallle PUAT^ Laguru vilama ulexlte 0 ?2-36- S p6e-&s- W P HpLp? r Boratera Vilama I II • ulexlte s 22-34-g5S P66-54-15N P HOLO? ' Ceno Bayo utoxlio s 22-33 S0S 066-&3-3gyy P H0L07 Lagynjla ;s 2300- S 066-32'- W* P inyolte, ulexile clay QUAT Liberlad ;s 2316-16S gM-44-2Vyy ulexUe Loma Blanca borax, inyoite; minor ulexile. colemanite; realgar, travertine, sullur, orpimeni, calcite, trace hydroboracile, letuggile. iaragonlte, montmorilionlte, lllite, chlorite. s 2303- S 066-27- Vy DO llncalconlle gypsum LMIO 6 99 MA Maria Teresa !s 25;15:I6S P67 00 02W P ^re ;s 2f4B. S pi6-4i- W 9 ^ylexlie 'travertine OUAT ojq de Ague ]s 23 00- S 066-42- W 3> ulexite travertine OUAT RIo Alumbrlo Spring Area :ulexi(o travertine, tula. onyx, calcite, Fe and Mn 23 po-igs g66:^:0gyy oxides, halite PLKHIUAT Ariluiar Mine 22-59-24S p6e-30-06W 3» ulexlte travertine, onyx, Fe and Mn oxides PUO CalkJ>ar s 23 00- 8 066 35- W 3> ulexite ;lraver1ine, Fe oxides OUAT Caftuetas |s 22-59-10S pe6-30-20W SP ulexite travertine. Fe oxides OUAT Oanlel Mine 's 22-59-018 66e-29-16W 3» ulexile? icu' OUAT San Maicos s 23 00- 8 066-30- W ulexile .travertine, onyx OUAT Votcancllo ;S 23 00- 8 066-33- W y ulexite icaiclte, travertine, halite? OUAT Sejer Center>arlo io 24-52- 8 066-42- W p/-8n ulexile, borax, brine jhalile, mirabjite, LI, K, Mg OUAT Analuya Project p Is 24-50-563 P66-47-37W ujexite i OUAT Boroquirntca S^rnjcal Mln^ \s 24-49'- S 066-43- vy p ^ulexite OUAT ^Qenlina s 24 S3- S P66-4S- W p ^ulexite jhalile OUAT MaoQle 's 24-54- S b67-44-30W p ^ulexite ^halite OUAT Mataio Prospect ;S 24-54-30S 066-44-30W p ulexile OUAT Mana Lulsa Ml Occurrence 's 25 07-228 0e6-50-40W p ,ulexile OUAT? Putmamatca Mine !s 24-57-058 066-44 22W i» uleaile OUAT Salbi liu Anlolalld 's 2S 44- 8 067-55 W [U uluxilu lialitu*. nvpsurn. liAvetlioe MIOPLIO OlC3N Table 1. Borate deposits. • jDISTntCT DEPOSIT ASSOCIATED MINERAU MM DEPOSIT NAME or SITE? LATITUDE LONOmJOE TVPE(S) 1 BORATE MMERALS ('•dominant minaralliatlon) AGE 1 Satar da Cauehari Julexlle, borax, colemanlte. howMe gypsum. Iravertlne. tula, calcile. clay D 23-45 S 066-4S- W P/OD LMiaPUO QUAl Campamenlo Primero de Mayo S 24-01-3SS 066-47 SSW P 'uleiite clay QUAT CartotaCorlna S ^24 03- S 067 50- W P julOKlle? HOLD CirKO O^urrence s |23-39-33S 06e-41S3W P uleNite QUAT OelenM hll-M OccurrerKos s ,23-56-3jS 066-46'4tW P iuleille, borax? QUAT El Pprverilr [s |23-44-3^ 666-44 0BW P ulexite travertine, sand, clay QUAT? La Inundada s ]?3-54-62S 666-45-45W P Iborax, ulexite .Clay QUAT Mascota 's |23-3S06S 066-4IOOW P ^ulexlie Iravertlne QUAT? San Pedro *s '23-58-47S 0e6-47-12W P 'utexlte, borax ^clay QUAT? Stberla •s :23-46-53S 066-44-23yV P ;ulexHe travertine QUAT? Salar (to tnuhuasi 's t2415- S 067-38- W P jborates? halite 8alard« Jama ulexlle, lincalconlle? gypsum, halite, mIrablMe. clay D 23-20- S 067-00- W P QUAT? Benito Ml ^s |23-22 S3S 066-59-53W P ulexite halite, gypsum QUAT? Jama Mlra :S |23-l5t4S oe7-oo-oow P ulexlle gypsum, halite QUAT? Maria Lulsa S .23.24.07S 066-S7-19W P |ulejdte ^gypsui^ halite QUAT? ^an Fiandsco ;S ;23-1fl-36S 067-01.3SW P ulexlle ,halite, gypsum. QUATV Salar da LIultalllaco |Ulexlle haillo* ,0 ,24-51- S 068-16-30W P QUAT Adeia |24.49 S6S 068.14-40W P ,ulexlle QUAT s 1 Salar da Olarot *0 [h n- i P66.40- W' P ulexije, borax h^te, gypsum, clay QUAT? Et Cpn^r s ;23-24-36S 066-39-07W P ulexlle halite, gyp^urn oiiATv Grupo San Nicolas ulexlle gypsum, halite s 23-26 t3S 066-3a20W l» QUAT? Santa Ines s 23-27-54S 066-39-29W P j ulexlle gypsum, haltle Yacare s ;23-28-45S 066-43-1SVy P ^ulexlle QUAT? Salar da Pasioa Grandaa ulexlle. inyolte, hydroboraclte. halite*, gypsum, iravertlne. brine, clay D 24 40- S 067-20- W BO/P/BR [meyerhotlerlte, brine PLEISHOLO Betina Mine [s |24-33 &eS 0e6.39.43W P julexile ,halite*, clay Hao Boralera Blan» Lila 24-30-24S O66.43-OOW P lulexile, iriyoile Iravertlne Pl£IS Coronel Gorrotli !s ;24-33-2js 066.42-09W P ulexlle halite, cjay QUAT Salar da Pocltoa o Quiron lulexlte. Inyolto? halite*. mkabUlle. aragonile, gypsum, clay 24-30- S 066-59- W P 1 PLEtSHaO Ducus IV IS 24-t7-3SS 067 04-04W P lulexile QUAH Dona Emma S ,24-20 02S 067 02-&4W P i ulexite QUAT? Salar da Poiualoa ib *24-43- S 066-4~9- W P ^eille, borax? jhalite*, clay, organlcs QUAT? Margarita '.s |24-39-S0S 067-47:3gW ' San Mateo Mine Is |24-39-4gS 066-46-20W P iulexHe ^halite*, clay, organlcs QUAT Salar da Pucar ;S '24-t5- S 067-S5- W P ulexlle? halile Salar de Rio Grande 'd |25-05- S 068-10- W P ^ulexlle ^mirabilite*, halite, ihenatdile QUAT Salar de Santa Maria ^ulexllo, colomanite, hydroboracile. irona. sullale, halite ;24 04 S 067-20- W P/BO jlnyoite Sanla Maria Mine !s ,24-05-223 g67-2t-33W P/BD jborates trona, clay Salar de furllart iborax, uloxila halite, calcite. Li. A&. dolomite, benlonite s 23-08'3US P66-37-25yy QUAT? Salar del Hombra Muerto jbrlne (ll). ulexite, borax, inyolte gypsum, halile. travertine, sodhjm sullate. .2523 S 067 06 W pimmo t realgar, orplmont. anltydrlle QUATPLEiSlMli 20 de Febrero 's '25-25-tOS 067 02 t0W p lliluxltti? ' QUAT Calchaqulna ,'25-25-20S 066-2Bt2W p julexile? ' QUAT? Centonaiio s |25.2M7S 066-29 WW p 'ulOHltO QUAT? Delia !s '25-23 62S 066 28 2SW f> ulODle? QUAT ON H ' i' 1'"' 11 l|i1 ^ 11 {

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Z9I Table l. Borate deposits. DISTniCT DEPOSIT ; ASSOCIATED MINERALS MM DEPOSrTNAME or SrTE? ; LATITUDE LONGinJOE TYPE(S) BORATE MINERALS ('•dominant mlneralliation) ACE • Monle Ainaiillo hydroboraclle; lesser Inyolte, utevlte gypsum, anhydrite, orplment. realgar, rare S i24-42-50S 06e-41-30W (1) halite; Mn & Fa oxkles IKUO Monte Azul S '24-40-40S 066-4M0W 60 hydroboracite; lesser inyolle orplment LMiaPLiO Monte Blanco S |24»39-0SS 066-40-45W BO ;hy^qbpraclie, iny^te Iravertinp, gypsurn ^omo Mqnle Gds ;S !24-45-20S oee-4o-3sw ulexite, Inyolte LMiapub Monle Marron 'inyoite; lesser colemanile, hydroboraclle 1 gypsum, anhydrite ;S |24-4S-aOS 066-4t-30W BO LMIOPUO Monle Verde ; colemanlte. Inyolte; lesser hydroboraclle, clay, gypsum, anhydrite ;S i24-42-S0S 06fi-4p-soyy BO ;ulexlie IMP Santa Elena S I24-34.46S 0e6-3B-40W k) I hydroboracite, le»er inyolle gypsum LMldPUO Sania Elvira ;S i24-33-30S oe6'3i-36w ED lulexite 'halite*, gypsum IWIO-PUO Sanla Rosa {colemanlte. hydroboracite; lesser Inyolle. gypsum, clay |Ulexite. rare meyetholferlte. noblelle. S 24<36-30S 066-39-30W BD igowerlie IWIOPUO Socacastro 's !24-I2- S 0e^56-30vy ,ulexite, pinnolle travertine, onyx Unnamed p ,s |22*34-05S 066 S1-64W . Armenia '• Othulla area s 139-40' N 04SOO- E BD7 borax, lincalconlle (rona*, halite*, tennardile, travertine QUAT? HOLD? BoUvUi ' 1 ' CuevlUs J 0 Laguna Buscti o Kaltna "s ;22<36-35S P87I2-45W UBR brine HOP Laguna Cachl ulexlle. bnne irona*, halile, brine, thermonatnte. s ,2t-43-45S 067 se-3pyy P/BR dlatomite. clay ICLO Laguna Caplna Sui s ;2i-5s-3bs 067-34-20W P/BR ,y|exlte, biino, probortita lime, Li, K, halite, gyp&um 1^0 Laguna Celeste s ;22-12-33S p67 06-l6W L/p ^^rme (B LI) NpLO Leguna Chlar KKota ulexlle, b'ine halite*, sulfur, gypsum, sytvite, Li, calcile, s .2I-35- S 06BQ4- W UBR clay Laguna Cl>ojllas brine 'li. Sr. K, Mg s 122-22 30S 067 p5-36W yoR HOtO Laguna ChuBuncant brine sodium sullate*, Ll, K s ;2l-32-4&S 067-53 00W a\ Hao Laguna Colorado ulexite. brine trona*, mirabiute*, halite, dlatomite, clay iS !2?!1'20S 067-46-3pyy p HOU) Laguna Corulo 'brine, ulexite halile, gypsum, clay is ,22-2S-4SS 067 pp ppW t^BR QUAT Laguna Hedionda Norto ' 'Ulexlto. brine Imlrablllte*. nalive sullur, halite s 21-34- S 06B 03- W P Hao Laguna Lorornayu is 22-24-30S 067-12-30W UBR bnne (B) Ll, K, Mg, Na, St In brine QUAT Laguna Marna Khurnu ulexiiti, bnne halite, aullur, arsenic minerals?, clay ;S i22I5-42S oe7p4-3pw P NOLO Laguna Ramaditas brine gypsum*, calcite I2l-3a- S 0680S- W P/UR Hao Laguna Sacat>aya uluxiiu, brino 'halllo s Iia-3B-4PSI 06B-57-45W pmn QUAT Laguna Vuide bnne calcile. clay, halite, organlcs :S |22.47-40S 067-4B-20W lyiiR Hao Lagunas Paslos Grandes ulexilo. bnne gypsum, clay, catcile, halite. Li. K ^2t-3a-aos 067 47 40W p »

Boratera ^ ChalMil Sur s •22-3A- S 067-34- W P ulexite gypsurn HOLO Ch^lNIrt Pampa Easi s s 067:33- w P ulMlle HOLO Chaltvid Pampa Nodh 's 22-2B- S 0e7-35- W p borax, ulexHe, colemanile? clay HCXO Herrera Pampa s 22-34-30S 067-32'30W p ulexiie, colemanile? HCXO Salar d* Chiguana lUtexlie. brine halite* 0 ,21 OB-pOS P6B-02-4SW p HCXO la Cairtllana |s |2i-pB-43S p6B-p4-5&W p lulexkle ,halite HOLO Satar de Colpasa ulexiie. U-B brines halite*, gypsum, day. dlatomite. K ;0 .ie-22> s 066 pa- w p QUAT Salar t9-46S Q6B-2a*33W p HOLO i Islma !s |20-2S'52S 066-38 2QW p gypsum HOLO laqueca 's '20M-23S 06B-26-S7W p i gypsum HOLO Salar de Luth)ues brine, ulexiie ;S ,22 23-55S p67-tg tow P/BM t CKJAT Salai de Ollague ulexite halite ^s .2M0-30S pesMppw p ' HOLO Salar de Uyunl brine, ulexite halite*, Li*. sodium aullate. syivite, clay, Mg .D ,20-00- S 066-00- W P/UR ' OUAT Llipl-Ulpl ;s 2b-48-13S 067-24-18W p i ulexite, brine clay Hao Rio Grande (Boratera Pampa) s 20-43-36S 067 I5-01W P/BR brine, ulexite gypsum halite, day, Fe oxides Hao Salmuera del Rio Grande s 2Q-3?; S 067 t9- W GR 'brine halite, U, K QUAT Salmueras M Salar do Uyuni !s ^20-'00- S oeeoo- W biir)e, ulexite hatjte, U| sylvlte, clay, gypsum, K, Mg QUAT Salar Laguanl ulexite, brine hallle .D 20 S6-3IS 06816 10W P NOLO PajoTKha 's 20-&2-33S 06816 28W P uloxito »CLO Chile * * Cebdiar s '22 29- S 069 06- W P cotemanite? gypsum LPUOPLEIS? Lagunas Bravas D |26-i9. S 0e8-37- W P7 julexite La&T|zas S J9-29- S 069-44. w P 'ulexite Marta Elena 's '2219- S 069-40- W N nitrates*, lodales*, chromates. halite Hao Pampa Tamarugal i ulexite, colemanile halite, potassium salts, carbonates. D S 069-40- w P? nitrates*, lodates*, chromates PUOHOLO Chug-chug !s ]22-oe- S 06906- w SP? ^ulexite chrornates El Toco ulexite, colemanile gypsum ;s 22 0B- S 069-20- W P/UD7 1 LPUO? Pampa Joya 'ulexiie? gypsum s i2t-S2-4pS 069-31 40W P HOLO Quebra^ de Oarrera [s '22 00- S 066-10- w ;ulexito OuUlagua ;o ;2l-47- S 069-30- W P? :ulexile, borax? ciay (B4 Salar CosapKta ,'s ,17 50 S 069 06- W Salar de Agua Antarga s ]25-35- S 068-50- W P iulexilQ hallle* QUAT Salar de Agues Callenles julexlte yypsum, halite s 2500 S 068-37- W P OUAT Salar da Aguas Caltenies Norte (Zenobia) ulexite, brine gypsum, halite, clay .s ;23 07- S 067-25- W P QUAT HOLO Sajar (to Aguilar ;S I2&S0- S w P lUlexile? halite OUAT Salar de Ascolan ulexite dlatomite. halite, gypsum, mirabiiite S 2t 33- S 068 18- w P QUAT Salar de Aiacama j brine Li*. K, halite, gypsum 0 2330 S 06815- w P/BH ONvD Table 1 Bcxale deposits DtSTRICT OEPOSfT ASSOCIATED MMERALS MM OEPOSrrNAME orSrTE? LATTTUDB LONGOUDE TVPEISi BORATE MINERALS ('•dominant minaraliiatlon) ACE

TamblHo haliie, gypsum S 23 07- S 06B06- W P QUAT Ttlomonte S ,23 48- S 0M07- W P OUAT Tilopozo S ]23-47. S 068-V5- W halite, gypsum QUAT Salar de Carcote o do San Manin S '21-23- S OeB-23- W P ,utexll6 ^halite, gypsum, clay OUAT Satai da Carlquimas 0 |l9-26> S 06B-48- W P ,ulexlte OUAT Salar de Gorbea S |25 2S- s 06B-40- W P ulexlle QUAT Salar de Infieles ulexite halite S ,25 SB- s 0e9 03-30vy P OUAT Salar da La tsia s i2S-4S- s 068 37- W P ulexile hallle? Salar de Las Partfias 0 2SS1- s 0e8-30 30W P ulaxile? OUAT Salar de Maricunga ulexite hallle, travertine, lula s ,26-56- s yy P OUAT? Salar de OHague ulexite halite S 21-10'30S 06B-IS00W P Hao Salar de Pajonalea ulexite halite s .25-»Q. s 06B-48- vy P QUAT? Salar de Pedernales ulexile halite, gypsum, clay, anhydrite, tachyhydrlte s ,26-14- s 069-07- vy P QUAT Salar da Plntadoi ulexite Ihenardite*. mkabilile, bloediie. halite. 0 ,2p-3fl- s 069-38 W gypsum, hydro glauberlte. glauberite oyAj Diana s 'ig-2a- s 069 45-30W ? ulexile Satar de Punia Negra ulexile halite, gypsum s ,24-37. s g68j§- yy P OUAT? Saljr ^ S^lff 0 s 06905- W P ulexile, bnne mirabllllo, halira, gypsum QUAT Boral^as ^ ChHcaya s 18-49- s 069 05- W P ulexite QUAT Salar del Huasco ulexite gypsum, dlalomiie. halise, thenardile. clay s .20-ia-45S 06B-50-3aW P QUAT Salar Oulsquiero ulexite. brine hallle. gypsum, clay. Lt. K S ,23-l5- s 067-17- W P QUAT-HOLO TALTAL D Alemania S ,25-27.21S 069-49-56W N unspecihed ,nllrales*, lodales*, chromates, halite HOtO? Fl^ (le Chile s .2S-I2-36S g69-4&-4ayv N unspecilled nitrates*, lodates*, chromates HOLO? Sartia Lucia s |2&'27.34S 070-Qpp6w N 1unspecified nitrates*, lodales*, chromates HpLO? Tarapaea D 1 Hum^rstone s .20l0-2gs 069-46 P4yy N unspecified ;nilraies*, Ip^les*. chfomates NOLO? Negreiros S ;ie-49 04S 069-46-50W N junspecified nitrates', lodates', chromates HOLO? North Lagunas s ;20'55-27S 069-38-35W N unspecilled 'nitrates*, lodates*, chromaies Hao? Victoria s |20-4SI4S 069-42-38W N unspecified :nllrates*, lodates*, chromaies, halite HOLO? Tocopina 0 Pedro de Valdrvia unspecilled sodium nilrales*. lodales*, cfuomales, halite s 122-36- s 009-41- W N ICLO Prosperidad S |2IS3-37S 069-40 I3W N 'unspecified Hao? Sania Fe S ;2l-52nS 069-36-56V^ N iunspecilied ^nllrates*, lodates*, chromates Hao? Vega Carvajal s t'22-29- 06906- W xolamarille? igypsum puapiEiS?

! China Bango Laku S ;3l-50- N 089 ?5 E P |borax hpy? Sail Lake s '33 30- N 087-45- e p/afi • bora*? Hao Clialaka s |32-00 N 082 30 E p Iborax, Iincalconite, tirine sudium caibunale', li, K. Mg Hao Outlall Loho 8 '30 55 N 088 45 E p borax, iincalconite. brine clay itao o Table t Borale deposits. DtSTRtCT DEPosrr ASSOCIATED MINERALS MM OEPOSrTNAME iofSrrE? lUTITUOE LONGfTUOE TYPE(S) BORATE MMERALS ('•dominant mineraliiailon) AGE

Qeerhunstia :32-05- N 08p-tS- E P borax, ulexitu halile, gypsum, anhydrite QUAT Hepmg 's datotite Llaontng Provlnc«MI mi Gaoiaigou S 4108- N 126-10- E szaibelyile, ludwigite?. suanlle? magneslta, magnelito, rare earths pnon Houxianyu s 40-39- N 122-31- E 9< 'szaibelylte, ludwiglta?, suanlle? .magneslte, magnetite, rare eanhs pnon Llapnlng Province Borate Mine S U stalbelylle Ougquangou s /Q-28- N 124-0^ E 9< 8»|b^lle, lu^jgile?, suanlte? ^magneslte, m^gnetltfi, rare earihs PRon Wudaogou 's N i24-44* E » .siaibelyita, ludwiglte ^rnagnasita, magnelile, rare earihs pRon Zuanmlaogou 's *40-45- N i24-4l8- E szaibetylte, tudwiglle?, suanlta? ^magnasite, magnetite, rare earihs PROT QiNpIng :S ]2'6-i5- N i12-25- E SK? PSW? OInghal PlatMu ;8 P Oaldam Batin borax. tir>calconite. ulexite, plnnolte. halite*, potash*, gypsum*, clay, sodium 0 37-30- N 095-00- E P/BR ^kurnakovlle, brine sullate. Mg. Li. I. Iraverllne PUOHOLO Bielietan s '38-10- N 094-05- E P io-o Da Chatdan Lake utexlte. kurnakovite, indehte, borax. potash*, halite, gypsum*, travorline. Mg Li. i s ..37-50- N 095 00- E P plnnolte HOLp Ik&aydam Lake s BD/BR ulexitjs? Mahal ]s 37-t7N 094-I3E P7 ^ulaxite, plnnolte ,mlrabillle7 QUAT barhan Salt Pan borates, brine ! halite, sytvlte (potash)*, carnalhte, oypsuf"' u 38-00- N 095-00- E P/BR inirabilite* QUAT West Ta>itnaler Lake 's 38-30- N 093-25- E P uleiite? halite? and other avaporites Mac Xiao Chaldan Lake s .3?-3P- N 095-to- E P utexlte, pinnulte haljte, mirablllte, Ca-Mg carbonates HCXO Viliping [s .3§:<5- N 09300- E P potast)?, aodium rnlnerats? KX-O Yeshan *s [3300- N 118-30- E SK W0T7 Yin Lake s 28-15- N 088-15- E P NOLO Ztiabuye Salt Lake s 3200- N 084-00- E P borax halite, gypsum? HOLO Zhacang kurnakovito, indente. inyolte, ulaxlte, gypaum*, halite* s ,32-25- N 082-15- E P plnnolte MP»-P

• Ecuador Nono s oo-os-oos 078-34 55W y unspecified Li San Ntcolas s 02-38 S1S 078-58 18W a> ' unspecified LI, Mn QUAT

Germany ' Hamburg [s 153 30- N oippo E M Iboracjte potash*, gypsum, halite, anhydrite imw Stasslurl boracite. stalbolyito potash* (carnallto, syMlo), gypsum, halite s 51-51- N 011-35- E M IPQM

Greece Katlova&si Basin • Samos Island . 37-46- N 026-13- E BO? colemanitQ. ulexite celestite, gypsum, clay

• India ! Puga Valloy borax halite, sulfur*, sodium sulfate, sodium ,D ^33 55- N 078 25 E I"? carbonate, gypsum, halite l«XO QUAT

• 1 1 tran 1 Abhin j33-20- N p53--4f E p ulexite lhalite, clay H^aOUAT Dett-ti-Shotoran 0 120-28 N 055-44- E p ulexMe HOLQ^AT Tonkar ]s 136-13- N 057 38- E p uleiito? , HOtO-QUAT 1 Italy ' Tu&canv 0 42-:iD- N on-:io- E sasbolitu. bone itiid caibun UloxiUu naOQUAT Table 1 Borate deposits. t IWSTRICT OEPOSCT ASSOCIATED MINERALS Mt4 DEPOSIT NAME lorSrTE? UTTTUDE LONGmiOE TVPE(S) i BORATE MMERALS <*sdomlnani mIrMralliaUon) AGE

Ka2akh6tan Inder ^hydrobofaclie. szaibelylie. Inderlte. gypsum, clay, carbonates, sylvlte, anhydnte .s 48 33 N 51 48- 1 M cotemanlle. pdceile, Inyolte ulexilo R9M Lake Indor borax, hydroboraclle. sralbalylle, brine. sylvile. bromides, halile 'utexlle. Inyoile. colemanlte, pricelte. iS 48 30- N 5I-55- £ BR Inderlle LQUAT

Mexico H^qsllo *s 2904- N 110-58- W GO colemanlle men La Salada 's 30S9-30N ni-27-30W GO Mesa del Alamo howtlle, minor colemanlte zeolites- cNnoptlloiite, phiiliptlte, calctle. As ;S 30-3S-3SN n0&4-40W GO MO Tubulama j colemanlte, howlile, ulexlle, mcalllsteiite. zeolite, gypsum, clay S 30SeS2N iji-29-43yy Bp/P wardsmlthlte

' North Korea Kh(^don 38&2- N 126-27- E U ludwiglle Raiiakurt 3900 N I25-45- E U ludwlglle

Peru Chljlicolpa 0 17I3- S 069-54- W SP/P ulexlte, borai, brme halile, clay, epsomile, halite QUAT Cualqiuer Cosa Concesion s W-12-50S 069-54-20'w Iborax, ulexlte epsomite, halile Alguna Cosa s "l7l2-50S 069-54-20W P? jUlexlle, borax, brine clay Laguna Blanca ,s t7-38-30S 069-33-308 P ^B LI brine clay, chlorides, sullales Laguna Salmas ulexile. inyotte; minor proberlite. halite, gypsum. Ihenardile, montmoilllonite. s .I6-22- S 07I-0B-30S P hydroboraclle, biino Illita HO^

' t Hussia Cilnraa 's 45-00- N 034 00- E m 'brine 0UAT7 Q^nSQ^lK fPoQ .s 4f3p- N t35-30- E »7 'daiollie P^pG7 Kamchatka Peninsula R 56 00- N 161-00- E 3* bilne, other Klyuchevskoya-Dlmltryavskoye s 55.00- N 156 00- £ Rj lourmaline CREH Tazhefan (Lake Baikal) ;S ,5!-45- N 104-00- E azoproit .

' ' Tajikistan Churkurkul borax, lincalconile trona, halite*, tennardile, hanksile, burkeile. s 39 00- N 073-30- E Itiermonatrlle, traverllne, clay HOLO-OUAT Lyanger Lake borax, imcalconiie irona*. halite*, lennaidile. hankslte. ,s 38-55- N 070-50 E if buikeile, Iheimonatiite. liaveitine, clay Saskykul Lake borax, tincalconlle ,Irona*, halile*. tennardite. hanksite. burkeile, Ihermonalrile, clay, LI. Iraverline, ;S 37 40 N 073 00 E if ' clay ^^UAT Shorkul Lake i borax, iincalcontto Irona*. halile*, iennardilo, hanksilo. s 38 23- N 074-10- E burkeile. Ihermonalrile, Li, travertine

Turkey BIgadIo colomanilo. ulexHe. pncuite. calilo, gypsum, hentonile. zeolilos hydroboracdo, moyorholleriio. (houiandile, clmoptiiotilu, anatcimo. probertlle. howlile, inyoilo, (er&cliilu. chaba/ile), chlorite, anhydrite, celestile, szalbelyile, (unuHilo. ttvadavile tllilu. k-spai, qudiU. opal CT. aiagontle. D 3U 2B N 02U-II- E (1) dolumilu tMO Tablo 1 Borate deposits. ; jwSTBICT OEPOSTT ASSOCIATED MINERALS MM DEPOSrrNAME lor SrTE7 iLATTTUOE LONGfTUDE TYPE(8) ! BORATEMINERALS ('•dominant mlneralltatlon) AGE I Acep ;ulexite, colemanllei minor Inyolto. bentonlle. gypsum, calcile, aragonlla. mayarholfotilo dolomlle. /aollles (heutandite, cllnoplilolile). k-spar, opal-CT. Illile, ct>k)rlle S ;a9-27SSN g2B-120pE GO OM Ankara Nos. 2 and 3 's !39-2S-55N 028 07-46E OO ^colemanile, ulexlle clay BAO Avsat colemanite. ulexMe, meyert)ollerite. calcite, aragonile. dolomite, anhydrite, prlcQlte, howlltQ gypsum, zeolites (heulandile, clinoplilolite). k-9par, quartz. opal CT. monlmoiillonile, ;s BU chlorile. Iiliia Begendikler colomanile, uloxlte. meyerhottefile benloniia. calcile. aragonite. dolomite, zeolliea (haulandlte. clinoplilolite), k-spar, ,s ,39-29-2SN 02a-1310E BD opal CT. chlorile. illlle, quartz Qoreke icoiemanila, ulaxlla, howlllQ, bentonlle, calcilo, aragonile, dolomlle, .meyerhollerlte zeohtea (heulandile, cllnoplilolile), k spar. .§ ,39-27>p5N p28n-40E GO opal CT. chlorite, illlle. quartz BAO Oomuz Deiesl colemanila. ulexlla, howllle. bentonlle. calcile, aragonite. dolomlle. meyeiholleilte zeolites (heulandile, clinoptllolile), k spar. s 39 27 00N 028 10-40E a) Opal CT. chlorile, Illlle, quarU QAO Emircam colemanite, ulexlle calcite. aragonile. dolomlle. anhydrile. gypsum, zeolites (heulandile. clinoplilolite), k'Spar, quartz. opal-CT, montmorlllonlle. s O) chlorile. liiiie Ounevi colemanlle, ulexlle: minor inyolle, bentonlle. gypsum calcite. aragonile, meyerhoflerlte, hydroboraclle. lunelille. dolomite, anhydiile, cete&llle. zeolites proberllle (heulandite. cllnoplilolile). k spar. quart/. s 39-26-3SN 028 t3-35E ED opal CT. chlorite, illlle aso Haimantcik ;S '39-4S- N 029-12- E GP ! colemanite clay Isiklar colemanlle. ulexlle. hydioboraclta calcile, aragonite. d(^omlle. anhydrite, gypsum, zeolites (heulandile. clinoplilolite). k-spar. quartz. opal CT. montmorllionlie. s uo chlorite, illlle Kirechk ulexlle. colemanlle: minor bentonite. calcile. aragonile. dolomlle. meyerhollerlle, pilceile, inyotte. zeoliles (heulandite. cllnoplilolile. analclme), hydroboracite, tunnellile k-spar. opal CT. quartz, chlorile. illite ;S 39-27-2gN 028-14-3PE aj BAO Kufiplnad < ulexlle, colemanlle: ler&chlle, inyoile, benionlte. calcilb. aragonile. dolomite, meyerhollerlle. howllle zeoliles (heulandile. cllnoplilolile). k-spar. ;S ;39-2S0SN 028-I4-2SE BU quartz, chlorite, Illile EMO Meiarbasl colemanite. uloille, prlceile. calcile, aragonite. dolomite, anhydrite, hydroboraclle j gypsum, zeolites (heulandite, clinoptllolile, analcime), k-spar. quartz. opal CT, s BU monlmorlllonlle, chlorile, illlle Salmanii colemanlle. ulexlte. Inyolle benlonlle. calcite. aragonita. dolomite, zeolites (heulandile, cllnoplilolile), k spar. • S ;39-26-2&N 028 08 05E UD quartz, chlorile. ililte culeniankle, uluilte. Iu&&et Inyollo, calcite, aiagonlle. dolomlle, anhydrite, mttyerhollertlo. pnceile. howlila gypsum, zeolites (heulandite, cllnoplilolile). k-spar, quart/. opal CT. iirantmorlllonilti. SiniAv s j ai cfilorlto, illlle Tulu colotnanilo. nilnor ulohilo calcile, aragonile, dolomile, anhyddte. gypsum, /eolltes (heulandite, cllnoplilolile), k spar, quad/, opal CT. montmodllonile. s IV chlurile, illilo OJ 1 — • Tablo 1 Borate deposits DISTRICT DEPCSfT 'ASSOCIATED MINERALS MM DEPOSrrNAME iOfSrTE? ilATTTUOE LONCmJDE TYPE(S» (BORATE MINERALS i(*«domlnant mineralluilon) ACE

Tulu DegUmen *S |3B-2? 028..05-55E BO colemanile bentonile 940 calcite, aragonite, dolomite, anhydrite. ;gypsum, zeoliles (heulandite, cllnoptiloiiie). 'k spar, quartz, opal CT, montmorillonite. Yonikuy S 00 ^cpjemarute, ulexile chlorite, lllite Emat 1 colemanite; lesser ulexlle. hydroboracile. otpimeni, realgar, ceiesllle, calcite, gypsum. meyerhotlerlle; rate cahnlte, leruglle, native sullur, zeolites (clinoptilolile). ;o 39-I6- N 029-IB- E O) lunellite. veatchite A 'smecllle. chloilte, lllile MO Oerekoy ;s '39'10 00N 02^19 30E PP ^col^rnanlie ;catclle, rnontmprll|onjle, illiie, chlorite Espey I ' colemanile, less ulexiio, hydroboracile; bentonite, realgar, cafclie, celestlle. rare meyerholferlte, veatchttO'A, orplmeni. nalive sullur, iillte, chlotiie ;s 30-2t-3ON 029-f7.50E BO iunellile, cahnlte Goktepci colemanile. ulexlle gypsum, calclle, monlmorillonile, lllile. s 3B 15 30N 029.16-0SE DO chlorite MO Hamarrtkoy ]s ;3en SON 029.18-20E BO ,colemanile calcite, montmorillonlle, illlle, chloille MO Hisarcik colemanile. minor ulexlle. hydroboracile, realgar, calcite, celestlle. orplmeni, gypsum. rare calmite. teruggite native sullur, monlmorillonile, iillte. chlorite s <39M00N 029*16 OOE BO Killik colemanile: minor ulexlle, hydroboracile. monlmorillonlle, realgar, native sulfur, meyeihoKetile; rare vealchlte, tunellile. calcite, illlle, chlotlle s 39-2 ISSN 029.I6.00E BO cahnlte MO Kesteiek colemanite. ulexlle. proberlite; rare smectile, illlle. calcite, quartz, zeoliles. s ^39-40- N 028-45. E 60 hydroboraclte chlorite BAQ Ktrka borax, lincalconite. colemanite, ulexite. smeclile, dolomite, calcite, lignite, realgar. kernite. inyoito, minor moyoihollorlto. orplmeni, celestite, illlle, chlotlle, zeolites hydroboraclte. Mg kurnakovile. lunelhle. 39-20- N 030-30- E 60 Inderborlte. inderlle MIO 1519 MA Kucukler s 39-31 3SN 028 20 3SE eo colemanite M07 Selench Oa&ln ;38-42- N 028-45- E po ^colernanite clay Sultat)caylr-Azi2iye prtaelte; minor colemanite, ulexlle, gypsum, bentonile, zeoliles (clinoptilolile). howlite lllile. chlorite, opal CT, K-spar. sanldine. s :39 52 N 028 08- E quartz LTttU

' i Turkmonlstan K^!A§aQarOpl Gull 0 4V00- H 053-30- E w ,brine ^Mg QUAT

' • United States-Arizona Aguila :S '35-54. H 113 pa­ W p brine QUAT Gila Ber>d S '32-57. N ns 45- VV Float colemanite LTERT?

United States • Calltornia Ash Meadows Zeohio Deposit 's '3557. rj 11615. w ^searlesile zeoliles*, clay, opal, calcile PIEIS? CAUC(M)AGG£T AREA cotemanile, b boating shafe, minor relestUe, gypsum, calcite ,D _34-57. N n6-48- w uo howltle, bakenlu? MIO 13-17 MA American Borax Mlnu •s 34 56 N IIfl-57- w m B buanng shale MIMIO Cenlertnial Mine S BD colemanile calcilu MLMIO ColumtMiS Mino (Gem Borate) s i34 48 N 116 S3 w BD B-bearmg shale MLMIO Pacific Mine (Old Dorale) 1 colemanile. howlite, bakenlu?, B bearlng calcile, celeslllo, gypsum ;S 34 57- N !!§ w aj sliale MLMtO Paltn Uorate Co Minu '34-55- N 116 48- w BO B-bearing stialo MLMO Union 's !34-57- N ne-49 WE BO/P TERT Webtein Minerals Mine •S ;34-57. N 116S2- W uo B beanng shalu MLMIO Cluna Laku s 35 43- N 117 37 W l» iileiilu. bnnu? haltle. clay QUAT Tablu 1. Borate deposits. DISTDICT oeposrr ASSOCIATED MINERALS MM DEPOSfTNAME or SriE? UTTTUDE LONGITUDE TYPE(8) BORATE MINERALS .('•dominant minerslliatlon) AGE

' CLEM LAKE AREA Oqrax Lake "s |3e &9- N 122-40- W mi jbiino, borax Irona, gaylusslte, hatlle QUAT Lake Hachinhama Cotumbian mud borax? DEATH VALLEY colemanile. ulexile. probertite; minor calclle. dolomite, gypsum, celesllte. clay .0 BD/P hydroboraciie HpLp UwtlpeM' Blialandll jcolemanite, proberiite. ulexlle calclle s ^36-20-30N 1 ie-4l-02W tX) LAtK) Boraxo (Thompson) 'colemanile. ulexile. probertlle clay s 36-20 23N n6-42-17W O) IMiO Coikscrew s 36-2I-57N ii6-45-54W BO fcolemanlle. ulexlle, probertile calcile LJ^ DeBfily s QO icolemanlle calcile IMO EaQle Borax WorKs s |36I2-1SN 1 ie-5l-4SW P ulexile QUAT East Coleman s |36.^.17N n.6-^-41W DO ^colemanile ,calclle LMIO Qower Gulch s '36-24 SaN i j6-5poavy GO ^coiemanlje, ulexlle cak:|to, gypsum LMIO Grar)d View ;s ]36{8t6N 1 i6-4p'3aw GO xolernanite calclte 1Mb Harmony Borax Works ulexile s 36-3I-3SN 116-S3-3SW P QUAT Inyo 's '36-29 S1N 116-42 plW BO .colemanile, ulexlle, probeiiiie calcile IMP LilaC s '36Mt^ ue-29-42W BO jcolomanile calcile Lifzy V. Oakley s [36I7-53N ilB:4P-26W BO ^colemanite ^calcile LMIO GMV Low ;S colemanile Lower Biddy McCarthy 's 36-igUN n6-40-34W VD colemanile calclte LMIO Maria 8 36IS-30N tl6-32 SOW BO 'colemanile, minor ulexile calclle LMIO Monle Blanco s 36-23 I4N n6-46-40W BO colemanile, ulexlle. probertlle calclle LMIO P^uja s .36-13-57N \ io-2e-4Byy BO ,cplemanlte? LMIO Played Out ^s ^36-20-10N n6-39-i&vy kt colerrianite, ulexile calale Ll^ Terry colemanile, minor hydroboraciie, ulexlle calcile, zeoilies (chaba/iie, cilnopiilolile. s 36-I7-26N ne-33-t2W BO phillipslle, anak:lmo), gypsum IMO Upper Biddy McCanhy *s ]36-t903N n6-40 0SW BO colemanile, ulexlle calclte LMIO While Monster • Sigma •s '36-t9-l^ tl6-4l*25W BO colemanile, ulexlle, probertlle calclte IMO Wi^w* No 3' 's '36-17-45N ii6-39-4ew BO ; colemanile. ulexlle, pro^rllle calclte LMO widow No, 7 's *36I7-<7N t|6-38-54W BO ico/ernarWte, uloMlle calcUe IMO Fori Ca^ Pepp&il •S N 116-25; W P/BD colemanile anhydfile, gypsum, celesiiie, irona, halile Gerstley 1 s '36 0f05N n6-t3-55W BO ulexite. colemanile, proberiite calcile I!MIO 6 MY Qerslley II 36 02-10N 1 ie-l4-3SW QO colemanile, ulexite, minor probertlle calclle LMIO 6 MY Hector 'colemanile, howlile heclorlle', leolltes, anhydrite, clay, oypsum. 3f46- N l!6-27- W calclte, iravertlne MIO 19 23 MY Koehn Lake [s .35-le- N !!7-53- W P ^ulexite |halile, gypsum CKJAT KRAiyiERAREA ;R n Kramer 'borax, kernlte, llncalconile, ulexite. calcite, realgar, stlbnite. native arsenic and columanlte, proberlllu sullur. smecllte. illlto, leldspar. mica ,35 02-2eN 1 I7-41-j4W 00 i MIO 18 20 MY Rho A • Upper and Lpwer '34-46-OON H7-32-60W BO ; colemanile realgar, oiplntenl^ caklte Rho B • Upper and Lower 's '34-2OS6N i 17-32 21W BO 1 colemanile catello. ar&enk: minerals? MO? Sunray (Rho) s 34-47-50N 1 I7-34-15W ID colemanite MO? Owens Lake ; brine, borax soda ash* s 3625- N 1I7-57- W ! QUAT Saline Valley ]R |36-43- N 117-50- W P ,bofax?, ulexite? OMAT Beatles Lake brine, borax, ulexile Irona*. halile. LI, K, aragonlte, dolomite, gaylussile, calclle, aragoniie, nahcolile, s N 11724- W 11) Ihenaidite, inifdUilile UUAT 0 030( Table I Borale deposlls i iDISTRICT OEPOSCT ASSOCIATED MINERALS MM DEPOSfTNAME or SITE? LATmJOE LONGOUOE TYPE(S) BORATE MMERALS ;(*adominanl mlneralliailon) AGE 1 VENTURA COUNTY AREA/FRAZIER MTN. ' colemanlle. pricelle gypsum jo :34-47- N 119-04 W eo MID IS MY Alia Claim S oo colemanlle Bilter Creek s ,34-46-OSN I19 06-30W eo ^cplemanlje gypsum TWT7 Borate No. 3 ,s GO colemanlle 0/y«n 0 CMm BD colemanlle Columbus Mine 's |34-47-04N 1 19 03-43W colemaqlle, pricelle ,gypsum Denver Claim ]s CD ^colemanlte Pra/ler Mine s |34-46-33N M9 04-57W m xofemanite, prIceHe gypsum, (raverllne? MI07 I5MY7 Frisco s BD colemanlle Ives Properly •S |34-4b-35N n9-ig-20W GP ;ptlc^e^ ,gypsum Ives Turuiel 's |34;4S-S0N n9 07-18W BD colemanite? gypsum Jessie 'S GD cojemanlle Kij>g and Oueen s BD coiernanUe? Mane s BD cotemanlte, pricelle Middle Fork Borale Prospects s 34-46*t1N n9-07-2gw BO cotemanlie. pricelle gypsum TCRT North Fork Borate Deposits s 34-45-30N n9 09 00W BO pricelle TERT PInpche s BO colemanlle Rusland ]s eo colemanite Russell Mine 's '34-46 55N 119p4-13Vy op colemanlle, priceile gypsurn, selenlte THTT Stufablehetd and Halloway ]3V4S-20N iig-07S0W ep cplem^nlte, pricelte gypsum Thomas Boyle Tick Canyon (Lang. Sterling) colemanite. howlite, proberlite. ulexlle, s ,34-2Q-S5N 118-21-53W 0) veatchlie M|0 20 MY Tuscan Sprlrigs *s |46I4-27N 12208-3BW £P? United Slitet • Nevada Anniversary Mine/CallvUle Wash colemanite; minor ulexlle hectorite. gypsum, dolomite, halite, s ;36-12-5&N 1 14-42 2BW UBD catareous clay, celeslite MMIO 13-16 MY Cave Spring 's '|^-49 0iN 117-5119W OC searleslle calclle PUG Cotumbut Marth ulexlle halite*, clay p ;38 02-46N 117-&9-21W P NOLO Borax Works •

CakmviUe Borax Works 's jsB-pl-tSN n7-56:35W P ,ulexlle , halite ^CU) China Borax Works 's 3B02-20N 117-S9S0W ulexlle hallle HOLD Old Borax Works 's |3B04>2QN 1t7Sa-05W P ,ulexlle |hallte HOLD Dixie Maish 's 39-4anN 117-5B-MW P ulexite halite*, biine, day. gaylussite OUAT Eagle Marsh i® ;39-43-4GN 119 02 31W P borax, brine ,halite, mirablNte, Iheiiardlte OUAT Hot Springs Marsh (Eagle Marsh) brine ^s m cm Fish Lake Marsh s |37 54-12N 1 17-S5-4BW p ulexile, minor borax sodium sullale, halite Hao Pacilic Borax Co {37S4-28N 117-SS-41W p iborax, ulexite QUAT Qertach Hoi Springs |s i4p-44-3aN II9 26I0W a* ulexlle OUAT Nor^ Sand Springs p ]s 1 ulexlle, brine, borax poiabh? QMM Ore Car Mine 's 1 ? borates ' f Rhodes Marsti borax, ulexite halite*, sodium sullales*, Irona, gaylussiie. D j30l713N 1 16-04 29W p thenardlle, ntlrabllile, glauburito OUAT Sample Sile 1133 ;37 S3 56N 117 55-13Vy f? QUAT Sand Sonnns Marsh (Salt Wells) s 30-20- N ne-su- w p uluxito. bu

ON Table V Borale deposits. DtSTRlCT DEPOSIT ASSOCIATED MINERALS MM DEPOSIT NAME or SfTE? iUTTTUOE LONCmJOE TYPE(S) i BORATEMMERAL8 ('•dominant mlr>eralliallon) AG£

Sttver Peak Mar&ti brme. ulexile lithium*, hectorite, gypsum, halite, clay, tula S 37-45 tON tt7-38-20W P/BR CBi Stfver Peak Range S 37-5t-3IN n7S3-06W eo uleille 0JO Soda Lake 39-3t-3tN t1852*25W m brina sodium Mrbonale QUAT Teols Marsh borax, ulexile. tmcakunlle, brine. zeolite, trona. halite, gaylusslte, magnesia. s 36-t2-27N t162t 12W p soarlesMo lime QUAT WMIe Basln/Cenlral Muddy Mlnji CDlemanile. minor ulexite hectodte, gypsum, (ravertine, smeclite. s ,36 t9-S2N t t4-34-27W BD celestlte MMIO 13-16

United States New Mexico •

Lake Lucero :32-40-31N 10e-2S00W p borax? halite, sodium sullate

United States • Oklahoma West-Central Oklahoma |34-00- N 100-30- W M

• United States Oregon Alvord Desert 42-3t-49N t IB-27-24W Alvord Valley (Lake Alyofd) .42-20- N 11B-3S- W P/SP borax sodium carbor)a^, soAum sulfate OUAT Lone Ranch (Cheico) S [42 06- N w OD prlceite aragonile Summer Lake (eastern playa) S |4i-S0- N 120-41- W P/BH brind soda ash*, sodium sullate*, potash?. Mg

Yugoslavia Jarancfot colemanile. howlite. soaitasila, zeolites, magnesite. coal. cak:ite, gypsum 0 .4326- N 020-40- E DO luneberglte MO Krenma s '43-50* N 019-35- E 807 spafieslle magneslte^ d^rnlte MO Loparl-Slbosnica s '44-38- N 018-50- E BD? searleslle Vallevo-Mlonkra s 44-t6- N 020-00- E UD searlesile dolomite, oil shale MAO Table! Borate doposiis. HOST ASSOCIATED VOLC ASSOC. DEPOSIT NAME ROCKS nOCKS AGE jsPGS? PROD? COMMENTS

Boralera de ChalMri Sur lacuslrtne sediments, evaporlles SPP ChaUyid Pan^pa Easi iacusirjne sedmenis, evaporlles N ChalMf) Pampa North lacustrine clay N Herreia Parrpa lacustrine sediments N Salar da Chiguana lacustrtne sediments, evaporlles ignimbrite, dacitic lo andesite Hows and lulls MIOHOLO S La Carrillana lacustrine sediments, eyapori^s OT Salar de Colpasa lacustrine mud, limestone, gypsum, halite dacilic lo andesite volcanics LMK>HOLO Y Salar da Empaia lacustrine sediments, evaporlles. clay volcanics ffP Islrna lacustrine sediments, evaporlles N Laqueca lacustrine sediments, evaporites SPP Salar de Lurlques lacustrine sediments, evaporites ignimbrite, iJacltic to andesillc (ufl MOHOU) s Salar de ORague lacustrine sediments, evaporites dacitic to andesite (lows See Chile MROS record lOIOlOO and tults LMK>HOiO N Salar da UyunI tacusinne sediments, avaporlies tuff, basalt iMiatKKO S Llipl-Lllpt mud lull, basalt N Rio Grande (Boratera Pampa) lacustrine-lluvlal mud, clay lull, basalt LMIO-HOLO SPP SalfDuera del Rio Giancto lacustrine se^q^nts, ovaporites N Salnjueras del Salar ^ Uyuni lacustrine sediments, eyapprltes volcanics N Salar Laguani lacustrine sedlmenis, evaporites ignimbrite, dacitic lo andesite Hows and tults M&IIOLO S Pa)or>cha lacustrine sedlmenis, ovaporites volcanics N Chile Cebollar limestone U Ugunas Bravas lacustrine sediments, avaporlies yplcanlcs N Las TUas Ma/la Elena alluvium, colhivlum, caliche N Pampa Tamarugal sand, carbonate, CAltche, halite. tull. andesile, rhyolite conglomerate Chug chug j y ffP Ei Toco limestone, (anglomerate, ignimbrllo. tuff, andesile, rhyoilto rhyollte, andesite CRET N Pampa Joya lacustrine and alluvial sedimonis and Jgnlmbritu, rtiyolile. evaporites andesile t 3f Ouebrada de Barrera Oudtagua lacustrine slit, clay Satar Cosapitla N Salar de lacu^ln^ sediments, evaporites iyoicanics N Salar de Aguas Calientes j lacustrine sediments, evaporites rhyoklic to basallic lulls I 1 and flows MO-tlOlO u Salar do Aguas Callonles Norlo (Zonobia) iclay, mud. sand, gypsum !lgnimbrile, dacilic- andesilic lull, basalt IWK>PLI0 u Salar de Aguilar Ijacuslrine sediments, uvapuiiios ^volcanics 'c^ !Y N Salar de A&cutari lacustrine sill, clay, dtatomlle. evaporites andesilic Mows and lull : LMK>PUO Y SV Salar de Atacama lacustrine clay, mud. sill, evaporlles (lacilu lull, andobile 1 mOI'LElS Y Table 1 Borala deposlls HOST ; ASSOCIATED VOLC 1 ASSOC. DEPOSTTNAME ROCKS ROCKS LAGE SPGS7 PROD? COMMENTS

Argentina Acatoque lacuslrlne clay ^daclle, andeslte 'MIOPUO lossll N Aldjandra Occurrence N Alei Prospecl N Archlbarca Ravine area A(^iana alluvium Y H Uri ^ajluylurn Completely mined out. Los Bayos sedlmanis basalt |QUAT ]y Oeppsll la mined out Tropa Pele allium 'Y SFP Berta Prospect N Blanca Liia Mine lacustrine evapontes, clay, sand Boralera da Antuco alluvium J lull, basalt, andeslte MLPTIO V Prod 1940-1949 Ce||i Occurrence lull, clay, Sana, tull dacite ,M0 N Coyaguaima argiillle. shale, andslofie dacite lull contains about 10,000 1 borate, 3 deposlls PUO Y S El Toto Y N La Mucar clay, sand U Small deposlls in several depressions Laguna Quachalayle lacustrine sedirnents? N Laguna Quayatayoo sand, clay S ^tow Rio Alumbro apringa Baraloyoc Mine Iacuslr1r)e sedLELS N Cerro Bayo lacuslrlne sediments and evaponles andesite. dacite .PUOPT£« Lagunlla clay, sand dacite tull, ignlmbrile *PIBS N Ubertad Boraje almost erillrely rplned out. Loaia Blanca tullite, clayslonti. lull lull, dacite. rhyodaclln

TTHTMLO lossil Y Maria Teresa av ^re pianlHc rnBjarnojrphlc rocks N PJo de Agua stiale, mudslone 'Y SV Rio Alumbrio Spring Area conglomerate, lull, sandstone, claystone. basalt, andeslle 11 spring aproni argilllte. quaililte .RAN Y ETP Aniu/ar Mine shale, slItstMe, sandstone volcanics .MO 'y SPP Deposit is almost exhausted Calichar ^sedim^rits Jgnimbille N Canueias sandstone, schist 'Y Deposit IS exhausted. 3 springs. Oanlel Mine ,aiiuvlum: sliale. siiistone dacite PUO 'Y Deposit is eihausled San Marcos shale, mudstone, sandstone dacite lull RIBS Y 1 Votcancllo dacite lull, Hows, sediments dacite lull MO Y SH> Prod uloxite in IBSO's Salar Centenarlo claystone, slllslpn^ sand lull, basalt, andusile ;MIOPLIO S Anatuya Prospect jacustilne sediments, evaporiies N Soroquimica Samlcal Mines lacuslriria sediments, uvaporiles V La Argentina lacustrme sediments, evaponles 3^ Maggie lacustrine sediments, evaponles BV Mataro Prospecl lacustiine sediments, uvapontos H Maria Luisa Ml Occurrence ,lacuslrlne sediments, evaponles N Purmamarca Mine lacustrme sadirnents, avapontos Salar do Aniolalla lacustrme sedimenls. ovaporltes U Table 1 Borate (teposils ' HOST ASSOCIATED VOLC ASSOC, OEPOSTTNAME ROCKS ROCKS .AG£ SPGS7 PR007 COMMENTS

Salar de Ciucharl lacuslrlne silt. sar>d, clay, ovaporiies Silar ii S3 km x 80 km Y S Campamento Prlmero (to Mayo iacustrtne sediments, ovaporiies Y CailotaCofina ;lacusir1r)e se^ents^ $y§fiorlles ;lull, andesile, daclte .MOPI^ S9 ClrKo Occurrence ;lacusit1ne sediments, avaporltes U Defen>a l-ltJl Occufrertces |iacu^rlne se^men^j fyapgrljes U El Pofvenir I'scystrlne sarid, ciay SPP La inundada lacustrine sand, clay ' S Mascota lacustrine sand, mud ffP San Pedro Jacustrine mud, clay Y Siberia Jacuslrlne silt, clay N Salar Incahuasl N Saiar de Jama lacustrine clay, other sediments. volcanlcs e ovaporiies ffP Maria lulsa lacustrine sediments, evaporltes U FrarKisco lacuslrlne sedimenis, ovaporiies U Salar de Uullalllaco lacustrine sediments and evaporltes s Adela lacustrlrie sediments, evaponies N S^ar da Olarox laucslrlrie sediments 9P ElCpric^ Jacuslrlne sediments, evaporltes 3^ Orupo San Nicolas lacustrine mud. calcareous sandstone. salt, other Sff Sar>ia Ines liriiy sand Yacara lacustrine sediments, evaporltes N Salar de Pattot Grandei clastic sediments, gypsum, tullaceous lull, dacile, andesile rks ,LMIC>PL£IS SP Betlna MMe lacuslrlne sediments, ovaporiies S Bqraiera Blanca Ilia .lacuslrlne mudstone, sandstone ^dacite, andesile [EQUAT Y Y Coronel Oorrotll ^iMus^ne clay SPP Salar de Pocltot o Qulron lacustrine sediments, ovaporites andesile OUAT S Oucus IV llacustrlno sediments, evaporltes N Dona Emma .lacuslrlne sedimenis^ evaporltes s Salar de Poxuelos lacustrine silt, clay, sand 7 Mar^illa San Mateo Mine i lacustrine sediments, evaponies V Salar de Pucar ^lacuslrlne sediments N Salar de Rio Grande liacustrlne sediments, evaponies 9*' Salar de Santa Maria lacustrine sedimenis Y ' Santa Maria Mine liacustrlne cla^, Uill ;iull S Sitlar de Turllarl jgreen benlonlllc mud. sand, clay. lilhlc lull tullaceous sediment l*UO S Salar del Hombre Muedo sst, clysl, lull, evap, Isl. congi lull, basalt ,TERT KEIS? Y 20 de Febrero Jacustrine sediments, evaponies Calchaqulna lacustrine sediments, ovaporiies SV Cuntenatlo ^lacustrine sedimenis, evaporltes Oetia lacuslrlne sedimenis, evapoiilos ap Table 1. Borate deposlls. ' HOST ASSOCIATED VOLC ^ASSOC. DEPOSfTNAMe ROCIS iROCKS AGE :8PQS7 PROD? COMMEKTS

Tincalayu sandslona. clayslona. evaporlies, lull. tull. basalt In N-central part ol salar. Sljes Fm overlies conglomerate thick halite sequence

,1X1(0 M Salar del RIncon lacuslilne limestone, sand, silt. evaporlies SPP Angela jBcusUlne sediments, eyaporites N Anjnco lacustrine sediments, eyaporites N Carolina .lacustrine sediments, evapojlles S Eduardo N Nelly lacustilne sediments, evaporlies 1 SaUna Talisman lacustrine sediments, halile N San Eduaro lacustrine sediments, ovaporiles N Salar OlabliHos clay. sand, gypsum, sail, oolian votcanics sediments ca4 Y Y Salar Ralonaa silt, clay, halite lossH 1 Aeghyr Occurrence ^lacustrine silt, clay N Eaperania Prospecl lacustrine sill, clay N Sallna da Una Larj y do Palrlquia tutlaceous clay ignlmbrlte, othr volcanlcs C84 gi' Hutr>cul Prospecl tacustnne sediments N Salinas Grandat lacustrine ctaystone, slilstone. limestone, sandstone, gypsum Y Bahla Blanca lacjistrln^ ^edimenU, eyapmiles U Dofalera La Aguadita lacu&trrne sedtnients, evaporites 39 Boraiera de Nino Muerio Jacustrine sediments, evaporites Sff Boralara de Pozo Cavado lacustrine sediments, evaporites 9P Boratera de Tras Morros lacustrine clay SPP Caucharl Minj lacustrine sediments, evaporites ap Sania Maria Ml lacustrine sediments, evaporites i u Silvia Jacustrine sedirnents, eyaporites N Valparaiso lacustrine sediments, evaporites u Vlclotla lacustrine sediments, avapoiltes u Salinas Orandes Prospecl lacustrine mud, salt u San Anionio SP San Eduardo N San Luis N Sarrania da Sljaa day. lull, other lacustrine sedimenls. tull evaporites roftsfj Y Alejandro mudstona. tuti, other lacustrine lull sediments, evapoilles N Andina imudstone, sandstone luti, andusllu, daclle EPLEJS lossti Anna lacustrine mudslone, sandstone, lull lufl LWiaPLIO los&ll N Elsa lacustrine mud, clay, caltche, sand N Hlorro indio Prospecl clay, lull lull ,iMiaptio U Juanita &attilslqne, niudstuiie, clayblonu, gypsum 1 La Esperar)ia mud&tune. lull tull EtUO 31' La Paz clav&lorto. tull, Qvpsuni lull IMiOPLlO 1 Tabto r Borala deposits. HOST ASSOOATEO VOLC ASSOC. DEPOSIT NAME ROCKS ROCKS AGE SPGS7 PR0D7 COMMEmS

Monle Afnarillo clayslone. mudslone. sandstone, tull, tull gypsum MO S Monte A/ul mudslone, lull lull LMK>PUO SFP Mopja Blanco claystone, tuti, sandstone ;iuii LMK>PLiO tossll N Monte &is mudstone, tull \u\\ jlMO-PUO N Monte Marron mudslone. gypsum, minor lull Jull ^LMiaPUG N Monte VefUe clayslone, sillstone. tull, sandstone ^lutl LMO N Santa Elena mudstone, tuti, gypsum lull LMIQPLX) N Santa EMfa mudstone. lull 'lull LMiaPUO N Santa Rosa sandstono, mudslone, claystone. lull. lull gypsum S Socacastro red sdttrnenjs, gravel, aand ^cite lull and Hows N Unnamed Y OT

ArmanlK Oihulla aroa travertina, shale, conglomerale (ossll Y

Bolivia Cuevitas N Laguna Bu&ch o Kalma lacustrine sediments, ignimbrile Ignini^^e. d^ite IMOHOLO N LaQuna Cachi iacusirine sodimenis, evaporiies volcanics MiOHOLO U Laguna Capita Sur lacustrine sedimenU, evapontes andeslte, pyroclasllcs LMiaOUAT Y Laguna Celeste lacustrine sediments y^canlcs 'OUAT N Laguna Chlar Khola lacustrine sediments, evapontes vo4canlcs ;LMiaQUAT N Laguna Cho|llas lacustrine sedimenls. evapontes dacitlc lo andesiio |Volcanlcs ^LMl&^OLO .V N Laguna CbuHuncanl lacusltine sediments, evapontes dacilic lo andeslte .volcanics, ignlmbrlte LMiaHOLO N Laguna Colorado clayslone, dlatoimle. other lacustrme dacilic to andeslie sediments votcanics, Ignimbrile LAtUaHOLO Y N Laguna Coruto lacustrine sedimenls Ignlmbrito, daclie. andesite ,QUAT ,Y N Laguna Htidionda Notle Iacusirine sediments, evaporilos dacilic lo andosllo tull. ignlmbrlte iMtafiOLO N Laguna Loromayu lacuslrino sediments, volcanics ,volcanics 'QUAT N Laguna Mama Khumu lacustrine sediments, evapontes ignlmbnie, dacttlc to , andeslte Hows and tufis 12 \s S Laguna Ramadilas mud. carbonate, gypsum ,lgnimbnte. daclilc lo : andeslie Hows and lulls jLMlOHOLO N 1 Laguna Sacabaya lacustrine sodimenis and evaponles ignimbrite, dacitlc to andeslte Hows and lulls IMiaHQLO Y Layuna Verde lacustrine llmestono, olhor sediments, ash, ulher volcanics 'ush QUAT N Lagunas Paslos Grandes laciislrine llmeslone. ovaporiles lonimbrite, dacilic lo andeslie Hows and lulls MlOHOLU Y S Salar de Challvirl lacusinnu sudlmoots, uvaputiius Ignlmbnto. dAciilc lo ' andeslie Hows and lulls ,LMlO iXXO Y av Huraltira da Chailvitl Nmle lacustnne s^eilimonts, uvapontes N Table 1. Borate deposiis HOST ASSOCIATED VOLC ASSOC. OEPOSTTNAME Rocte ROCKS AG£ SPGS7 PfKXn COMMENTS

Tambillo lacuslrlne sedimonts?, evaporites dacltic andesitic luHs and (lows PLK>PI£1S Ttlofnonle lacuslrine sedimenis?, evaporites ignlmbrile, dacite, andesite, basall ,PUOPl£IS SFP Tilopoxo lacusUlne sedlmenis?, ovapofi^s ^dadle tyd :puo Y Salar da CaiccHe o de San Martin lacustrine ciay. silt, evaporites .andesite itovn and lulls LlkvPUO N Salar de Cariquimas lacustrine sedimer^ls. evaporites S Salar de Gorbea iacuslrlne sediments, evaporllos ^volcanics C8^ SPP Salar de Infteles tacusirine aodimeMi, evapotUoi dac'tlc andesitrc {uffs and Hows MO N Salar de La Isia lacustrine sedlmenis, evaporiies volCBnlcs C84 N Salar de las Partnas lacustrine sadlments, evaporiies Salar de Markur>oa lacustrine sediments, evaporites ihyolitic lo andesitic (loiMs and lulls LTHin Salar de OUague lacuslrine sedlmenis, evaporites ignimbrlle, rhyoliiic lo andesitic Mows and tulls IWiaPLMD N Salar de Palonales lacu&tnne sediments, evaporites rhyoKlic lo basaltic volcanlcs MtOHOLO N Salar de Pedernales lacustrine sediments, evaporites lull, dacite, andesite SFP Salar de Plntadoa lacu&lrino silt, sand, evapoiites volcanlcs S Diana Salar de Punia Negra lacuiilrlne sedimonis, evaporiies rhyoliilc lo basaltic volcanlcs MIOHptg N Salar de Surire lacuslrine sedimonis, evaporllos volcanlcs "iWPLBS S Bor^eras ^ Chjicaya lacuslrine sedimenis, evaporites volcanlcs ,PUOPL£lS Salar del Huasco lacustrine sedimenis. evaporiies rhyoliilc to andesitic ^volcanlcs MMIOPUO SV Salar Oultqutero sill, clay. mud. evaporites ignlmbrile, dacite lull. ;basalt, andesile LMK>PLIO TALTAt Alemanla caliche Flm ^ Chile caliche Santa Lucia caliche Tarapaca Humberslone caliche Negrekos caliche North Lagunas caliche Victoria caliche Tocopllla Pedro do Valdivia calichu, alluvium, colluvium

Pfospeddad caliche Sanla Fe caliche Vega Carvajal limoslono

China Bange Lake lacu&lntie eyapofjlHs, mud Bangyu Sail Lake lacustiino evaporites, mud Ct^laka lacu&liine evaponles. mud Ouilall Lake Idcustdno clay laclivo iriine 00 CO Tablet. Borate deposits. HOST ASSOCIATED jVOLC ASSOC. DEPOSrrNAME IROOQ Inoos lAGE SPGS? PR007 COMMENfB

• mud N Hoping ^granodiortte U Liaontng Provinoe IMIr>ea Gaotaigou marble S Houxlanyu marble S M§9'l'nQ P!9y!nc? Ouflquangou ^carbonates S Wu^ogqu ^dolomlllc marble S Zuanmlaogou Y Qiiiping carbonates Y Qlnghal Plateau Y Qaidam Baiir) lacustrine sediments, evaporlles • i Y Y Blellelan iM^lrlne ^aporites, mud 'Y N Da Chaidan Lake lacustrine evaporites, mud y Y Iksaydam Lake Matial lacustrine se^enls, eyaporites S QarhanSalt Pan mud, halite, sIH. sand U West Taljinaler Lake Jacustrlne evaporites. mud N Xiao Chaldan Lake lacuslune mud, sand S YiHptng lacustrjne ey^orltes, mud N Yeshan melasedlmenls N Yin Lake lacusUlne evaponles, mud N ZliatHjye Salt Lake lacustrine evaporiles, mud Y Zhacang lacustrine evaporites, mud Y

• • Ecuador None ,volcank:s N San Ntcolas volcanlcs N

Qemmny Hamburg Igypsum, haUle, anhyiklte, clay B B recovered as byproduct ol potash prod Stassluit gypsum. haUle, anhydrite, clay B recovered as byproduct oi potash prod B

t • Qreece ; Karlovas&i Basin • Samos Island tud, clay, riiarl :iuti N only V sm bodies recognited

India ' ! t Ruga Valloy jhalile, mud, gypsum lull S i ! jY i Iffln ! I A&hm ^h^ile, mud ! Ueh-eShnloran |evaponies, mud ' 1 Tuiikdr iimeslunu, clay, ovapuriles av

Italy Tuscany buUuntinls. vulcanlr.s volcanics Table 1 Borate deposits HOST ASSOCIATED vote AS&OC. OEPOSTTNAME ROCIG ROCKS AGE SPQS? PROD? COMMENTS

Kazakhsltii inder 'gypsum, clay Y Lake Inder evaporlles, brine, mud

Y

• ' Mexico Hamos||o Jacuslrine sedlmenjs? N U^ta^ ^conQlomerate. sandstone, luM itull, basalt .LTERT U Mesa del Alamo lull, tullaceous mudstone. sandstone, 'iult ^ stiale TCRT N Tubutama shale, sandstone, limestone, volcanlcs voicanics SMt at lower grade . ,M0 N

' ' North Korea Khol-don S Deposit described as *p

Peru Chilli colpa Jacustrlne se^entsj evaponles basallj aridesilo y Cualqluer Cosa CorKesion 'Y Atguna voteaniclastic and la^^rlne sediments voicanics TERT-QUAT? EPP Uguna UarKa lluvloQiaclal sedim,er)ls7 N Part ol this satar is in Chile Laguna Salinas sandy mud tutt, andesite. dacite S

Russia ' CrtrMB Y palnegotftk (Boi) volcanlcs Y Kamctiaiha Peninsula basall N Klyuchevskoye-Oimllryevftkoye pugmatlle U Batkal) skarn . N

• TafiMatan Chutkuikui cidy. caibonalo ,Y N Lyanger Lake clay, salts, (raveriine ,Y N Saskykul Lake clay, salts, travertine '

.y U Shorkul Lake clay, salts, travertine ,Y , N

' Turkey BIgadie inad. Iimestono, gypsum, voicanics, lull lull, basalt, oD&icJian 12 rriinos. ^uveral iltiposils

00 EMO Y u\ Table 1. Borate deposilj HOST {ASSOCIATED VOLC ASSOC. DEPOSTTNAME iROCKS Iroos AGE SPGS? PROP? COMMEWre

Acep mail. clay. lull. Iimeslone ilull. obsidian

LTHRT Ankara Nos. 2 and 3 Jacuslrlne sedlmenls Avsar

Begendtklor Iimeslone, clay, lull lull, obsloian

Boreke Iimeslone, clay, lull iuti, obsidian

LT£RT Ooniu/ Deresi Iimeslone, clay, lull luH. obsidian

LTERT Emiicam

GunevI Nmestone, clay, lull ^ull

Harmanlcik marl, clay, Iimeslone luO discovered by drill inlercepi (siklar

Kireclik Iimeslone, clay, lull lull, obsidian

Kuflplnari Iimeslone. clay, lull tuti, obsidian

Mezaibasi

Salmanii lacuslnne sedimertls

Simav Tulu

00Os Table 1 Borate deposits. HOST ASSOCIATED VOLC j ASSOC. DEPOSTTNAME ROCKS iROCKS AGE SPGS? PR007 COMMENTB ! Tutu Oegirmen Ilmeslone, clay, lull lull

Yenlkoy Emot ilmeslone, congI, clay, lull, agglomerate. lull, andeslle several deposits sandstone MO V Oerekoy ^clay, mail, lull lull Y Espey gypsum, shale, limestone, mad. tuft lull largesl dep In dlstrk:t, underground

Y Gokiepe clay, mart, tufi lull I UO U Hamamkoy clay, mail, lutt, limestunit 'lull MO U HIsarclk Ilmeslone. shale, marl, lull, llgnlio lull Impoftanl deposit, open pM

MO Y Ktliik marl, lull, clay lull

Y Kestelek clay, tult, limestone, mail lull 3 beds BID Y Kiiha clay, lull, marl, congl. Itmeslone, basalt lull, basall, andesite

MO Y Kucuklef lacuslrme sediments 9V Selendl Oasin clay, marl, Ilmeslone, jull lull N SuUancaylt-AzUiye illmeslone, tuti, gypbum, lignite tuil

, LTEHT Y

Turkmenislan Kard-Baga

• • United States-Arizona Aguita ^lacustrine se^enls N GUa Dend N

United States - California Ash Meadows Zeolite OeposM jluH, inudslona ^tull. basall ITERTPIBS V O CAUC(M}AGGETAREA ; Shale, Ilmeslone volcanics, agglomerates i ,Y R» Ameiican Bwai Mine 'shale FP Cenletmlal Mine 1 shale, Ilmeslone volcanics IP Columbus Mine (Gem Boiale) ; shale fV Pacific Mine (Old Boiale) lacuslrme shale. Iimestonu vulcanics U sequunctt is 30 rn IIUcK 1 IF ' Palm Bofalb Co Mine lacusliine stialu 1 Union |lBCusltlne sediments u ! Weslorn Minerals Mtnu lacustrine shale fp 1 00 China lake mud. evaporiles Y Y 1 VI 188

i I i I iif J £ S Z I s i! 1 f Als i- 8: fc'jfetzziji

='.i i 5 fc fc 81 s e tS sis ISs ii

su« 111!! nil ill 111 11 III! Ill I; 1 Si I II liii .Hi .Hi n .liiillli .Si % ii I II 11 ft 1 1# H If i! ilii If

n 11 I 1 I

I i fi i illli 1 i iiliilil fJijiiilf iiliitfi ill iifj ii Table \. Boiate depostis HOST ^ASSOCIATED VOLC ASSOC. OEPOSTTNAME ROCKS ROCtS AGE SPG87 PROD? COMMENTS

VENTURA COUNTY AREA/FRAZlEfl MTN. Shale, limestone basalt MO fossil V Aita Claim u Blltar Creek jBCu&trine shale, limeslone basall Y Borate 3 U 0/yjn D CiMlm U Columbus Mine lacustrine shalfj limeslone basblt Y 1 • • Oanver Claim U Fruier Mine lacustrine shale, limestone basall MO Y Frisco U Ivas P/o^rty Jacusirine shale basalt N Ives Tunnel jacusthne shale basalt N J^sle U Kng and Queen U Mane U Middle Fork Borate Prospects gypsum, shale, limestone basalt N North Fork Borate Deposits lacustrine shale basalt Y Pirioche U R^lai^ U Russ^Mrie lacustrine shale, limestone basalt Y Slubbletleld and Halloway Jacuslrine shale, limestone basalt Y Thomas Boyle Tick Canyon (Lang. Sterling) lacustrine shale, limestone lull, basalt, andeslte ,EM07 Jossit Y Tuscan Springs N

United States - Nevada Anniversary Mine/CalfvlUe Wash limeslone, cateareous shale, lull lull stromatolites Y Cave Sprtr>g calcllic to dolomitic cjaystjne N Columbua Marsh mud. silt, sand Borates on E side of marsh; diagram In Y Papke Borax Works ,

1 CalmvWe ^orax Works mud, silt, sand Y China Borax Works mud. sill, sand Y Old Borax Works imud, silt, sand Y Ulxie Marsh lacusirlne sediments and evaporiies S Eagle Maiih 'lacusliine and aHuvlal sediments y Y Hoi Springs Marsh (Eagle Marsh) lacustrine sediments, evaporiies U ' Fish Lake Marsh clay, silt S diagram In Papke Pacilic Borax Co Qerlach Hoi Springs u North Sand Sp{|ngs lacustrine sediments , Y t pro Cai Mine carbonates N Rliotles Mv&l) lacustrine and alluvial sedlntenis 1 marsh is 3 sq ml, 40 acie borale area In n- Y N central part Samjiltt Sittt 1133 lacu^ldiiti sucllnionlb 'lull N Sand Sprtnos Mar&h (Sail Wolls) lacusltiite sodimunls Y S Table 1. Borate Ueposlls. HOST ASSOCIATED VOLC ; ASSOC. DEPOSfTNAME iROCKS ROCKS AGE !SPG87 PH007 COMMENTS t ' Si^er Peak Marsh lacustrine sediments and evaporltes lull LI. possible salt producer U SiK'er Peak Rarigo xalcaroous chale, limestone, ash S Soda Lake ^lacustilne sediments T S Teels Marsh ' lacustrine arul alluvial sediments lull diagram in Papke, borates in NE part ot playa, Y llral discovery ol natural borax In Nevada White OasirVCentral Mudc)/ Mtns 'limestone, calcareous shale, dolomlle. lull Sttveral small deposits here 'tulfaceous rocks S

United StatBS • New Mexico

1 Lake Lucero '

United States • Oklahoma • Weat-Central Oklahoma

United States • Oregon Alvofd Oesejl Ali^rd Valley (Lake Atvord) Jacustrlne sediments basalt "Y Y Lone Ranch (Chetco) seiperitinlte Y Summer Lake (eastern playa) lacustrine sediments basalt LTERTPUO? Y N

YugosMa Jarandol clayslone, chert, lull tuti, andeslle MO Y N Kremna dolomite, magneslte N Loparl-Sibosnica , shale, marl |lull N Veljevo-Mlonlca lull. marl. clav. dolomite lull MMO U 191 APPENDIX B: CATEGORICAL CLASSIFICATION OF VARIABLES FOR BORATE DEPOSITS

[-1 = not present; 0 = presence is questionable or present only in trace amounts; 1 = present; 2 = mineral has been produced or is dominant in the mineralogy of the salar.] BORATE MINERALS • • MINS MINS MINS MINS ^MINS ;MINS MINS DEPOSIT NAME MDCEO IBRME CA-NA CA NA BMS XA-SI !cVMg ulex , prob Iny meyer cole pric

Acazoque AQTN 1! 1 1 2 1 -1 -1 -I •1 -1 Archlbarca Ravine area AGTN' 1,: -1 2 -1 1 -1 l' -l' -1 z' -i -1 -1 •1 -1 Boratera de Antuco AQTN' 1L -1 2 -1 -1 R -1 -1 2 -1 •1 • 1 -1 •1 Celtl Occurrence AGTN' i! 0 2 •1 •1 2; -i • i -1 •1 •1 Coyagualma AGTN; i; .1 2 -1 -1 l" -l' -i 2; -1 •1 -1 •1 •1 Laguna Quayatayoc AGTN' 1; 0 2 •1 •1 -1^ 2; -1 •1 -1 •1 -1 Lagunlla AGTN i; 0 1 -1 1 -L' -1 1'; -1 2 • 1 -1 •1 Loma Blanca AGTN' r -1 1 -1 o' -1 r -1 2 •1 1 -1 Ojo de Ague AGTN' 2 • 1 • i •1 L' -1 -1 2' -1 •1 • i •1 • i Rio Ajurnbrlo AGM 1; -1 2 • 1 •1, ' -1 -1 2 -1 -1 • 1 -1 • 1 Salar Cenlenarlo AG"M: r 1 2 •1 2' -1 •1 -1 •1 -1 Salar de Aniofalla AGTN' i; 6 0 -1 -1 •1 i' -1 -i 6' -1 •1 -i •1 • 1 ^!ar^ Cauchari \ 0 2 • 1 1 •1 2 -1 •1 • 1 •1 • 1 Sajar da Jama AGTN i 0 2 V -1' -1 2] •\ • i -1 -i • 1 Salar de LIullalllaco AGTN' 1 0 1 •1^ r -1, -1 1' i • 1 • 1 • 1 • i Salar de Olaroz AGTN L' 0 2 • 1 -1 1, -1' -1 2. -1 -1 • 1 -1 • 1 Salar de Pastos Grandes AGTN i 1 2 •1 L' 0 -1 2' -1 0 • 1 -1 Salar de Pocltos o Quiron AGTN' 1 0 2 -1 1 -1 -1 2 -1 0 • 1 -1 • 1 Salar de Pozuelos AGTN 1 ; 0 2 • 1 1 T -1 -1 2 -1 -1 • 1 • 1 -1 Salar de Rio Grande AGTN^ R 0 2 • 1 -1 1 -1 -1 2, -1 -1 • 1 • 1 • 1 Salar de Santa Maria AGTN r 1 1 •1 r -1 -1 1 -1 • 1 • 1 • 1 • 1 Salar de Turllarl AGTN 1! 1 1 -1 2 •1 1, -1 -1 1 -1 • 1 -1 • 1 • 1 Salar del Hombre Muerlo AGTN^ 1 2 2 0 •1 2 -1 0 • 1 -1 • 1 Tincalayu AGTN' r -1 1 1 2 1 ^ \[ -I' -1 1 Q 0 • 1 • 1 Salar del Rlncon AGTN L' 2 2 -I 1 •1 1, -1 -1 2 -I • 1 • 1 • 1 • 1 ^|ar Dlabjlljos AGTN 1; 0 2 •1 1 •1, i' -1 -1 2' -1 -1 • 1 • 1 -1 Salar Ralonas AQTN' r 0 2 -1 • 1 •l' i' •]' -1 2; -1 •1 • 1 • ) • 1 Sallna de LInl Lari AGTN: ij 0 1 •1 -l' 1 ; -1 •1 • 1 • 1 -1 Salinas Grandes AGTN! M ' 2 -1 -1 -1, i' -1 -1 2| -1 • 1 -T -1 • 1 Serranla de Sljes AQTN' 1! -1 1 -1 •' 1 •1 Dzulla Area ARMN I! -1 •1 •1 1 •1 t; -1 -1 • R -1 -1 • 1 • 1 • ) Laguna CachI BLVA' I; 2 1 -1 -1 •1, -1, -1 r 1 • 1 • 1 -1 • 1 Laguna Caplna Sur BLVAI l' 2 2 •1 •1 •L' 2; i • 1 • 1 -1 • 1 Laguna Chlar Kttola BLVA; 1 ' 2 1 •1 -1 i' -i' -1 i 1 -1 • 1 • 1 • 1 • 1 Laguna Chojilas BLVA; 1: 2 •1 •1 -1 1• '1 • 1 • 1' -1 • t • 1 • 1 -1 Laguna Chu|luncan| BLVA, 1 [ 2 -1 -1 -1 h ^ • 1, -1 • 1 -1 -1 • t Laguna Colorado BLVA^ L' 2 1 •\ -1 \] r -1 T; -1 -1 • 1 -1 • 1 Laguna Coruto BLVAI ', 0 1 -1 -1 T -1 -1 -1 -1 -1 Laguna Hedlonda Nori^ BLVA; 1 i 0 0 -1 -) 1 i -1' -1 0! •! -1 -1 • 1 • 1 Laguna Mama Khumu BLVA' l' 0 2 •1 •1 2' -1 •1 •t • t • 1 Laguna Ramadlias BLVA! '! ' •T •1 •1 -1, 1 -v -1 •1! •' • 1 • 1 • 1 • 1 Laauna Sacabava BLVA' 1 i 2 2 •1 -1 •l' 2 -1 • 1 -1 • t UJVO MMS MINS MINS MINS MNS :MMS 'MMS DEPOSFTNAME iMIXED IBRME CA-NA OA NA BMQ RCA-SI ica-Mg IBST ulex 1 prob Iny mayer cole pric 1 ! Lagunas P^sto^&andes ^VA; I; 2 1 •1 1, 1 -1 •1 -1 -1 -1 Salar de Challviri BLVAI t' 1 2 -1 1 ) L' 2' -1 • 1 -1 •1 -1

Salar de Chlguana BLVA! !i 0 1 -1 -1 l' 1 -1 •t -t -I •1 Salar de Colpasa BIVA I; 2 0 -1 -t •li -1 0! -1 •1 -i •1 •1 Salar de Empexa BLVAi 1 1 •1 -1 •li -i 1' -1 • 1 • 1 •1 • 1 Salar da Ollague BLVAI 0 1 •1 -1 1 R • I| -1 1 -t -1 -I -t -t Sajar de UyunI BL^ L| 2 2 •1 •1 R 2 -1 •1 • t •1 •1 Sajar LaguanI BLVW ti b 1 -j •1 R -I; ^ 11 -1 •1 • I •t • 1 Pampa Tamargal OLE : r 0 0 •1 0 •I -1 • 1 -1 Salar Agua Amarga ca£ ' L' 0 2 -1 •1 t' • i; •! 2 -1 •1 • 1 •1 •1 Salar de Aguas Callentes OLE ' 0 2 •1 •1 I • 1' -1 2' -1 •1 • 1 -1 -1 Salar de Aguas Callentes Norii OLE ' 1 1 2 •1 •t t' •1 •! 2' -i •1 • 1 -1 •1 Salar de Agullar PP. 1 0 0 • ! •1 0; -1 •1 • 1 -1 • 1 Salar de Ascotan ca£ ' \ 1 2 • i •1 V 1 • 1 • 1 2' -1 •1 • i •1 -1 Salar de Atacama OLE ' t' 2 -1 • 1 -1 1^ 1 -1' -1 -t • 1 -1 -t Salar de Carcote •) Cll£ ^ '! 0 1 -1 1 •'! !, -1 -1 -1 •1 -1 Salar de Huasco OLE ' 0 1 -1 •1 i' i r -1 •t • 1 •1 -1 Salar de Infleles Cl£ ' l' 0 0 •1 •1 t 0' -1 •i •1 •1 -1

Salar de Isia Cl£ 1; 0 1 • 1 • ^ 1 1 1 -1 • t -1 •1 -1 Salar de Marlcunga Cl£ 1 0 2 • t • 1 1 1 1 • 1 -1 2' -1 • 1 • 1 -1 • 1 Salar de Pajonales CIE ' L' 0 0 j -l] r t -i' -1 0 -t • 1 • 1 -1 • 1 Salar de Pedernales OLE ^ 1 0 2 -1 r 1 -i' -1 2 -1 • t • 1 • 1 -1 Salar de Pintados OLE ] 1, 0 2 -1 -i! 1 -1 -) 2\ -1 • 1 • 1 • 1 • 1 Salar de Punta Negra OLE ^ r 0 1 • i r i' } 'li -1 • 1 • 1 -t •i Salar de Surire aL£ ' t' 2 2 • 1 • 1 r 1 •i; -1 2] •! • 1 -1 • 1 -1 Salar Quisqulero OLE 1 L! 2 2 • 1 •1 1, 1 •i_ -1 2 -1 • 1 -1 -1 • 1 Chalaka CINA! J' 2 •1 • i i' 1 • ij -1 -1! -1 • 1 • 1 -1 •1 Da Chaldan Lake CINA| 2 1 •1 1 0 1 •1 -1 1" -1 • 1 •1 •1 -1 t Oujlall Lake CINA ; 1 ^ 2 •1 • t 1^ •1. •I •1. -1 -1 -1 -1 • 1 Geerkunsha CINA 1 1 ^ 1 1 • ! 1 i' • i! -t 1' -1 • 1 • 1 • 1 • 1 Qaldam Basin CINA 1 '' 1 •1 1 t -ll •! 'i -i • t -t -1 -1 Xiao Chaldan Lake CINA ' 1 0 1 -1 t' -li -1 1' -t • 1 • t • 1 •1 Zhabuye Salt Lake CINA 1 li 0 -1 • 1 1 i' • i| t • t • t -1 •1 Zhacang Caka CINA i 1' 0 0 0 t^ 1 oj -1 • 1 •I •1 Samos Island-KarlovassI Basin GPB:' 1J -1 0 0 •t -1 0; -1 • t • t -1 -) Puga Valley INDA j 1; -1 • 1 • 1 • I! 1, • I! -1 •' •! -1 • t -1 Ashin IRAN ; o' 0 1 • t -I! -1 1; -i • 1 -1 -1 -1 Lake Inder KAZK' 1; 1 0 0 I' 1 -1 oi -1 • 1 Mesa del Alamo •1 1 • 1 • I MWX)_ '1 •' •'! •' • 1 1 Tubulama MXCO' l' -1 0 2 1' o! -t 0' -1 • 1 • 1 • I Chllllcolpa PBU ' 1; 0 2 •1 1 -ti -t 2 -1 -1 • 1 •1 Laguna Salinas PBU ' t 1 2 1 o! -1 2 0 I • 1 •1 vO •1^ 1

MINS MINS MMS MINS jMMS !MMS jMINS DEPOSIT NAME MIXED BRME CA-NA OA NA BMQ ; CA-SI iCa-Mg iKr ulex prob Iny meyer cole pric 1 1

Chukurkul TJIK r 0 •1 2 r 1^ -1 •' -1 •1 -1 -1 Lyanger Lake TJIK 1 0 •1 2 r l' •1 •l' -1 •1 . t •t •1 Sasyk-kul Lake TJIK 1 0 -1 •1 2 1^ 1 f' •1 •1 -1 •1 •1 -1 Shorkul Lake TJIK i; 0 -1 -1 2 r i -i •1 -i -1 •1 •1 BIgadIc TFIKY ' •' 2 -1 0 0 2 0 2 1 Emet TRKY L; -1 1 2 -1 1 i' 0 t' -1 -1 1 2 •1 Harmanlclk TRKY I' -1 2 -1 1 1, l' -1 •I -1 -1 • 1 2 •1 Kesteiek TPKY ]' -1 1 2 •1 r 1 •1 1 ^ 1 • t • 1 2 -1 KIrka TTi

Owens Lake USCA r 2 •1 •1 1 r 1 i' •1 •1 -1 •1 •1 •1 -1 Hho A and B USCA 1 -1 -1 2 1 1 1 •1 • 1 -1 • 1 •1 2 Searles Lake USCA \ 2 1 -1 1 1 1 • 1 t -1 -1 •1 •1 -1 Tick Canyon USCA: 1 -i 0 2 •1 i' 6 o' 0 • 1 •t 2 •1 Ventura USCA 1: -1 •1 2 •1 i' • 1 • 1 -1 • 1 •1 2 1 ,! C^llvllle Wash/Annlvarsaiy Min USNV -1 1 2 -1 1 -1 2 -1 i •' • 1 -1 Cave Spring ysw -1 -1 •1 •1 r_ • i • T -1 •1 •1 •1 •1 Columbus Marsh USNV 1' 1 2 •1 -1 r r i| •1 2 -1 -) -1 •1 •1 Dixie Marsh USNV r 1 2 •1 -( 1 1 i • 1 2 -1 • 1 •1 -1 -1 Fjsh Lake Marsh USNV 1 2 2 •1 1 r r . 1 2[ -1 -1 •1 -I •1 Hot Springs Marsh/Eagle MarsI USNV 11 2 •1 r 1 ij • 1 • 1 -t •t -1 Rhodes Marsh USNV 1; 1 1 •1 • 1 •! •1 •1 •1 •1 1 Sliver Peak Marsh USNV! 1 ^ 2 •1 t" •i o\ -i •I -1 •1 •t

Sliver Peak Range USNV; r -1 1 -1 1^ 1| -) 1' •\ •1 -1 -1 • 1 Soda Lake USNVI 1' 1 •1 1; i! • 1 -1 -1 •1 •1 ,! Teels Marsh USNV! '! 2 1 •1 r -1 • 1 •1 •t •1 White Basln/Cenlral Muddy Mt USNV! li -1 2 r i' -1 • 1 •1 2 -1 Lake Alvoid ueoHi i! 1 •1 r ) 1 -1 •1 -1 •1 •1 Jarondai YUGO' 1, -1 2 -1 • 1 • 1 2 • 1

Kremna VUQO ij -1 •t i' -1 • 1 •1 •1 • 1 VuilevO'Mlonica YUGO^ 1' -1 •1 1 • 1 •1 •I •1 •1 UlVO DEPOSrTNAME borax line ker ilnd kurn pinn howl hydro lerug tun Marl

Acazoque 2 • 1 •1 •1 •'i •1 Archlbarca Ravine area 1 -1 • 1 -1 • l' -1 • 1 Boratera da Antuco -1 -1 •1 -1 Colli Occuirence • 1 -T -T -i' -1 • t • 1 1 " ' -1 -1 -1 Coyagualma -1 •1 -1 •{ t •1 Laguna Quayalayoc •1 •1 •1 •l' -1 •1 Lagunlla • 1 • 1 -1 •1 * 1 > >1 •1 Loma Bjanca -i -1. -1 • 1 •1 Ojo de Agua -1 •1 •V -1, -i! • i •1 -) •' Rjo Alumbilo •t •i' -tl -1^ -1 • 1 •1 •1 Salar Canlenarlo t 1 -1 •1 • i' -) • 1 Salar de Antolalla 1 • 1 -1 -1 -1 -i • i -i • 1 Salar de Caucharl 1 -1 -1 -1 -1 •1 • 1 •1, -1 •1 Salar de Jama • 1 •1 -1 -1 -1 -1 • 1 • T -1 • 1 Salar de LIullalllaco •1 •1 •T -i' -1 -1 • 1 •1 • 1' • i •1 Salar de Olaroz •1 •i' -1 -1 -1 -1 •1 •1 -1 • 1 1 Salar de Pastes Qrandes • 1 -1 • 1 -1 -1 -1 • 1 • 1 Salar de Pocilos o Quiron • 1 •1 •1 -t -i' -1 • 1 •1 •i' -1 -i Salar de Pozuelos •1 •1 -1 -1 -1 •1 •1 • 1, -1 • 1 Salar de Rlq Grande -1 -1 •1 -) -1 -1 -1 -1 -1 Salar de Santa Maria •1 • 1 -i' -1 -T -1 • i • i •i' -1 • i Salar de Turllarl 2 -1 •1 -1 -1 -1 • 1 • 1 • 1 -1 • 1 Salar del Hombre Muerto 0 •1 -1 • 1 V • 1 TIncaiayu 2 1 r o| i' -1 -1 -1 o' -1 Salar del RIncon 1 • 1 • 1 • 1 -1 • 1 Salar DIabllllos 1 •1 .1 1 .1 1 1 -1 • 1 •1 -1 • 1 Salar F^tmies -1 -1 -i' -i' -1^ -1 -1 -) -1 Sallna de LInl Larl -1 • 1 -1 Salinas Grandes •1 -1 •v. -1, -1, -1 • 1 • 1 • 1 Serranla do Sljes •1 -1 ' -1 * 1 -1 • t • i' -1 • 1 Dzulla Area 1 1 • i| -i' -T 1 -i -1 -i Laguna Cachl -1 -1 •1; -1 -1 -1 •1 -t -1 Laguna Caplna Sur -1 -1 -1 - 1 ' - 1 - 1 -1 -1 •i| -1 -1 Laguna Chlar Kkota •1 -1 " 1 j • 1 *1 *1 • ) • 1 • 1 Laguna Cho|llas •1 -1 •1, -1 • 1 -1 •i' -1 -1 Laguna ChulluncanI -1 -1 • 1 • 1 •ij -'i -i! •' •1• t -1 • 1 Laguna Colorado •1 -1 • 1( • 1 • 1 -1 • 1 •1 • 1 Laguna Corulo -1 -1 •ii -1 -1 -1 • 1 • 1 •i' -1 -1 t 1' «* Laguna Hedlonda Norta •1 -1 • 1 • 1 -1 •) • 1 Laguna Mama Khumu •1 •1 • 1 • 1 •i' -1 • 1 Laguna Ramadltas •1 -1 •11 -1, -i' -1 • 1 • 1 •1 -1 -1 Laquna Sacabava •1 •1 •i' •\ r 1 • 1 • 1 • 1 vO ON DEPOSrTNAME borax tine ker ilnd kurn 'pinn howl hydro terug 'tun searl 1 !

Lagunas Paslos Grandes •1 • 1 •t •1 Salar de Challvlrl 1 • 1 •1 •1 -l' -i -i Salar de Chlguana •1 •1 • 1 • 1 • 1 -1 • 1 Salar ^ Colpasa •1 -1 •', -i! •'! •' • 1 • i •V •' -1 Salar da Empexa -t •1 • t • I -I Salar da Ollague -1 •1 -1 • 1 • 1' -1 • 1 Salar da UyunI •1 • 1 •\ -1, • 1 • 1 • 1 -1 • 1 Salar l^guanl •1 • 1 -1 -1 • I •' -1 Pampa Tamargal •1 • 1 • 1 -1 • 1 Salar de Agua Amarga -1 • 1 •r -r -1 -1 • 1 • 1 •1. -1 • 1 Salar de Aguas Callentes -i -t -t -t • i Salar de Aguas Callentes Norte •I -) •1 • 1 •i' -1 • 1 Salar de Agujjar •1 •1 -1, -1 -1 •1 • 1 -1 -1 • 1 Salar de Ascolan •1 • t -i| -1 -i' -1 • 1 -1 •' -1 Salar de Atacama •t •t -1 i 1 -1 • 1 • I • t' t -i Salar do Carcole •1 -t -1 -1 •1 t -1 Salar de Huasco •1 •1 •1^ •'! -i! • i -1 -i' -1 • 1 Salar de Inlleles •1 • 1 •t' -t' -i' -1 • 1 -t •t -1 -1 Salar da La Isia •1 •1 •1 -1 -1 -1 • 1 • 1 •1 •\ •1 Salar de Marlcunga •1 -1 -1 -1, -1 -1 -1 -1 -1 -1 •1 Salar de Pajonales -1 •1 -T -i' -T -1 -1 -1 -i' -1 -1 Salar da Podernales -1 •1 •1 -t -1 -1 • 1 • 1 •1 -1 -1 Salar da Pintados •1 • 1 -t -t -1 -1 • 1 • I • I -) Sal^r ^ Punta Negra 1 •'! -1 • 1 • 1 •i' -1 • t Salar de Surlre •t -1 • 1 -1 •1 -1 -1 Sajaj Quisqulero -1 -1 •1 -1, -t -1 • 1 • 1 -1 -t -t Chalato t 1 •'i -y -i • 1 -1 -i -1 • 1 Da Chaldan Lake 1 -1 •l' 0 00 • I • 1 •i' -1 • t Dujlall Lake 1 \ • 1 • 1 •1, •' •1 Qeerkunsha 1 -1 • 1 • 1 •i' -1 • 1 Qaldam Basin t 1 • t' -T o' 0 • t -t • t -t • t Xiao Chaldan ^ke •1 -I -1 t! 0 • 1 • t • 1 Zhabuye Salt Lake 1 -1 •'! ?! 2*1 2 • i • 1 -i' -1 -1 Zhacang Caka • 1 • 1 1 1 1 1 • ) • 1 -T -1 • 1 Samos Island-KarlovassI Basin • 1 • 1 • 1 • 1 Puga Valley •1 -t; -t; 'i: -t -t • 1 -I •! -! Ashin •t • 1 • 1' • 1 ' -1 • 1 • 1 r -i -i Lake Inder •1 -ll 0 -l; -1 • 1 t •1 1 • 1 Mesa del Alamo •1 -1 -1 -1 -1 -I •' t • t Tubutama • 1 -i' -1 r -1 1 • 1 •i' -1 • 1 Chllllcolpa 1 •1 • ) •' -1 • t Laguna Salinas • t •V -V !i: -1 0 •1 1 • 1 vO DEPOSIT NAME borax tinc ker ilnd kurn pinn howl hydro terug tun •earl 1

Chukurkul 2 1 -1 •1 Lyanger Lake 2 1 •l' •)' -l' -1 -1 -1 -1 Sasyk-kul Lake 2 1 •1 -1. -1, -1 • 1 -1 Shorkul Lake 2 I • 1 • 1 •1• -1 •1 BIgadic •1 •i • V 1 •1 Emet -1 -1 •1 -1 •) -1 • 1 1 • 1 Harmanlclk -1 -1 -1 .) -1 -1 -1 Kesteiek • 1 • 1 • T -T -1 -1 * 1 1 * 1 •1 Klrka " o! o! •' -1 -1 Sullancaylr-Azlzlye -1 • 1 •i| -1 -1 -1 -1 •1 Ash Meadoyvs • 1 -1 -i' -i' -1 -1 • 1 •1 1 Borax Lake (Clear Lake) • 1 •1 -1 -1 -1 • 1 • 1 -1 Callco-Daggatt • 1 • 1 -1, -1 -1 -1 • 1 "1 -1 China Lake •1 • 1 •i' -i| -i' -1 • 1 -1 •1 Death Valley •1 • 1 -i' -i' -1 -1 -1 •1 -1 •1 Fori Cady •1 • 1 •1, -1 -1 -1 • 1 •1 •1 Qerstjey -1 • 1 •1 -i' -1, -i • 1 •1 • 1' -1 -1 Heclor • i • 1 -i' -1 -1 -1 •1 •1 -1 •1 Koehn Lake -1 • 1 •1. -1 -1 -1 • 1 •) •1, -1 •1 Ktarner 1 2 0 -1 -1 -1

Owens Lake 1 -1 •1 -1 -1 -1 • 1 -1 * 1 i -1 •1 Rho A and B • 1 -1 -1 1. -1 -1 -1 • 1 Searles Lake 1 -1 • 1 -1 •1 •'! •' •' Tick Canyon -1 -1 •1 -l' -l' -1 -1 •'! •' • 1 Ventura -1 -1 -1 -1 -1 -1 -1 -1 •1 Callvllle Wash/Anniversary MIn -1 -1 -1 -t -l' -1 • 1 •1 •1 Cave Spring -i -1 •1 -T -i' -1 • 1 -1 • 1' • 1 1 Columbus Marsh -I • I •1 -i -1, -1 • 1 •1 •)| -1 • 1 Dixie Marsh • 1 • 1 •1 -i' -r -1 • 1 •1 •ii -1 •1 Fish Lake Marsh 1 • 1 •1, -1 -i' -1 • i • i • 1 • -1 • 1 Hot Springs Marsh/Eagle Marsi -1 •i •1 •ij -i -1 Rhodes Marsh -1 •t' -t -i' -1 -1 -1 •1, -1 • 1 Silver Peak Marsh • 1 •i' -T -i' -1 • 1 • 1 • 1 •1 •t Silver Peak Range • 1 • 1 • 1 -1 • 1 -1 Soda Lake • 1 •i' •)' •)' -1 1 • 1 -1 •1 •1 Teels Marsh 1 •i' -T -T -1 • 1 • 1 • 1 •1 White Basin/Central Muddy Ml -1 -1 -1 -1 -1 -1 • t -1 -1 -1 -1 Lake Atvord -1 •i' -1 -t' -1 •1 • 1 • 1 •1 Jarondal • 1 •1; t -t -1 1 • 1 -i! -t Kremna -1 •i| -i' -1 -1 • 1 -1 • i! -1 1 Vallevo-Mlonica • 1 •1 -1 r 1 • 1 -1 -ii -1 1 v£> 00 NON-BORATE MINERALS DEPOSIT NAME GVP IHAL NASO !NACO CAL OOL ARAQ |ANHY s AS K U SR THAV I TUFA ZEO iCLAY 1 1

Acazoqua AQTN -1 -1 2; .1 •l| *1 ti -1 • 1 ! 1 •! -f • ^rMb^rca Raylns area AGTO -r p .1 •)' -i ,! Buratera de Aniuco AQTM -1 r -1 •1' -1 Cellj Occunenca AG™ ' •1l -1 -T -1 •1! •' -1' 1 Cqyagualma AQTW •1; i -l' -I 1; -1 1' -1 -1' -t Laguna Guayaiayoc AQTN •'! ' -1l -1 •\[ -1 •1' -1 • 1' -1 •ij -1 •1' 1 Lagunlla AQT^ -li -1 •i' .1 -1 -1 • 1 -1 -1 1 Loma Blanca AQTN •i; -1 i[ 1 ! -1 •'! •' -1! •1 •)[ 1 OJo de Agua AGTN . i; - i -1' -1 1; -1 nio Alumbrto AG™ •' 0 •i! -1 1' •\ r -1 1' t • 1 *1 •'! •' t Salar Centenario AGTN • 1 2 2; -1 -1 -1 •t -1 Salar de Aniolalla AQTN K 2 •i] -1 •)' -t 1, -1 Salar de Cauchatt AQTN i -1 -1' -1 V -1 •i| -1 •1 -1 1'. 1 •V \ Salar de Jama AQTN 1 \ \ • 1* -1 •1 -1 •1 -t •'t •' Sajar dj Uullajllaco AQTN •1. -1 • ) -1 •1; -1 •1 -1 Sajar de plaroz AGT^ i' 1 • 1* -1 • r -1 •ll .1 -i' -1 \ Salar de Pastas Qrandes AQTN r 2 •\] •\ •V 1 •i" -1 0 -1 1 -t Salar de PocHos o Qulron AQTN t 2 1' -1 1] -1 •1 -1 •1 -1 Salar de P^uelos AQTN •r 2 •\ -1 * 1' -1 •1' -1 -1, -1 • r 1 Sajar da Rjp Grande AQTN • t' i 2! -t -ij -1 •1' -1 Salar da Santa Maria AQTN •l' 2 2 • 1* -i •I -1 •i' -i Salar de Tutllarl AQTT^ •'! ' -1, -1 1' 1 •1 1 1 -1 • t -1 *v 1 Salar del Hombre Muerto AQTN 1, I ^ -1 •V -1 *1 2, -1 t -1 TIncalayu AQTN i' 1 • 1' -t •1' -1 •1' 1 •1' -1 Salar del Rlncon AQTN r 2 r -i -1* -1 1 -1 • 1' -1 Salar piablillos AQTN 11 1 •1 -1 • i' -1 -1 11 1 Salar Ralones AGTN •1 2 -1! -i -1] -1 •r 1 1 -1 • t • • I «' 1 Sallna de LInl Larl AQTN -1' • t ' 1' • 1 -1' -i Salinas Qrandes AGTN 1 [ 2 .1! .1 1 Serranla de Sljea AQTN l| 1 • 1^ 0 1' -1 •l! 1 Ozulla Area ARMT i| 2 *1! -1 i' 1 Laguna CachI BLVA -1; 2 t' -1 -tj .1 -ii -i 1 Laguna Caplna Sur BLVA 1 1 •1' -1 1 -1 .. .1 Laguna Ctilar Kkota BLVA 1, 1 • 1' '1 r -1 -1 • Solar de Empexa BLVA i! 1 1' •( •1! 1 1' -1 •1' -1 • i' 1 O O OEPOSfTNAME GVP IHAL NASO ^NACO CAL DOL ARAQ ANHY s AS K u !SR TRAV TUFA 2E0 ICLAY 1 Salar de Oljagua BLVA •l| 2 :l. -1 -1, -1, -1 • 1 .1 Sajar de Uyunl BLVA i • 2 1* -1 •l' -1 -1* -1 2" 1 •1. -1 Salar LaguanI BLVA • i| i -I -1 V -1 • 1 -1 • i -1 •1 1 PampaTamatgal ai£ 2 1 • { .1 ^ -1 -1 -1 •\ •1 -1 S^ar de Agua Amarga QUE -I • 1: -1 -1' -1 -T -1 Salar de Aguas Callentes ai£ r 1 •i' 1 •1* -1 •1 -1 \ 1 •1 -1 Salar da Aguas Callentes Norli ai£ 1 ^ 1 •V -1 • 1 -1 -1 -1 •1 1 Salar de Agullar CIL£ -1 1 * 1. ' * •1. -1 1 -1 • i -1 •1 't S^ar de Ascolan ai£ i' 1 -i -1' -1 Salar de Alacama OLE 1 i •V •' - i" -1 • 1 -1 Salar da Carcote OLE 1 1 -1 -1 -1 r -1 • } -1 -t -t Sajar de Huasco ai£ i! -1 r -i •y 1 •1' 1 1 • ! - Salar de Inlleles OLE • 1 1 •l" -1 •i' 1 • 1' y Salar de La Isia CIL£ •1' -1 • 1 -1 •V -1 •1 -1 • 1 -1 •1 -1 Salar ^Mancunga OLE • ij 1 •\ -1 -1 • 1 1 1 1 •1. * Salar de Pajonales CUE 1 •\\ -1 -l' -1 • i -1 -i' -1 Salar de Pedemales CUE 0' 2 •T -1 • T -i •i" -1 11 1 r -1 r 1 Salar de Pintados OLE 2 -1 -1 -1 • 1 -1 •1, -1 -1 -1 •i_ -1 Salar de Punia Negra OLE 1 1 -J • 1 -t -1' -I -1 -1 -i| -1 Salar de Surire OLE r 1 r -1 • T -1 •1' -1 1' -1 • -1 r -1 . Salar Quisqulero OLE r -1 -i -1 1' -1 •V 1 Chalaka CINA •1 -1 • 1 -t •1 -1 1 •\ -1 -1 •1 -1 Oa Cliald^ LaKe CINA 2 ^ •1 -1 Dujl^l Lake CINA •1 -1 • 1 -1 •i" -1 • i' -1 •) 1 Qeeikunstta CINA \ 2 • 1 -i • 1 1 •1' -1 • 1 1 '\ \ Qaldam Basin CINA 2; 2 -1 -1 • { -1 •y -1 • 1 1 *1' 1 Xiao Ctialdan Lake CINA -l' 2 i| -1 r 1 •i' -i -1 • 1, -1 -1 Ztiabuye Salt Lake CINA -i] -i • i' 1 •V Zhacang Caka CINA 11 1 • 1* -1 -1 -1 1 -1 -1' -1 -1 -1 Samos Istand-Karlovassl Basin UKC *1 •1 -1 •1 1 r '1 Puga yaljay INOA 1' 1 • 1. • * .1. -1 1' -1 Ashin IRAN •1; 1 •i -1 • -1 •V Lake Inder KA2K -1 * -1 • \[ -1 M^a del Alamo MXOC •1, -1 -i' -1 -1 •'! •* 1 -1 1 -1 Tubutama -1' -1 1. -1 • i -1 -1' 1 \[ -1 1* 1 Chllllcolpa -i -1 • i * 1 • \] -1 Laguna Salinas PBU • i_ -1 • 1 1 1 ChukuiVul TJIK -li 2 o; 2 \[ 1 • )[ -1 r -i 1' -i Lyanger Lake TJIK •V 2 o; 2 1' -1 •li 1 Sasykkul Lake rjIK •T 2 o' 2 • i' -1 1' -1 ) 1 -it 1 Shoikul Lake TJIK M ? o] 2 -1 -t 1 t \ -t -li 1 Blg^lc TTWY 1 i •) -1 1,' 1 1' 1 1! 1 •*, * *'i Emet TOKY • 1' -1 r -1 v ^ Harmanlclk TRKY • 1 1 •1* -t •1 j I Kealaiek TOKY -ij -1 •1. -1 i' -1 r -1 Klrtia THKY -1: -1 1 ^ 1 •1' 1 -t' -1 M O Sullancavii-Azi2lva THKY -1 \ •1 1 1 DEPOSIT NAME GYP HAL NASO jNACO CAL ioOL ARAQ |ANHY s AS K u \m TRAV TUFA ZEO CLAY 1 Mea^ws USCA -1. -1 -1 • 1 •1 • ij -1 -1 1 2. 1 Borax Lake (Clear LaKe) USCA \ -1 • 1 • 1 • i • 1. *1 Callco-Oiggatt USCA 1 -1 -1* -1 -i • 1 • 1 • j • i China Lake USCA 1 -1 -1 • 1 • 1 -1 *1 •l' 1 Oaath Valley •l' -1 -1 • i • 1 1 •' •' Fori Cady USCA l] t • t; 1 i' i • 1 • 1 • 1 -1 -1 Gerslley USCA • 1 -1 ii -1 •1 -1 -I • 1 • 1 -1 1 • 1 1

Hector USCA •' •1. 1 -1 • 1 • 1 * ! 1 * . 1 1 1 Koehn Lake U^ 1' 1 -i -1 -1 -i] -1 • 1 -1 • 1 1 -1 -T i Kramer USCA If -1 1* -i 1 1 • 1 • 1 -1 • 1* 1 Owens Lake USCA -1 -1 -1 • 1 • 1 •i! -1 • 1 1 Rho A and B USCA •'! •' \\ 1 •i' -1 -1 1 -1 • 1' -1 -1 Seartes Lake USCA i' t 2 2 r -1 • 1 -1 i] .1 • 1* -1 •1 1 Tick Canyon USCA •1 -1 V -1 • 1 •1 • 1 •i! -1 r i 1 1 Venjur* USCA t -1 -t -t • 1 • 1 *1 •1 \ Callvilla Wash/Arrnlyersary MIn USNV 11 1 • i -1 •V -1 • 1 •i • 1 •1. 1 Cava Spring USNV •1 -1 •t' -1 •\\ -1 • 1 • 1 • 1 -1 -1 1 • 1 1 Columbus Marsh USNV -1 2 •t -1 • 1 1 1 -1 -1 • 1 r -1 • 1 -1 •1 1 Dixie Marsh USNV •1 t •\] -1 *1 • 1 • 1 y -1 -1 -1 • 1, 1 Rsh Lalw M»8h USIW -t 1 y -1 -1 • 1 1 1 -1 -t Hot Springs Marsh/Eagle Mars! USW •l' 2 •i -1 r -1 -1 -1 • 1 -1 • T -1 Rhodes Marsh USNV •1 2 2 t -1 -1 • 1 -1 -1 -1 • 1 -1 Sliver Pe^ Marsh USNV 11 2 -1, -1 -l" -1 -1 -1 • 1 • 1 • 1 2 -1 • 1 *1 -1. 1 Silver Pe^ Baiige USNV •l' -1 •1 -t r -1 •i' -1 -1 -1 -I •] Soda Lake USNV •t -1 -l' 2 • i -1 -1 1 1 *v \ -i Teels Marsh USNV 2 ! \ -1 • -1 -1 • 1 • 1 K 1 * V *1 1 ^ 1 yVhite BasliyCenlral Muddy Ml USNV t 1 •i! •• • 1 • 1 • i 1 -i • i" i Lake Alvord iRnn •l' -1 r ' -T -1 -i • 1 •i •V 1 • i' -1 Jarondal vuao 1' -1 •'i •' -1 -1 • 1 -1 • 1 • 1 -1 1 1 Kjemna YUGO •1] -1 •V 2 • 1 \ -1 -1 -1 -\[ -1 Vallevo-Mlonica VUQO -T •) • 1 •) -l! 2 1 -1 • 1 • 1 • 1 -1

to o to 1

DEPOSIT NAME CHtOR MONT lU COAL MN |MQ ORGAN DIT SB FLO MICA OPAL P en 'n ONYX QTZ

Acazoque -1. -1 •1 -1 -1 -1 •1, -1 • 1, -t Archjbarca Ravine area 1 -1 •)' -1 •1 1 •'! •' i' -i Boratera de Antuco •t -1 1' -1 •)' -1 •1 -1 1 -1 Celll Occufrence •1 -1 •1 -1 Coyagualma r -1 •i' •) • t i •'! •' •1 -1 •T -1 Laguna Quayatayoc •) -1 • 1' I •1 •) r -1 •i' -1 • i' -1 Lagunlla •I -1 • 1 -1 •1 -1 •1 -1 •1 -1 •1 -1 • )' -1 Loma Kanca 1 1 1, -1 •1 -1 •1 -1 •1 -1 OJo de Agua • t -1 -i' -1 -r -1 Rio Alumbrto •1 -1 •i -1 -1 -1 •1 -1 Salar Cenlenario •V • 1 1 •r 1 •1 -1 •y -1 -1 •) Salar de Aniolalla •i' -1 • 1, -1 •1^ -1 •i| -I •1 -1 •'! •' • 1, -t Sajar de Cauchari -1 -1 -i -1 •V •' -i' -1 •1 -1 • 1 -1 Salar de Jama •1 -I -i' .1 • 1 -1 -i -1 -1 -1 • i' -1 1 -1 Salar do LIullalllaco -1 -1 • 1 -1 -1 •( Salar d« Olaroz -1 •i' -1 r 1 •V •' -i' i -1 i Salar de Pastos Qiandea • i' -1 •i' •« •i -1 1 -1 •1 -1 • i' -i Salar de Pocllos o Oulron • 1 -1 -1 -1 1 -t •V -1 -1 •1 -1 Salar de Pozuelos • 1 -1 -1 -1 -1 -1 •t •' •1^ -1 Salar de Rio Grande • 1 •) • 1 •« • t' -1 • (' -1 • 1 -1 Salar de Sania Maria • 1 •) •1 -t -i' -1 • j -1 •i' -1 Salar de Turllari • t 1 r -1 •) -1 •t -t •t -1 • 1 -1 •1 •) Salar del Hombre Muerlo • 1 -1 •1 -1 -1 -1 • 1, -1 •1 -1 •1 -1 •1 -1 Tlncalayu -1 -i •1 1 -i' -1 •1 -1 • i' -1 • i' -i Salar del RIncon -1 -t •i -1 •i' 1 • i' -t •1 -1 •i' -1 Salar DiabliUos •1 -1 • 1 -I • 11 *1 •'! •' • t Salar flatones -i' -1 •1 1 •\\ -1 •i' -1 •1, -1 Sallna de LInl Lart • 1 -1 •i' -1 •i' -1 •)' -t • )' •) •i' -1 Salinas Grandes • 1 •< •1 •\ •1 -1 •1 -1 • 1 -1 -1 Serr^nja ^ SIJos •) •1 -I •'! •' •'! •! • 1 • -1 DZMB Mee •i' .1 •i' -1 Laguna CachI r -1 •1; •) • i' j Laguna Caplna Sur -1 -1 * 1' *1 Laguna Chjar Ktola •i" -1 •li -1 •)! -1 1! « Laguna Chojilas •'! •' •i' -1 •l| -1 -I • ii -1 Laguna ChulluncanI -i' -t -1 -1 •l; -1 • 11 -1 Laguria Colqiado -1 -1 •?. -1 •i; -1 -i' -1 Laguna Corulo •'! "1 -i' -1 '' I '' •1 -1 -il -1 Laguna Hedionda Norle •ij 1 •1. -1 K -1 •il -1 Laguna Mama Khumu •i' -1 • -1 •r -1 •'! •' ? Laguna Ramadilas •) •1 1 • 1 •) •!i -t Laguna Sacabaya . r 1 •'! •! •I; .1 •'i •' •I, .1 Lagunas Paslos Grandes r -1 •'! •' • i' -1 Salar de Challvlrl • ) -1 •1 •) •t 1 •'! •' Salar de Chlguana r 1 •'! •' -1 -1 •1 1 •'! 1 •t; t Salar da Colpaaa • i' -1 •i' 1 •i' -t •i' -1 r 1 •i' -1 to Salar do Empexa o 1 1 • 1 • 1 r 1 1 1 1 1 •|i -1 •1 1 OJ DEPOSIT NAME CHLOR IMONT lU. COAL MN MQ OROAN DIT SB FID juMCA OPAL P BR in ONYX *QT2 ! 1 Salar de Ollagua •1 •1, -1 • 1 -1 Sajar de Uyunl •1; -1 •1* 1 • i •l' -1 • i' -1 •l' 1 Salar Laguanl • T -1 • 1 •1 •* -1 1 •1 t -i •V -1 Pampa Tamargal -1; -1 • i' -1 -1 -! -1 1 1 Salar de Agua Amarga -i' -1 -i; -1 •i' -t -1 -ij -i -i] -1 \ -1 Salar de Aguas Callanles •1, -1 • 1, -1 •1 •i' .1 •i' -1 .1 -1 Salar de Aguas Callentes Norti •i' 1 \ -1 • 1 •} -1 • 1 -1 •1 -1 Salar de Agullar •1 -1 • t •t • 1 1 •1 •i_ -t r -1 •\ -t Salar ^ Ascolan •1, •' • i •1 1 •] •] • T -1 r 1 •t' -1 Salar de Alacama -1 -1 •1* -1 •i V -i -1 -1 •i' -1 •1 -1 Salar de Carcote -i' -1 •1 •t r -1 • 1 •i] -1 • t 1 -i' -1 -1 t Salar de Huasco •1, 1 •A, 1 •* • 1 1 •] -1 •i. -1 Salar de Intleles -i -i •1 -1 -1 -i' 1 •1 -1 1 -1 •i' -i Salar de La Isia •1 -1 •1 1 •1 •1 -1 •i' -1 •1 -1 *v Salar de Maricunga • 1 -1 •1 -1 • 1 -1 t • i 1 •1 -1 • \[ -1 Sa)» de Pajon^lea .r -1 \ -1 • 1 • T -t • i 1 -1 -1 r 1 Salar de Pedemales -t' -1 r 1 • V -i • 1 -1* -1 •1 1 •1 -1 •i' -1 Salar de Pintados •1 -1 •1 -1 • 1 -1 • 1 •1 -1 •1 -1 •1 -1 •1 -1 Salar de PunIa Negra •1, -1 •1 -1 • -1 -1 -1 -1 •1 -1 -1 -1 Salar de Surtre •T -1 •1 •) • i' -1 •1 l * •1. -1 •\ -1 r -1 Salar Quisqulero • 1 -i • i" -1 *1 -1 -1 -i" -t -1 -1 r 1 Chalaka • 1 -1 • 1 1 -1 1 • 1 •1 1 •1 -1 1 -1 •1 -1 Da Chajdan Lake -1 -1 -1 -t. -1 • 1 •1 -1 • 1, -1 -1 *1 DuJIall Lake • T -1 • \ -1 -1 -1 • i -1 -1 -1 -1 -1^ -1 • i' -i Gserkunsha • T -i • 1 •i' -1 1 -1 • i' *1 Qaldam Basin -1, -1 •V •! • 1 • 1 -1 •}[ 1 Xiao Chaldan Uke •i' -1 • 1 • i' -i •{ -1 • y -1 Zhabuye Sail Lake •1 -1 • \ -i i •1 -i -i] -1 • T -1 - r • i Zliacang Caka -1 -1 •V 1 • 1 • 1 -1 • 1* -1 •V -1 .11 -1 S^os Island'Kadovaasi Basin • 1 -1 .l| -1 -1 -1 • 1 • 1, • t •\ -1 • 1 -1 Puga Valley •'i -lj -1 -1 - r - i -i" -i -i! -1 Ashin -1' -1 -T -i • i" -1 -1 •V •»' -1 Lake Inder • i' -1 • -1 • i' -1 • 1 -1 r -1 Mesa del Alamo •'! •' • 1^ -1 -1 -ii -1 \ -1 \ Tubutama " * 1 • • 1 -1 -i' -1 • i • r -1 -1' • t Chillicoipa -1 •1 • 1 -1 • i -l' -1 -1' -i -T -1 •)\ -1 Laguna Salinas 1 •1 • 1 • 1 .1 • 1. -1 Chukuiliul • 1 1 • 1 •*! • i' -i • i' -1 •t' -t Lyanger Lake "M •' •*! • \ • *1 • i! -1 Sasyk'kul Lake -1 •1 •)] -1 • 1 -1* -1 • i' -1 •\' -1 • 1 -1 Shorkul Lake • 1 -1 11 -1 • 1 • 1' -1 \ -1 t' • 1 -1 BIgadIc 1' 1 1 •1 • I «! • \[ -1 Emet i! -1 •V • 1 • i' -1 r -1 •y -1 Harmanicik •1 -1 -i -I i -1 -1 Keslelok 1 •1 -1 • 1 •\\ -1 •I -1 • 1 1 1, 1 Kirka •1 1 • 1 •V -1 •i' I • i' -1 lo Sullancavit'A2i2ivo 1 1 i' 1 • 1 -1 •I i •I •! •t •! o 4^ 1 t

DEPOSIT NAME CHIXM IMONT ILL COAL MN !MQ ORGAN DIT SB FLO iuiCA OPAL ip GR jlO ONYX ioTZ

Ash Meadows •1 -1 Borax LaKe (Cjear 1^^ •'! •' •1 •1 •1 •1 -1 Calico-Daggett •i' -1 •1 •1 •1 -) -t •l' -1 •'! •' China Lake -l' -1 •1 •1 •1 •1 -1 Oealh VaHey •'! •' •1 -1 •1 •1 -1 •) -1 •li -1 •1 -1 Foil Cady -i' -1 • i, -1 •V •' •1 •1 •1 •l' -1 •'! •' • i! -1 Gerstley •1 -1 •1 •1 •1 •1 -1 -i| -1 Meclor • 1 -I •1 •1 •1 •1 -1 •li "1 Koehn Lake •1i -1 •1 •1 •1 1 -i •i' i • 1! • j • i' -1 Kramer •1 •1 1 1, i •1 -1 •t -1 Owens Lake •l' -t • 1 1 -1i -1 •1 •1 •) 1 -1 •1 -1 •1 -1 Rho A and B • T -1 •1 -1 •1 •1, -1 •I -1 Seatles Ljke •'! •' •\ •1 •t • i -i •'! •' Tick Canyon -1 -t •1 -1 -1 •1 • 1 -1 •1 -1 1 -1 r -1 Ventura -1 -1 -1 -1 •1 •1 •1 •1 -1 -1 •1 -1 Cal|y|lle Wash/Anniversary Min -1 1 •1 -I •1 •1 -1 • i' • i •1 -1 -i' i Cave Spring -1 1 •y •' •1 -1 -1 -1 -i •1 -1 •1 -1 •i' -1 Columbus Marsh •1 1 -1 -1 -i' -1 •1 •1 •1 • 1 -1 • 1 -1 -1 -1 •1 1

Dixie Marsh •K •' •t •1 •1 • 1 -1 •1 -1 •\ -1 Fish Lake Marsh •)' -1 -i' -1 -) -1 -i • 1 -1 Hoi Springs Marsh/Eagle Mars • t -1 -1 -1 -1 -1 •1 •1 • 1 • 1 -1 • T -t r -1 Rhodes Marsh -1 -1 -1 •1 •' • 1 • 1 -1 r •) •1 -1 Silver Peak Marsh •'! •' •I •1 • I •' •!, •' -I -I Sljyer Pert Range •V •1 •1 • 1 •1 •) r -1 Soda Lake • i' -1 •1 •1 • 1 • 1 -1 -i' -1 •i' -1 Teels Marsh -1 -1 •1 1 -1 •1 • t • 1 -1 •1 -1 •1 1 •1 •' While Basln/Cenlral Muddy Ml • r -1 -I •1 • 1 • 1 -1 •i' -1 -1 -1 Lake Alvord •i' -1 •1 -t -1 1 i •t' -1 -i' -1 Jarondal •1 •1 • 1 •1 -1 •i' -1 -1 -1 •'1 ^ !

Iv> o CJl LITHOLOGY .SH/ DEPOSIT NAME MOST LST SST CONQ EVAPS !ALLUV DIAT iCHEHT TUFF FLOWS VOLC BASALT AND

Ac^qque AQTN' 1 -1 •1 l' -1 1 1 1 Archlbarca Ravins area AGTN' -1 -1 -1 -i •' '! L' -1 -1 .1 1 Boratera de Antuco AQTN^ -1 -i -1 • 1 •'! ' 1 1 1 1 \ Celll Occurrence AQTN t -1 1 -t • t' • 1 ^ (' -1 1 1 1 •1 1 Coyagualma AGTN 1 -1 1 1 1 -1 1 •V •' Laguna Quayalayoc AGTN, 1 -1 1 • 1 \ -1 • 1 -1 -1 -1 Lagunlla AQTN' I -1 1 -1 •l' -1^ t' -1 t -1 1 • I t Loma Blanca AQTN 1 • 1 -1 • 1 l' -1 1 •1 1 -1 -t Ojo de Agua AQTN, i -i •1 •1, -l' r -1 • 1 -1 •1 -1 Rjq Alumbrlo AQTN' 1 • 1 1 • 1 i' -1 1 1 1 1 1 Salar Centenario AQW 1 • 1 1 • 1 R -I^ R -1 1 1 t 1, 1 Salar de Aniolalla AQTN", i • 1 1 • 1 r ) . 1 .) 1 •1 1 Salar ^Caucharl AQTN' 1 -1 1 -1 1' -t I' -1 1 1 1 •V 1 Salar ^^rna AQTN 1 • 1 1 -1 1 -1 1 Salar de LIullalllaco AQTN 1 -1 . t -1 -1 . 1 • 1 • 1 Salar de Olaroz AQTN' 1 1 1 -1 1' -1 t' -t -1 . t Sajar ^ Paslos Qrandes 1 -1 1 1 1 -1 1 -1 1 1 1 •1 1 Salar de Pqcjlos p Quiron AQTO 1 -1 • 1 • 1 r -t^ . 1 i i •'! ' Salar de Pozuelos AQTN' 1 -1 1 • 1 -1 . 1 • 1 -1 Salar de Rio Qrande AQfN 1 • 1 -1 1, -1 1 -1 . t . \ • t -t Salar de Santa Maria AQTO 1 • 1 • 1 1' -1 1 . 1 1 • i' -i Salar de Turilarl AQTN' 1 • 1 1 • 1 r -1, 1 . 1 1 • 1 -1 Salar Hombre Muorlo AGTN 1 -1 1 1 1 -t' ' -1 1 1 1 1 -t Tjncalayu AQTN 1 1 1 1 R -I i' -1 1 1 1 '! -1 Salar del RIncon AQTN' 1 1 1 -1 ' -T i 1 1 1' -1 Salar Oj^llllqs AQTN 1 -1 1 1 1 -i' r -1 • 1 . 1 1 -1 -1 Salar Ratones AQTN' 1 -1 •1 -1 •'! • 1 • 1 Sallna de LInl Larl AQTN' 1 •1 -1 •1 r -1 1 . 1 1 •T -1 Salinas Qrandes AGTN^ 1 1 -1 -1 V -i' 1, -1 . 1 -1 •V Serrania de Sljes AQTN 1 -1 1 • 1 r -t I' -1 1 1 1 • 1 1 D/ulla Area ARMN' 1 -1 -1 1 •t Laguna CachI BLVA; 1 • 1 •1 -1 '! •' '! -1 1 1 1 • t 1 Laguna Capl^ Sur BLVA' 1 -1 -1 -1 t' -1 i' -1 1 1 1 Laguna Chlar Kkota BLVA! 1 • 1 •1 • 1 r • T; ii •) 1 1 1 r 1 Laguna ChoJIIas BLVA 1 • 1 -1 -1 ' i •' 1 i 1 •1 t Laguria ChulluncanI BLVA; 1 -1 -1 • 1 i' -1 1 1 1 Laguna Colorado . 1 BLVA -1 1 -1 ^ -T '! -i 1 1 1 •' ' Laguna Corulo BLVA; 1 -1 •1 -1 '! -1 1 1 1 •1, 1 Laguna Hedlonda Norte BLVA 1 • 1 •t • 1 t' -t t; -1 1 t 1 • V ' Laguna Mama Khumu BLVA 1 -1 •1 -t 1 • 1; 1 I 1 • 1 1 Laguna Ramadllas BLVA^ 1 1 -1 -1 1' -i' 1 1 1 • 1 1 IO o Laquna Sacabava BLVA' 1 •1 • 1 1 -1 1 t 1 • 1 1 •v] isH/ OEPOSFTNAME JMDST LST SST CONQ EVAPS iALLUV iDIAT CHERT TUFF FLOWS VOLC BASALT ;AND

Lagunas Pastos Grandes BLVA 1 1 1 1 Salar de Challvlrl BLVA' 1 -1 I' -T, -I' -1 1 1 1 •V ' Salar da Chlguana BLVA 1 • 1 V -T -1^ -1 1 1 1 • 1 1 Salar de Colpasa BLVA! 1 1 1 1 1 Salar de En^exa BLVA 1 1 1 1 1 Salar de Ollague BLVA 1 •1 -T -1^ -1 1 i 1 t Salar ^Uyunl BLVA 1 •1 1 1 1 Salar Laguanl BLVA 1 •1 1 1 1 Pampa Tamargal OLE ' 1 1 1 1 1 • t' 1 Salar de Agua Amarga OLE • 1 -1 • 1 -1 1 •1' -1 Salar de Aguas Caljenles OLE ^ 1 -1 1 1 1 r 1 Salar de Aguas Callentes Nort< CUE ' 1 •1 1 -T -I' -1 1 1 1 i' 1 Sal^r de Agullar CLE ' t -1 1 -1 -i' -1 1 Salar de Asc^an Cli 1 •1 1 1 1 ' Salar de Alacama OLE 1 •1 1 -t' •]' -1 1 1 1 11 1 Salar de Carcoie CLE 1 -1 1 •' •' 1 1 1 •( 1 Salar da Huasco CLE 1 -I 1 1 1 ' Sajar de jnlleles CLE ' 1 •1 r -i' -1^ -1 1 1 1 •'! 1 Salar de La Isia CtJE ' 1 •I . ^ 1 Salar de Marlcunga CLE 1 1 •1 -1 1 1 1 •1 1 Salar de Pajonales CLE 1 •1 -1 '! •'! •' t 1 1 Salar de Pedernales CLE ' 1 •1 -1 1 1 1 •i' 1 Salar de Pjntedps CLE I 1 -1 1 -T -1 -1 1 Salar ^l^njaNegra QUE ^ 1 -1 i! -i; -r .1 1 1 1 R 1 Salar da Surire CLE ; 1 •i R -1 -I' -1 1 Salar Quisqulero CLE 1 1 •1 1 -I! -1 -1 1 1 1 1 1 Chalaka Cl^ j 1 •1 I'-1 -I't -I'- -1 -1 1 1 1 1; 1 Da Chaldan Lake CINA i 1 -1 1 DuJIall Lake CINA j 1 -1 1; ^1; 1 -1 -1 Geerkunsha CINA J 1 -1 1, -1. •'! -1 ) 1 1 1 ' 1 1 Qaldam Basin CINA j 1 •1 1 Xiao Chaldan Lake CINA ' 1 1 • 1 -1! -1 -1 1 • 1 -1 Zhabuye Sajl Lake CINA' 1 1 1] -v •*! -1 1 1 1 1! 1 Zhacang Caka QNA' 1 1 1 1 Samos Island-KarlovassI Basin GPKI 1 t 1! -T -v -1 1 1 1 •ii 1 t Puga Valley INDA1 1 i| -ij -i; -1 1 Ashin IR^ 1 i! -li -1, -1 . 1 Lake Inder KAZ'K 1 1' -i' -I -1 Mesa del Alamo 1 •il -i' -T -1 1 1 Tubulama MXCO' I 1 1 i -1 -1 -1 t 1 I Chllllcolpa 1^1 1 •i| r -1^ -1 1 1 1 tsj o Laquna Salinas PBU' 1 •'I ' 1 1 1 1' 1 00 SH/ DEPOSrrNAME iMDST LST SST CONQ EVAPS IALLUV DIAT 'CHERT TUFF FLOWS VOLC BASALT lAND

Chukurkul TJIK 1 1 -1 •1 Lyanger Lake TJIK 1 1 -1 •1 •1 . t • 1 . T Sasyk-kul Lake TJIK ^ 1 -1 -1 -1 • t . 1 . 1 Shorkul Lake fJLK t •1 •1 . t Bigadlc 1 1 -1 •1 1 -l' .1 1 1 1 1 ^ -1 Emet 1 1 t 1 1, -l' 1 ) 1 t 1 ] 1 Harmanclk TRK/ 1 1 •1 -1 -1 -1 -t -1 1 . ^ 1 'I -1 Kesteiek TRKY' i i • i -1 1 1 1 Klrka TOKYj 1 1 • 1 1 -1; -1; -1: 'J 1 1 1 1. 1 Sujlancaylr-Azlziye TFIKY'; 1 1 • 1 •1 1 1 4 ' 1 1 • 1 1 Ash Meadows USCA' 1 • 1 • 1 •1 •1 -1 -1 -1 1 1 1 Borax Lake (Clear Lake) USCA! 1 -1 -1 -1 -1 1 • 1 -1 Cajll^-Daggett USCA 1 1 t -1 1 1 1 1 ^ 1 Chjna tjke USCA' i • 1 -1 -1 i' -t' -i' -1 t 1 Death Valley USCA' 1 1 1 1 i' -i' -i' -1 1 1 1 1 1 Fort Cady USCA 1 -1 • 1 1 1 -t -1 -1 1 1 1 1 1 Qerstley USCA' 1 1 1 1 1 1 1 1 *1 Hector USCA' 1 1 -1 -1 -1 -1 -1' 1 1 1 1 I Koehn Lake USCA' 1 • 1 • 1 -1 1 1 1 • 1 Kramer USCA! 1 1 1 •1 1 1 1 1 • 1 Owens Lake USCA' 1 1 •1 i 1 1 1 •! Rho A and B USCA' 1 • 1 1 -1 •1 -1 -il -1 • 1 i 1 Searles Ul^ USCA' 1 • 1 •1 i; -1. .i! .1 -1 ! 1 Tick Canyon USCA; 1 i 1 1 •1 -L! -1; -1 1 . t 1 i! 1 Venlura USCA; 1 1 ) •1 1 -r -ij -1 -t 1 1 t *1 Callville Wash/Annjversaty Mjn USNVL 1 1 1 -t 1 -!• -l' -1 1 .) 1 • 1 *1 Cave Spring ysNvj 1 1 -1 •1 . t Columbus Marsh USNV; i 1 •1 r -i' -ti -1 1 1 1 r 1 Dixie Marsh USNv' 1 -1 -1 -1 t 1' 1 Fish Lake Marsh USNV. 1 -t -1 -1 1 t 1 11 1 Hot Springs Marsh/Eagle Marsh USNv] 1 -1 -1 •1 • 1 • 1 Rhodes Marsh USNV; 1 -t • 1 •1 1 1 1 Silver Peak Marsh USNVj 1 -1 • t •t I -r -1 -1 1 1 t • 1 '1 Silver Peak Range USNV; i 1 • 1 •1 1 1 • 1 *1 f Soda Lake USNv! 1 • 1 • 1 •1 •1 •1 1 Teels Marsh tJSNVj 1 -1 •t • 1 -1j -1 -1 1 t 1 While Basin/Central Muddy Ml USNVj 1 1 • 1 •1 1 -1 -1 -i 1 1 Alvord Valley USCR; 1 • 1 • 1 •1 •1 -1! -1: -1 1 1 1, • ^ Jarondol VUQO; 1 1 • t •1 t -t' -t; t 1 1 1 Krenina YUQOj 1 1 • 1 •1 •1 -I; -ij -1 VallevO'Mlonlca YUQO 1 1 • t -1 1 1 M O vO I

',SPGS ' DEPOSIT NAME DACtTE RHVOL RHVOO LATITE AGGUm isTROMS isPGS i ACTIVE I CALICHE GRANITE

Acazoque 1 -1 •1 •I -I -ll 1 V •1 Archlbarca Ravine area • 1 -1 -1 -1 -T -i' 1' l' -1 •1 Boralera ds Aniuco 1 •1 •1 •1 •) Ceiy Occurrence 1 -1 •1 •1 1 -11 -1 •1 Coyagu^ma 1 -1 •1 •1 •1 Laguna Quayaiayoc -1 •1 •1 • 1 -1 -l' -1 •1 ygunila 1 •1 •1 -1 • 1 -v 1 -1^ -1 -1 Loma Blanca 1 -1 1 •1 -1 -1 1' -1 -1 •1 Ojo de Agua -1 •1 •1 •' V i; i! -1 •1 Alumbrlo 1 -1 •1 •1 -1 Salar Cenlenarlo 1 -1 •1 •1 -T -1 -1 I Salar de Antolalla •1 -1 -1 i' r -1 •1 Salar de Caucharl 1 -1 •1 •1 • 1 -1 1, 1, -1 -1 I Salm^ Jama -1 -1 -1 -1 -i' -1 r -i' -1 -1 Salar de LIullalllaco -1 -1 -1 -1 -1 -i' 1 -1 -1 •1 Salar de Olaroz •1 •1 -1 -1 -1 -1 1 -1, -1 •1 Salar de Pastas Qrandes 1 -) -1 •) • 1 • 1. 1, r 1 •> Salar da Pocllos o Quiron -1 •1 •i -1 -1 -T -1 Salar de Pozuelos •1 •1 •1 •1 -1 -i' 1, -1 -1 Salar de Rio Grande -1 -I •1 •1 -1 I ' -1 -1 -1 Salar de Sanla Maria •1 -1 •1 •1 • 1 r 1 -1, -1 •1 Salar de Turllari •1 -1 •1 -t • 1 -1 ^ ' •1 Salar de| Hombre Muerlo 1 •1 •1 •1 •1 -1, 1 • 1 < -1 •1 Tincalayu •1 -1 1 •1 • 1 -i' '. " M '' •1 Salar del RIncon • i •1 •1 •1 •i -i' -1 Salar Dlabllllos • 1 -1 •1 •1 • 1 -1. i! h 1 •1 Salar Ralqnes • 1 -i -i -1 1 ii -1 -1 Sallna de LInl Larl • 1 • 1 -1 -1 1 -i' .1 •1 Salinas Grandes • 1 •1 •1 -1 •' -1. i: -i; -1 •1 Serranja de Sljes 1 •1 • 1 •1 • 1 • 1 1 -i! 1 •1 Dzulla Area • 1 •t -i •1 • 1 -1' r -i! -1 -1 Laguna CachI 1 •1 •1 •1 1 1 -1 Laguna Caplna Sur 1 •1 • 1 •1 •1 Laguna Chlar Kkota 1 •1 • 1 •1 r -i' •1 Laguna Chojilas I •1 -1 •1 •1 laguna Chulluncanl 1 •1 -1 •t •1 1 -i: -1 -1 Laguna Colorado 1 •1 -1 •1 '! •') •' •1 Laguna Corulo 1 •1 • 1 •1 1 1' • 1 •1 Laguna Hedlonda None 1 •1 • 1 •1 •1 •)' •1 Laguna Mama Khumu t -1 • 1 •1 •y v 1-11 -1 •1 Laguna Ramadllas 1 • i • 1 • 1 • 1 -1 r -i' -1 •1 NJ t—' Laquna Sacabava 1 • 1 -1 •1 •1 1 1 r -1 • 1 O I 1

DEPOSrrNAME OACrTE RHYOL RHVOD LATITE AQGLOM 'STROMS 'SPCS ACTIVE CALICHE GRANITE

Lagunas Pastos Qrandes 1 •1 -1 -1 -j Salar de Chailvirl i -1 -l' -i' -1^ -l' -1 •1 Salar de Chlguana 1 -1 •1 -1 Salar de Cqlpau 1 -1 •1 •1 Salar de Empexa 1 -i -1 •1 Salar de Ollague i 1 -1 -1 •1 Salar dejJ^nl 1 -1 •1 v •'! •!, •1 Sgar LanuanI 1 -1 •1 -1 Pampa Tamargal 1 -1 •1 -1 Salar de Agua Amarga •1 •1 •1 Salar Aguas Callentes 1 1 •1 •1 •1 Salar de Aguas Callentes NorlE 1 •1 •1 •i' -i' r i' -1 •1 Salar de Agullar -1 -1 •1 Salar de Ascolan 1 1 -1 •1 •i! •'! 1, •'! -1 -1 Salar de Atacama 1 -1 •1 •i' •\ -T -T -1 -1 Salar de Carcote 1 •1 •1 -1 -1 -1 •' t •1 . 1 Salar de Huasco 1 -1 •1 Salar de Inlleles i •1 -1 •1 Salar de La Isia •1 •i -i' -1 -1 -1 -1 •1 Salar de Marlcunga 1 t -1 •1 •i' -1 -1 -1 •1 Salar de Peyonales 1 1 •1 •1 -i' .)• .r -1 -1 •1 Salar de Pedernales 1 1 -I •1 -1 Sajar de Pintados •1 •1 •'! -i! •' •' •1 Salar de PunIa Negra 1 1 -1 -1 •i. •'! •'! •' •1 Salar do Surire -1 -1 -1 -j' -T -1 -1 .1 -1 Salar Qul^ulerq 1 •1 •1 -1 • t' -1 1, 1 -1 •t Chalaka t 1 -1 •1 •1 Oa Chaldan Lake -1 -1 I -1 OujlBli Lake -1 •1 -1 •1 Qeerkunsha 1 1 •1 •1 •1 Qaldam Basin -1 •1 1 •i' -T i' r -1 •1 Xiao Chaldan Lake •1 •1 1 •1 Zh^uye SaU Lake 1 1 •1 •1 •1 Zhacang Caka 1 1 -1 •1 -t Samos Island KarlovassI Basin • 1 1 •1 •1 -1 Puga Valley • 1 •1 -1 •'i -y •t AshIn • t •1 •1 •1 Lake Inder • 1 •1 •1 •1 Mosa del Alarno • 1 -t •1 •1 Tubutama • 1 1 •1 t •t Chllllcolpa •1 •1 •1 Lagiina Salinas 1 •1 1 ! |Sf>GS DEPOSrTNAME DACrTE RHVOL RHVOD LATITE AGGLOM SmOMS ISPGS i ACTIVE i CALICHE GRANfTE

ChuKurkul •1 •1 -1 -1 Lyanger Lake -i •1 •1 •t Sasyk-kul Lake • 1 -t •1 •1 Shorkul Lake -1 •1 •1 -1 BIgadic 1 1 1 •1 '! •!; -ij -1; -1 Emat I • ) -1 -) -1 Harmancik -1 • 1 -1 •1 •1 Kesteiek -1 1 •1 -1 •i KIrka 1 • 1 • i •1 • i Sujtancaylr-A2|z|ye -1 1 • 1 •1 •!, •'! -y •' • 1 Ash Meadows -1 -1 -1 •1 • 1 Borax Lake (Clear Lake) -1 • 1 -1 -1 •'! -1' r -1 -1 -1 Callco-Daggetl -1 1 -1 •1 • f , i • 1 China Lake -1 -1 • 1 •1 1 Death Valley -1 -i -1 •1 • 1 Fort Cady -1 -1 -1 •1 • 1 Qerslley -1 1 • ) •1 -) Hector -i -1 • 1 •1 *1 '1 1' '1 *1 1 Koehn Lake -1 -1 -1 -1 1 Kramer -1 -1 • 1 •1 1 Owens Lake • 1 t • 1 •1 -y -1 t Rho A and B -1 • I • 1 •1 1 Searles Lake -1 -1 • t -1 t Tick Canyon -1 • 1 • 1 •t -1 Ventura -i • t • 1 -1 • 1 Callvllle Wash/Annlveisary MIn -1 -1 • t •t 1 Cave Spring • 1 • 1 • ! •1 • i Columbus Marsh • 1 1 • i •1 •i' -i' i! ij -1 • 1 Dixie Marsh -1 • 1 • 1 •1 •1. -i' -i; -i! •' • 1 Fish Lake Marsh • 1 1 -1 -1 • 1 Hot Springs Marsh/Eagle Marst • 1 -1 -1 •1 • 1 Rhodes Marsh -I 1 • t •1 1 i' i| i 1 1 Sliver Peak Marsh -1 • 1 • 1 •1 • 1 Silver Peak Range -1 • 1 -1 -1 -1 -1^ -ij .11 .1 -1 Soda Lake • 1 • 1 • 1 •1 • 1 Teels Marsh -t 1 • 1 •1 t While Basin/Central Muddy Ml • 1 -i -1 -1 • 1 Alvord Valley -1 t • 1 •1 • 1 Jarondoi • 1 • 1 • 1 • 1 • 1 Kremna • 1 • 1 • t •1 •V -M -ij -i; -1 • t VailevO'MlonIca -1 -1 • 1 •1 • 1 h-' N> APPENDIX C: ANALOGUE DATA SET Plj^PMs ;Terl Drainage Salar Water surf elevation Qua) jacus non-marina non-marine SITE LOG (8q km) (sq km) ar«a (sq km) (m) lEVAPS (sq km) (sq km) ;(sq km)

• • QUATBRNARY with BORATES

Ascotan OLE 1930 250 9,27; 3720' 1 236 0' 0 Busch 0 Kallna, Laguna BLVA 177 21 17^ 0 34 0: 0 CachI, Laguna BLVA 244 6.2 1.5' 4495! 1 6:2 0; 0 Capina, Uiiiuna BLVA 656 48 13 4387^ 1 48 0; 0 Carcote, Salar de QUE 579 102 2.V 1 1 102 0; 0 Challviri BLVA 1367 113 26 4394' 1 103 0; 0 China Lake USCA 2992 20 0 1 1 94 383 23 ChoJIIas, Laguna BLVA 159 5 2 5,2^ 4545^ P 5.2 0^ 0 Clayton Valley/Silver Peak Marsh USNV 1445 39 1 Ot 0' 73 Colorada, Laguna BLVA 1455 139 53^ 4278 1 139 0 0 Colurnbus Marsh USNV 992 116 1375 1 111 8.7; 57 Coruto, Laguna BLVA 327 25 131 4530 1 25 oj 0 F[sh Lake Marsh USNV 2516 10 1 6 7V 89 Koehn Lake USCA 2228 31 0 55; 1 109 346,' 75 Laguani, Salar BLVA 920 67 0.5 67 0' 0 Marna Khumu BLVA 55 7.3 7.3 4445 1 7.2 o| 0 Paslos Grandes, Lagurias B VA 655 125 17; 4440' 1 146 0; 0 L • * •" Rhodes Marsh USNV 526 24 1341 1 0 ol 7.4 Saline Valley USCA 1904 71 1 71 15 2 Searles Lake USCA 1844 106 2.6: 602^ 1 280 197; 1 Teels Marsh USNV 843 15 ' 1494; 1 20 o| 8.3 UyunI, Salar de BLVA 56954 13436 13436 0' 718 f 1

i 1 • * QUATERNARY without BORATES

• Alkali Flat (Goldfleld area) USNV 828 19 2.6 1 'i 55 Bicycle USCA 315 5.6 20 72I 0 Broadwell Dry Lake U^ 814 7 0 891 61 Coposa CILE 1063 88 81 15! 0 Coyote Lake USCA 634 24 25 41' 12 Cuddeback Lake USCA 559 12 12 38l 18 Deep Springs Lake USCA 505 35 35 5.7; 0 Dry Lake USNV 680 1 9 0 Oi 28 Emerson Lake USCA 842 1 5 165! 5.4 Galaxv Lake USCA 294 a.7 3 8 lei 0 5 j Pllo-Pleis Jert Drainage Salar Water surl i elevation Quatlacus |nqn-mar|ne non-marine SITE LOC (sq Km) (sq km) area (sq km) i(m) ,EVAPS (sq km) Ksq km) i(sq km) 1

Khara, Laguna BLVA 397 13 13: 4509 39: 0; 0 La Laguna. Salar de BLVA 331 0.6 3l' o[ 0 Laco, Salar del CIL£ 318 16 18' 0' 0.6 Lavic Lake USCA 354 9.3 9.4' 67 0,7 Leach Lake USCA 416 5,4 6.5; 39 5 0 Lucerne Lake USCA 1015 42' 44^ 3.5 Owl Lake US^ 357 3.6 3.7' 37^ 0 Racetrack 157 6.4 6.4 o| 0 Qry USCA 2098 152 173' 8 Troy Lake USCA 877 I-* 25, BO; 64 Tuyallo, Salar de ClUE 262 11 i 12: 0 0 Pllo-Qual Pjlo-Quat Tert Terl Pr^Cen Mes Mas Ktes Mes basalt yolcanlcs basalt volcanlcs mala-lg rx granite voles seds basic jntru SITE (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km)

QUATERNARY with BORATES

Ascolan 0 850 0 411 0 Busch 0 Kallna, Laguna 0 47 0 57 0 CachI, Laguna 0 85 0 100 0 Caplna, Laguna 0 266 0 308 0 Carcote, Salar de 0 103 0 260 0 Challviri 0 612 0 402 0 China Lake 420 0.4 0 0 12 946 13_ 15 ChoJIIas, Laguna 0 6B 0 18 0 Clayton Valley/Sllver Peak Marsh 23 140 0 140 30 5.8^ Colorada, Laguna 6 664 0 569 0 Columbus Marsh 37 21 103 149 1.4 13 Coruto, Laguna 0 246 0 3.5 0 Fish Lake Marsh too 134 1 5 114 617 20 30 Koehn Lake 9,1 26 20 73 40 660 Laguanl, Salar 0 644 0 31 0 Marna Khumjj 0 34 0 0 0 Paslos Grandes, Lagunas 0 194 0 201 0 Rhodes Marsh 29 0 5.1 113 13 15 11 Saline Valley 265 0 0 22 490 1.4, Searles Lake 17 45 16 20 105 455 Teels Marsh 1-4 26 202 206 4 7 ' 26 Uyuni, Salar de 0 10493 b 5001 0 612

QUATERNARY without BORATES

Alkali Flat (Goldfleld area) 25 21 1 131 6.2 4.6" Bicycle 9.5 0 I I 28 12 51 Broadwell Dry Lake 5 0 27 134 1 98 1.1 Coposa 0 490 0 238 52 Coyole Lake 0 2.4 0 38 142 52 Cuddoback Lake 0.8 39 0 29 107 Deep Springs Lake 6.8 0 0 0 135 Dry Lake 0 0 87 66 2.7 ' 43 Emerson Lake 15 0 0 0 299 13 Galaxy Lake 3.9 0 0 1 7 90 13 3 Pllo-Quat Pllo-Quat Tert Tert Pr«^en Ms Mas jMes Mes basalt yo|canlcs basalt volcanlcs meta-lg rx grarilte voles seds basic Intru SITE (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) |(sq km) (sq km)

Khara, Laguna 0 54 0 243 0 La Laguna, Salar de 0 202 0 0 0 Laco, Salar del 0 139 0 79 0 Lavic Lake 63 1.9 6 105 1.1 Leach Lake 0 0 0 6.3 159 6.2^ 7.4 Lucerne Lake 0 0 6 0 199 53' 12 Owl Lake 0 0 0 130 4.5 §2 Racetrack 0 0 0 0 19 Rogers Dry Lake 13 0 0 18 3B2 Troy Lake 55 0 36 102 too 27^ 0.4 Tuvajto, Salar de 0 153 0 28.1 0 P^O Paleo Prec undlff. 1 undlff. undlff. Lake voles seds daclle ; daclle luff and basalt area ^No. S(TE (sq km) (sq km) (sq km) (sq km) |(sq km) (sq km) (sq km) (sq km) Springs

QUATERNARY with BORATES

Ascotan 0 2 Busch 0 Kalina, Laguna 0 17' 6 CachI, Laguna 0 2 CaplnBj Laguna 0 10 Carcote, Salar de 0 2.1^ 1 Challvlri 0 16 : .

China Lake 13 i 7O o C ChojIJas, Laguna 0 Clayton Valjey/Sllver Peak Marsh 225 75 10 Colorada, Laguna 0 12 Columbus Marsh 9.2 75 19 5 Coruto, Laguna 0 1 12.6 22 Fish Lake Marsh 258 51 1 16 Koehn Lake 7.2 60 55 i ® Laguani, Salar 0 1 3 Mama Khumu 0 , 7.2 9 Pastes Qrandes, Lagunas 0 1 10 Rhodes Marsh 48 28 2 Saline Valley 443 22 17 Searles Lake 16 12 Teels Marsh 12 27 4.3 ' 7 UyunI, Salar de 950 85

QUATERNARY without BORATES

Alkali Flat (Goldfleld area) 58 2 Bicycle 0 0 Broadwell Dry Lake 0 0 Coposa 110 0 3 Coyote Lake 4 4 42 3 Cuddeback Lake 0 15 4 0 Deep Springs Lake 232 9 Dry Lake 3 1 0 4 1 Emerson Lake 18 30 2 Galaxy Lake 5 2 0 74 0 |0 H-' oo Paleo Paleo Prec undlff. undlff. undjff. Lake voles 8^8 daclle dacl^ tuft and basalt area No. SITE (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) (sq km) fSprinss

Khara, Laguna 0 12,6 1 La Laguna, Salar de 0 0 Laco, Salar del 0 1 Lavic Lake 0 0 Leach Lake 0 3.1 5 Lucerne Lake 41 39 0 Owl Lake 0.6 18 1 Racetrack 63 2 Rogers Dry Lake 1,5 0 4.8 0 Troy Lake 0 0 Tuvaito, Salar de 0 0 APPENDIX D: STEPWISE DISCRIMINANT ANALYSIS

This analysis was done using STATISTICAL'*'' with a dataset of 43 (mineralized and non-mineralized) and 20 lithologic variables. 221 DISCRIM.OUT.6 NO PSED, NO LOGPSED, NO GRT, NO LOGGRT

File: Discrim.txt: size: 47 32 HXSS«-9999.00 Exclude If: v0>43

STATISTICAl Variables currently not in the model

DISCRIM. Df for all F-tests: 1,37 STATS

Wilks' Partial p to 1-Toler. i N=39 Lambda Lambda enter p-level Toler. (R-Sqr.) i

LOGDRN .9014126 .9014126 4 04669 .0515837 1.000000 .0000000 i SALAR .9765100 .9765100 89004 .3515877 1.000000 .0000000 1 LOGSAL .7787524 .7787524 10 51189 .0025135 1.000000 .0000000 1 EVAPS .5958747 .5958747 25 09359 .0000137 1.000000 .0000000 1 QLAC .9756582 .9756582 92312 .3428954 1.000000 .0000000 1 LOGQLAC .9237064 .9237064 3 05602 .0887330 1.000000 .0000001 1 QSED .9901190 .9901190 36924 .5471284 1 .000000 .0000000 1 LOGQSED .8859371 .8859371 4 76369 .0354885 1 .000000 .0000000 j TSED .9784257 .9784257 81585 .3722392 1.000000 .0000000 1 LOGTSED .9996771 .9996771 01195 .9135333 1.000000 .0000000 1 QBASALT .9612126 .9612126 1 49304 .2294726 1.000000 .0000000 ! LOGQBAS .9985372 .9985372 05420 .8171870 1.000000 .0000000 j gVOLC .9658751 .9658751 1 30723 .2602410 1 .000000 .0000000 : LOGQVDL .7254863 .7254863 14 00027 .0006187 1.000000 .0000001 i TBASALT .9925479 .9925479 27780 .6012936 1.000000 .0000000 j LOGTBAS .9985963 .9985963 05201 .8208584 1.000000 .0000000 ! TVOLC .9657637 .9657637 1 31165 .2594503 1 .000000 .0000000 1 DOGrrVDL .9773032 .9773032 85928 .3599466 1 .000000 .0000000 ! SPG .8086221 .8086221 8 75685 .0053532 1 .000000 .0000000 I LOGSPG .5090913 .5090913 35 67851 .0000007 1 .000000 1 .0000000 1

I STATISTICAl Discriminanc Function Analysis Sunmary I DISCRIM. I Step 1, N of vars in model: 1; Grouping: BDET (2 grps) jsTATS I Wilks' Lambda: .50909 approx. F (1,37)=35.679 p<0.0000

Wilks' I Partial | F-ranove | 1-Toler. N=39 Lambda | Lambda | (1,37) | p-level Toler. (R-Sqr.)

DOGSPG I .9999999 .5090913 I 35.67851 .0000007 1.000000 .000000 I 222

ISTATISTICAj Discrimirjant Function Analysis Sumnary IDISCRIM. I Stiep 2, N of vars in model: 2; Groining: BDEP (2 grps) jsTATS I Wilks' Lambda: .38264 approx. F (2,36)=29.041 p<0.0000 i Wilks' Partial F-remove 1-Toler. I I N=39 Lambda Lambda (1,36) p-level Toler. (R-Sqr.) !

LOGSPG I .5958747 | .6421551| 20.06122 | .0000729 ( .9996643 ( .0003357 cVAPS I .5090913 | .7516215 11.89645 .0014505 .9996643 I .0003357

STATTSTICAl Discriminant Function Analysis Sunmary DISOUM. 1 St:ep 3, N of vars in model: 3; Grouping: BDEP (2 grps) STATS 1 Wilks' Lambda: .35933 approx. F (3,35)= 20.801 p<0 0000

1 Wilks' 1 Partial | F-remove 1 ! 1-Toler. N=39 1 Lambda j Lambda | (1,35) j p-level ! Toler. (R-Sqr.)

LOGSPG 1 .5461302 1 .6579608 i 18.19465 i .0001439 1 .9992067 .0007933 EVAPS i .4741278 I .7578808 j 11.18141 1 .0019793 i .9981976 .0018024 LOGQSED 1 .3826440 1 .9390774 1 2.27062 1 .1408206 1 .9980457 .0019543

|STATISTICA| Discrindnant Function Analysis Sunmary iDISCRIM. I St:ep 4, N of -"/ars in model: 4; Grouping: BDEP (2 grps) iSTATS ! Wilks' Lambda: .31157 approx. F (4,34)=18.781 pxO.OOOO

I Wilks' 1 Partial I F-remove j | i 1-Toler. N=39 j Lambda Lambda (1, 34) p-level { Toler. 1 (R-Sqr.)

LOGSPG 1 .4730675 .6586146 17.62351 .0001829 1 .9849139 1 .0150861 EVAPS i .3844447 .8104396 7.95254 .0079549 i .9945728 | .0054272 LOGQSED 1 .3810650 .8176273 7 58374 .0093873 1 .4119079 1 .5880921 QSED 1 .3593324 .8670780 5.21216 .0288028 1 .4093489 1 .5906511

iSTATISTICA] Discriminant Function Analysis Sunmary jOISCRIM. I Step 5, N of vars in model: 5; Grouping: BDEP (2 grps) isTATS I Wilks' Lambda: .28266 ajprox. F (5,33)=16.750 p<0.0000

j Wilks' Partial F-remove 1 1-Toler. N=39 1 Lambda Lambda (1,33) p-level 1 Toler. (R-Sqr.)

LOGSPG .4367702 .6471573 17.99224 .0001686 1 .9652089 .0347911 EVAPS .3437900 .8221850 7.13695 .0116359 1 .9940326 .0059674 LOGQSED .3802398 .7433704 11.39240 .0019007 1 .2942922 .7057078 QSED .3245083 .8710377 4.88585 .0341216 1 .4086997 .5913002 LOGQBAS .3115692 .9072111 3.37522 .0752037 1 .5282923 .4717077 223 1 H H Discriminant Function Analysis Suninary ! [DISCRIM. i Step 6, N of Vcurs in model: 6; Grouping: BDEP (2 grps) 1 STATS 1 Wilks' Lambda: .26820 ajprox. F (6,32)= L4.552 p<0 0000 1 1 1 i Wilks' Partial | F-ranove 1 1-Toler. ! 1 N=39 i Lambda Lambda | (1,32) I p-level i Toler. (R-Sqr.) !

I LOGSPG 1 .4282219 .6263056 i 19.09327 1 .0001227 1 .9295249 .0704751 1 I EVAPS 1 .3340958 .8027570 1 7.86262 i .0085069 i .9633091 .0366909 1 1 LOGQSED 1 .3642792 .7362422 | 11.46396 1 .0018932 1 .2913590 .7086411 1 1 QSED 1 .3123228 .8587198 1 5.26477 1 .0284694 1 .4020085 .5979915 1 1 LOGQBAS 1 .3106524 .8633372 | 5.06547 1 .0314101 1 .3997604 .6002396 1 1 LOGTSED 1 .2826590 .9488386 | 1.72544 1 .1983347 1 .6119950 .3880050 i

iSTATISTICAl Discriininanc Function Analysis Sumnnary |DISCRIM. I Step 7, N of vars in model: 7; Grouping: BDEP (2 grps) ISTATS I Wilks' Lambda: .23759 approx. F (7,31)=14.211 p<0.0000

Wilks' Partial F-ranove ! 1-Toler. i N=39 Lambda Lambda (1, 31) p-level 1 Toler. (R-Sqr.) 1

LOGSPG .4159997 .5711334 23. 27804 .0000355 1 .8271081 .1728919 1 EVAPS .2743999 .8658580 4. 80264 .0360550 1 .9441919 .0558081 ( LOGQSED .3432660 .6921493 13.78802 .0008050 1 .2714775 .7285225 ! QSED .3018971 .7869944 8. 39037 .0068604 1 .3337873 .6662127 i LOGQBAS .2969038 .8002301 7.73886 .0091153 1 .3469171 .6530830 1 LOC?rSED .2708226 .8772949 4. 33589 .0456607 1 .4672920 .5327080 1 LOGTVOL .2681977 .8858812 3.99340 .0545148 i .6295229 .3704771 i

jSTATISTICAj Discriminant Function Analysis Sunmary IDISCRIM. I 8, M of vars in model: 8; Grouping: BDEP (2 grps) !STATS I Wilks' Lambda: .21272 ajprox. F (8,30)=13.879 p<0.0000

Wilks' Partial F-rarvove 1 1-Toler. ! N=39 Lambda Lambda (1, 30) p-level 1 Toler. (R-Sqr.) !

LOGSPG .4021182 .5289969 26.71110 .0000145 i .5061963 .4938037 i EVAPS .2551113 .8338292 5-97859 .0205674 1 .9011544 .0988456 1 LOGQSED .3025267 .7031423 12.66562 .0012626 1 .2703394 .7296606 1 QSED .2938253 .7239652 11.43846 .0020164 1 .2881439 .7118561 1 LOGQBAS .2704190 .7866285 8. 13744 .0077802 1 .3408729 .6591271 1 LOGTSED .2221542 .9575300 1. 33061 .2578042 1 .4163831 .5836169 1 LOGTVOL .2673638 .7956173 7.70657 .0093856 1 .3794560 .6205440 1 LOGDHN .2375913 .8953159 3. 50773 .0708573 1 .2749605 .7250395 1 |STATISTICA| VarizJalas currently not in the model

DISCRIM. 1 Df for all F-tescs: 1,29 STATS

1 Wilks' Partial I F CO 1 1-Toler. N=39 1 Lambda Lambda j encer p-level i Toler. (R-Sqr.)

SALAR j .2126705 .9997706 I .0066547 .9355443 ( .3585885 .6414115 LOGSAL 1 .2092558 .9837178 1 .4799993 .4939340 1 .2244045 .7755955 QLAC 1 .2126753 .9997934 1 .0059941 .9388200 1 .3612679 .6387321 LOGQLAC 1 .2126815 .9998222 1 .0051571 .9432436 j .5218223 .4781777 TSED 1 .2127142 .9999760 1 .0006966 .9791243 1 .3009384 .6990616 QBASALT i .2124768 .9988602 1 .0330925 .8569163 1 .3924690 .6075310 QVOLC 1 .2125210 .9990677 1 .0270630 .8704723 1 .3197166 .6802834 LOGQVDL 1 .2116904 .9951628 i .1409594 .7100614 1 .4841146 ! .5158855 TBASALT i .2111861 .9927922 1 .2105423 .6497633 j .8041675 .1958325 LOCJTBAS 1 .2119903 .9965729 I .0997273 .7544187 1 .5088063 .4911937 TVDLC 1 .2127164 .9999864 1 .0003941 .9842972 j .3115229 .6884770 SPG 1 .2124366 .9986711 i .0385907 .8456320 i .2486620 1 .7513379

iSTATISTICAl p-levels DISCRIM. 1 STATS

BDEP 1 g^l:0 g_2:l

g_l:0 1 .0000000 g_2:l 1 .0000000

ISTATISTlCAl F-values; df = 8,30 | IDISCRIM. i i I STATS 1- + I i I 1 i BDEP I g_l:0 I g_2:l i

( g_l:0 I — ! 13.85311 j 1 g_2:l 1 13.85311 i 1

ISTATISTICA Squared Mahalanobis Distances IDISCRIM. I STATS I I BDEP g_l:0 gr_2:l i g_l:0 .00000 15.05151 I g_2:l 15.05151 .00000 H 225

1STATISTICA Suitniary of Stepwise Analysis [DISCRIM. I STATS I I Variable F to 1 Enter/Retnove \ Step entr/rem | df 1 ! df 2 p-level 1

1 LCXSSPG -(E) 1 1 35.67851 1 1 1 37 .0000007 1 i EVAPS -(E) 1 2 11.89645 1 1 1 36 .0014505 I 1 1 1 IJOGQSED -(E) 1 3 2.27062 1 - 1 35 .1408205 1 ! QSED -(E) ! 4 5.21216 i T i 34 .0288028 i j LOC32BAS -(E) i 5 3.37522 i i i 33 .0752036 i 1 LOGTSED -(E) 1 6 1.72544 1 11 32 .1983344 1 1 LOGTVDL -(E) j 7 3.99341 1 11 31 .0545147 1 1 IJOGDRN -(E) 1 8 3.50773 1 11 30 .0708573 1

I STATISTICA I Suntnary of Stepwise Analysis (DISCRIM. j I STATS I

Variable 1 No. of 1 i i Enter/Remove ! vars. in j Lambda F-value 1 df 1 i df2 p-level

LOGSPG -(E) ! 1.000000 1 .5090913 35.67851 1 1 i 37 .0000007 , EVAPS -(E) i 2.000000 1 .3826440 29.04111 1 2 ! 36 .0000000 1 IJO(33SED -(E) j 3.000000 1 .3593323 20.80096 i 3 1 35 .0000001 i QSED -(E) 1 4.000000 1 .3115692 18.78126 1 4 1 34 .0000000 ^ LOSQBAS -(E) 1 5.000000 1 .2826590 16.74969 1 5 1 33 .0000000 • LOGTSED -(E) 1 6.000000 1 .2681977 14.55249 1 6 1 32 .0000001 i LOGTVDL -(E) 1 7.000000 1 .2375913 14.21088 1 7 1 31 .0000000 1 LOGDRN -(E) 1 8.000000 1 .2127193 13.87887 1 8 1 30 .0000000 1

ISTATISTICAI Chi-Square Tests with Successive Roots Removed (DISCRIM. i iSTATS I

I Roots I Eigen- | Canonicl | Wilks' | | | i I Removed | value \ R | Laittida | Chi-Sqr. | df | p-level |

0 I 3.701031 i .8872884 | .2127193 | 51.07680 | 8 | .0000000 | 1 STATlSnCA Standardized Coefficients jDISCRIM. for Canonical Variables 1 STATS 1 1 i ! Variable ! Root 1

1 LOGSPG 1.08715 1 EVAPS .48396 1 liCGQSED -1.18101 1 QSED 1.10309 1 LCGQBAS .89168 1 LOGTSED -.35994 1 LOGTVDL .82714 I LCGDRN -.69541

1 Eigenval 3.70103 ! Cum.Prop 1.00000

ISTATIsnCAl Raw Coefficients I jDISCRIM. I for Canonical Variables! I STATS I i

! Variable | Root 1

LOGSPG ! 3,.25798 EVAPS 1 1,.27302 LOGQSED 1 .90276 QSED i .01270 LCGQBAS 1 .70986 LOGTSED i .28297 LOGTVDL ! .77417 LOGDRN ! -1..47043

Constant | ,38622

Eigenval ! 3.,70103 Cum.Prop 1 1,,00000 ISTATTSTICA Factor Structure Matrix | IDISCRIM. Correlations Variables - Canonical Roots| !STATS (Pooled-within-groups correlations) |

I Variable Root 1 j LOGSPG .510436 I EVAPS .428074 I LOGQSED -.186513 j QSED .051927 i LOGQBAS .019895 ! LOGTSED .009343 i LOGTVDL .079215 I LOGDRN .171905

iSTATISTICAl Means of Canonical Variables| IDISCRIM. 1 1 i STATS i 1 i t" 1 ! 1 i ! Group ! Root 1 1

1 g_i:0 i -2.13165 j ! g__2:1 1 1.64719 1 ISTATISTICA Unstandardized Canonical Scores IDISCRIM. jSTATS I Case Group Root 1

I Ascotan g_2:l .11066 I Busch g_2:l .89860 I Cachi g_2:l .95645 j Capina g_2:l 2.54140 j Carcoce g_2:l .15191 I Challviri g_2:l 2.77773 I China g_2:l 1.95334 I Chojllas g_2:l .93634 I Clayton g_2:l 2.63950 I Colorada g_2:l 2.47515 j Coluitibus g_2:l .57475 i Coruto g_2:l 2.53359 i Fish g_2:l 1.60898 I Koehn g_2:l 2.41685 j Laguani g_2:l .12317 I Mama g_2:l 1.28860 I PGrandes g_2:l 2.39897 I Rhodes g_2:l 1.72545 I SalineV g_2:l 1.95129 j Searles g_2:l 2.01778 I Teels g_2:l 2.08587 j Uyuni g_2:l 2.07173 1 PJ-kali g_l;0 -1.03857 I Bicycle g_l: 0 -2.71958 I Broadwell g_1:0 -3.65091 ! Coposa g_i: 0 -1.06127

STATISTICA Unstandardized Canonical Scores DISCRIM. STATS Case Group Root 1

Coyote 1 g_i 0 1 -1.99915 Cuddeback 1 g_i 0 j -4.62445 DeepSpg ! g-i 0 I -1.61450 Dry i g_i 0 1 -2.37719 Emerson 1 g-i 0 1 -3.18533 Galaxy 1 g_i 0 1 -3.45598 Khara 1 g_i 0 i -.90279 Laguna 1 g_i 0 1 -3.11543 Laco 1 g-i 0 1 -.10464 Lavic 1 g_i 0 1 -2.06100 Leach 1 g_i 0 1 -2.44425 Lucerne 1 g_i 0 i -7.37294 Owl 1 g_i 0 1 -2.89483 Racetrack 1 g_i 0 1 -2.35779 Rogers 1 g_i 0 I -2.34965 Troy 1 g_i 0 1 -1.86191 Tuyajto i g-i 0 1 -1.06932 !STATISTICA Classification Functions; grouping: BDEP IDISCRIM. !STATS

1 1 g_i--o 1 gL.2:l 1 Variable p=.43590 1 p=.56410

1 LCGSPG -16.9199 1 -4.6085 1 EVAPS -3.5383 1 1.2722 1 LOGQSED .7920 j -2.6193 ! QSH3 -.0506 1 -.0026 1 LiOGQBAS -.8995 1 1.7830 1 LCGTSED -4.5547 j -5.6240 1 LOGTVDL -5.6574 i -2.7319 I LOGDRN 33.0773 1 27.5208

1 Constant -37.1464 ! -37.4327

I STATISTICA-I Classification Ifetrix [DISCRIM. I Rcws: Observed classifications I STATS i Columns: Predicted classifications

1 Percent 1 g_i:0 1 g_2:i Group 1 Correct 1 p=.43590 ! p=.56410

g 1:0 1 95.2381 1 20 ! 1 g_2:l 1 100.0000 1 0 1 22

Total 1 97.6744 1t 20 1 23 i STATTSTICA i Classification of Cases IDISCRIM. j Incorrect classifications are marked with

Observed i Case Classif. 1 p=.43590 1 p=.56410 i

1 Ascotan g_2 1 ! g_2 1 i g_i 0 1 i_ 1 Busch 91.2 1 1 g-2 ! g-1 0 1 1 Cachi g_2 1 i g-2 1 I 9-1 0 i 1 Capina g_2 i_ i g_2 1 1 9—1 0 1 1 Carcote g_2 1 i g-2 1 1 9-1 0 1 Challviri g_2 1 i g-2 1 ! g-1 0 1 1 China g_2 1 1 9-2 1 1 g-1 0 1 Chojllas g_2 1 1 g-2 1 1 g-1 0 j Clayton g_2 1 1 g-2 1 1 9-1 0 ! Colorada gL.2 1 1 g-2 1 1 g-1 0 ] Columbus g_2 1 ! g-2 1 ! 9-1 0 i Coruto g_2 1 1 g_2 1 1 g-1 0 i Fish g_2 1 1 9-2 1 i g-1 0 ! Koehn g_2 1 i g-2 1 1 g-1 0 1 1 i Laguani g^2 1 1 9-2 1 1 g-1 0 1 Maitta g_2 1 1 g_2 1 1 g-1 0 i PGrandes g_2 1 1 g-2 1 i 9-1 0 j Rhodes gL.2 1 i g-2 1 1 9-1 0 i 1 SalineV g_2 1 1 g-2 i_ i 9-1 :0 i 1 Searles g_2 1 1 g-2 1 i g-1 :0 i 1 Teels 91.2 1 1 9-2 1 1 g-1 :0 1 1 1 Uyuni 9-2 1 1 g-2 1 1 g_i 0 1 1 Alkali g_i 0 1 g_i 0 1 g-2 1 1 i j Bicycle g_i 0 1 g_i 0 ! 9-2 1 j Broadwell g_i 0 1 g-i 0 1 9-2 1 1 1 Coposa g_i 0 i g-i 0 i 9-2 1 i 1 1 1 Coyote g_i 0 i g-i 0 i g-2 j. i Qiriri(=hack g_i 0 i g-i 0 1 g-2 1 i j DeepSpg 9-1 0 i g-i 0 1 g-2 1 1 j Dry 9-1 0 ! g-i 0 1 g-2 :1 1 i Eitverson 9-1 0 1 g-i 0 1 g_2 1 ! 1 Galaxy g_i 0 1 g-i 0 1 g-2 1 i 1 Khara g_i 0 1 g-i 0 1 g-2 i 1 Laguna g_i 0 1 9-1 0 1 g-2 1 i 1 'Laco 9-1 0 1 9-2 1 1 g-1 •0 1 1 Lavic g_i 0 1 g-1 0 1 g-2 :1 1 1 Leach 9-1 0 1 g-1 0 1 g-2 1 1 1 Lucerne 9-1 0 1 g-1 0 i g_2 :1 1 i Owl 9-1 0 i g-1 0 1 g-2 :1 1 Racetrack 9-1 0 1 9-1 .0 1 g-2 i 1 1 Rogers g_i 0 1 9-1 0 1 9-2 i 1 1 Troy 9-1 0 1 g-1 0 1 g-2 :1 I I Tuyajto 9-1 0 1 g-1 0 1 g-2 :1 1 231

ISTATISTICA Squared Mahalanobis Distances fron Group Centroids IDISCRIM. Incorrect classifications are marked with * STATS I I Observed i g_l:0 g_2:l 1 Case Classif. 1 p=.43590 p=.56410

j Ascotan g_2 1 i 12 55743 9.8904 i Busch g_2 1 1 16 54567 7.9236 Cachi g_2 i_ 1 12 46858 3.4093 i Capina g_2 1 1 23 46612 2.4283 1 Carcote g_2 1 1 9 20539 6.2266 1 Challviri g_2 1 1 26 23413 3.4102 i China g_2 1 1 37 87103 21.2775 1 Chojllas g_2 1 1 16 71621 7.8090 ' Clayton g_2 1 i 27 61732 5.8381 1 Colorada g_2 1 1 23 63125 3.0941 1 Columbus g_2 1 1 12 79043 6.6160 ! Coruto g_2 1 1 25 50654 4.5278 i Fish g_2 1 1 20 13947 6.1486 1 Koehn g_2 1 1 36 78811 16.6916 1 Laguani g_2 I 1 9 48728 6.7257 1 Mama g_2 1 ! 25 60366 14.0341 1 PGrandes g_2 1 i 21 82553 1.8641 1 Rhodes g_2 1 1 21 22875 6.3576 1 SalineV g_2 1 1 26 27890 9.7010 1 Searles g_2 1 ! 22 42541 5.3449 ; Teels g_2 1 1 19 60137 2.0063 Uyuni g_2 T_ 1 39 83891 22.3507 i Alkali g_i 0 i 7 42976 13.4482 j Bicycle g_i 0 i 4 78724 23.5103 i Broadwell g_i 0 ! 5 13661 30.8983 i Coposa g_i 0 1 7 92186 14.1119 1 Coyote g_i 0 1 11 01408 24.2923 ! Cuddeback g_i 0 1 7 71310 40.8325 1 DeepSpg g_i 0 i 13 03283 23.4040 1 Dry g_i 0 1 7 45610 23.5914 1 Elnerson g_i 0 i 10 07764 32.3206 1 Galaxy g_i 0 1 2 63799 26.9264 I Khara g_i 0 1 6 79322 11.7855 j Laguna g_i 0 i 24 21710 45.9318 i 'Laco g_i 0 1 7 74631 6.7064 j Lavic g_i 0 1 6 30535 20.0510 i Leach g_i 0 1 5 89004 22.5322 1 Lucerne g_i 0 j 46 68542 100.5770 j Owl g_i 0 ! 4 94710 24.9946 1 Racetrack g_i 0 1 9 30215 25.2909 1 Rogers g_i 0 i 9 55464 25.4818 1 Troy g_i 0 1 6 71693 18.9580 1 Tuyajto g_i 0 1 7 49400 13.7448 ISTATISTICA 1 Posterior Probabilities joiSCRIM. ! Incorrect classifications are marked with " I STATS i

1 1 Observed 1 g_i:0 ! g_2:1 1 i Case Classif. 1 p=.43590 1 p=.56410 1 1 1 Ascotan g_2: 1 I .169194 1 .8308061 1 i Busch g_2 1 1 .010263 i .9897367 i j Cachi g_2 1 I .008265 1 .9917352 1 i Capina g_2 1 1 .000021 1 .9999791 1 1 Carcote g_2 1 1 .148396 1 .8516043 1 j Challviri g_2 1 1 .000009 1 .9999914 1 1 China g_2 1 1 .000193 j .9998074 1 i i Chojllas g_2. 1 j .008912 i .9910884 1 Clayton g_2. 1 I .000014 1 .9999856 j Colorada g_2 i .000027 1 .9999732 i Columbus g_2 1 i .034057 i .9659429 • Coruto g_2 1 j .000022 j .9999785 j Fish g_2 1 1 .000707 1 .9992926 i 1 Koehn g_2 1 1 .000033 1 .9999666 i 1 Laguani g_2 1 .162651 1 .8373491 j 1 Mama g_2 1 i .002370 1 .9976302 i 1 PGrandes g_2 1 i .000036 1 .9999642 1 i Rhodes g_2 1 I .000456 i .9995444 1 j SalineV g_2 1 1 .000194 1 .9998059 1 Searles g_2 1 i .000151 i .9998490 1 Teels g_2 1 j .000117 1 .9998832 i 1 TJyuni g_2 X 1 .000123 1 .9998769 1 i Alkali g_i 0 I .939991 1 .0600087 1 i Bicycle g_i 0 1 .999889 1 .0001112 ! 1 Broadwell g_i 0 1 .999997 i .0000033 i 1 Coposa g_i 0 1 .944653 1 .0553474 ! 1 Coyote g_i 0 1 .998310 i .0016901 i j Cuddeback g_i 0 j 1.000000 i .0000001 1 i DeepSpg g_i 0 i .992809 I .0071907 I ; Dry g_i 0 1 .999594 j .0004056 i 1 Elnerson g_i 0 1 .999981 ; .0000191 i 1 Galaxy g_i 0 1 .999993 1 .0000069 ] j Khara g_i 0 1 .903636 i .0963639 1 i Laguna g_i 0 1 .999975 1 .0000249 ; 1 'Laco g_i 0 1 .314798 j .6852025 1 i Lavic gL.1 0 i .998662 1 .0013383 i 1 Leach g_i 0 j .999685 j .0003148 1 Lucerne g_i 0 1 1.000000 1 .0000000 1 Owl g_i 0 .999943 1 .0000574 1 Racetrack g_i 0 .999564 1 .0004364 1 Rogers g_i 0 1 .999550 1 .0004500 g_i 0 1 .997164 1 .0028355 1 Troy 1 1 Tuyaj to g_i 0 1 .946221 1 .0537792 1 Exclude If: v0<44 Deposits not used to calculate discriminant function. jSTATISTICAl Classificacion Matrix IDISCRIM. I Rows: Ctoserved classifications I STATS 1 Columns: Predicted classifications 1 1 1 Percent 1 g_i:0 1 g_2:l j Group 1 Correct 1 p=.43590 11 p=.56410 i g_l:0 I 100.0000 1 1 1 0 1 g_2:l ! 100.0000 i 0 1 3

1 Total 1 lOO.OOOO i 1 1 3

ISTATISTICA Classification of Cases IDISCRIM. Incorrect classifications are marked with I STATS I I Observed I 2 Case I Classif. p=.43590 i p=.56410

Goldstone ! g_i::0 1 g_l:;0 i g_2:. 1 1 Sacabaya ! 9-2::1 1 g_2::1 1 g_l::0 i Clayton 1 g_2::1 1 g_2::1 ! g_i::0 1 Coipasa 1 g_2:; 1 1 g_2:;I 1 g_l::0 j

ISTATISTICA Squared Mahalanobis Distances frccn Group Centroids | IDISCRIM. Incorrect classifications are marked with * I 1 STATS I Observed g_l:0 g_2:l I Case Classif. D=.43590 p=.56410

! Goldstone g_l:0 6.92043 19.64600 ' Sacabaya g_2:1 15.67515 15.65687 I Clayton g_2:l 26.64525 5.51290 I Coipasa g_2:l 26.32043 20.01214

j STATISTICA Posterior Probabilities IDISCRIM. Incorrect classifications are marked with I STATS I Ctoserved g_l:0 g_2:l I Case Classif. p=.43590 p=.56410

Goldstone 1 g_l:0 1 .9977732 .0022268 Sacabaya 1 g_2:l 1 .4336509 .5663491 Clayton 1 g_2:l 1 .0000199 .9999801 Coipasa 1 g_2:l 1 .0319234 .9680766 APPENDIX E: PRECIPITATION/RUNOFF CALCULATIONS Base runotf

Drain jSalw Lake PRESENT ^(mm) ^ SIT Inflow vol PPT VOL E IJOC Station area larea area PE P 1ST AE D S (m3)/yr i (m3)/yr Papreclp, T'temp, E>evap 1 PEopotentlal evapotransplrllon, ST- storage of moisture In soil; AEa actual evapotransplratlon; 0= water dellcit: Ss water surplus; R " runotf 1

QUATERNAHYwHh BORATES . BLVA E=1.5 m/yr ave ' '

i

Busch 0 Kallna, Laguna BLVA UyunI 177 21 17 602 175 0 123 479 0 22.1E+6' 31.0E+6 Cachl, Laguna BLVA UyunI 244' 6.2 6O2' 123; 0 123 479 0 1.7Et6' 30.0E+6 Caplna, Laguna BLVA UyunI 656^ 48 1.3 6O2' 123^ 0 123 479 0 2.0Et6' 80.7E+6 Chjlly|rl, Salar de BLVA UyunI 1367^ 113 28 602 123' 0 123 479 0 42.0E+6: lee.iE-^e Chojllas, Laguna BLVA UyunI 14l| 5.2 5.2 602 123 0 123 479 0 7.8E+6' 17.3Et6 Colorada, Laguna BLVA UyunI HSSj 139 53 602 123^ 0 123 479 0 79.5E+6' 179.0E+6 Coruto, Laguna BLVA UyunI 327' 25 13 602 123' 0 123 479 0 19.5E+6' 40.2Ei6 Laguanl, Salar de BLVA UyunI 920^ 67 0.5 602 123 0 123 479 0 75O.OE+3' 113.2Et6 Mama Khumu BLVA Uyuni 55! 7.3 7.3 602 175' 0 123 479 0 g^sE+a^ 9.6Et6 Pasjos Qr^^s, Lagunas BLVA UyunI 655i 125 12 602 123' 0 123 479 0 80.6E^6 UyunI, Salar de BLVA UyunI 56954^ 13438 0 602 123^ 0 123 479 0 7.0Et9

Colpasa BLVA Uyuril 26022^ 2215 184 602 123' 0 123 479 0 276.0E+6j 3.2Ef9

1 1 i USA- evap = 1.75- Call). 2.54m/yr ave

1 Ctilna Lake USCA Trona 2992 20 0 1021 90; 90 931 0 269.3Et6 Koehn Lake ukiA Mojave 2228' 31 0,5 953^ 122 '22 831 0 I.OEtS 271.8Et6 Saline Valley USCA Trona 1904' 71 0 1021' 9o! 90 931 0 ; 171.4E+6 Beatles Lake USCA Trona 1044] 106 2.6 1021 90, 90 931 0 5.2E+6 166.0Et6

' ' USA- evap= 1.1-2.2 Nev m/yr ave

to U) en Base runoff

Drain Salar Lake PRESENT '(ntm) ; SIT Inflow vol IPPT VOL E LOO Station area area ^ area PE P ST AE 0 S (m3)/yr i(cn3)/yr ' ' Popreclp, T'tamp, E>evap 1 PE=potenllal svapotransplrtlon, ST- slorage ol moisture In soil; AE= actual evapotransplrallon: Da watsr 1 dellcit: S= water surplus: R = runott

Clayton Valley/Silver PeaK Marsh USNV Qoldlleld 1445^ 39^ 0 6B1^ 153' 153 508 0 9.3E+6' 221.1E+6 Columbus Marsh USNV Tonopah 992' tie; 0 646' 123! 123 523 0 6.4E^6| 122.0E^6 Fish Lake Marsh USNV Qo|d|leld 2516 10| 0 681 153; 153 508 0 16.1E^6 3B4.9Ef6 Rhodes Marsh USNV Tonopah "526| 24' 0 646' 123; 123 523 0 3.4E+6^ 64.7E+6 Teels Marsh USNV Tonopah 843 15 0 646 1231 123 523 0 5.4E+6' 103.7E+6 PP« Runoff Ppt Runoff PP« Runoff Ppt Runoff PP» Runoff SIT Runoff coef 'I2-50K 42.56K 38-4 IK 38-4 IK 37-2'jK 37-29K 2I-26K E 27-28 27-28K 21-26K P'preclp, Tatemp, Eaevap ' PE'potentlal evapotransplrtlon, ST- storage ol moisture In soil; AE=> actual evapotransplrallon: D- water deficit: S= water surplus: R = runoff ,

QUATERNARY with BORATES •

pt. It Busch 0 Kallna, Laguna 713.5E-3 1 700.0Et3i 94.6Et9 1,1Et6 l32.6Et9 Caclil, Laguna 55.PE-3 492,0Et3j 12.6Etg 738.0Et3 9.9Et9 Caplna, Laguna 24,2E-3 4926Et3; 23.9Et9 738.0Et3 11.7Et9 Challvlrl, Salar de 240.8E-3 492.0Et3| 201.6Et9 738,0Et3 2S2.0Et9 Cliojilas, Laguna 449.7E-3 ^ 492,gEtl 34,7Et9 738.0Et3 46.8Et9 Colorada, Laguna 444.2E-3 492.6Et3' 353.BEt9 738.0Et3 477.0Et9 Coruto, Laguna 484.8E-3 492.0Et3 86.0Et9 738.0Et3 117.0Et9 Laguanj, Salar de 0.6E-3 492.0Et3' 25.6Et9 738.0E+3 4.5Et9 f^ama Khumu 986.0E-3 700.6Et3' 39.9E+9 l.tE+6 56 9Et9 Pastos Qrandes, Lagunas 223.4E-3 492,0Et3; 88.1Et9 738.0Et3 108.0Et9 UyunI, Salar de 70,6E-3 ! 4?^QEt3; 3.4Et12 738.0Et3 2 9Et12

Colpasa B6.2E-3 ' 492.0Et3^ 17Ett2 738.0Et3 1.7Et12

I i

dry PMZ) dry to pt 25-dry: 24- (12) 1 P + (2) !P» i China Lake 31,3E-3 720,0E+3 67.5E+9 540.0E+3 373.8E<9 972.0Et3 91,1Et9i 216.0Et3; 20,2Et9 1.1Et6 gp9.1Et9 Koehn Lake 3,7E-3 976,0E+3 8.0E+9 732.0E+3 332,2Et9 1 3Et6 I0.8E+9j 292.8Et3! 2.4Et9 1.5Et6 a27.4Et9 Saline Valley 31.3E-3 720.0E+3 42 QEtQ S40.0Et3 237.8E<9 972.0E»3 58.0Et9| 216.0Et3! 129Et9 1.1ET6 57e.5Et9 Searles Lake 31,3E-3 720.0E+3 41.6E+9 540,0Et3 230.4Et9 972.0Et3 56.2Et9i 216.0Et3! 12.5Et9 1 lEt6 S60.3Et9 ' • I i dry 38K: 37K pt, Pt p=l 4-1 7, pt(1.2) (1 2) 1-

1 PPI Runoff PPI Runoff Ppt Runoff Ppt Runoff Ppl Runoff SIT Runoff coaf 42-50K 42-56K 3B-4tK 38-4 IK 37.29K 37-29K 21-26K E 27-28 27-28K 2I-26K Papreclp, Tstemp, Eeevap PEspotentlal evapolransplrllon, ST- storage ol n[\olslure In soil; AE° aclual evapolransplrallon; 0- water dellcll; Sa water surplus: R = runoll

Clayton Valley/Silver Peak Marsh 41.9E-3 1.2E»6 74.1E+9 S50.8E^3 33.3E«9 1.7E+6 100.0E+9 367.2E+3 22.2E^g 1.4E+6 580.8Ei^9 Columbus Marsh 52.1E-3 984.0Et3 50.9E+9 442.8E^3 22.9E'f9 ).3E+6 68.7E+9' 295.2Ef3 1S.3E'f9 1.1E+6 331.8Et9 Fish Lake Marsh 41.9E-3 1.2Et6 129.0E'f9 550.8E+3 56.1Et9 1.7E+6 174.2E+9^ 367.2Et3 38.7E+9 1.4E+6 1.0E+12 Rhodes Marsh 52.1E-3 984.0Et3 27.0E+9 442.8Et3 12.1E+9 t.3Ef6 36.4Ef9' 295.2Ef3 8.tEf9 1.1E+6 175.9E+9 Teels Marsh 52.1E-3 g84.0E'f3 43.2E+9 442.8Ef3 ig.SEfO t.3E^6 58.4E+9 295.2E+3 13.0E+9 1.iE+6 28t.9Etg glacial advance Ppt Runoff PP« Runoff ;ppt Runoff Ppi Runoff Ppt Runoff SIT 20-19k 20 -19K 18k-17k 18-17K 15k-14 15 14K 13-1tK bp 13-11K E 16.0E+0 16K P^preclp, Totemp, E>evap PE=potenllal evapolranspirtion, ST- storage ol moisture In soil; AEs actual avapotransplrallon; D= water dellcll; waler surplus; R ° runoll ,

• QUATERNARY with BORATES no xtenslve colder. I+, pt; Sim to 'p4 30-40%, t- glaclatlon, dryer 18k 6; water too dry >20°S, e-, budget p- warming Busch 0 Kallna, Laguna 350.0E+3; 44.26+9 31S.pEf3 39.8Et9; 175.0E+3 22.1Et9 525.0Et3 68.2Et9 708.8Et3 90.8Et9 CachI, Laguna 246.0E+3' 3.3E+9 221.4Et3 3.OE+9' 123.0E+3 I.7E+9' 3e9.0E+3' a.SEtg 49B.2Et3 7.9Et9 Caplna, Laguna 246.0E+3' 3.9E+9 221.4E+3 3.5Et9 123.0E+3 2.0Et9 36g.0Et3^ 10.7Et9 498.2Et3 1t.2Etg Challvlrl, Salar de 246.0E+3, 84.0Et9 221.4E43 76.6E+9 123.0Et3 42.pE'f9 369.0Et3' 136.1E+9 498.2Et3 176.?Et9 ChoJIIas, Laguna 246,dE+3^ 15.6E+9 221.4E+3 14.0E+9 123.0^3 7.8E+9; 369.0Et3; 24.4Etg' 4g^2Et3 32.3Et9 Colorada, Laguna 246.0E+3' 1S9.0Ef9 221.4Ef3 143.1E+9 123.0Ef3 79.5E+9 369.0Et3' 249.2Et9 4g8.2Et3 329.2Et9 Coruto, Laguna 246.0E+3 39.0Ei9 221.4E+3 35,1Et9^ '.23.PE+3 19.5E+9' 369.0Et3 60.9E+9 498.2Et3 80.6Et9 LaguanI, Salar ds 246.0E+3' 1.5E+9 22i.4Et3 1.4Et9, 123.0Et3 750.0Et6^ 369.0Et3 9.0E+9 498.2Et3 7.kt9 Mama Khumu 350.0E43 19.0Et9 315.0Et3 17.1Et9' 175.0Et3 9.5E+9 525.0E + 3 29.0E+9 7bB.8Et3 38.8E+9 Pastes Qrandes, Lagunas 246.0E+3 36.0E+9 221.4E+3 32.4E+9, 123.0E+3 18.0E+9 369.0E+3' 58.8E+9 4g8.2E+3 76.2Et9 UyunI, Salur ds 246.0Ef3 9B0.7E+9 221.4E+3 882.7E+9' 123.0E+3 490.4Et9| 369.0Et3^ 1.9Et12| 49B.2Et3 2.3E + i2

Colpasa 246,0E+3^ 5S2.0Et9 22).4Et3 406.8Et9 l23.0Et3 276.PE+9' 369.0E+3' ).0E+12' 498.2E+3 I.2E+12

pt (1.4- pt (1.4), t- 'l5-dry; or pt pt(1.2-2) 1.7). I- (1.2-2) dry China LaKo 288.0Ei^3' n3.2E+9 252.0Et3 99.0Ef9, 90.0Et3 8.4E+9, 252.0Et3i 99.0E+9; 378.0Et3 148.5Et9 Koehn Lake 39g.4E+3j 90.2Et9 341.6E+3 78 9E + 9 122.0Et3 I.OE+9' 34i.6E+3j 78.9Et9' 512.4E+3 l18.4Et9 Saline Valley 2B8.6E^3 72.0Et9 252.0Et3 63.0Ef9' 90.0E+3 5.4E+9| 252OE+3' 63.0Et9! 378.0E + 3 94.5Etg Searles Lake 2a8.0E+3' 69.7Ef9 252.0Et3 6I.OEf9! 90.0E+3 5.2E+9; 252.0Et3^ 61 OEtO, 378.0E+3 91 5Et9 1

pt (1.4- p» (14) 'pt (12) p, (12) 1.7), t- glacial advance Ppt Runoff Ppl Runoff Ppl Runoff >pl 'Runoff Ppl Runoff SIT 20-19k 20-r9K 18k-17k 18-17K 'i5k-14 'l5-14K 'l3-11K bp 13-1 IK E 16.0E+0 16K Pspreclp, T'temp, E>eyap PE=potenllal evapotransplrtlon, ST- slorage of moisture In soil; AEs actual evapotransplratlon; Ds water dellclt; S= water surplus; R = runod

Clayton Valley/Silver Peak Marsh 489.6Ei^3^ 100.4Et9 428.4Et3 87.8E+9! 163.0E+3 9.3E+9| 367.2Et3^ 22.2E+9 5508E+3 33.3Ef9 Columbus Marsh 393.6E'f3| 59.4E'f9 344.4E+3 52,0E+9! 123.0E+3 6.4Etg' 29S.2E«3l 1S.3E+9' 442.8Et3 22.9Ei9 Fish Lake Marsh 489.6E+3; 174.BE+9 42B.4Ef3 1S2.9Ef9' 153.0Ef3 16.1E+9 367.2E'f3, 38.7E+9 S50.8Ef3 S8.1Efg Rhodes Marsh 39i6E«3| 3i.5Et9 344.4E+3 27.6E+9| 12i0E+3 3.4Ei9 295.2E'f3; 8.IE+9' 442.8E+3 12,1E+9 Teels Marsh 393!6Et3' 50.5E+9 344.4E+3 44.2E+9' I23.0E+3 5.4E4^g 2g5.2E+3' 1X0E^9! 442.8E+3 19.SE^9 Ppt Runoff .Ppt ' Runoff Ppt Runoff PP« Runoff Ppl SIT 10k tOK 9k-8K 9-8K E ,6k-7 6-7K 5K-4 S-4K 0-3K P'predp, TBternp, Eseyap ' ' PE-potentlal evapolransplillon, ST- storage of moisture In soil; AE= actual evapotransplratlon; D= water dellcit; S= water surplus; R = runotl aUATERNARy wllh BORATES

warm, dry; 1 onset Holo climate

Busch 0 Kallna, L^guna 175.0E+3 22.1E+9 350.0E+3 44.2E+9 31S.0Et3 39.eEt9 3Sp.pEf3 44.2E+9| 525.0E+3 Caclil, Laguna 123.0E+3 1.7E+9' 246!6E+3' 3.3E+9 221,4E+3 3.6Etg 246.6E+3 3.3E+g 369.0E+3 Caplna, Laguna 123.0E+3 2.0E+9 24'6.6E+3 3.9Ef9 221.4E+3 35E+9 246.0E+3 3.9E+9 369.0E+3 Challvlrl, Salar da 123.0E+3 42.0E+g: 246.0E+3 84.0E+g 221.4E+3 75.6E+9 246.0E+3 84.06+9 369.0E+3 Chojllas, Laguna 123.0E+3 7.8E+9 246,0"E+3 15.6Et9 221.4E+3 14.0E+9 246.0Et3 li6E+9 36i0Et3 Colorada, Laguna 123.0E+3 79.5E+9 246.0e+3' 1S9.0E+9 221.4E+3 143.1E+9 246.0E+3 159.0E+9 369.0E+3 Coruto, Laguna 123.0Et3 19.5Et9 246.0E+3' 39.0Et9 221.4E+3 35.1E+9 246,0E+3 39.0E+9 369.0Ef3 LaguanI, Salar de t23.0E+3 750.0Ei6i 246.0E+3' 1.5E+9 221.4E+3 1.4E+9 246.0Et3 1.SE+9 369.0Et3 Mama Khumu 175.0E+3 9.5E+0| 350,0Et3^ 19.0E+9; 315.0E+3 17.1E+9 350.0E+3 19.0Ef9 52S 6E+3 P^tos Grandas, Lagunas 123.0E+3 18.0E+9 246.0E+3' 36.0E+g' 22I.4E+3 32.4E+g 246.0E+3 36.0E+9 369.0E+3 UyunI, Salar de t23.0Et3 490.4Ef9 246.0E+3^ 980 7E+9 221.4E+3 882.7Et9 246.gE+3 980.7E+9 369.0E+3

Colpasa 123.0E+3 276.0Et9 246.0E+3' 552.0Et9, 221.4E+3 496.8Etg 246.0E+3 SS2.0E+9 369.0E+3

P»(l 2-2)

China Lake 126.0E+3 49.5E+9 t80.0E+3; 16.9Et9^ 180.0Et3 16.9Ef9 216.0Et3 20.2E+9 270.0Et3 Koetin Lake 17O.0E+3 39.5E+9 244.0E+3: 2.0Et9' 244.0E+3 2.0E+9 292,8E+3 2.4E+9 366.0E+3 Saline Valley 126.0E<3 3I.5E+9 180,0E+3i 10.7E+9' 180.0E+3 10,7Et9 216.0Et3 12.9E«g 27O,0E+3 Searlos Lake 126.0E+3 30.5Et9 180 OE+3^ t0.4E+9; ieO.OEt3 10.4E*9 216.0Et3 12.5E + 9 270.0E»3

' p + (1 2) end last major pluvial Ppt Runolt iPpt Runoff Ppt 1 Runoff Ppt Runoff Ppt SIT 10k iOK '9k-8k '9-8K E 6k-7 i6-7K 5K-4 5-4K ,0-3K P-preclp, Tatemp, E>evi|p PE=polenllal evapotransplrtlon, ST- storage of moisture In soli; AE= actual evapotransplratlori; 0= water deficit; 8= water surplus; R = runoff

Clayton Valley/Silver Peak Marsli 183.6Ef3 11.1Et9; 306.0E'f3^ 18.SE+9| 306.0Et3i 18.SE+9 367,2E+3 22.2Et9j 4S9.0Ef3 Columbus Marsh 147.6E+3 7.6E+9; 246.0E+3' 12.7E+9' 246.0E+3I 127'E+9 295.2E+3 15.3E+9; 369.0E+3 FIsf) Lake Marsh 1B3.6Et3 19.4Etgi 306.0E43 32.3Etg 306.0Et3| 32.3E'>9 367,2E+3 3a.7E+9i 459.0E+3 Rhodes Marsh 147.6E+3 4.0E+9| 246.0E+3' 8.7E+9| 246!oEf3' 6.7E+9 295.2Et3 B.1Ei9 3e9.0Ei3 Teels Marsh 147.6E+3 6,5E+9! 246bE+3 10,8E+a 246,0Et3i 10,86+9 295.2Et3 IS.OEtO' 369.0E«3 10K 10K 20K 20K 28K 2BK

Runoff |TOTAL :T0TAL TOTAL TOTAL TOTAL ! SIT "pPT(m) 'INFLOW (M3) PPT (m) INFLOW (M3) PPT (m) INFLOW (M3) relerence E 0-3K Pspraclp, Tntemp, Eaevap ' PE=potentlal evapolransplrtlon, ST- storage ol moisture In soil; AE= actual evapotransplratlon; D= water dellcH: S= water surplus; R = runoll

t • • QUATERNARY wllh BORATES arid ,Lauer and Frankenbatg, 1983; zone 23. Kessler, 1983; Markgral and 30S Bradbury, 1982; Markgral, 1989; Clapperton and Sugden, 1988; Seltzer. 1990 Buscti o Kallna, Laguna 66.3E+g 1.7E+3 2t6.6E+9 3.8Et3 481.eE+g 5,9E+3. 70a.8Et9, CachI, Laguna 5,0E+9 1.2E+3' 16.2Et9 2.7E+3 3B.7E+9 4.1E+3, 61.2E'f9, Caplna, Laguna 5.9Et9 ! 1.2E+3| 19.tEt9 2.7E+3 50.3E+9 4.1Et3' 86.OE+9' Challvlrl, Salar de t26.0Ef9 I.2E+3' 4n.6E+9 2.7Et3 926.2Ei9 4.1Et3i 1.4Et12 ChoJIIas, Laguna 23.4E+9 ! 1,2E+3 76.4E+9 2.7Et3 i70.6E+9 4,1E+3; 252.1E+9 Colorada, Laguna 23e.5E'»9 1.2E+'3| 779,iE+9 2,7E+3 I.7E+12 4.iE+3' 2.6E+I2' Corulo, Laguna 5B.5Et9 1.2Et3| t9l.tEf9 2.7Et3 426.2Ef9 4.1E+3: 629.3Et9 LaguanI, Salar de 2.3E+9 1,2E+3' 7.4e+9 2.7E+3 27.6E+9 4.IE+3' 57.7E+9 Mama Khumu 28.5E+9 • 1.7Et3| 93.0E+9 3.8Et3 206.4E'f9 5.9E+3: 363.3E'f9! Pa^s Grandes, Lagunas 54.0E^9 1,2Et3| 176.4E+9 2.7Et3 397.8E+9 4.1E+3 S93.9E+9. UyunI, Salar de 1.5Et12 i 1-2E+3! 4.8E+12 2.7Et3 I1.3E+12 4.iE+3; ii6E+12

Colpasa B^B.OEfg ' 1.2E+3; 2.7E+12 2.7E+3 6.3Et12 4.IE+3' 9.7E+12;

• Smith, 19 ; Phillips and others. •1994; Spauldlng, 1984; i 'Bedlnger, 1989 i China Lake 25.31+9 972.0E+0i t2B.BE+9 2,2Et3 597.0E+9 3.8Et3| I.5E+12' Koehn Lake 3.0E+9 I I.SEtS^ 4B.9Et9 3.0E+3 4l6.2Et9 5.2Et3j I.2E+I2' Saline Valley 16.1E+9 ' 972.6E+6' B2.0E+9 2.2Et3 379.9E+9 3.8Et3j 971 3E+9'; Seailes Lake IS 6Et9 972.0E»0;t 79.4Et9 2 2E»3 367.9Ef9 3.8E+3j 940.7E+9

' 1 WInograd and Thordorson, 1975; Ttiomas, 1964; Spauldlng. 1984; Bedlnger, 1989, Langboln and others. to 1949 W 10K 10K 20K 20K 28K 28K

. Runoff TOTAL TOTAL TOTAL TOTAL TOTAL TOTAL SIT PPT (m) INFLOW (M3) PPT (m) INFLOW (M3) PPT (m) INFLOW (M3) reference E 0-3K P'preclpj Tstemp, E^eyap PE^polenllal evapolransplrtlon, ST- i sloraga ol moisture In soil; AE= actual evapotransplratlon; 0= water dellclt: S= water surplus; R = runoll

Clayton Valley/Silver Peak Marsh 27.8E+9 I.6E+3 3.6E+3 351.3E+9 5.8E+3 954.3E49^ Columbus Marsh la.lEfQ i.3E+3 67.4E+9 2.9Et3 223.3Et9 4.7E+3 570.3E+9 Fish Lake Marsh 48.4Ef9 1.6E+3 171.0E+9 3.6E+3 ai1.6Ef9 5.8Ef3 1,7E+t2' Rhodes Marsh 10.IE+9 1.3E+3 35.7E+9 2.9Et3 tia.4Et9 4.7E+3 302,4E+9^ Teels Marsh i6.2E+g 1.3E+3 57.3E+9 2.9Ef3 t89.7E+9 4.7E+3 484.6E^9' 245 REFERENCES

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