Stress modeling of the Nazca plate: advances in modeling ridge-push and slab-pull forces

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Authors Cox, Billie Lea

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Link to Item http://hdl.handle.net/10150/557971 STRESS MODELING OF THE NAZCA PLATE:

ADVANCES IN MODELING RIDGE-PUSH AND SLAB-PULL FORCES

by Billie Lea Cox

A Thesis Submitted to the Faculty of the DEPARTMENT OF GEOSCIENCES

In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE In the Graduate College THE UNIVERSITY OF ARIZONA STATEMENT BY AUTHOR

This thesis has been submitted in partial ful­ fillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules . of the Library„ Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permis­ sion for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the mate­ rial is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

R. M. RICHARDSON ' Date Assistant Professor of Geosciences ACKNOWLEDGMENTS

I am very grateful to my thesis advisor, Professor Randall M. Richardson, for suggesting this thesis topic, convincing me that finite elements could be understandable given time and effort, and for patiently guiding my pro­ gress, supporting my work with a research assistantship and computer time. I want to thank Professors Spencer R. Titley and William R. Dickinson for reading my thesis, and for stimu­ lating my interest in plate tectonics through course lectures. The Department of Geosciences supported me with teaching assistantships in mineralogy, and I also received a research assistantship from Dr. Dennis K. Bird. Further Support for my graduate studies came from Amoco and Conoco scholarships awarded by the Geophysics Committee, and from earnings from summer employment with GeothermEx, Inc., and Sohio Petroleum Company. I appreciate all of this support. I want to express a special thanks to Murray C. Gardner for encouraging me to pursue graduate studies at the University of Arizona, and for sending flowers at the right times. And finally, I want to thank my mother, Marcilie G. Cox, for providing a coastal haven from desert heat and allergies, and for the moral support I needed to see my way through to the completion of this thesis.

iii TABLE OF CONTENTS

Page TABLE OF CONTENTS ...... iv LIST OF ILLUSTRATIONS ...... vi LIST OF TABLES ...... ix ABSTRACT x I. INTRODUCTION . . ; ...... 1 II. DESCRIPTION OF THE NAZCA PLATE ...... 6 East Pacific Rise Ridge Boundary ...... 11 Galapagos Spreading Center Ridge Boundary . 13 Chile Ridge Spreading Center and Transforms ...... 15 South American Trench Boundary ...... 16 Intraplate Features ...... 20

III. STRESS DATA . . . . » ...... 24

IV. DESCRIPTION OF MODELING METHOD 30

Elastic Modeling ...... 31 Viscous Modeling ...... 38

V. MODELING PLATE-DRIVING FORCES 40 Ridge-Push Forces ...... 40 Distributed Ridge Forces Applied to the Nazca Plate ...... 48 Line Ridge Forces Applied to the Nazca Plate ...... 48 Slab-Pull Forces ...... 51 Drag Forces ...... 57 Transform Fault Shear Forces ...... 63 Hot Spot Forces ...... 63 Distant Forces From Other Plates . . . . . 64 iv V

TABLE OF CONTENTS— Continued

Page VI. STRESS MODELS ...... 65 Distributed Ridge Models ...... 65 DR Models ...... 65 DRD Models ...... 68 Refined Grid Models ...... 71 Line Ridge Models ...... 74 LR Models ...... ■ 74 LRD Models ...... 78 Slab-Pull Models ...... 78 SD Models ...... 78 Angle Dependent Models ...... 80 Age Dependent Models ...... 83 Combined Ridge-Push and Slab-Pull Models . 87 DRSD Models ...... 87 LRSD Models ...... 90 Viscous Models ...... 90 VII. CONCLUSIONS ...... v 97 REFERENCES 101 LIST OF ILLUSTRATIONS

Figure Page 1. Location map of the Nazca plate . . . . . „ . 7 2. Nazca plate boundaries and intraplate

f e a t U r e S oeeeoeoeooeepoooo IQ

Topography along the East Pacific Rise Ridge Boundary . .■ „ . • . . . , ...... 12 4„ Segmentation of the South American Subduction Zone 17 5. Distribution of intraplate earthquakes in the Nazca plate recorded between 1901 and 1981 . . 25 6. Location of the 1965 and 1944 intraplate earthquakes ...... 26 7. Triangular elements on a half-sphere . . , . . 32 8. Finite element grid of the Nazca plate (coarse) oopeppopppopeooao 35 9. Finite element grid of the Nazca plate (re fined) 9***99 99*90 * 9*9 37 10. Plate-driving forces acting on the Nazca plate * ...... 41 11. Test case for comparing distributed ridge and line ridge forces 46 12. Distributed ridge forces on the Nazca plate . . 49 13. Line ridge forces applied to the Nazca plate . 52 14. Constant slab-pull forces on the Nazca plate . 56

15. a. Angle dependent slab-pull forces b. Age dependent slab-pull forces ...... 58 vi vii LIST OF ILLUSTRATIONS— Continued

Figure Page 16. Drag forces balancing distributed ridge forces e o <» o -< <> • -•• « o o 62 17. a. Stress state for Model DR-a b. Stress state for Model DR-b . 67

18. Stress state for Model DRD--a • » • v ° o 69 19. a. Stress state for Model DRD-b be Stress state for Model DRD-C o • • • ° ° 70 20. a» Distributed ridge forces for refined grid be Stress state for Model *DR-a » •- • o o 73 - ' 21. ae Stress state for Model *DRD-a be Stress state for Model *DRD-b - • » • «, o 7 5 22. a. Stress state for Model LR-a be Stress state for Model LR-b » • * - o 76 23. Stress state for Model LR-(: » • > • • « < • e 77 24. a. Stress state for Model LRD-a b. Stress state for Model LRD-b • - e a o 79 25. a. Stress state for Model SD—a b. Stress state for Model SD—b a « • •• ° o o 81 26. a. Stress state for Model SD-c b. Stress state for Model SD—d e • • • « o 82 27. a. Stress state for Model SD-ang b. Stress state for Model SD-ang2 . . a o o 84 28. Stress state for ModelModel SD-ageSD-age ...... 8528. 85 29. Composite of stress states for Models SD-c, SD-ang, SD-ang2, and SD-age ...... 86 30. a. Stress state for Model DRSD-1 b. Stress state for Model DRSD-2 ...... 88 31. a. Stress state for Model DRSD-3 b. Stress state for Model DRSD-4 . , . . . . . 89

32. a. Stress state for Model LRSD-1 b. Stress state for Model LRSD-2 , ...... 91 viii LIST OF ILLUSTRATIONS— Continued

Figure Page 33. Stress state for Model LRSD-3 Stress state for Model LRSD—4 . . . « . . . 92

34. fd Stress state for Model V-DR A Stress state for Model V-DRD ...... 94

35. ftirQ Velocities for Model V- -DR Velocities for Model V--DRD o o o e o o e o 96 LIST OF TABLES

Table Page 1. Plate Motion Data Used in Nazca Plate Stress Modeling ...... 9 2. Description of Nazca Plate Models ...... 6 0

ix ABSTRACT

The forces which drive the plates are evaluated by finite element stress modeling of the Nazca plate, where stresses resulting from various combinations of forces are compared with the record of intraplate earthquakes and other stress data. Both elastic and viscous rheologies are modeled. Advances in modeling both ridge-push and slab- pull forces are presented. Ridge forces are distributed over the entire plate, and then compared with line ridge force models. Angle and age-dependent slab-pull models are compared with constant slab-pull models. The distri­ buted ridge force models produce more realistic stresses and represent a significant improvement over line ridge forces. Age-dependent slab-pull models fit the data better than other slab-pull models. Angle-dependent slab-pull models do not fit the data in regions of shallow dipping slab segments. Both elastic and viscous models with drag forces are less correlatable with the stress data than models without drag forces.

x I. INTRODUCTION

The earth's lithosphere is made up of about a dozen plates, defined by seismicity, and although we can directly observe and measure the relative motion of the plates, we have no direct method for measuring the forces which drive the plates and must rely on theoretical modeling. The object of this thesis is to utilize one of these methods, stress modeling, to investigate the role and relative importance of possible forces in.driv­ ing and stressing a single plate, the Nazca plate. The forces considered are ridge-push, slab-pull and resistive drag at the base of the plate. The Nazca plate is modeled by the finite element method as in Richardson (1978) where combinations of the various plate-driving forces are applied and the resulting

stress states compared with the stress data. Several advances to this earlier work are presented here. One improvement is a new, more realistic way of modeling ridge-push forces, by distributing the ridge-push over the entire plate. Distributed ridge forces are also modeled with a refined grid. Advances in modeling slab- pull forces include both age-dependent and angle-dependent

slab-pull models. A fourth innovation is the use of an incompressible viscous rheology for two of the eight

1 distributed ridge models„ The viscous solution results in velocities and stresses rather than displacements and stresses obtained from elastic modeling. The relative velocities of the plates were worked out by Minster et al. (1974) and then improved by Minster and Jordan (1978) by inverting data from transform fault azimuths, spreading rates and earthquake slip vectors. The relative strength of the various plate-driving forces were then studied by inverting the data on velocities and plate geometries, minimizing the net torque action on each plate (Forsyth and Uyeda, 1974; Chappie and Tullis, 1977). Intraplate stresses for various driving force models were calculated by the finite difference technique (Solomon et al., 1975, 1977; Richardson et al., 1976) utilizing elastic rheology and comparing the stress states of the models with the earthquake data. The ridge-push forces were found to be at least comparable to any of the other forces acting on the lithosphere. The results of stress modeling were improved by the finite element modeling technique and a finer grid (Richardson, 1978; Richardson and Solomon, 1979) showing that ridge-push was required for all models which matched the stress data.

Drag forces that were resistive could fit the data, while driving drag force models did not correlate with the

stress data. , Viscous stress modeling of the global set

Of plates by Richardson (1982, 1983) indicated that ridge-push may be the most important plate-driving force on the basis of predicting the direction and rate of rela­ tive plate motion, while the effective force of slab-pull may be less than half the ridge-push. In this thesis, new ways of modeling ridge-push and slab-pull forces are applied to elastic models of the Nazca plate, and the effects of a viscous rheology are also tested. The Nazca plate is ideal for stress modeling be­ cause it is a small oceanic plate with nearly comparable lengths of both ridge and trench boundaries. The size is important because a small sized plate economically allows detailed modeling with a fine grid* Oceanic plates are easier for modeling stresses than continental plates because oceanic lithosphere is young and relatively homo­ geneous , and is not so complicated by the preservation of past stress states. The section which follows this introduction in­ cludes a detailed description of the Nazca plate bound­

aries and intraplate features. In detail the Nazca plate is surprisingly complex with, asymmetrical spreading along the ridges, and a segmented subduction zone. A fossil

spreading ridge in the middle of the plate, and the presence of several aseismic ridges and island seamount chains are potential sources of stress. This stress is modeled by distributing the ridge forces. The stress data for the Nazca plate is the sub­ ject of the third section. This data includes the set of intraplate earthquakes, extensional features along the plate boundaries, and a new kind of stress data from VLB! (Very Long Wavelength Interferometry) and lunar laser ranging techniques. The next section describes the use of the finite element method to model stress for both elastic and viscous rheologies, and is followed by a section which explains how the driving forces are calculated. These driving forces include ridge-push, slab-pull and resis­ tive drag, and other forces which are not modeled but are described such as transform fault resistance, radial push from hot spots and distant forces from other plates. Thirty different models represent combinations of the plate-driving forces and variations of the initial and boundary conditions. These models are described in section six, followed by the conclusions. Distributed ridge forces are found to be a more realistic method of modeling ridge-push than simple line ridge forces. The refined grid was found to result in nearly identical stresses to those of the coarser grid, indicating that the coarse grid, with approximately 5° grid spacing in the plate interior, is sufficient for stress modeling of the Nazca plate. Slab-pull models with age-dependence fit the stress data better than other slab-pull models. Ridge-push models without drag forces fit the data better

than ridge models which were balanced by drag forces. The viscous models with distributed ridge forces alone qualitatively matched the relative velocity data for the Nazea-South American plate boundary. However, if drag forces were added to the viscous distributed ridge model, the resulting velocities indicated non-plate-like behavior„ II. DESCRIPTION OF THE NAZCA PLATE

The Nazca plate is a small oceanic plate in the Southeast Pacific Ocean, extending southward from lati­ tude 5° N to 40° S and westward from longitude 75° W to 115° W. It is bounded by the Cocos plate on the north, the Pacific plate on the west, and Antarctic plate on the south, and the South American plate on the east (Fig. 1). The plate is squarish in shape, pinched at the north end and elongated to the southeast, with a total area of approximately 1.6 X 1 0 ^ cm'2. The thickness of the plate is not known in detail, but estimates of oceanic plate thickness based on thermal models (Parsons and Sclater, 1977) indicate a range from

essentially zero at the ridge crest to over 125 km for 80 my old lithosphere. The maximum thickness of the Nazca plate, based on a maximum age of 50 my (Herron, 1972), would be 92 km, using the following equation from Turcotte and Schubert (1982) :

Yl = 2.32. (kt)1/2 (2.1) where YL is the thickness of the lithosphere, k is the

thermal diffusivity, and t is the age. A constant thick­ ness of 50 km is used for the Nazca plate modeling. The

6 Eurasian Plate

r'N orth American Plate Juan de Fuca Plate

Caribbean Philippine Plate Arabian Plate Plate Pacific Plate Cocos Plate

African Plate \

/ South Indian Plate Nazca Plate American Plate

Transform F ault------Ridge Axis Subduction Zone Mi LI Unknown ' — Antarctic Plate

75° 90° 105° 120° 135° 150° 165° 180° 165° 150° 135° 120° 105° 90° 75° 60° 45° 30° 15° 0° 15° 30° 45° 60° 75° 90'

Figure 1. Location map of the Nazca plate (From Turcotte and Schubert, 1982) effect of doubling the plate thickness is to halve the stress magnitudes. The relative motion poles for the Nazca plate and adjacent plates, as well as the absolute motion pole in the hot spot reference frame are taken from Minster et al. (1974) and Minster and Jordan (1978) who inverted a data set of spreading rates, transform fault azimuths, and earthquake slip vectors. The 1974 plate motion models were used in previous stress modeling of the. Nazca plate by Richardson (1978) to determine the direction of plate­ driving forces. In the present stress modeling, the more recent plate motion data from Minster and Jordan (1978) were used to determine the direction of some of the forces These poles and rotation rates appear on Table 1. The Nazca plate includes significant lengths of all three kinds of plate boundary: a subduction zone or convergent boundary adj acent to South America, and spread­ ing centers and transform faults along the Other three boundaries. The length of spreading ridge along the East Pacific Rise boundary is nearly the same as the length of the South American trench, making it feasible to test the roles of both slab-pull and ridge-push forces. The plate also contains intraplate ridges, seamounts, hot spots, and two possible microplates. The Nazca plate boundaries and intraplate features are shown in Figure 2 and described below. TABLE 1„ Plate Motion Data Used in Nazca Plate Stress Modeling (from RM-2 and AMl-2 models of Minster and Jordan, 1978)

RELATIVE MOTION

Latitude, Longitude, Rate, 10 ^ Plate Pair ____ °N °e degrees/year

Nazca-Pacific 56.64 -87.88 15.39 Nazca-South America 59.08 -94.75 8.35 Nazca-Antarctic 43.21 -95.02 6.05 Cocos-Nazea 5.63 -124.40 9.72

ABSOLUTE MOTION

Nazca Plate 47.99 -93.81 5.85

When viewed from above the pole, the first named plate moves counterclockwise with respect to the second. 10

i2.ri\v 90**/ gO\J I JO w lOOiV l COCOS PLATE S' , Panama

-o*

Awrw AMCKICAlJ PLATE -|0°S

-20WS

e a Stem /nA^bCt** 1 • O " o • *_^ £4ST£f/tar -s/ter /Sl A k )J> -MTS

^ r - . .

-40*S ANTARCTIC PLATE

Figure 2. Nazca plate boundaries and intraplate features

(Numbers indicate whole rates in cm/yr. Arrows indicate direction of relative plate motion. Double lines are ridges. Dashed lines are transform faults. Solid line is trench.) 11 East Pacific Rise Ridge Boundary

The East Pacific Rise portion of the Nazca plate boundary separates the Nazca plate from the Pacific plate to the west, and extends 4,000 km south from the Galapagos triple junction at 2° N, 2° W to a poorly defined triple junction with the Chile Ridge at about 35° S, 110° W (Rea, 1981). The East Pacific Rise is spreading more rapidly than any other ridge, with a whole rate of approximately 16 cm/yr (Rea, 1981). Rea and Scheidegger (1979) observed that the East Pacific Rise spreading rates have fluctuated during the past. Also, spreading is asymmetrical south of the Garret Fracture Zone at 13.5° S, spreading faster to the east than to the west. Although variable spreading rates and asymmetrical spreading may be important to the state of stress of the Nazca plate, they have not been included in the present modeling. The East Pacific Rise has a complex topography, ascending to the south in three broad steps. The regional depth of the rise is around 2,850 m between 8° N and 4° S, ascending to 2,650 m between 5° S and 22° S. South of the Easter plate the axial depth is around 2,350 m (Rea, 1981). The axial ridge tends to deepen at intersections with offsetting fracture zones, with the exception of the

Garret Fracture Zone (Fig. 3). This complex ridge topog­ raphy is an indication that the constant force per unit EAST PACIFIC RISE

2200 2200

2400 Easter 2400 Plate

2600 ■ 2600

2800 • 2800

3000 3000

Figure 3 Topography along the East Pacific Rise Ridge Boundary (after Rea, et al, 1979) 13 length for ridge forces assumed by Richardson (1978) was an oversimplification. The present East Pacific Rise portion of the Nazca-Pacific plate boundary is young, and began forming in Late Oligocene by three large westward jumps from the now fossil Galapagos Rise. The jumps covered a distance of 900 km, spanning a time period of 2.5 my, and coincid­ ing with similar adjustments involving the Mathematician's Ridge at 5° N to 20° N, and the opening of the Gulf of California (Anderson and Sclater, 1972). This realignment may have arisen because of the breakup of the Farallon plate and/or complex interactions of the East Pacific Rise with North America (Anderson and Sclater, 1972). Since we are dealing with a single plate in this modeling, stresses from outside the Nazca plate boundaries are ignored. How­ ever , stress resulting from the elevation of the fossil Galapagos Rise above the surrounding sea floor, as well as variations in stress resulting from the complex topog­ raphy of the East Pacific Rise will be included in this new modeling.

Galapagos Spreading Center Ridge Boundary

The Galapagos Spreading Center, also called the

Cocos-Nazca Spreading Center, is an asymmetrical, moderate- velocity spreading center which extends from the Galapagos triple junction on the west, to the Panama,Fracture Zone 14 at 83° W,along one large and three smaller ridge segments offset by transforms (Fig. 2). The spreading rate along the Galapagos Ridge was very rapid in the past, with a whole rate of 14 cm/yr, but now is spreading at a moderate 6 to 7 cm/yr (Hey et al., 1977). Scheidegger et al. (1981) claim that most of the older crust of the Nazca plate was formed at the Cocos-Nazca Spreading Center. Recent accre­ tion on the center is asymmetrical, with more material added to the Cocos plate than to the Nazca plate (Hey

et al., 1977) The Galapagos Spreading Center is not a simple spreading ridge, but can be divided into four different regions (Johnson et ad., 1976), The western segment, located between the Galapagos triple junction and 98° W, is very rugged and has a rift valley characteristic of slow spreading ridges. The central portion, between 98° W and the Galapagos Plateau, has moderate relief and no well developed rift valley. The Galapagos Plateau is

an elevated region which may be entirely of Pleistocene age (Johnson and Lowrie, 1972) and contains the Galapagos hot spot, and several box-shaped depressions which may

be submarine canyons or grabens. The fourth segment is the eastern Galapagos Spreading Center, which has a rela­

tively subdued relief, no rift valley, and may represent a recent axial shift to the south (Johnson et al., 1976). The stresses resulting from these complexities cannot be 15 modeled with simple line ridge forces, but are modeled with distributed ridge forces.

Chile Ridge Spreading Center and Transforms

The Chile Ridge boundary extends from approxi­ mately 35° S, 110° W, to the Chile Margin triple junction at 46° S, 76° W (Herron et aT., 198]). The Chile Ridge was not recognized as a major plate boundary in early papers because the area was remote and the data were sparse (Herron et al., 1981). Most of the west side of this boundary consists of transform faults, with rugged relief. The east side is almost a single ridge segment with low bathymetric relief superimposed on a gradual increase in depth away from the ridge crest (Klitgord et al., 1973). The Chile Ridge may be a remnant of the former Galapagos Rise (Klitgord et al., 1973). The whole spreading rate along the Chile Ridge has averaged 5.6 cm/yr over the past 700,000 yr, slowing from a previous rate of 11.2 cm/yr before 5.12 my B.P. (Herron et al.,

1981). Herron et. al. (1981) studied the collision of

Chile Ridge with the subduction zone at the Chile Margin triple junction. Continental seismic activity stops

60 km north of this triple junction and there is a gap in volcanism landward from the triple junction north to the intersection with the fracture zone at 49 S (Herron et al., 1981). This is also within the region which slipped during the 1960 Chilean earthquake, the largest earthquake ever recorded (Ms =8.3, Mw = 9.5; Kanamori, and Cipar, 1974; Kanamori, 1978). The Chile Ridge col­ lided with the subduction zone 300,000 years ago, but the spreading process does not appear to have been modi­ fied by proximity to the subduction zone (Herron et al., 1981). However, this may have affected the stresses within the adjacent South American plate.

South American Trench Boundary

The subduction zone between the Nazca plate and the South American plate is divided into two sections, separated by the Grijalva Scarp (Fig. 4). The northern trench extends southward from the Panama Isthmus to the

Grijalva Scarp, near 4° S, and is much shallower than the Peru-Chile Trench to the south. The entry of the Carnegie Ridge into the subduction zone during the past 3 my may have shoaled the trench off Ecuador, which has a minimum axial depth of only 2,920 m (Lonsdale1978) . The Ecuador Trench is subducting younger (less than 27 my old) lithosphere from the Cocos-Nazca Spreading Center, while the Peru-Chile Trench is subducting litho­ sphere up to 50 my old originating from the fossil

Galapagos Rise (Lonsdale, 1978). 17

is’ go° 7«r 70° Lf* iV

5£T6 m e /v r SOUTH p£^u AMERICAN) SEGMENT PLATE

N orth CHILE Segment 30*

N AZ_CA P late.

Figure 4. Segmentation of the South American Subduction Zone (After Barazangi and Isacks, 1976) O "

'■ 18 The northern subduetion zone is very complex because of the proximity of active and extinct ridges, transforms, and possible hot spot traces to the trench. Pennington (1981), using seismicity data, divided this subduction zone into three segments: the Bucaramanga segment in the north, and the Cauca and Columbia-Ecuador segments to the south. There may be a tear between the Bucaramanga segment, which is dipping at a 20 to 25 degree angle, and the other two segments, which are dipping at

35 degrees (Pennington, 1981). Because of the complexity of this region, and its small area relative to the rest of the Nazca plate, only the Ecuadorean segment was in­ cluded in the stress modeling. This segment is moving obliquely with a rate of 9 cm/yr (Lonsdale, 1978). The Peru-Chile Trench extends from 4° S to 45° S, and subduction between the Nazca plate and the South American plate is occurring at around 9 cm/yr (Minster and Jordan, 1978). Barazangi and Isacks (1976, 1979) attributed the transition from the flat Peru segment to the steeper North Chile segment to a major tear in the descending Nazca plate, basing their argument on first motion studies of P waves. Hasegawa and Sacks (1981) argue on the basis of ScSp observations that instead of a tear, there is contortion in the shallow Peru segment.

They argue further that the Peru segment dips initially at an angle of 30 degrees, then bends below 100 km, where 19

it then subducts nearly horizontally. Whether a tear or a contortion, the lengths of the slab segments seem to be different, and the tectonics of the Andes Mountains show the same segmentation as the Nazca plate slab (Jordan et al., 1983). Schweller et al. (1981) observed five morphotec- tonic provinces along the Peru-Chile Trench, from a data set of over 200 bathymetric profiles, showing distinct changes in tr&nch depth, axial sediment thickness, exten- sional fault structures, and dip of the seaward trench. These provinces are similar to the angle-dependent seg­ ments of Barazangi and Isacks (1976). Grellet and Dubois (1982) found a correlation between the rate of subduction, the age of the subducting slab, and the depth of the trench

Increasing subduction rate and older lithosphere both correlate with deep trenches. This correlation was con­ sistent with either elastic or viscous rheologies for the oceanic lithosphere (Grellet and Dubois, 1982). The age of the subducting slab varies from as young as 12 my at the north end, to a maximum of 50 my

in the middle, and becoming as young as 3 my at the south end near the Chile Margin triple junction. Age affects the thickness and density of the subducting slab (Wortel

and Vlaar, 1978; Wortel and Clotingh, 1981) and young

lithosphere may be less dense than the mantle into which it is being driven, causing shallow dip angles (Sacks et al., 1978). Other factors which may contribute to the complexity of the South American subduction zone are the subduction of buoyant aseismic ridges and seamount chains (Vogt et al., 1976; Pilger, 1981) and the curvature of the South American subduction zone (Rodriguez et al., 1976). The possible contributions of slab age and slab dip angle will be considered and evaluated in the slab- pull stress modeling.

Intr aplate Feature s

In addition to the plate boundaries, the Nazca plate has several other important geologic and tectonic features: possible hot spots, microplates, several aseismic ridges, a fossil ridge, and island seamount chains (Fig. 2). At least two hot spots or mantle plumes have been proposed for the Nazca plate, one in the Galapagos Islands and one either west of or beneath Easter Island (Johnson and Ldwrie, 1972; Pilger and Handschumacher, 1981). Hot spots are thought to be narrow plumes of mantle material which rise and spread radially in the asthenosphere. As oceanic plates move over the hot spots, basaltic volcanism occurs, forming linear aseismic ridges (Johnson and Lowrie, 1972). The hot spots could locally affect the state of stress in the Nazca plate by a variety of mechanisms, including the heating of the plate. However, in terms of this paper, only the effect of the elevation of these regions has been included in the distributed ridge models discussed below.

The Nazca plate also has two regions described as possible microplates. The Easter plate and the Panama plate are complex regions along the East Pacific Rise and Cocos-Nazca Spreading Centers, respectively. The Easter plate is a small 3.2 my old plate defined by seismic, magnetic and bathymetric data. There are two active spreading centers along the east (Este) and west (Oeste) boundaries, and active fault zones along the north and south borders (HandSchumacher et al., 1981). The Este Ridge is more active, spreading at greater than 13 cm/yr, while the Oeste Ridge is spreading at less than 2 cm/yr (Engeln and Stein, 1983). This may lead to the future "capture" of the Easter plate by the Pacific plate (Handschumacher et ad., 1981). In the present modeling, the Easter plate has been treated as part of the Nazca plate. The Panama platelet (Lonsdale and Klitgord, 1978) is bounded by the Panama Fracture Zone, the South American and Cocos plates, and some poorly defined boundary between the Carnegie and Malpelo Ridges. The platelet encompasses part of the thick sediment filled Panama Basin, which dis­ plays many extensional features (Van Andel et al., 1971). 22 The now seismically active transform at 83° W, the Panama Fracture Zone, may have recently jumped westward, detach­ ing the region from the rest of the plate (Van Andel et alo, 1971? Lonsdale and Klitgord, 1978; Pennington,

1981). In modeling the Nazca plate, this platelet is not included because of its complexities, poorly defined boundaries, and small size relative to the Nazca plate. The Galapagos Rise, a fossil ridge in the middle of the Nazca plate, extends from near 15° S to 30° S . It is elevated up to a kilometer above the surrounding sea floor (Hammerickx and Smith, 1978). The East Pacific Rise spreading jumped from the Galapagos Rise and became active 6.5 my B.P. However, the Galapagos Rise may have continued spreading after the jump, up to 4 my B.P., so that the two ridges were both active for a period of over two million years (Anderson and Sclater, 1972). Aseismic ridges, which include the Nazca Ridge and the Cocos Ridge, may have been formed syncronously with adjacent sea floor at the mid-oceanic spreading centers (Pilger, 1981). These are continuous features, unlike island seamount chains such as the Juan Fernandez and Easter Island seamount chains, which are discontinu­ ous and may have been formed by thermal anomalies (Pilger, 1981). The subduetion of these possibly buoyant ridges and islands may be responsible for shallow dips and the segmentation of the subduction zone (Pilger, 1981; 23

Pennington, 1981). In the present modeling, the effects of the elevation of the ridges and islands are considered in the distributed ridge models. III. STRESS DATA

The stress data for the Nazca plate consists of the record of intraplate earthquakes (Pig. 5). One of these occurred on November 25, 1965 with a magnitude (m^) of 5.75, located at 17.1° S, 100.2° W. Mendiguren (1971) used both body and surface wave data to determine the source mechanism. The analysis indicated nearly east-west maximum horizontal compression. Two earlier earthquakes were recorded in 1944 and the first motion studies of the P waves were consistent with the mechan­ ism solution of the 1965 earthquake. The location of these earthquakes is shown on Figure 6. Bergman and Solomon (1980) studied 159 oceanic earthquakes to determine their association with large bathymetric features and pre-existing faults. They con­ cluded that large earthquakes are often associated with old zones of weakness which appear to be reactivated by the present stress field. One earthquake (m^ of 5.0), located along the Nazca Ridge at 21.3° S, 82° W, occurred on December 8, 1964. Bergman and Solomon (1980) sug­ gested that the Nazca Ridge may be a weak zone, but that the bathymetry may also be contributing to the stresses. The November 25, 1965 earthquake occurred on the

24 25

IlFw U 0*« 105*M IOO'm 9^ MAGNITUDE o 0.00 M 3.99 X 3.99 It 9.99 A 9.99 It 9.90

Figure 5. Distribution of intraplate earthquakes in the Nazca plate recorded between 1901 and 1981 (Earthquake epicenter map is from NOAA) 26

COCOS

PACIFIC

S. AMERICA

NAZCA

ANTARCTIC

Figure 6. Location of the 1965 and 1944 intraplate earthquakes (Plate boundaries are defined by earthquake epicenters; boundaries are as described in Figure 2. Arrows indicate orientation of hor­ izontal compression axis inferred from the focal mechanism of the 25 November 1965 earth­ quake. The segment of the Peru-Chile trench boundary that failed during the 22 May 1960 earthquake is hatched. After Richardson, 1978.) southwest flank of the Galapagos Rise, near the Mendana Fracture Zone, and Bergman and Soloman (1980) suggest that this earthquake was responding to the stress field of the East Pacific Rise. The epicenter of another Nazca plate earthquake, recorded on May 28, 1972 (m^ of 4.9) was located at 32.78° S, 92.2° W, just east of the

southernmost trace of the fossil Galapagos Rise (Fig. 6), Because of its small size, there has been no attempt to determine a fault plane solution. Studies of oceanic intraplate earthquakes world­ wide indicate that oceanic lithosphere older than 20 my is under deviatoric compression (Sykes and Sbar, 1973; Wiens and Stein, 1983). Most of the Nazca plate east of the 1965 and 1944 earthquakes is older than 20 my, and so might also be in a compressive state of stress. The number of intraplate earthquakes per unit area of oceanic floor and per unit volume of lithosphere decreases with

lithospheric age (Wiens and Steip, 1983) indicating that

stresses might be greater in younger lithosphere hot too distant from the spreading ridges. A recent study by Hilde and Warsi (1983) claims that the Mendana Fracture Zone near 10° S is undergoing rifting with the creation of new oceanic lithosphere at the subduction zone. They suggest that the Nazca plate may be undergoing, extension in this region in response to subduction-induced stresses along a zone of weakness. 28 which may lead to the separation of the entire Nazca plate in 35 my. Another region of extension is the Panama Basin, in the northeast corner of the Nazca plate (Van Andel et al. , 1971) . A new kind of stress data from VLBI (Very Long

Wavelength Interferometry) and lunar laser ranging is being accumulated (Bender et al., 1979; Smith et al., 1979; Allenby, 1979; Clark, 1979; Niell et al., 1979). This new data has the potential to measure distances between widely separated stations with an accuracy of centimeters. Relative plate motions and internal defor­ mation of plates could be measured on time scales of years or less. The Goodard Space Flight Center has developed a highly mobile satellite laser tracking system called TLRS2 (Transportable Laser Ranging System) which arrived on Easter Island in early January, 1983, and began routine

tracking in March of 1983. The station is going to col­ lect data for six months, be moved to a new site, then return annually to Easter Island to measure baselines between the Nazca plate and the Pacific and South American plates (Nasa, 1983). Permanent stations are located at

Arequipa, Peru and Maui, Hawaii. Stress modeling of the Nazca plate will be valuable for evaluating this new data

and for possibly guiding the location of future data

collection stations. 29 The choice of model rheology and plate thickness can be constrained by experimental data from rock defor­ mation studies (Kohlstedt and Goetze, 1974; Kirby, 1980). Kirby (1980) observed that the maximum strength of the lithosphere is reached at some critical depth, and that below this depth strength falls off rapidly due to increas­ ing temperature. The strength maximum increases in both magnitude and depth with increasing age of lithosphere, and the strength distribution is strongly influenced by the state of stress. Except for lithosphere less than 2.5 my old, the elastic strength of oceanic lithosphere is predicted to be in the kilobar range (Kirby, 1980). The effective elastic thickness varies from 2 to 54 km, based on studies of the flexure of oceanic litho­ sphere (Watts et al., 1980). Further, oceanic lithosphere appears to be able to support stresses of at least a kilo- bar for long periods of time (Watts et al., 1980). The Nazca plate is here modeled as an elastic plate 50 km thick. An elastic lithosphere of 50 km would have stresses twice the magnitude of the stresses of 100 km thick litho­

sphere, but the distribution of stresses would be the same. Thus, the choice of model thickness does not affect the results of attempting to fit the orientation of the Nazca

intraplate earthquake data, or a general sense of compres­ sion or extension in any region of the plate. IVo DESCRIPTION OF MODELING METHOD

The Nazca plate is modeled as a linearly elastic medium, using the displacement method of finite elements in which all external loads are balanced by internal strains (Zienkiewicz, 1971; Bathe and Wilson, 1976). The plate is divided into a discrete number of regions of finite area (elements), connected at a finite number of points (nodes). The displacements of the internal points within a given element are approximated by some polynomial function of the nodal displacements„ The dimension of the matrix of polynomial functions is determined by the number of degrees of freedom (coordinate directions of displace­ ment) at any point and the total number of degrees of freedom for an element. Therefore the necessary calcula­ tions are simplified by minimizing the number of nodes per element and the number of degrees of freedom per node.

The Nazca plate model is made up of constant strain triangular elements with two in-plane degrees of freedom per node, in the latitudinal and longitudinal directions. Therefore, there are six degrees of freedom per element. In addition to decreasing the number of degrees of freedom needed to solve the problem, the con­ stant strain triangles are also a good choice of element 30 31 because they can approximate displacements on a sphere while still retaining their planar geometry, since three points on a sphere define a plane„ Any other kind of element would lead to a less satisfactory approximation to a sphere. The elements can be visualized as triangles situated on a sphere, with springs between the nodes (Fig. 7). The triangles are deformed as a result of forces applied to the nodes.

Elastic Modeling

Strain at any point in the element can be deter­ mined from the displacements of the node points. Element stresses can then be found from stress-strain relation­ ships. For a two-dimensional isotropic elastic medium in a plane state of stress, Hooke's law leads to the follow­ ing relationship between stress and strain (Zienkiewicz,

1971) : 1 V 0 511 G11 v 1 0 a22 522 0 0 1—v 512 012 2

(4.1) where o^j is the stress, is strain, E is Young's Modulus, v is Poisson's Ratio, and [C] is the elasticity matrix. MODES

Figure 7. Triangular elements on a half-sphere 33

For each constant strain triangular element, the two displacement degrees of freedom, and , for an

interior point in the element, are functions of the six nodal degrees of freedom. A strain operator matrix [B] is computed for each element. This matrix depends on the geometry and area of the element, including the rela­ tive difference in nodal locations. A stiffness matrix [K] is then calculated for each element as (Zienkiewicz, 1971) :

[K.] = [C\] [B^] h dxdy (4.2)

area where h is the element thickness. The local element stiffness matrix [K^] can then be transformed into the global coordinate system and added to a global stiffness matrix [K]. The equilibrium condition for a finite ele­ ment approximation to an elastic medium is (Zienkiewicz, 1971):

[K] {U} = {F} (4.3)

The solution of the equation for displacements leads to:

{U} = [K]"1 {F} (4.4)

where {U} is the vector of unknown nodal displacements, and {F} is the vector of all equivalent nodal loads.

The inputs to any problem are thus the elastic properties, 34 the geometry of the grid, and any forces acting on the system. The solution of Equation 4.4 used here incorporates the Wave Front solution technique of Irons (1970) and Orringer (1974). This technique is based on Gauss elim­ ination, and trades external computer storage and core space off against each other. A Certain number of degrees of freedom are assembled, sent to storage, and later re­ trieved for further calculations. The maximum number of degrees of freedom required at any one time in in-core storage is called the front width and depends on the ele­ ment numbering scheme. The front widths for the coarse and fine grids for the Nazca plate were 30 and 42 respec­ tively. The first grid used for modeling the Nazca plate was modified from one used by Richardson et al, (1979) for global modeling. The modifications included a better fit to the plate boundaries from two bathymetric maps of the Southeast Pacific Ocean (Mammerickx and Smith, 1978; A.A.P.G., 1981). This grid is composed of 116 nodes and 183 elements, for a total of 236 degrees of freedom (Fig.

8). For the distributed ridge models, discussed below,

elevations of node points were needed, and the grid points were moved in some cases to include the bathymetric detail that might otherwise have been missed by the grid. The 17 2 total area of this grid was 1.601 x 10 cm . #o°w

IO°S,

z o ms

30*5

4 0 mS

izo'kj no°w 90"*/ 70°U/

Figure 8. Finite element grid of the Nazca plate (coarse) (There are 183 constant-strain triangular elements with six degrees of freedom per element and a total of 116 nodes.) A finer grid was also constructed to see if it would give significantly different results for the eleva­ tion-dependent distributed ridge force models„ A grid with approximately 2-1/2 degree spacing was constructed (Fig. 9), utilizing 467 elements and 264 nodes. The 17 2 total area of this grid was 1.599 X 10 cm „ The re­ sults of the distributed ridge force models for the two grids are compared and discussed later. Elastic constants used in the modeling, appro­ priate for oceanic lithosphere, were 7 X 10"*"1 dyne-cm 2 for Young's Modulus and 0.25 for Poisson's Ratio. The finite element method allows the material properties to vary on an element by element basis. However, the mate­ rial properties of an oceanic plate are relatively homo­ geneous and there were no data which would indicate the need for ah inhomogeneous model, except possibly along the plate boundaries. An inhomogeneous model with a viscous rheology along the subduction zone boundary was included in the Nazca plate stress modeling and is dis­

cussed later. Calculated stresses represent an average across

the plate thickness, with the vertical component removed. They are, in a sense, stress differences or a kind of deviatoric stress, except that the vertical, rather than hydrostatic stress has been removed. The calculated stress represents the actual stress field if one assumes 37

u o * n n o 1 N

Figure 9. Finite element grid of the Nazca plate (refined) (There are 467 constrant-strain triangular elements with six degrees of freedom per element and a total of 264 nodes.) 38 that the material contains no memory of past stress states. In order to constrain rigid body motion, a minimum of three appropriate degrees of freedom must be constrained. One point is pinned from motion in both the latitudinal and longitudinal directions and another point is chosen so that there is no rotation about the pinned point.

- • Viscous Modeling

The oceanic lithosphere can be modeled with either viscous or elastic rheologies and still fit the data on oceanic flexure at subduction zones (DeBremaecker, 1977; Grellet and Dubois, 1982). The major advantage of viscous modeling is the ability to include the data set s ■ on present-day relative plate motion as well as the data on intraplate stress as constraints on the driving mechan­ ism. The viscous equations are homologous to the elastic

equations where stress is related to strain rate by the material property of viscosity. The viscous equation:

aij = ^ ^kk + 2 v ^ij ^4,5) where ^ is the stress, £ is bulk viscosity, £ is the shear viscosity, and is strain rate, and be solved in the same way as the elastic equations by using appropriate,

values for the shear and bulk viscosities. Thus, if you have solved an elastic problem in terms of the Lame con­ stants e and p for unknown displacements, you have also solved the equivalent viscous problem in terms of the viscous constant %■ and p for unknown velocities.

The volumetric strain rate 4 ^ must be zero for an incompressible Newtonian fluid. This can be accom­ plished if the bulk viscosity £ becomes infinite. Thus, for

_ E V ! A e “ (1+v) (l-2v) V ° a Poisson's ratio of 0.50 fulfills this requirement of incompressible fluid flow. The viscosity of the litho- 24 sphere is on the order of 10 P (deBremaecker, 1977), and appropriate values for Young's Modulus are chosen to achieve this viscosity. The subduction zone is modeled with a viscosity which is a factor of 20 lower than the rest of the plate. V. MODELING PLATE-DRIVING FORCES

The plate-driving forces are not well understood, but attempts to model the forces, and then match the re­ sulting model stress states or plate motions with actual observations, have shown that the three most significant forces seem to be ridge-push forces, slab-pull forces, and drag forces along the base of the plates (Forsyth and Uyeda, 1975; Chappie and Tullis, 1977; Richardson, 1978; Richardson et al., 1979; Carlson, 1981). These forces are illustrated in Figure 10. The methods of modeling these three major forces for the Nazca plate are discussed below, followed by a brief description of other potential forces acting on the plate.

Ridge-Push Forces

Ridge-push forces arise from horizontal density differences resulting from thermally induced elevation and thickness variations throughout the oceanic litho­ sphere. The lithosphere thickens as the cooling iso­ therms descend deeper into the mantle (Hager, 1978). The oceanic lithosphere then sinks to compensate for the thickening, and the depth of the sea floor increases with the age of the lithosphere (Sclater and Francheteau,

40 Figure 10. Plate-driving forces acting on the Nazca plate

(Fr and Ft are forces per unit length of ridge and trench, respectively, acting in the direction of relative plate motions; Fp is drag force per unit area, resisting the motion of the other forces; V is fixed so that torques due to Fr and FT are balanced by drag forces. From Richard­ son, 1978.)

H 42 1970; Parsons and S.clater, 1977; Hager, 1978) „ The follow­ ing equation describes the variation in lithospheric thick­ ness due to cooling from Parsons and Sclater (1977):

h = 2 (kt)1//2 erf-1 (Tj/1^) (5.1) where h is the lithospheric thickness, k is the thermal diffusivity, t is the age of the lithosphere, is the temperature of the lithosphere, and Tm is the temperature in the mantle. Parsons and Sclater (1977) also describe the variations in the depth of the sea floor for young oceanic lithosphere (less than 70 my old) by the follow­ ing equation:

d = 2500 + 350 t1//2 (5.2) where d is the depth of the sea floor. The variation in sea floor depth resulting from isostatic compensation

is given by Hager (1978) :

dt = db / ((Pi - Pw)/(pl " pm )) (5.3)

where d^_ is the depth to the top of the lithosphere, d^

is the depth to the bottom of the lithosphere, and p^, p , and p are the densities of the lithosphere, sea- . w m water, and mantle respectively. If isostatic compensation is assumed, the hori­

zontal mass difference from the change in depth of the base of the lithosphere is equal to the horizontal mass 43 difference from the changes in elevation of the sea floor (Hager, 1 •fe}. Numerical modeling of mantle flow by Hager (1978) and Hager and O'Connell (1981) shows that these ridge-push forces may be more important than slab- pull forces. This theory is supported by previous stress modeling by Richardson (1978) where models with predom­ inately ridge-push forces matched the stress data better than models with predominately slab-pull forces. The horizontal ridge-push forces, perpendicular to the ridge crest, are analogous to glacier flow (Frank, 1972) and give rise to compressive stresses in the litho­ sphere which decrease close to the ridge crest, diminish­ ing to zero at the ridge crest. Lister (1975) describes this force as:

FR = 1/2 h 1 g (P]L - pw ) (5.4) where FR is the horizontal ridge-push force, h is the drop in height from the ridge crest reference height, 1 is the lithospheric thickness, g is the gravitational constant, and p, and p are the densities of the litho- ^1 ^w sphere and seawater, respectively. The ridge-push force can also be quantified using thermal and time parameters as (Parsons and Richter,

1980):

(5.5) FR = 9 “ pm Tm k t 44 where a is the volume expansion coefficient, is the mantle density, k is the thermal diffusivity, is the temperature of the mantle, and t is the age of the litho­ sphere. Parsons and Richter (1980) show that this driving force is proportional to the geoid anomaly associated with the ridge. Estimates of the magnitude of this ridge-push force per unit length of ridge, utilizing thermal models, range from 1 to 5 x 10 15 dyne/cm, averaging between 100 and 500 bars across a 100 km thick plate (Forsyth and Uyeda, 1975; Lister, 1975; Chappel and Tullis, 1977; Richardson, 1978). An independent calculation of ridge- push force from distributed ridge forces on the Nazca plate will be described below, and the magnitude will be compared with the estimates from thermal models. Previous finite element stress modeling of the Nazca plate by Richardson (1978) utilized a constant force 15 per unit length of 1 x 10 dyne/cm along the ridge bound­

aries in the direction of relative plate motion. These directions were taken from the RMl model of Minster et al.

(1974). This kind of ridge-push modeling will be referred to as line ridge force, and is adequate as a first approxi­ mation of ridge-push forces. However, line ridge force models have three weaknesses. For the region near the ridge crest the horizontal compressive stresses due to the ridge-push do not decrease in the model, while they 45 would decrease in reality. Secondly, there should be force contributions from regions of elevated topography within the Nazca plate, such as the fossil Galapagos Rise and the aseismic ridges and island seamount chains. Potential forces from these elevated regions are not included in the line ridge force models. Finally, the ridge force itself should be distributed over the entire area of the plate, rather than concentrated at the ridge crest (Hales, 1969? Lister, 1975? Hager, 1978). A new way of modeling ridge-push, by distributing ridge forces due to topographical gradients, was developed in order to improve the ridge-push stress modeling. Dis­ tributed ridge forces as well as line ridge forces were first applied to a test case, and the resultant stresses of the two types of forces were compared. In the test case, a strip of elements 2,000 km long, 100 km wide, and

100 km thick was used to approximate a 100 km segment of ridge crest pushing across 2,000 km of plate (Fig. 11). The right side of the strip was pinned to approximate the behavior of a subduction boundary in between major seismic slip events. The topographic gradient from the ridge crest to the abyssal sea floor was calculated from the depth equation (Eg. 5.2) for young ocean floor described above (Parsons and Sclater, 1977). The distributed ridge forces were then computed for each element from the follow­ ing equation: *400-* Km

Figure 11. Test case for comparing distributed ridge and line ridge forces 47

FDR = Ap 9 a h (sin 0) (5.6) where FDR is the distributed ridge force for the element,

Ap is the difference between the lithospheric and seawater densities, a is the area of the element, h is the thick­ ness of the lithosphere, and 0 is the angle of the slope of the bathymetry. The total force applied to the line ridge test case was the same as the total force applied to 23 the distributed ridge test case, 2 x 10 dyne, equivalent 7 2 to a stress of 5 x 10 dyne/cm , or 500 bars over the 100 km thickness. Stresses resulting from the two cases were differ­ ent. For the line ridge force case, the stresses were compressive and equal in magnitude for all of the elements. For the distributed ridge case, the stresses were also com­

pressive, and were equal in magnitude to the line ridge stresses on the non-elevated portion of the strip, approxi- 8 9 mately 6.5 x 10 dyne/cm . However, the magnitude of the

stresses on the ramped portion of the strip decreased 8 2 toward the ridge crest, from 6.5 x 10 dyne/cm to 6.6 x 10 7 dyne/cm 2 , nearly an order of magnitude decrease in stress. Therefore, the two cases resulted in identical stresses for regions with no topographic relief far from the ridge, but the distributed ridge force resulted in a better approximation of stress near the ridge crest and in areas of relief away from the ridge crest. Distributed Ridge Forces Applied to the Nazca Plate

The nodal elevations for the Nazca plate were taken from a bathymetric map of the Southeast Pacific Ocean (Mammerickx and Smith, 1978). A computer sub­ routine was used to calculate the dip of each element and to apply a force in the direction of dip to each element which was proportional to the dip angle and the area of the element (Eg. 5.6). In other words, the force is due to the weight of the element and the sine of its topo­ graphic gradient. The force was distributed equally between the three nodes of each element. If the element had no slope, there was no force applied to its nodes. Also, if any nodes were pinned, no forces were applied to the pinned nodes. These distributed ridge forces are plotted on Figure 12. A comparison with a bathymetric map of the data verified that angles and magnitude of forces corresponded with topographic gradients.

Line Ridge Forces Applied to the Nazca Plate

In some models, line ridge forces were applied to nodes along the ridge boundaries, proportional to the length of ridge associated with the nodes. The direction of the force is the direction of relative plate motion of

the corresponding plate pairs from Minster and Jordan

(1978; Table 1). The force for each node was computed 49

Figure 12. Distributed ridge forces on the Nazca plate

(The arrows originate at node points and are proportional to the topographic slope of each element. The actual forces are also propor­ tional to the area of each element but the vectors presented here have been normalized to show the slope direction.) 50 as a product of the sum of the half-distances between adjacent nodes and 1.00 x 10‘L dyne/cm, making the force constant per unit length of ridge crest, equivalent to 200 bars across a 50 km thick plate. The distance between nodes was computed by first converting the node location to xyz (cartesian) coordi­ nates : x = cos (lat) cos (long)

y = cos (lat) sin (long) (5.7) z = sin (lat)

The arc-cosine of the dot product for the position vectors of the two node points gives the angular distance between the nodes. To input the force in the direction of lati­ tude and longitude, the following steps were taken. First, the relative velocity in the xyz coordinates for each node point was computed by finding the cross product of the position vector of the node point and the pole of relative motion. These relative velocity vectors, V^., V^., and Vg, were then converted to latitudinal and longi­ tudinal vectors, u^at and u^on, according to the follow­ ing relationship:

Ulat ^ -Vx cos (lon.g)°sin (lat) -V sin (long) sin (lat) + Vz cos (lat) (5.8)

J^on = V cos (long) - sin (long) 51 The velocity vector, (Ulat, ) was first normalized to unit length, then multiplied by the sum of the half­ distances belonging to each node, and scaled so that the

average stress across the plate was 100 bars„ The force vectors for the line ridge forces are shown on Figure 13 =

Slab-Pull Forces

Slab-pull forces are primarily derived from gravitational or negative buoyancy forces resulting from the entrance of a cold dense oceanic lithosphere into a hot, less dense mantle. This negative buoyancy force is described by McKenzie (1969) and Davies (1980) to be:

FT = g a Tm p2 h3 Cp V (sin 0)/(24 K) (5.8) where a is the thermal expansion coefficient, p is the density of the slab, H is the thickness of the slab, C is the heat capacity, v is the veolocity of subduction,

0 is the dip angle of the slab, and K is the thermal con­ ductivity. This force is enhanced by the thickening of the lithosphere near the trench due to the cooling effect

described above under ridge-push forces. The slab-pull forces may also receive a contribution from two major pressure-induced phase transitions in the mantle, one from

olivine to spinel at 350 to 400 km depth, and the other from spinel to post-spinel at 650 km depth. The olivine- spinel transition is elevated in the descending slab, 52

Figure 13. Line ridge forces applied to the Nazca plate (Vectors originate at nodes along spreading ridges and are applied in the direction of relative plate motion, proportional to the length of ridge segment belonging to each respective node.) 53 contributing a significant force to the total slab-pull forces (Schubert et al., 1975). If these slab-pull forces are transmitted to the surface plate, then slab-pull has the potential to be the dominant plate-driving force. While ridge-push forces are On the order of 100 bars across a 100 km thick plate, those predicted for slab-pull are on the order of kilobars (McKenzie, 1969; Smith and Toksoz, 1972; Chappie and Tullis 1977; Davies, 1980). Resistive forces due to friction may significantly reduce the pull of the slab and may be as great in magni­ tude as the gravitational forces pulling the slab (Forsyth and Uyeda, 1975; Chappie and Tullis, 1977; Davies, 1980). The record of large magnitude earthquakes along the sub- duction zone is evidence for the resistance to plate motion at the trench. Since the forces acting on the surface plate are the sum of a slab-pull and slab resistance term, the resulting net slab-pull may well be of the same magni­ tude as ridge-push forces, between 100 and 500 bars for a 100 km thick plate or up to a kilobar for a 50 km thick plate. The South American subduction zone, described earlier, is very complex, with large variations in both age and dip angle of the subducting slab. The dip angle might have a significant effect on the slab-pull force, since a smaller dip angle would decrease the component 54 of the negative buoyancy force acting down-dip along the

slab, as well as increasing the friction between the Slab and overridging plate. Therefore, the subducting slab along the South American trench would have a variable pull, and these variable forces would result in a different stress state than would result if the pull were constant along the trench. The age of the descending slab may also affect the slab-pull forces since older lithosphere is thicker and would have a greater pull (Molnar and Atwater, 1978? Wprtel and Clotingh, 1981). Age varies greatly along the Nazca plate subduction boundary, from 11 my at the north end, to 50 my near 30° S , to 3 my near the Chile Margin triple junction. This age variation would also cause a variation in stresses along the boundary and into the plate. The effects of both age and dip angle variations have been

included in the present model for the Nazca plate. Another factor which could conceivably affect the slab-pull force is the crossover depth, the depth along the slab where the stress on the slab changes from downdip tension to downdip compression (Chappie and Tullis, 1977). This crossover point should represent the depth where the deviatoric stress is zero, and would be the depth below which slab-pull forces are not transmitted to the Nazca plate. Earthquake fault solutions for the Nazca plate sub­ duction boundary do not give any clear evidence that this 55 crossover depth varies, along the Nazca plate boundary

(Isacks and Molnar, 19.71; Barazangi and I sacks, 1976 and 1979; Stauder, 1975; Chinn and Isacks, 1983)„ Therefore, the effects of variable crossover depth have not been included in the Nazca plate modeling. Slab-pull forces on the Nazca plate are modeled by applying a line force along the length of the trench, scaled in the case of constant force per unit length to l x 10 15 dyne/cm, equivalent to 200 bars deviatoric tension across a 50 km thick plate. Slab-pull forces are applied in the direction of relative plate motion between the Nazca and South American plates from Minster and Jordan (1978, Table 1). For the case of constant line force per unit length of trench, the procedure follows that of Richardson

(1978) and Richardson et al. (1979) in previous Nazca plate and global plate modeling. The forces for this case are shown on Figure 14. In addition to the constant slab-pull model, angle and age-dependent slab-pull models have also been considered. The angle dependent model forces were multiplied by the sine of the dip angle, and then scaled so that the total torque exerted was the same as that of the constant line force model. A second angle-dependent model, where the force,was multiplied by the sine squared of the dip angle, was run in order to include the added effect of 56

Figure 14. Constant slab-pull forces on the Nazca plate

(Vectors originate at nodes along the trench boundary and point in the direction of rela­ tive plate motion, proportional to the trench length belonging to each respective node.) 57 friction exerted by a smaller dip angle. These angle dependent forces are shown in Figure 15.

The age dependent model was constructed using an equation from Carlson et al. (1983), which also includes a velocity dependence:

Fc = S v t3/2 (5.9) where S is a slab force constant, v is the absolute 3. velocity of the plate, and t is the age of the lithosphere. These age dependent slab-pull forces were also scaled so that the total torque from the slab-pull force was the same as that for the other slab-pull models. The age dependent forces appear on Figure 15. The results of these various slab-pull models are discussed later.

Drag Forces

The movement of the plates over a viscous asthen- osphere may lead to drag forces which resist the plate motion. The magnitude of these forces is unknown, but may be less than a few bars (Melosh, 1977) or as great as 10 bars, depending on the velocity and area of the plate (Richardson, 1978). These drag forces may not be signifi­

cant for oceanic lithosphere (Chappie and Tullis, 1977) .

However, there will be a large net torque acting on the Nazca plate if only ridge and slab forces are modeled. If

the plate is to be in mechanical equilibrium, there must p 0® ♦ » id's * 10® 3 - p p

»'s- 20* S-

3DeS- 30® 3-

40s 3 - 40® 3 -

90® 31 30® Si U0®M 110* M lOO'H 90k H 80l H 70k H 120 M 110* M 100® M 90k W oo^h

Figure 15. a. Angle dependent slab-pull forces b. Age dependent slab-pull forces

(Force vectors originate at trench nodes and point in the direction of relative plate motion. The angle dependent forces shown here are for the sine squared of the dip angle.) 59 be some balancing forces. As discussed later, forces from distant plate boundaries and from transform faults prob­ ably do not contribute significantly to the torque balance. Thus, drag forces are a likely candidate for the source of resistive forces to balance the net torque acting on the plate. Drag forces are thus chosen to balance the total torque due to boundary forces from ridges and slabs.

The drag forces are assumed to be proportional to an absolute velocity of the plate where the pole of rota­ tion of the plate is determined by the torque pole of other boundary forces. Thus, the rotation pole need not bear any relationship to an absolute reference frame de­ fined by hot spots. A linear drag law is assumed where the force acts in a direction opposite to the absolute velocity:

FD C Vabs — Cmabs (5.10) where C is a constant, Vahg is the absolute velocity of a point on the plate with radius r and a)a^g is the ab­ solute rotation pole for the plate determined from the torque pole of the non-drag forces. The constant C is chosen so that a velocity of 1 cm/yr produces shear stress of one bar. The absolute motion poles for the models are shown on Table 2, along with the magnitude of the non-drag torque. The drag forces for one of the dis­ tributed ridge force models is shown on Figure 16. TABLE 2. Description of Nazca plate models

32 : : Ht 1 : ' ' ~ Torque x 10 Deg. Deg. Rate, 10 Deg. Deg. Model dyne/cm Latitude Longitude deg/yr Latitude Longitude Figure

DR-A 2.324 60.6 N 52.5 W 17a

DR-B 2.394 61.4 N 52.4 W —— “ --- - — — — 17b

DRD-A 2.324 60.6 N 52.5 W 2.6 33.9 N 74.4 W 18

DRD-B 2.735 63.1 N 61.8 W 3.1 32.2 N 80.2 W 19a

DRD-C 2.790 63.0 N 61.1 W 3.2 32.9 N 79.7 W 19b

*DR-A 2.295 64.0 N 66.0 W — — “ ——— 20b

*DRD-A 2.295 64.0 N 66.0 W 2.7 31.6 N 82.4 W , 21a

*DRD-B 2.743 65.3 N 70.8 W 3.1 35.7 N 83.8 W 21b LR-A 2.731 61.6 N 41.1 W — — — — —— --— 22a LR-B 2.731 61.6 N 41.4 W --— — — — — 22b

LR-C 3.629 60.2 N 59.8 W LO 1 1 ^ 1 Z0 J*3

LRD-A 3.629 60.2 N 59.8 W 16.6 N 82.9 W 24a

LRD-B 3.629 60.2 N 59.8 W 5.4 16.6 N 82.9 W 24b SD—A 3.364 66.2 N 79.7 W 3.9 32.0 N 95.8 W 25a

SD—B 3.364 66.2 N 79.7 W 3.9 32.0 N 95.8 W 25b TABLE 2— Continued

-7 Torque x 10 ^ Deg. Deg. Rate, 10 Deg. Deg. Model dyne/cm Latitude Longitude deg/yr . Latitude Longitude Figure

SD-C 3.364 66.2 N 79.7 W 3.9 32.0 N 95.8 W 26a SD-D 1.273 79.0 N 53.1 W 3.6 39.5 N 90.0 W 26 b SD-ang 3.364 64.6 N 80.9 W 4.9 19.3 N 94.8 W 27 a

SD-ang2 3.364 63.6 N 81.4 W 5.5 14.2 N 94.4 W 27b SD-AGE 3.364 65.6 N 80.1 W 4.3 26.7 N 95.4 W 28 DRSD-1 11.278 65.0 N 71.5 W 13.0 32.8 N 84.6 W 3 0 a

DRSD-2 14.587 65.8 N 77.8 W 16.9 32.7 N 87.2 W 30b

DRSD-3 17.916 66.1 N 81.9 W 20.8 32.6 N 88.9 W 31a

DRSD-4 21.256 66.3 N 84.7 W 24.7 32.6 N 90.0 W 31b LRSD-1 6.899 64.5 N 77.1 W 9.2 23.2 N 88.0 W 32a

LRSD-2 10.230 65.5 N 84.3 W 13.1 25.9 N 90.2 W 32b LRSD-3 13.577 65.8 N 88.2 W 17.0 27.3 N 91.4 W 33a

LRSD-4 16.930 66.0 N 89.5 W 20.9 28.2 N 92.2 W 33b V-DR 2.324 60.6 N 52.5 W — — — ~~ — 34a Cl V-DRD 2.324 60.6 N 52.5 W 2.6 33.9 N 74.4 W 34 b H 62

Ml

o'

10*

20*

SO*

40*

80*

Figure 16. Drag forces balancing distributed ridge forces

(The force vectors originate at the nodes. In this figure, the drag forces are balancing in the torque due to distributed ridge forces.) Transform Fault Shear Forces

Shear stress acting along transform faults would resist plate motion. This resistance is evidenced by seismic activity along the faults. Estimates of shear stresses along the San Andreas Fault by heat flow measure ments indicate a few hundred bars maximum (Brune et al., 1969). Extrapolation of in situ measurements to depth along the San Andreas by Zoback et ad. (1980) did not resolve the issue of the magnitude of shear stresses along the San Andreas, because the stress measurements could be explained by both low and high shear stress fault models. Schols et al. (1979) interpreted local thermal metamorphism and argon depletion along New Zea­ land’s Alpine fault to indicate a shear stress of at least a few kilobars. Theoretical modeling of plate motion by Forsyth and Uyeda (1975), however, showed that shear forces along transforms were hot an important part of the driving mechanism of plate tectonics. Transform fault resistance has not been included in this present modeling of the Nazca plate.

Hot Spot Forces

Hot spots may be the result of hot mantle plumes, and the forces produced by these hot spots would be 64 radially outward directed. Chappie and Tullis (1977) estimated that these forces would produce little or no net force if on a single plate. Hager and O'Connell (1981) stated that small scale density contrasts, such as would be produced by the hot spots, would not exert a significant net force. Driving forces from hot spots on the Nazca plate have not been included in the model­ ing, except to the degree that the elevation pushes on the surrounding plate for the distributed ridge models.

Distant Forces From Other Plates

There are potential forces from outside the Nazca plate, but these forces are ignored in the one plate problem. Richardson (1978) observed that ridges, being composed of hot material, do not transmit stresses well

from one side to the other. Transform faults and slab margins may transmit stresses from outside the Nazca plate, although the nature of how well they are trans­ mitted is not known. To the extent that a wide variety of slab pull models are considered, variable forces transmitted from the South American plate to the Nazca plate are at least partially considered. Transform faults have been discussed above, and since the total length Of

transform fault boundary is relatively small (except the Nazca-Antarctic boundary) they will be ignored. VI„ STRESS MODELS

The results of the stress modeling are shown on Table 2 and on Figures 17 through 35. The model names have the following meanings:

DR — ;— Distributed Ridge

DRD -- Distributed Ridge with Drag

LR -- - Line Ridge LRD -- Line Ridge with Drag SD — -— Slab Force with Drag V — ■--- Viscous Rheology

The results of varying the initial and boundary condi­ tions for each of these kinds of models are described below, followed by the results of combining various ridge and slab models.

Distributed Ridge Models

DR Models These models have a pinned subduction boundary

and no drag forces. The subduction boundary nodes are pinned in both the latitudinal and longitudinal direc­ tions to approximate the behavior of the boundary in between major stress release events. In model DR-A the 65 66 entire subduction zone (16 node points) was pinned. The total torque due to the distributed ridge forces was 32 2.32 x 10 dyne-cm. For model DR-B, the three northern­ most subduction zone nodes were unpinned. The total 3 2 torque increased slightly to 2.40 x 10 dyne-cm. The poles for this distributed ridge torque were only mar­ ginally affected by this change in boundary conditions (Table 2). The stress states of the Nazca plate for these two models are Shown on Figure 17. The only difference in the two models is that there is much less deviatoric tension in the northeast corner of the plate for model DR-B than for model DR-A. The Nazca plate can be divided into five different stress regions for the DR models. The region along the Spreading ridges shows compression oriented parallel to the ridges . A .second region is in the vicinity just west of the 1965 earthquake, where the stress is biaxial com­ pression. A third region is to the east and south of the earthquake, covering most of the interior of the plate, where northwest-southeast to east-west uniaxial compres­ sion occurs. A fourth stress region is located to the southeast, where primarily east-west and northwest-

southeast compression occurs, with a smaller secondary compression axis. And finally, the northeast and south­ west corners of the plate show deviatoric tension. •

* i <4,i— < J

/,XX' v / XX /: \\ r % XX XX x x 3 s "-O' X X

l— 1 IOC B«ur^

Figure 17. a. Stress state for Model DR-a b. Stress state for Model DR-b

(Principal horizontal deviatoric stresses are represented by arrows. Compressive stresses have no arrowheads. Deviatoric tensional stresses have outward pointing arrowheads. Tensional stresses smaller than the depicted arrowheads are not shown. Stresses are centered at element centroids and are displayed for only some of the elements for ease of viewing. See text for desription of models.) 68 The 1965 earthquake is located in an area of stress transition between two regions of different stress: biaxial compression to the west, and northwest-southeast uniaxial compression on the east. This may be a region of instability because there is a change in stress orienta­ tion and therefore is an area where earthquakes might be more likely to occur.

D.RD Models These models have distributed ridge forces and drag forces which balance the torque due to the ridge forces. In model DRD-A, the entire subduetion zone was pinned. In model DRD-B only three degrees of freedom were pinned on the subduction boundary, the latitudinal and longitudinal directions at the Chile Margin triple junction, and the longitudinal direction at the northern­ most node point. In DRD-C, three degrees of freedom were pinned in the interior of the plate, rather than along the subduction zone. The stress states in the interior of the Nazca plate for the DRD models is significantly different from the non-drag DR models (Figs. 18 and 19). The two types of models are similar to the west of the 1965 earthquake where there is biaxial compression, and along the East

Pacific Rise, where there is compression parallel to the 69

\ I i

Figure 18. Stress state for Model DRD-a

(See Fig. 17 for explanation of symbols. See text for description of models.) __JL£

& \

o I

Figure 19 Stress state for Model DRD-b Stress state for Model DRD-c

(See Fig. 17 for explanation Of symbols. See text for description of models.)

o 71 ridge. However, in the DRD models most of the plate is in a state of nearly north-south compression, with a small region of east-west compression along the subduction boundary adjacent to Peru. Deviatoric tension occurs at the northeast and southwest corners again, and in addi­ tion, there is tension in the center of the plate and in the southeast corner.

Model DRD-B differs from DRD-A in the following ways. There is more east-west tension in the middle of the plate. Also, the tension in the northeast corner is no longer present, and the east-west compression adjacent to Peru vanishes. The torque pole shifted slightly to the north and west for model DRD-B, and the rotation rate increased. Model DRD-C is practically identical to the DRD-B model, with slightly more tension in the northeast corner.

Refined Grid Models A refined grid was created to test the sensitivity of the model results to grid size. Models with the re­ fined grid are denoted by *DR. The resulting stress models below are not significantly different from those using the coarser grid. This indicates that the coarser grid is probably adequate for stress modeling of the Nazca plate and that future modeling does not need to be as detailed as the fine grid. In model *DR-A, similar to model DR-A, the subdue tion zone is totally pinned and there is no drag force.

The total torque is almost the same as for the DR models, 32 2.30 x 10 dyne-cm. The pole for the torque is slightly north and west of the coarser grid pole for model DR-A. The distributed ridge forces for the refined grid are illustrated on Figure 20. The stress state for model *DR-A (Fig. 20) is very similar to DR-A with the same five stress regions described earlier. However, the biaxial compressive region to the west of the 1965 earth­ quake in model DR-A extends eastward to longitude 90° W in the *DR-A model. Another difference is that there is less tension in the southwest corner for the refined grid model. Model *DRD-A is analogous to DRD-A with the sub- duction zone pinned, balanced by drag. The refined grid absolute velocity pole is almost 10 degrees further west than that of the DRD-A model. The rate of rotation is slightly faster for the refined grid, but the stress states of the two models are essentially identical. Model *DRD-B has three points pinned on the sub- duction zone, analogous to model DRD-B. The pole for absolute motion is further north and west than that of model DRD-B, and the rate of rotation is slightly slower. The stress states for models DRD-B and *DRD-B are nearly w ■

4 , t •' '// T 4 *- * - * » >?A fj; > 1 /|V X ! 1 f n - ;r( l* * * 4 ; ; ‘vr 9 1 1 A

Jg W / 9 I

uo* n liei" m ico'* m k* m 1*4 H• m

Figure 20. a. Distributed ridge forces for refined grid b. Stress state for Model *DR-a

(See Fig. 1] for explanation of force vectors. See Fig. 17 for explanation of stress symbols. See text for description of models.) 74 identical. The stress states of models *DRD-A and *DRD-B are shown on Figure 21.

Line Ridge Models

LR Models

The LR models have a line ridge force which is equivalent to 200 bars across a 50 km thick plate, and no drag. Model LR-A has a completely pinned subduction zone, and only the East Pacific Rise ridge forces were applied. The total torque was 2.73 x 10"^ dyne-cm, about 18 percent larger than the total torque on the distributed ridge models. Model LR-B is identical except the subduction zone is only partially pinned. For both of the models the stress state is very similar (Fig. 22) with uniform compression in the direction of plate motion, and one area of biaxial compression in the northwest corner of the plate. For model LR-B, the northeast corner becomes

north-south instead of east-west compression. In model LR-C the line forces for the Galapagos Spreading Center and the Chile Ridge were added. The torque pole shifted westward, even further westward than

the distributed ridge model torque pole. The total 32 torque increased to. 3,62 x 10 dyne-cm. The stress state did not change significantly (Fig. 23). UD* M 110* M 100 M

a. Stress state for Model *DRD-a b. Stress state for Model *DRD-b

(See Fig. 17 for explanation of symbols. See text for description of models.) Figure 22. a. Stress state for Model LR-a b . Stress state for Model LR-b

(See Fig. 17 for explanation of symbols. See text for description of models.)

-j CTi iue 3 Srs sae for stateLR-cModel Stress 23.Figure See text for description ofmodels.) fordescription textSee S eFg 1 frepaaino symbols(Seeof for 17explanation Fig. LATITUDE

77 LRD Models

The LRD models have line ridge forces at all three ridges equivalent to 200 bars, and the torque from this line ridge force is balanced by drag. Model LRD-A has a totally pinned subduction zone, and the torque pole is much further south and west than the pole for the LR models (Table 2). The absolute velocity was much slower than that of the distributed ridge models. The stress state for LRD-A (Fig. 24) differs from the LR models primarily because the east-west compression diminishes east of the 90° W longitude. Also, tension in the middle of the Chile Ridge is present. Model LRD-B has only three degrees of freedom constrained from motion on the subduction zone. This has no effect on the torque pole, but the stress state changes. The LRD-B model stress state (Fig. 24) has compression parallel to the subduction zone along the subduction boundary and tension across the Chile Ridge.

Slab-Pull Models

SD Models The slab-pull SD models have line forces along the subduction zone which average 200 bars across the 50 km thick Nazca plate, and the torque is balanced by drag forces. Model SD-rA has three degrees of freedom pinned along the subduction zone. Models SD-B and SD-C Figure 24. a. Stress state for Model LRD-a b . Stress state for Model LRD-b

(See Fig. 17 for explanation of symbols. See text for description of models.)

V£> have three degrees of freedom pinned within the plate. 32 The torque fof these models is 3.36 x 10 dyne-cm, similar to the total torque of the LR models (Table 2). The stress states for these three models are almost identical (Figs. 25 and 26), and all show deviatoric tension in the direction of plate motion from about longitude 95° W to the subduction boundary. There is also a secondary stress axis along the subduction zone, which is north-south compression. Model SD-D was run with only slab-pull along the north end of the subduction zone to see what effect this would have on the north-south compression along the southern part of the Peru—Chile trench. The compression was still present on the south end (Fig. 26), even though there was no pull on this end. This may indicate that the north-south compression is related to the geometry of the subduction zone. These models are essentially stress-free in the vicinity of the 1965 earthquake.

Angle Dependent Models The first angle dependent model, called SD-Ang, had three degrees of freedom pinned in the interior of the plate, and the forces were balanced by drag. The slab forces were multiplied by the sine of the angle of dip of the slab and then scaled so that the total torque was the same as for the SD models. The only difference Figure 25. a. Stress state for Model SD-a b. Stress state for Model SD-b

(See Fig. 17 for explanation of symbols. See text for description of models.)

H00 Figure 26. a. Stress state for Model SD-c b. Stress state for Model SD-d

(See Fig. 17 for explanation of symbols. See text for description of models.)

00 K> 83 between this model and SD-Ang2 was that the latter model forces were multiplied by the sine squared of the dip angle. These forces are shown on Figure 15. The stresses for these two models are shown on Figures 27 and 29. The stresses for SD-Ang are tensile over most of the plate east of longitude 100° W. The magnitude of the stresses are greatest in the northeast corner, in the middle of the trench, and in the southern border of the plate, responding to the larger dip angles in these sections. The two regions of shallow dip show north-south compression. The stresses on model SD-Ang2 were similar to those of model SD-Ang except there was more compression along the shallow zones because the differences in the angle-dependent forces were accentuated.

Age Dependent Model . The age dependent slab-pull model, called SD-Age, had three degrees of freedom pinned in the interior of the plate, and was balanced by drag. The total torque was scaled to that of the other slab-pull models, 3.364 x 32 10 dyne-cm. The stresses for this model are displayed on Figures 28 and 29. The stresses are entirely tensionsi, in the direction of plate motion, and are greatest between 20° and 35° S, where the slab is the oldest. There is a small component of tension perpendicular to Ml *•

Figure 27 Stress state for Model SD-ang Stress state for Model SD-ang2

(See Fig. 17 for explanation of symbols. See text for description of models.)

00 85

Figure 28. Stress state for Model SD-age (See Fig. 17 for explanation of symbols. See text for description of models.) 86

Figure 29. Composite of stress states for Models SD-c, SD-ang, SD-ang2, and SD-age (See Fig. 17 for explanation of symbols. See text for description of models.) 87 the major tensional stresses. Tension along the slab north of 10° S and south of 40° S disappears where the subducting slab is the youngest.

Combined Ridge-Push and Slab-Pull Models

DRSD Models These models combined a distributed ridge force, a slab-pull force, and were balanced by drag. Three degrees of freedom were pinned in the interior of the plate. The distributed ridge force was scaled differ­ ently from the previous distributed ridge models, a factor of .348 larger. The slab-pull forces were increased pro­ gressively from 200 bars to 800 bars in the four DRSD models. The total torque resulting from the non-drag 32 forces ranged from 11.28 to 21.26 x 10 dyne-cm. The stress states for these four models are shown in Figures 30 and 31. As expected, the west side of the plate indicates predominately compression and the east side indicates mostly tensile stresses. The region of the 1965 earthquake fits the data best for the first of these models, DRSD-1, where the forces from distributed ridge forces and slab-pull forces are nearly the same. As the slab-pull increases in models DRSD-2, DRSD-3 and

DRSD-4, the region becomes increasingly tensile, although the north-south compression remains. M» HI M f H

O'

10* s ao's

90* S

40* S

90*9 U0*M Figure 30. a. Stress state for Model DRSD-1 b . Stress state for Model DRSD-2

(See Fig. 17 for explanation of symbols. See text for description of models.)

00 CO J / ^

/j J 4 4 - ” y \

. i 1 1

\ 'its*' \ 4— ;

t ---4 ^30 3aci 1 sJ-r--- i 120* M no*M 100* N 90 M 90M 70 120 M 110” M 100” M

Figure 31. a. Stress state for Model DRSD-3 b. Stress state for Model DRSD-4

(See Fig. 17 for explanation of symbols. See text for description of models.) 90 LRSD Models

The LRSD models combined a line ridge force with slab-pull forces, balanced by drag forces. The line ridge and slab-pull forces were equal on LRSD-1, equivalent to 200 bars compressive and tensile stress respectively across a 50 km thick plate. The other three models had slab-pull forces equivalent to 400, 600 and 800 bars tensile stress combined with a line ridge force of 200 bars. The total torque from the non-drag forces for these 32 four models ranged from 6.90 to 16.93 x 10 dyne-cm, and the pole of absolute motion moved increasingly northwest­ ward, responding to the increasing pull from the slab.

The stress states for these four models are shown on Figures 32 and 33. The first of these models, LRSD-1, is dominated by the line ridge force, except along the subduction zone where tensile stresses occur. The com­ pression in the region of the 1965 earthquake is still present in model LRSD-2, with about half of the plate in compression, and the other half dominated by tension. The slab-pull forces dominate the line ridge forces in the models LRSD-3 and LRSD-4.

Viscous Models

Stresses and velocities for two viscous models were calculated using distributed ridge forces, and then compared with the relative velocity data for the Figure 32. a. Stress state for Model LRSD-1 b. Stress state for Model LRSD-2 (See Fig. 17 for explanation of symbols. See text for description of models.)

VO I-1 tv N Y

Figure 33. a. Stress state for Model LRSD-3 b. Stress state for Model LRSD-4

(See Fig. 17 for explanation of symbols. See text for description of models.)

VOKJ 93 Nazca-South American plate boundary. The first model V-DR had distributed ridge forces, no drag, and a totally pinned subduetion zone. The second model, V-DRD, had distributed ridge forces which were balanced by drag forces, with a pinned subduction zone. Elements along the subduction zone had a viscosity that was smaller than plate interior viscosity by a factor of 20. The stresses resulting from the two models are shown on Figure 34. Model V-DR is similar to the elastic DRD-A model, with the following differences. There is less tension in the northeast corner for the viscous model, and there is less compression in the interior of the plate relative to the Subduction zone. Large biaxial compressive stresses occur along the subduction zone, and the largest stresses are located in the southeast region of the plate. A line of tension crosses the plate in an east-west trend at around 23° S. The viscous V-DRD model differs from the elastic DRD-A model in the following ways. First, there is less compression along the East Pacific Rise boundary, and the compressive stress axes change orientation along the trace of the ridge. Also, in the viscous model there is a linear trend of tensile stresses between 20° S and 30° S.

A third difference is that there is more east-west compres­ sion in the northern part of the plate for the viscous case. »V IV W IV

0* - x^- \ o* - i '

>K + 10* 3 -

\ \ \ ao's- aoe 8- /

\ * 30* 3* ' 1 \ >

I \ 40*9 l------< 72.0 Baits

80 Sio *M 110* H 100* M 80l M e 1 * 70fcll

Figure 34. a. Stress state for Model V-DR b. Stress state for Model V-DRD

(See Fig. 17 for explanation of symbols. See text for description of models.)

VO The velocities for the two models are displayed on Figure 35. The data for the displacements were in­ verted to obtain the best fitting pole of rotation (Richardson, 1982). The velocity pole for the V-DR model was located at 17.8° N, 53.5° W, with a rate of 1.6 degrees per million years. The rate is not signifi­ cant because it depends on a trade-off between the magnitude of the forces and the viscosity of the plate. Increasing the viscosity by a factor of two will decrease the velocity by one-half to the observed rate of 0.8 degrees per million years (Minster and Jordan, 1978). Such an increase in viscosity is well within the uncer­ tainty of the appropriate viscosity for the lithosphere. The location of the velocity pole was over 50 degrees away from that of Minster and Jordan (1978, Table 1), indicating at best a qualitative agreement between the two poles. The velocities for the other viscous model, V-DRD, were scattered (Fig. 35) and not resolvable into a single pole of rotation, indicating that this model did not behave as a single plate. m i n M l ft

O' v ^v: / / / i jj : f id ' s 5v \ \ (v to'3 4 x\l\ \ 4\ x X\ \ \ ^ Sk >* \ \ v \ \' • ‘ ao's \ > • X* u ao's 1 • \ \ f 1 ~ r i # 4 ‘ \ \ \ ^ >» * ♦ i - 4 , - 30'3 N \ 30'3 y 4 ux 4 & y N X ' / / ‘‘ ( V x X • f 40* 3 40'3 X .* r & ♦ # * X X » ♦ •

5 0 '3 : 50'3 5 0 'N 120'H 110'N lOO'M 80* M 80*8

Figure 35. a. Velocities for Model V-DR b. Velocities for Model V-DRD

(Velocity vectors originate at element centroids. See text for description of models.) VII. CONCLUSIONS

By comparing the various stress models with each other and with the stress data, the following conclusions can be made. 1. The stress states for the distributed ridge models are significantly different from those of the line ridge models. The distributed ridge models represent an improvement over the previous models, because they are probably more realistic, reflecting several different Stress regions in the Nazca plate. There is compression in the vicinity of the 1965 earthquake, and this region is also an area of stress transition. Deviatoric tension in the northeast corner of the plate agrees with the extensional features observed in the Panama Basin. 2. The use of a refined grid, with approximately

2.5° grid point spacing, for the distributed ridge force models does not significantly change the stress state of the models. This indicates that the coarse grid, with approximately 5° grid point spacing, is sufficient for modeling distributed ridge forces on the Nazca plate. 3. The inclusion of drag forces results in very different models for both line ridge and distributed ridge models. The stresses are rotated approximately 90 degrees in both cases when drag forces are introduced. 97 98 The drag force models do not fit the stress data as well as the models without drag. This may indicate that drag forces are hot significant for the Nazca plate, or that the drag forces are more complex than modeled.

4. Age-dependent and angle-dependent models show some of the possible variations in stress along the com­ plex subduction zone. The age-dependent models are in better agreement with the proposed rifting along the Mendana Fracture Zone at around 10° S. The other slab- pull models show north-south compression in the region of the Mendana Fracture Zone, which is just the opposite orientation expected in an area which may be experiencing rifting. 5. The angle-dependent slab-pull models are in poorest agreement with the stress data for the region of possible extension near the Mendana Fracture Zone. This region is one of the shallow dipping slab segments described by Barazangi and Isacks (1976) and yet the resulting stresses are compressive parallel to the trench. Since the shallow angle stress results do not fit the data, a shallow subduction angle in this region may not be appropriate. Hasegawa and Sacks (1981) suggested that the slab is contorted rather than segmented, and that the entire length of slab dips initially at a 30 degree angle. The contortions of the slab occur at a few hundred kilom­ eters depth which is below the cross—over depth for 99 transition from down-dip tension to down-dip compression„ Therefore, a contorted slab model would have a uniform dip angle in the upper region where slab-pull forces occur. The stress results favor this contorted model over the segmented model.

6. Combination models which have both slab-pull, ridge-push, and drag forces, with increasing amounts of slab-pull fit the data best when the ridge-push and slab- pull forces are approximately equal, or when the slab- pull is at most twice the ridge-push force. This result agrees with previous stress modeling of the Nazca plate by Richardson (1978). The absolute velocities become exceedingly high as the slab-pull is increased (Table 2) but this is a function of the torque magnitude which could be scaled down. 7. The viscous models of distributed ridge forces with no balancing drag roughly agree with the relative velocity direction for the Nazca-South American plate boundary. The viscous models with drag forces result in non-plate behavior where it is impossible to obtain a single pole of rotation for the plate. This suggests that the drag forces may not be important, or that perhaps they should be modeled in a different manner. The viscous models allow expansion at the three ridge boundaries. Since the southern ridge boundary has significant amounts of transform fault lengths between the ridge segments, 100 the viscous model should somehow be constrained from expanding along the southern boundary. This might result in more realistic velocity directions. Several areas of future research could signifi­ cantly improve the stress modeling of the Nazea plate. The addition of transform fault resistance is one obvious area of improving the driving-force modeling. Another area of future research might be the effect of modeling thickness variations as a function of age throughout the entire plate. The inclusion of the two microplates, the Panama and Easter plates, might lead to a better under­ standing of the dynamics of ridge and transform fault jumping. Other improvements would include the thermal effects of hot spots and for viscous modeling, the con­ straint of expansion along the southern boundary. REFERENCES

American Association of Petroleum Geologists, Plate tec­ tonic map of the Circum-Pacific region, southeast quadrant, 1;10,000,000 scale, Tulsa, Oklahoma, 1981. Allenby, R. J„, Implications of V.L.B.I. measurements on American intraplate crustal deformation, Tectono- physics, 60, T27-T35, 1979- Anderson, R- N., and J„ G. Sclater, Topography and evolu^ tiori of the East Pacific Rise between 5°S and 14°S, Earth- Planet. Sci- Lett-, 14, 433-441, 1972. Barazangi, M., and B . L. Isacks, Spatial distribution of earthquakes and subduetion of the Nazca plate beneath South America, Geology, £, 686-692, 1976. Barazangi, M., and B. L. Isacks, Subduction of the Nazca plate beneath Peru: Evidence from spatial distribu­ tion of earthquakes, Geophys. R. Astron. Soc., 57, 537-555, 1979- Bathe , K. J., and E. L. Wilson, Numerical methods in finite eletnent analysis, Prentice-Hall, Englewood Cliffs, 1976- Bender , P. L., J. E. Faller, J. Levine, S. Moodey, M. R. Pearlman, and E. C. Silverberg. Possible high- mobility LAGEOUS ranging station. Tectonophysics, 52, 69-73, 1979. Bergman, E. and S. Solomon, Oceanic intraplate earthquakes: implications for local and regional intraplate stress, J- Geophys. Res - 85, 5389-5392, 1980. Brune, J. N., T. L. Henyey, and R. F. Roy, Heat flow, stress, and rate of slip along the San Andreas fault, California, J. Geophys. Res., 74, 3832-3827, 1969.

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