Tectonic Analysis of Northwestern South America from Integrated Satellite, Airborne and Surface Potential Field Anomalies

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TECTONIC ANALYSIS OF NORTHWESTERN SOUTH AMERICA FROM INTEGRATED SATELLITE, AIRBORNE AND SURFACE POTENTIAL FIELD ANOMALIES

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for

the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

Orlando Hernandez, B.S., M.S.

*****

The Ohio State University

2006

Dissertation Committee: Approved by

Dr. Ralph R. B. von Frese, Adviser

Dr. Hallan C. Noltimier Adviser Dr. Michael Barton Graduate Program in Dr. Douglas E. Pride Geological Sciences °c Copyright by

Orlando Hernandez

2006 ABSTRACT

Northwestern South America is one of the most populated regions of the Americas with more than 80 million people concentrated along the Andes Mountains. This region includes a complex and dangerous mosaic of tectonic plates that have produced devastating earthquakes, tsunamis, volcanic eruptions and landslides in the last decades.

The region’s economic development has also seriously suﬀered because the region is poorly explored for natural resources. To more eﬀectively assess the tectonic hazards and mineral and energy resources of this region, we must improve our understanding of the tectonic setting that produced them.

This research develops improved tectonic models for northwestern South America from available satellite, airborne and surface gravity and magnetic data integrated with global digital topography, seismic, and GPS plate velocity data. Reliable crustal thickness estimates that help constrain tectonic stress/strain conditions were obtained by inverse modeling of the magnetic anomalies and terrain compensated gravity anomalies. Correlated positive Terrain Gravity Eﬀects (TGE) and Free Air Gravity Anoma- lies (FAGA) suggest that the crust - mantle interface under the northwestern Andes is closer to the surface than expected, indicating that these mountains are not isostatically compensated. Correlated negative FAGA anomalies observed along western

South America and the Greater and Lesser Antilles islands are associated with isostatically disturbed mantle displaced by subducting oceanic plates. Subtracting TGE

ii from the terrain-correlated FAGA (TCFAGA) yield compensated terrain gravity ef- fect (CTGE) anomalies that characterize the Andes Mountains with deep roots of low density crust displacing denser underlying mantle and thickening the local crust.

FAGA and TGE correlate at all levels of compensation, but the correlations are especially strong where the compensation is less than 100%. Correlated first vertical derivative FAGA (FVD(FAGA)) and differentially reduced−to-pole total field (DRTP) magnetic anomalies show crustal thickness variations and states of magneto-isostatic compensation. Continental crustal thickness estimates for the North Andes are in the range from roughly 34 km to 55 km, conforming well to and extending regional seismic constraints. The analysis highlights crustal deformation from plate collision and subduction in Northwestern South America.

Inversely correlated FVDFAGA and DRTP magnetic anomalies suggest thickness variations in the lower crust and thermal eﬀects in terms of the Curie isotherm. Directly correlated FVDFAGA and DRTP magnetic anomalies indicate thickness variations of the upper crust due to the formation of recent topography.

iii To Olga Lucia, Camilo Andres, Carolina and Alejandra

iv ACKNOWLEDGMENTS

I thank the Government of The Unites States of America, through the FUL-

BRIGHT Fellowship Program and The Ohio State University for this opportunity to pursue my doctorate at OSU. I also thank the Government of Colombia and The

Universidad Nacional de Colombia for endorsing my application and for granting me authority to study abroad.

I am deeply and indebted grateful to my advisor Pr. Dr. Ralph R. B. von Frese for his tutelage and academic advice over the years. I also thank Drs. Hallan Noltimier,

Michael Barton, Douglas Pride and Terry Wilson for their guidance, encouragement, review and criticism of my research work.

I want to extend my thanks to Mohammad Asgharzadeh, Timothy Leftwich, Laramie

Potts, Luis Gaya-Pique and Hyung Rae Kim for their assistance and cooperation during my stay at the Ohio State University.

This work has been partially supported by grants from FULBRIGHT - LASPAU,

COLFUTURO and Sociedad Minera Kedahda S.A. I also thank the Planetary Geo- dynamics Branch at NASA’s Goddard Space Flight Center for providing access to satellite gravity and magnetic data.

v VITA

October 26, 1962 ...... Born - Pacho, Colombia

December, 1988 ...... B.S. Geological Sciences, Universidad Nacional de Colombia

August, 1995 ...... M.S. Exploration Geophysics ITC, Delft, The Netherlands.

1989-1997 ...... Geologist, Geophysicist INGEOMINAS, Colombia

1997-2006 ...... Associate Professor Universidad Nacional de Colombia

PUBLICATIONS

Hernandez, O., R. R. B. von Frese, Crustal modeling of Northwestern South Amer- ica from spectrally correlated free-air and terrain gravity, Journal of South American Earth Sciences (in review).

Acosta J. E., Hernandez, O., Analisis neotectonico al Este de Pasca, Cundinamarca. Geologia Colombiana, Vol 23. 2000

Romero, O. F., Hernandez, O., Exploracion geologica y analisis mineralogico de los depositos de esmeraldas de San Antonio de Yacopi, Cundinamarca. Geologia colombiana, Volumen 22, 1999.

vi FIELDS OF STUDY

Major ﬁeld: Geological Sciences

Studies in: Geomathematics Dr. Ralph. R. B. von Frese Geophysics Drs. Hallan Noltimier and Ralph. R. B. von Frese Petrology Drs. Michael Barton and Phil Westerhoﬀ Historical Geology Drs. Michael Barton and Loren E. Babcock Structural Geology Drs. Terry Wilson and Hans Diederix Exploration Geophysics Drs. Colin V. Reeves Sally Barritt and Rob Sporry Geographic Information Systems Drs. Ekkehard Jordan and Cees van Westen

vii TABLE OF CONTENTS

Page

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vi

List of Tables ...... xi

List of Figures ...... xii

Chapters:

1. INTRODUCTION ...... 1

1.1 Nature and Signiﬁcance of the Problem ...... 2 1.2 Objectives ...... 6 1.3 Description of procedures ...... 6 1.3.1 Data Compilation ...... 7 1.3.2 Data processing ...... 7 1.3.3 Data interpretation and integration with geology ...... 9

2. THEORETICAL GRAVITY AND MAGNETIC MODELING ...... 11

Abstract ...... 12 2.1 Introduction ...... 13 2.2 Forward Modeling of Gravity and Magnetic Anomalies ...... 14 2.2.1 Isostatic models of mountainous topography ...... 15 2.2.2 Isostatic model of depressed topography ...... 20 2.2.3 Isostatic model of an oceanic ridge ...... 20 2.2.4 Local body gravity eﬀects ...... 23

viii 2.2.5 Sedimentary basin gravity eﬀects ...... 23 2.2.6 Dipping crustal interface ...... 26 2.2.7 Generalized oceanic - continental subduction ...... 30 2.2.8 Estimating the angle of subduction ...... 30 2.3 Conclusions ...... 32

3. ISOSTATICALLY DISTURBED TERRAINS FROM SPECTRALLY COR- RELATED FREE-AIR AND TERRAIN GRAVITY DATA ...... 34

Abstract ...... 35 3.1 Introduction ...... 35 3.2 Spectrally correlated free-air and terrain gravity ...... 37 3.3 Analysis of anomaly correlations ...... 42 3.4 Discussion of results ...... 50 3.4.1 Digital terrain model (DTM) ...... 53 3.4.2 Free-air gravity anomalies (FAGA) ...... 53 3.4.3 Terrain gravity eﬀects ...... 54 3.4.4 Terrain-correlated free-air gravity anomalies ...... 55 3.4.5 Terrain-decorrelated free-air gravity anomalies ...... 57 3.4.6 TCFAGA and FCTGE anomaly correlations ...... 57 3.5 Conclusions ...... 59

4. CRUSTAL THICKNESS AND DISCONTINUITY ESTIMATES ...... 61

Abstract ...... 62 4.1 Introduction ...... 63 4.2 Crustal modeling ...... 63 4.3 Comparison with Airy MOHO estimates ...... 64 4.4 Comparison with seismic MOHO estimates ...... 68 4.5 Crustal cross-sections ...... 71 4.5.1 Paciﬁc subduction zone - Andes Mountains - Guiana Craton 71 4.5.2 Guiana Craton-Andes Mountains-Caribbean subduction zone 74 4.5.3 Middle American Trench - Caribbean Plate - North American Plate ...... 77 4.6 Crustal discontinuities of the North Andes Microplate ...... 81 4.7 Discussion ...... 90 4.8 Conclusions ...... 93

5. CRUSTAL MODELING FROM MAGNETIC DATA ...... 95

Abstract ...... 96 5.1 Introduction ...... 97 5.2 Core Field and external ﬁeld reductions ...... 99

ix 5.3 Diﬀerential Reduction to the Pole (DRTP) ...... 101 5.4 First vertical derivatives of FAGA (FVD(FAGA)) ...... 105 5.5 Spectral correlations of CHAMP DRTP (TMFA) and FVD (FAGA) estimates ...... 105 5.6 Aeromagnetic anomalies of the North Andes Microplate ...... 109 5.7 Discussion ...... 114 5.8 Conclusions ...... 117

6. CRUSTAL THICKNESS VARIATIONS AND SEISMICITY ...... 119

Abstract ...... 120 6.1 Introduction ...... 121 6.2 Zero Curvature of crustal thickness variation ...... 122 6.3 Seismic data compilation ...... 123 6.3.1 ANSS Catalog ...... 123 6.3.2 RSNC historical and instrumental seismic catalog ...... 125 6.3.3 Recent seismicity in the RSNC catalog ...... 129 6.4 Discussion ...... 133 6.4.1 Ocean-continent collision zones ...... 133 6.4.2 Ocean-ocean collision zones ...... 138 6.4.3 Continent-continent collision zones ...... 139 6.4.4 Oceanic spreading ridges ...... 139 6.4.5 Transform faults ...... 139 6.4.6 Cratonic zone ...... 139 6.5 Focal mechanism solutions ...... 140 6.6 Conclusions ...... 142

7. CONCLUSIONS AND RECOMMENDATIONS ...... 143

Appendices:

A. TWO DIMENSIONAL GRAVITY AND MAGNETIC ANOMALIES DUE TO A POLYGON BY GM-SYS ...... 151

A.1 Gravity Anomaly due to a Polygon ...... 153 A.2 Magnetic Anomaly due to a Polygon ...... 155

B. FRACTIONAL VERTICAL DERIVATIVES ...... 160

BIBLIOGRAPHY ...... 162

x LIST OF TABLES

Table Page

1.1 Compiled geographical, geological and geophysical databases and sources of information...... 8

2.1 Correlation coeﬃcients of gravity eﬀects for an isostatically compensated mountain range, for observations at the surface, 20 km, 50 km, 100 km, 150 km and 200 km altitude, and 100% and 50% isostatic compensation ...... 16

2.2 Densities (gm/cm3) and magnetic susceptibilities (cgs) for intrusive bodies and host rocks modeled in Figures 2.6 and 2.7...... 26

2.3 Correlation coefficients between FAGA and TFMA for an intrusive body with different rock composition affecting a sedimentary host rock . . . . 28

2.4 Correlation coeﬃcients between FAGA and TFMA for a sedimentary basin hosted within maﬁc and metasedimentary basements ...... 28

2.5 Correlation coeﬃcients between FAGA and TFMA for a layer dipping at 15o, 30o, 45o, 60o, 75o and 90o inclination...... 28

2.6 Correlation coeﬃcients between FAGA and TFMA for a subduction zone model at 0 km, 20 km , 50 km, 100 km, 200 km, and 350 km altitudes...... 30

3.1 Correlation coeﬃcients (CC) between the gravity anomalies at 20 km altitude for the area from −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude in northwestern South America...... 50

5.1 Correlation coeﬃcients (CC) between the FAGA in Figure 5.6, FVI(FAGA) in Figure 5.5, CHAMP total ﬁeld magnetic anomalies (TFMA) in Figure 5.2 and the CHAMP DRTP TFMA in Figure 5.3 at 400 km altitude for northwestern South America from −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude...... 109

xi LIST OF FIGURES

Figure Page

1.1 Tectonic framework of northwestern South America (Trenkamp et al., 2004) showing the plate boundaries and major faults (black lines) . . . 3

2.1 Airy model of an idealized isostatically compensated mountain range with gravity effects, evaluated at 0 km, 20 km, 50 km, 100 km, 150 km, and 200 km altitude. (a) Geologic model showing topography, densities and crustal-mantle interface. (b) Anomaly profile conventions. (c) TGE at 100% isostatic compensation. (d) Edge effects in TGE and FAGA at 100% isostatic compensation. (e) FAGA at 100% isostatic compensation. (f) TGE, FAGA and RGE and FAGA at 100% isostatic compensation. (g) RGE at 100% isostatic compensation (h) TGE, FAGA and RGE at 50% isostatic compensation...... 17

2.2 Flexure model of an idealized isostatically compensated mountain range with gravity effects evaluated at 0 km, 20 km, 50 km, 100 km, 150 km, and 200 km altitude. (a) Geologic model showing topography, densities and crustal-mantle interface. (b) CC between Airy and flexural gravity anomalies. (c) TGE at 100% isostatic compensation. (d) Edge effects in TGE and FAGA at 100% isostatic compensation. (e) FAGA at 100% isostatic compensation. (f) TGE, FAGA and RGE and FAGA at 100% isostatic compensation. (g) RGE at 100 % isostatic compensation. (h) TGE, FAGA and RGE at 50% isostatic compensation...... 18

2.3 Airy gravity model of an isostatically overcompensated mountain range evaluated at 20 km altitude. (a) Geologic model. (b) Gravity Anomalies: RGE overcompensates TGE making FAGA negative. In this case, the equilibrium could be reached by isostatic rebound to increase TGE and diminish RGE to make FAGA approach zero...... 21

xii 2.4 Isostatic overcompensated topographic depression with lateral crustal density variation and mantle upwelling evaluated at 20 km altitude. (a) Geologic model. (b) Gravity anomalies: TGE are negative, “anti” RGE overcompensates TGE so that FAGA are positive. In this case, the isostatic state of equilibrium could be reached by crustal subsidence lowering the upwelled mantle and diminishing RGE to make FAGA approach to zero. TGE and FAGA are negatively correlated ...... 22

2.5 Gravity eﬀects of isostatically overcompensated oceanic ridge with underplated material evaluated at 20 km altitude. (a) Geologic model of a volcanic ridge (b) Gravity anomalies: TGE are positive and RGE are strongly negative making FAGA negative. The model shows how FAGA can also be aﬀected by density variations in the mantle ...... 24

2.6 Gravity and magnetic responses evaluated at 20 km altitude of igneous intrusions aﬀecting a sedimentary sequence. (a) Geologic model. (b) Gravity anomalies: TGE is equal to zero. FAGA is positive. (c) To- tal magnetic ﬁeld anomalies. The gravity and magnetic anomalies are positively correlated...... 25

2.7 Gravity and magnetic anomalies for a sedimentary basin estimated at 20 km altitude and 50 km station interval. (a) Geologic model. (b) Negative FAGA for a sedimentary basin with diﬀerent basement rock types. (c) Negative TFMA for basin thicknesses of 1 km, 2 km, 3 km, 4 km, and 5 km within maﬁc basement...... 27

2.8 Gravity and magnetic anomalies for a dipping interface beneath thin overburden evaluated at 20 km altitude at a 10 km station interval. (a) Negative FAGA for 15o, 30o, 45o, 60o, 75o and 90o inclination.(b) TFMA for 15o, 30o, 45o, 60o, 75o and 90o inclination ...... 29

2.9 Gravity and magnetic anomalies of a subduction zone evaluated at 20 km altitude and a 100 km station interval. (a) Geological model with an oceanic plate subducting under a continental plate. (b) The FAGA at 0 km, 20 km, 50 km, 100 km, 200 km, and 350 km altitude and (c) corresponding TFMA...... 31

2.10 Subduction zone modeling with 15o, 30o, 45o and 60o angles of inclination estimated at 20-km altitude at a 100-km station interval. (a) Geologic model. (b)FAGA and (c) corresponding TFMA...... 33

xiii 3.1 Topography/bathymetry of northwestern South America with superposed regional tectonic features between −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 38

3.2 Free-air gravity anomalies (FAGA) at 20 km elevation for the study region (Lemoine, et al., 1998). Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 39

3.3 Terrain Gravity Eﬀects (TGE) at 20 km elevation for the study region by Gauss-Legendre quadrature integration. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 41

3.4 Terrain-correlated FAGA (TCFAGA) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection. . 43

3.5 Terrain-decorrelated FAGA (TDFAGA) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection. . 44

3.6 FAGA-correlated TGE (FCTGE) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection. . . . . 45

xiv 3.7 FAGA-decorrelated TGE (FDTGE) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection. . 46

3.8 Summed local favorability indices (SLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing TCFAGA-peak to FCTGE-peak correlations for SLFI ≥ 8.7226. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 48

3.9 Summed local favorability indices (SLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA-trough to FCTGE-trough correlations for SLFI ≤ −8.7226. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 49

3.10 Diﬀerenced local favorability indices (DLFI) between TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA- peak to FCTGE-trough associations for DLFI> 4.8904. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 51

3.11 Diﬀerenced local favorability indices (DLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA-trough to FCTGE-peak associations for DLFI<- 4.8904. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 52

4.1 Compensated terrain gravity eﬀects (CTGE) at 20 km elevation for the study region obtained by subtracting TGE from TCFAGA. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 65

4.2 Gravity MOHO obtained from the inversion of CTGE showing deep MOHO beneath the mountains and oceanic ridges. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 66

xv 4.3 Seismic MOHO from the CRUST 2.0 model (Bassin et al., 2000) showing deeper MOHO below the mountains and oceanic ridges. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 67

4.4 Airy MOHO obtained the hydrostatic equilibrium principle. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 69

4.5 MOHO diﬀerences by subtracting gravity MOHO from Airy MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 70

4.6 MOHO diﬀerences by subtracting gravity MOHO from seismic MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 72

4.7 MOHO diﬀerences by subtracting the seismic MOHO from the Airy MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western- Central ranges. This map was produced using the Albers equal-area conic projection...... 73

4.8 Gravity, seismic and Airy MOHO estimates at 5oN latitude from −90o to −58.5o longitude. MOHO diﬀerences are greatest at the volcanic ridges and Andes Mountains...... 75

4.9 Gravity, seismic and Airy MOHO estimates at the Guiana Craton and North Andes − Caribbean subduction zone along (OoN, −78oW) to (23.5oN, −75oW)...... 76

4.10 Gravity, seismic and Airy MOHO estimates at the Caribbean − North American plates along (12.5oN, −90oW) , (16oN, −58.5oW)...... 78

xvi 4.11 Crustal proﬁle at 5oN latitude along −90oW to −79oW across the Cocos and Malpelo Ridges that is consistent with TCFAGA. Oceanic crustal thickening partially compensates TGE. The complete matching of observed and calculated gravity anomalies required the inclusion of underplated material that was less dense than the mantle...... 79

4.12 Two dimension P-wave velocity versus depth model across the Malpelo Ridge and Eastern Panama Basin showing an ophiolitic sequence with thinned oceanic crust and less dense underplated material in the upper mantle. The dashed line indicates a change in velocity gradient (Trum- mer, 2002)...... 80

4.13 Crustal profiles showing the different angles of subduction along the Nazca-North Andes plate boundary zone that are required to satisfy the TCFAGA. The TCFAGA map is also given in F igure 4.14. The TCFAGA map and crustal profiles were produced in Cartesian coordinates with origin (1’000.000 N, 1’000.000E) at the National Observatory of Bogota...... 82

4.14 TCFAGA of northwestern South America at 20 km altitude and interpreted plate boundaries and intracrustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 83

4.15 Plate boundaries and intracrustal discontinuities of northwestern South America interpreted from TCFAGA at 20 km altitude. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 84

4.16 Profiles (W-E) of the northern Andes Microplate showing the subducting oceanic slab under the continental crust as interpreted from TCFAGA at 20 km altitude. (a) Profile A-A: Two main continental roots were modeled below the west-central and eastern ranges, respectively. Smooth MOHO variations are observed below the Guiana Cra- ton. (b) Profile B - B: A single continental root was modeled below the west-central ranges. No clear continental root below the incipient eastern range is evident and the MOHO below the Guiana Craton is relatively flat...... 86

4.17 Surface FAGA and interpreted crustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 87

xvii 4.18 Plate boundaries and intracrustal discontinuities interpreted from surface FAGA. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota. 88

4.19 The tectonic realms and blocks of northwestern South America interpreted from geological and geophysical data (Cediel et al., 2003). . . . 89

4.20 Surface complete Bouguer anomalies and interpreted plate boundaries and intracrustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 91

4.21 Plate boundaries and intracrustal discontinuities interpreted from surface Bouguer anomalies. This map was produced in Cartesian coordinates referred to an origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 92

5.1 Core magnetic intensity (color), inclination (white contours) and declination (black contours) for northwestern South America from IGRF- 10 (NOAA, 2006). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 100

5.2 CHAMP total magnetic ﬁeld anomalies (nT) at 400 km altitude for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 102

5.3 Diﬀerentially reduce-to-pole CHAMP magnetic anomalies DRTP(TFMA) at 400 km for Northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 104

5.4 Crustal magnetic susceptibility values for northwestern South America calculated by linear inversion of DRTP CHAMP magnetic anomalies. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 106

xviii 5.5 First vertical derivative (FVD) of the free-air gravity anomalies (FAGA) at 400 km for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 107

5.6 Free-air gravity anomalies (FAGA) at 400 km elevation for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western- Central ranges. This map was produced using the Albers equal-area conic projection...... 108

5.7 Peak-to-peak correlations between FVD(FAGA) and CHAMP DRTP (TFMA) at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection. . 110

5.8 Trough-to-trough FVD(FAGA) and CHAMP DRTP (TFMA) at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 111

5.9 FVD(FAGA) peak-to- CHAMP DRTP (TFMA) trough correlations at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 112

5.10 FVD(FAGA) trough-to-CHAMP DRTP (TFMA) peak correlations at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection...... 113

5.11 Total magnetic ﬁeld anomalies at 20 km altitude for the North Andes Block with interpreted crustal discontinuities superposed (blue lines). This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota...... 115

xix 6.1 ANSS seismic catalog for 1966-2006 for three categories of earthquake magnitudes: M=3-4 (minor earthquakes), M= 4.1-5.5 (intermediate earthquakes), and M ≥ 5.5 to 10 (major earthquakes). Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. Yellow and blue zones correspond to thicker and thinner crust, respectively. This and succeeding ﬁgures were created using the capabilities of Oasis Montaj (Geosoft, 2006)...... 124

6.2 RSNC historical seismic catalog for 1643-1991 of earthquakes with magnitudes from M=3.0 to 4.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 126

6.3 RSNC historical and instrumental seismic catalog for 1643-1991 of earthquakes with magnitudes from M=4.1 to 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 127

6.4 RSNC historical seismic catalog for 1643-1991 of earthquakes with magnitudes M > 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also display. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 128

6.5 RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes from M=3.0 to 4.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 130

6.6 RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes from M=4.1 to 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 131

6.7 RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes M > 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 132

xx 6.8 RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 0 km to 10 km. Crustal discontinuities interpreted from gravity anomalies and thezero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 134

6.9 RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 10 km to 30 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 135

6.10 RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 30 km to 70 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 136

6.11 RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths to the hypocenter from 70 km to 300 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively...... 137

6.12 Main stress axes determined by the Reches Method (Reches, 1983; Reches, 1987) from 94 focal mechanism solutions of the Central Moment tensor catalog (CMT) reported by Harvard University (CTM, Harvard, 2006) for the period 1976-2000 and event magnitudes M = 5.0 (Vargas et al., 2005)...... 141

xxi CHAPTER 1

INTRODUCTION

1 1.1 Nature and Signiﬁcance of the Problem

The plate tectonic setting of northwestern South America (Figure 1.1) is characterized by the convergence of the North Andes microplate and the Nazca, Caribbean and South American plates (Bird, 2003 ; Cediel et al., 2003; Trenkamp et al., 2001;

Pindell, 2006). This is one of the most populated regions of the Americas with more than 80 million people concentrated in urban areas along the Andes Mountains. The region is also subject to devastating earthquakes, volcanic eruptions, landslides and other tectonic hazards due to the complex interactions of the crustal plates. However, the dense vegetation that covers most of the rock exposures seriously limits conventional geological mapping in this region. Thus, the tectonic setting is much more poorly known for northwestern South America than it is for the mountainous backbone of the

Americas north to Alaska and south to Patagonia (Ramos, 2006).

Kellogg et al. (1985) deﬁned the Panama block in southeastern Central America using seismic and geodetic data and inferred that it is moving northwards relative to the Caribbean plate and eastwards relative to the South American plate. Mann and Kolarsky (1955) suggested that the converging boundary between Panama and

North Andes microplates is near the Panama-Colombia border. Kellogg et al. (1985) deﬁned the North Andes block within the western, central and eastern Cordilleras of

Colombia, Ecuador and Venezuela, respectively. From geologic and seismicity data they inferred that it moves about 10 mm/a towards 55oE with respect to South America or about 17 − 19 mm/a northwestwards with respect to the Caribbean plate. Dewey and Pindell (1985) presented a contrasting tectonic model interpreted from geologic data whereby during the last 9 ma the Central block moved about 275 km at 31 mm/a northeastwards with respect to South America, and the Maracaibo block moved even further northwards about 105 km at12 mm/a. Perez et al. (1997) studied the Benioﬀ

2 Figure 1.1: Tectonic framework of northwestern South America (Trenkamp et al., 2004) showing the plate boundaries and major faults (black lines)

3 zone of seismicity within this slab, and showed that it terminates eastwards near

Curacao-Aruba.

The CASA project (Kellogg, 1985) compiled GPS data and quantiﬁed the relative velocities of the Panama and North Andes microplates. Van der Hilst and Mann (1994) from seismic data interpreted the Caribbean plate as subducting beneath the South

American Plate to a depth of 275 km with 17o of eastwards inclination. Moore and

Sender (1995) mapped the triple-junction of the Cocos-Nazca-Panama plate and the complex relative plate movements. Trenkamp et al. (1996) deﬁned the motion of North

Andes block with respect to South America for a 78 mm/a dextral component and a 45 mm/a compressive component on their common boundary. Perez et al. (1997) interpreted the Caribbean-North Andes and South America triple-junction as lying at the intersection of the Bocono fault (North Andes-South America), San Sebastian

- El Pilar fault (Caribbean - South America), and a seismically active dextral fault trending NW (ND-CA).

Bird (2003) presented a comprehensive compilation of the local tectonics of the area, with a set of plate boundaries interpreted from topography, volcanism, and seismicity, taking into account relative plate velocities from magnetic anomalies, moment tensor solutions, and geodesy. Compiling observations from seismic, gravity, magnetic, tomography and satellite techniques, Cediel et al. (2003) presented the tectonic assembly of the North Andes block deﬁning four tectonic realms including the Guiana

Shield, the Maracaibo sub-plate, the central continental sub-plate and the western tectonic realms. Collot et al. (2005) described the boundary between the North Andes microplate and the South American plate as a mega thrust that is apparently reacti- vated in an oblique dextral-normal sense in Ecuador and continues into Colombia along the Borde Llanero fault system to the Merida Andes in Venezuela. Although much work has been done, the tectonic model for the area is mostly supported from data of the

4 uppermost crust. To advance our understanding of the hidden deeper geology and tectonic forces of the North Andes microplate and its surroundings, I developed the ﬁrst comprehensive crustal model of northwestern South America from integrated satellite, airborne and surface gravity and magnetic anomalies. Satellite gravity and magnetic observations mapped the major anomalies measured in hundreds of kilometers providing unique insights on plate boundary zones from the surface to the crust-mantle interface at depths up to about 56 km.

Airborne and surface gravity and magnetic data provided regional and local anomalies respectively measured in tens of kilometers to kilometers for constraining shallow tectonic features at the plate boundary zones and intraplate regions. Therefore, the integration of gravity and magnetic observations from multi-altitude observations also integrates interpretations at diﬀerent depths providing a comprehensive three- dimensional crustal model from the crustal surface to the interface of the crust with the mantle or the MOHO.

Crustal magnetic anomalies have been widely associated with crustal magnetization variations along plate tectonic boundaries (e.g., von Frese et al., 1996). Thus,

I analyzed magnetic data from the Ørsted and CHAMP (Challenging Minisatellite

Payload) satellite missions, as well as gravity observations from EGM96 to model regional composition variations of the crust and the upper mantle. I also estimated crustal thickness variations and thermal perturbations that help control earthquake- producing stresses along the boundaries of the Nazca, Caribbean and South American

Plates and Panama,Costa Rica and North Andes Microplates.

5 Critical geological problems that I addressed include: Assessing stress controlling crustal thickness variations and crustal discontinuities. Establishing the tectonic features that control the region’ s earthquake and volcanic threats. Optimizing the use of multi-altitude geophysical data in the exploration of mineral and energy resources.

1.2 Objectives

The aim of this project is to use available gravity and magnetic observations from satellite, airborne and surface surveys in conjunction with new developments in crustal isostatic modeling to develop new insights on the crustal tectonic features and evolution of Northwestern South America. Improved knowledge of the crustal thickness variations can yield important constraints on the local stress ﬁeld (e.g., Kim, et al.,

2000) that in combination with regional plate tectonicstress ﬁelds provide new insight on earthquake hazards within northwestern South America. In addition, these results may contribute to exploration of the region’s mineral and energy resources to promote the economic development.

1.3 Description of procedures

Initially, hypothetical isostatic models were constructed to show examples of isostatic states of compensation for idealized mountain ranges, volcanic ridges, subduction zones and crustal discontinuities. Then, observed regional potential ﬁeld anomalies were interpreted in terms of the crust-mantle interface and related to isostatic disturbances of the crust from tectonic, thermal, and other geological forces. The methodology applied in this research project includes data compilation, data processing, qualitative and quantitative interpretation, and integration of the results with geological data.

6 1.3.1 Data Compilation

Disparate satellite, airborne and surface potential ﬁeld data sets were compiled and standardized for regional analysis and modeling of northwestern South America

. The compilation included geological, seismological and geodetic data sets. Satellite data oﬀered regional spatial coverage, whereas the coverage from airborne and surface surveys was much less complete. Regional satellite geopotential data helped augment or extend the analysis between local near-surface surveys that provided important local constraints on the tectonic features of the study area. Table 1 summarizes sources and types of datasets compiled for this study.

1.3.2 Data processing

The geophysical and geological data sets were converted into a common digital for- mat to facilitate interpolation, gridding, spectral analysis, inversion, trend surface analysis, and other quantitative processing objectives (von Frese, 1980; Reeves, 1991; Kim,

2000; Leftwich, 2005). The geophysical and geological data sets were integrated using GIS tools including digitization, rasterization, reclassiﬁcation, data overlaying and overlapping, conditional retrieving, logical boolean sorting, analytical signal modeling, and neighborhood assessments for visualization purposes (Hernandez, 1995; Borrough, et al., 1998; Kessler, 2006). Software was developed and integrated with commercial software to facilitate the quantitative analysis and digital display of the analytical results.

The crustal thickness map for northwestern South America was calculated using spectral correlation analysis between terrain and free air gravity anomalies. Terrain

7 ANALOG AND DIGITAL DATA SOURCE OF INFORMATION Satellite EGM (Earth Gravity Model) The Ohio State University. 96 Satellite GRACE (Gravity Recovery The Ohio State University, NASA. and Climate experiment) data Ørsted The Ohio State University, ØRSTED. Satellite CHAMP (Challenging Min- The Ohio State University, NASA. isatellite Payload) Magnetic data Topography 96 Digital elevation model The Ohio State University, NOAA. Digital Elevation Model Universidad Nacional de Colombia Free Air Gravity Anomaly map of Colombian geological survey (INGE- Colombia OMINAS). Complete Bouguer Gravity Anomaly INGEOMINAS. map Crustal thickness seismic database http://mahi.ucsd.edu Geologic map of Colombia INGEOMINAS. Aeromagnetic data of Colombia INGEOMINAS, ECOPETROL, USGS. Seismological databases INGEOMINAS, ANSS, USGS.

Table 1.1: Compiled geographical, geological and geophysical databases and sources of information.

8 gravity eﬀects were modeled by spherical coordinate Gauss Legendre quadrature integration of topography data. Gravity and magnetic data were combined by the application of the spectral correlation theory to separate core, lithospheric and external

ﬁeld components in CHAMP magnetic anomalies. Crustal discontinuities and crustal thickness variations were mapped and integrated with seismological data using GIS overlapping and superposition operations in the spatial domain.

1.3.3 Data interpretation and integration with geology

Crustal models were developed using geophysical, geological and geodetic datasets.

These data sets included seismic data, GPS stress and strain models, and maps of the geology, ore deposits, sedimentary basins, and volcanic and earthquake activities.

In Chapter 2, I investigated the gravity and magnetic responses of hypothetical geological models and their isostatic responses using available forward modeling techniques. Based on these models, I evaluated the contributions of spatial variation of density and magnetic susceptibility contrasts in the respective gravity and magnetic anomalies and their spectral correlations. This new modeling was focused on free-air gravity and terrain gravity anomalies for analyzing and interpreting observed data from northwestern South America.

In Chapter 3, I examined the spectral correlation of free-air and terrain gravity anomalies for their isostatic compensation state using Gauss-Legendre quadrature integration. By spectral correlation analysis, terrain-correlated and -decorrelated anomalies were obtained for separating gravity anomalies associated with the core-mantle and crust-mantle interfaces and intra-crustal density variations. Normalization and local favorability indices were developed to facilitate qualitative and quantitative interpretation of the complex spatial distribution of gravity anomalies.

9 In Chapter 4, I investigated the terrain-correlated gravity eﬀects for Moho estimates and crustal thickness variations. I obtained comprehensive MOHO estimates for northwestern South America that are consistent with the gridded topography, bathymetry and gravity observations. I compared the gravity MOHO against sparse Seismic MOHO to show the remarkable improvement of the gravity MOHO estimates. I also compared the gravity and seismic MOHOs against the theoretical Airy Moho. Crustal discontinuities from satellite and surface data were related to the tectonic processes and evolution of the North Andes microplate.

In chapter 5, I focused on extracting the crustal components in the CHAMP magnetic data and their spectral correlation with the ﬁrst radial derivative FAGA anomalies at satellite altitudes. Satellite, airborne and surface magnetic data were integrated and combined with gravity models to investigate the magnetic eﬀects of the crustal thickness variations. The analysis focused on the magnetic interpretation of crustal discontinuities of the North Andes microplate.

In chapter 6, I investigated the edges of crustal thickness variations calculated from the curvature of the crustal thickness estimates and their associated seismic and magnetic responses. Zero curvature values were used to separate the thicker and thinner crust. These models were combined with historical and instrumental seismic catalogs for stress/strain modeling of the region and evaluating the seismicity of local crustal discontinuities and plate boundaries.

In Chapter 7, I summarized the methodologies and results from the hypothetical models and spectral analysis of observed gravity and magnetic data for applications to seismic hazard analysis and exploring for minerals and fossil fuels. I also considered recommendations for expanding this research.

10 CHAPTER 2

THEORETICAL GRAVITY AND MAGNETIC MODELING

11 ABSTRACT

The phenomenon of isostasy concerns the equilibrating response of the crust to the imposition and removal of loads. The isostatic condition of the crust and the terrain were evaluated using the modeled gravity eﬀects of idealized crustal models. The idealized crustal models represented major tectonic features of the study area and included the mountain range, volcanic ridge, topographic depression, igneous intrusion, sedimentary basin, and fault and subduction zone models. These models were implemented by interactive forward modeling of gravity data to better understand how free-air, terrain and crustal root gravity anomalies interact for various states of isostatic compensation. The models facilitated interpreting spectrally correlated terrain and free-air gravity anomalies for isostatic disturbances of the crust.

The analysis suggested that the isostatic condition of the crust strongly aﬀects correlations between the free-air gravity anomalies and the gravity eﬀects of the terrain.

Additionally, the magnetic response for some of the idealized models was obtained and correlated with gravity anomalies. These models were useful for improving the interpretation of gravity and magnetic anomalies at multi-altitude observations.

The idealized models were also used to investigate the non-uniqueness condition of the potential field anomalies, in particular where anomaly superposition and inverse correlations occur. The results indicated that isostatic disturbances of the terrain greatly enhance correlations between the gravity effects of the terrain and free-air anomalies. Furthermore, these correlations are relatively insensitive to the differences

12 in models of crustal isostasy at altitudes that are large compared to the relief of the crustal terrain.

2.1 Introduction

The main purpose of this section is to develop theoretical geological models that provide insight on the free-air gravity and magnetic responses of isostatically disturbed terrain. The geologic models represent simpliﬁed geologic features that are relevant for the tectonic analysis of Northwestern South America and the isostatic conditions of the North Andes mountains.

Simple idealized geologic models commonly help to explain the basis of isostatic compensation. For example, Keary and Vine (1996) graphically described the inverse correlation of gravity anomalies with topography showing free-air, Bouguer and isostatic anomalies over an idealized mountain range for various levels of isostatic equilibrium ranging from 100% to 0% compensation. However, these models did not include the associated terrain gravity eﬀects or the multi-altitude variations of the gravity anomalies. Watts (2001) examined isostatic properties of crustal structures using the

Airy and Pratt models in explaining crustal structures, and introduced examples of the

ﬂexure model of isostasy. Turcotte and Schubert (2002) also presented compensation models for observed geoid anomalies and estimated the forces required to maintain topography and the geoid. Apart from these studies, however, few examples of gravity modeling of free-air and terrain gravity eﬀects at multi-altitude elevations and continental scales are available.

In the section below, I develope theoretical crustal models applicable to northwestern South America to illustrate possible relationships between terrain and free-air

13 gravity and magnetic observations. These results extend to multi-altitudes the surface relationships usually described by the Bouguer anomaly in common textbooks on geophysics (e.g., Reeves, 1991; Keary and Brooks, 1992; Telford, et al., 1994).

2.2 Forward Modeling of Gravity and Magnetic Anomalies

Gravity anomalies of the hypothetical geological models were calculated by forward modeling using the software capabilities of GM-SYS. This software for 2.75 D forward and inverse gravity and magnetic modeling allows intuitive, interactive manipulation of the geologic model (Northwest Geophysical Associates, 1999). GM-SYS is based on published algorithms (Talwani et al., 1959; Talwani and Heirtzler, 1964; Won and

Bevis, 1987; Parker, 1994) that are described in more detail in Appendix A.

For a constant density crust overlying a constant density mantle, the free-air gravity anomaly (FAGA) in mGals may be expressed by:

F AGA = T GE + RGE, (2.1)

where

TGE = Terrain Gravity Eﬀects (mGals) and

RGE = Root Gravity eﬀects (mGals).

Estimating the gravity anomalies of the idealized models involved the following procedures:

1. The TGE were estimated using a single density contrast.

2. The MOHO interface was estimated using an eﬀective density contrast between

the mantle and crust and varying the MOHO relief until the TGE were nulliﬁed.

This approach assumes that terrain loads on the crust deﬁned by the topography

14 and its density contrast to air are compensated by mass diﬀerentials across the

MOHO.

Simple and complex geological models were evaluated to obtain their superimposed gravity eﬀects at 0 km, 20 km, 50 km, 100 km, 150 km and 200 km altitude. The magnetic responses were also determined for some of the models using simplistic magnetic susceptibility values for the crustal materials and considering the mantle to be non- magnetic. The TGE, FAGA and RGE were graphically displayed using MATLAB

(Mathworks, 2005). Procedures were developed to extend the GM-SYS forward modeling capabilities to do isostatic analysis and to integrate the GM-SYS and MATLAB capabilities.

The correlation coeﬃcient (CC) such as between TGE and FAGA (Davis, 1986;

Isaaks and Srivastava, 1989) was calculated by:

# · σ2 (T GE, F AGA) CC (T GE, F AGA) = , (2.2) σ2 (T GE)σ2 (F AGA) where σ2(T GE, F AGA) is the covariance between the two signals with variances

σ2(T GE) and σ2(F AGA). CC varies between +/- 1.0, where CC = 1.0 implies positive or direct correlation between the signals, CC= -1.0 implies negative or inverse correlation, and CC ≈ 0 is generally taken to indicate no correlation between the signals, but the interpretation is not unique (von Frese, et al., 1997).

2.2.1 Isostatic models of mountainous topography

Figure 2.1 (a) shows the basic terrain model that consists of positive topographic relief over a ﬂat crustal surface. The mean crustal thickness is 35 km with a varying crustal root into the mantle. The densities used were 2.85 gm/cm3 for the continental

15 CC 0 km 20 km 50 km 100 km 150 km 200 km

FAGA(Airy,F lex)100% 0.7235 0.8008 0.8435 0.868 0.8719 0.8803

FAGA(Airy,F lex)50% 0.9968 0.9974 0.998 0.9987 0.9991 0.9993

RGE(Airy,F lex)100% 0.9931 0.9947 0.9962 0.9977 0.9985 0.9989

RGE(Airy,F lex)50% 0.8736 0.8863 0.9035 0.9245 0.9398 0.9514

TGE(Airy,F lex) 0.8565 0.8706 0.8874 0.9076 0.923 0.9354

Table 2.1: Correlation coeﬃcients of gravity eﬀects for an isostatically compensated mountain range, for observations at the surface, 20 km, 50 km, 100 km, 150 km and 200 km altitude, and 100% and 50% isostatic compensation

crust and 3.3 gm/cm3 for the mantle. The gravity eﬀects were modeled at a station interval of 10 km at the surface and 20 km, 50 km, 100 km, 150 km, and 200 km altitude along a 5000 km proﬁle oriented perpendicular to the mountainous topography.

The TGE, RGE and FAGA were calculated for the Airy and flexure isostatic models in Figures 2.1 and 2.2, respectively. In the absence of MOHO relief (e.g., RGE=0), the models equal the Pratt model where the terrain is compensated by intracrustal mass differentials. This situation tends to be limited to continental crust that is dominated by high heat flow such as occurs west of Rockies in North America (Watts, 2001). In this study, I focused on the isostatic properties of the Airy and flexure models that are more appropriate for representing the geology of northwestern South America.

Figures 2.1 and 2.2 give the gravity responses for the Airy and ﬂexural isostatic models, respectively, at the compensation levels of 0%, 50% and 100%. Table 2.1 shows how these gravity components correlate with each other at the various altitudes of observation for the varying levels of isostatic compensation.

The isostatic condition of the crust deﬁnes the correlation between TGE and FAGA.

For instance, a topographic high can be partially or completely compensated by a

16 Figure 2.1: Airy model of an idealized isostatically compensated mountain range with gravity effects, evaluated at 0 km, 20 km, 50 km, 100 km, 150 km, and 200 km altitude. (a) Geologic model showing topography, densities and crustal-mantle interface. (b) Anomaly profile conventions. (c) TGE at 100% isostatic compensation. (d) Edge effects in TGE and FAGA at 100% isostatic compensation. (e) FAGA at 100% isostatic compensation. (f) TGE, FAGA and RGE and FAGA at 100% isostatic compensation. (g) RGE at 100% isostatic compensation (h) TGE, FAGA and RGE at 50% isostatic compensation.

17 Figure 2.2: Flexure model of an idealized isostatically compensated mountain range with gravity effects evaluated at 0 km, 20 km, 50 km, 100 km, 150 km, and 200 km altitude. (a) Geologic model showing topography, densities and crustal-mantle interface. (b) CC between Airy and flexural gravity anomalies. (c) TGE at 100% isostatic compensation. (d) Edge effects in TGE and FAGA at 100% isostatic compensation. (e) FAGA at 100% isostatic compensation. (f) TGE, FAGA and RGE and FAGA at 100% isostatic compensation. (g) RGE at 100 % isostatic compensation. (h) TGE, FAGA and RGE at 50% isostatic compensation.

18 crustal root (RGE) into the mantle. The isostatic anomaly can be estimated from

TGE plus RGE. The isostatic anomaly is equal to FAGA over the central part of the

ﬂat topographic high, representing a simple method for assessing the mountain’s state of isostatic equilibrium. Thus, the correlation between TGE and FAGA can help to assess the isostatic condition of topographic features.

Gravity anomaly analysis can not distinguish between the Airy and ﬂexure models

(Watts, 2001). This is because the compensation occurs at depth and the diﬀerences in the anomalies produced by the root are negligible. Thus, gravity solutions require augmentation by magnetic, seismic reﬂection and refraction and other data (Keary and Vine, 1990).

FAGA is close to zero in Figures 2.1(e) and 2.2(e) at the central part of the mountain range where the RGE essentially cancels the TGE. However, FAGA and

RGE still show a positive regional correlation because the RGE can not fully negate the edge effects of the mountain in the TGE that are thus present in the FAGA. These edge effects are reduced with altitude, so that the RGE increasingly negate the TGE and the correlation coefficient between FAGA and TGE approaches zero. Thus, at altitudes that are large compared to the terrain relief, such as 20-km altitude, the correlation between FAGA and RGE or TGE for 100% isostatic compensation is close to zero.

The gravity curves obtained by these models in Figures 2.1 and 2.2 are useful for interpreting the correlations between FAGA, TGE and RGE. They are applicable for assessing the isostatic condition of the Andes Mountains and isolated topographic highs of Northwestern South America.

The curves in ﬁgures 2.1 and 2.2 show that TGE decreases more rapidly than

FAGA from the surface to satellite altitudes. Thus, the higher altitude observations are most eﬀective for resolving regional isostatic disturbances of the terrain. However,

19 as the altitude of observations increases the spatial resolution of the potential ﬁeld anomalies decreases.

Figure 2.3 shows the Airy gravity modeling for an overcompensated mountain range. Here, the crustal root is too thick and overcompensates for the topographic load so that the resultant FAGA is negative. TGE and FAGA are negatively correlated. The isostatic equilibrium will be achieved by crustal rebound reducing RGE as is invoked in glacial rebound and erosional processes (Turcotte and Schubert, 2002).

2.2.2 Isostatic model of depressed topography

Figure 2.4 models the gravity components for a topographic depression underlain by a root composed of metamorphic and mantle rocks. For this case, the root was designed to overcompensate for the excess terrain mass.

The TGE are negative for the topographic depression whereas mantle components produce a positive RGE. Lateral crustal variations represented by the metamorphic rocks produce an additional local positive crustal anomaly. The combined eﬀects produce a large positive ”anti-root” eﬀect that makes FAGA positive.

TGE and FAGA are negative or inversely correlated. This example of anomaly superposition may help to interpret positive FAGA over trenches, subduction zones, cratonic areas and isostatically overcompensated topographic lows. It also can be useful to model possible impact craters and mass concentrations or ”mascons” in other regions of the world (Watts, 2001).

2.2.3 Isostatic model of an oceanic ridge

Figure 2.5 shows the crustal model of an overcompensated oceanic ridge along with the related gravity components. The oceanic ridge produces a positive TGE but the anomalous underplated material that is less dense than the mantle produces strong

20 Figure 2.3: Airy gravity model of an isostatically overcompensated mountain range evaluated at 20 km altitude. (a) Geologic model. (b) Gravity Anomalies: RGE overcompensates TGE making FAGA negative. In this case, the equilibrium could be reached by isostatic rebound to increase TGE and diminish RGE to make FAGA approach zero.

21 Figure 2.4: Isostatic overcompensated topographic depression with lateral crustal density variation and mantle upwelling evaluated at 20 km altitude. (a) Geologic model. (b) Gravity anomalies: TGE are negative, “anti” RGE overcompensates TGE so that FAGA are positive. In this case, the isostatic state of equilibrium could be reached by crustal subsidence lowering the upwelled mantle and diminishing RGE to make FAGA approach to zero. TGE and FAGA are negatively correlated

22 negative RGE so that FAGA are negative. The TGE are negatively correlated with

FAGA and RGE. This example shows how mass variations in the mantle can also be recorded in FAGA. This model may be useful to interpret the gravity response of the Cocos, Carnegie, Malpelo and Beata volcanic ridges and related mantle density reductions.

2.2.4 Local body gravity eﬀects

Figure 2.6 gives the gravity and magnetic eﬀects of a local body represented by a granitic intrusion that is supported by the rigidity of the crust. Table 2.2 gives the mean density and magnetic susceptibility values used to evaluate the geopotential anomalies at 20 km altitude. The magnetic anomalies were calculated with the induction inclination of 90o.

The ﬂat topography yields TGE that are equal to zero. The intrusive igneous rock aﬀecting the host sedimentary sequence produces positive FAGA and positive total

ﬁeld magnetic anomaly (TFMA). The FAGA and TFMA are positively correlated as listed in Table 2.3. The amplitudes of these anomalies vary with the sign of the density and magnetic susceptibility contrasts between the igneous intrusions of granitic, granodioritic and gabbroic rocks and the host sedimentary rock. This model will be useful to detect shallow igneous intrusions aﬀecting sedimentary basins in the study area.

2.2.5 Sedimentary basin gravity eﬀects

Figure 2.7 shows the negative FAGA and TFMA for sedimentary inﬁll at the oceanic trenches and sedimentary basins. These anomalies reﬂect the lower density and magnetization of the sediments relative to the basement rocks. The amplitudes of the negative FAGA and TFMA increase with the increase in thickness of the basin.

23 Figure 2.5: Gravity eﬀects of isostatically overcompensated oceanic ridge with underplated material evaluated at 20 km altitude. (a) Geologic model of a volcanic ridge (b) Gravity anomalies: TGE are positive and RGE are strongly negative making FAGA negative. The model shows how FAGA can also be aﬀected by density variations in the mantle

24 Figure 2.6: Gravity and magnetic responses evaluated at 20 km altitude of igneous intrusions aﬀecting a sedimentary sequence. (a) Geologic model. (b) Gravity anomalies: TGE is equal to zero. FAGA is positive. (c) Total magnetic ﬁeld anomalies. The gravity and magnetic anomalies are positively correlated.

25 Rock Type Density gm/cm3 Mag. suscep (cgs) Granite (felsic rocks) 2.75 0.0025 Sedimentary rocks 2.35 0.0001 Granodiorite (inter- 2.85 0.035 mediate) Gabbros (maﬁc rocks) 3.1 0.070 Meta sedimentary 2.85 0.0003 basement Intermediate base- 2.9 0.03 ment Maﬁc basement 3.2 0.08

Table 2.2: Densities (gm/cm3) and magnetic susceptibilities (cgs) for intrusive bodies and host rocks modeled in Figures 2.6 and 2.7.

The asymmetry of the magnetic anomalies shows that this model was evaluated with the inclination of 40o. The FAGA and TFMA are positively correlated as shown in

Table 2.4. The correlation can be increased by reducing the TFMA to the pole which is equivalent to evaluating the models with the geomagnetic ﬁeld inclination of 90o.

The strongest negative FAGA and TFMA occur for the sedimentary basin within maﬁc basement. The negative anomaly amplitudes increase in magnitude as the thickness of the sedimentary sequence increases. These models are useful for interpreting the gravity and magnetic eﬀects for trenches, sedimentary basins and tectonic grabens.

2.2.6 Dipping crustal interface

Figure 2.8 shows the gravity and magnetic responses for a horizontal slab with a dipping edge at various angles of inclination. The FAGA and TFMA are positively

26 Figure 2.7: Gravity and magnetic anomalies for a sedimentary basin estimated at 20 km altitude and 50 km station interval. (a) Geologic model. (b) Negative FAGA for a sedimentary basin with diﬀerent basement rock types. (c) Negative TFMA for basin thicknesses of 1 km, 2 km, 3 km, 4 km, and 5 km within maﬁc basement.

27 CC Granite Granodiorite Gabbro FAGA, TFMA 0.9301 0.9240 0.9234

Table 2.3: Correlation coefficients between FAGA and TFMA for an intrusive body with different rock composition affecting a sedimentary host rock

CC Felsic Rock Maﬁc rock Meta sedim FAGA, TFMA 0.8249 0.8249 0.8225

Table 2.4: Correlation coeﬃcients between FAGA and TFMA for a sedimentary basin hosted within maﬁc and metasedimentary basements

correlated for the six dip angles of the slab model listed in Table 2.5. These correlations increase as the angle of inclination of the crustal interface decreases. This model is useful for interpreting crustal discontinuities associated with plate boundaries and major fault systems.

CC 90o 75o 60o 45o 30o 15o FAGA, 0.7576 0.7590 0.7609 0.7645 0.7726 0.8032 TFMA

Table 2.5: Correlation coeﬃcients between FAGA and TFMA for a layer dipping at 15o, 30o, 45o, 60o, 75o and 90o inclination.

28 Figure 2.8: Gravity and magnetic anomalies for a dipping interface beneath thin overburden evaluated at 20 km altitude at a 10 km station interval. (a) Negative FAGA for 15o, 30o, 45o, 60o, 75o and 90o inclination.(b) TFMA for 15o, 30o, 45o, 60o, 75o and 90o inclination

29 CC 0 20 km 50 km 100 km 200 km 350 km FAGA, 0.0074 -0.2108 -0.2358 -0.2683 -0.2786 -0.2216 TFMA

Table 2.6: Correlation coeﬃcients between FAGA and TFMA for a subduction zone model at 0 km, 20 km , 50 km, 100 km, 200 km, and 350 km altitudes.

2.2.7 Generalized oceanic - continental subduction

Figure 2.9 gives the gravity and magnetic responses for an oceanic-continental collision model. This model includes a subducting oceanic plate, a trench ﬁlled with soft sediments, and continental crust with a mountain range and crustal root into the mantle.

The positive FAGA over the oceanic crust become negative over the trench. Both positive and negative FAGA are observed over the mountain range. The FAGA decrease in amplitude and frequency from the surface to satellite altitudes.

The strongly positive TFMA over the continental crust become negative over the trench. Negative TFMA are observed at the edges of the crustal root and above the descending oceanic plate. The TFMA decrease in amplitude and frequency from the surface to satellite altitudes. Table 2.6 shows that the gravity and magnetic anomalies are inversely but weakly correlated with the CC decreasing from 20 km to 200 km satellite elevations and increasing again at 350 km altitude.

2.2.8 Estimating the angle of subduction

Figure 2.10 gives the geopotential anomalies at 20-km altitude for the subduction where the descending oceanic plate is dipping at 15o 30o, 45o and 60o. At the trench, the negative FAGA and positive TFMA are attenuated at low angles of inclination.

30 Figure 2.9: Gravity and magnetic anomalies of a subduction zone evaluated at 20 km altitude and a 100 km station interval. (a) Geological model with an oceanic plate subducting under a continental plate. (b) The FAGA at 0 km, 20 km, 50 km, 100 km, 200 km, and 350 km altitude and (c) corresponding TFMA.

31 Over the continental crust, regions of relative thicker crust are associated with negative FAGA and positive TFMA. Table 2.6 shows that the inverse correlations between gravity and magnetic anomalies become somewhat stronger with increasing inclination.

These models are useful for interpreting the gravity and magnetic responses of a subducting slab at low (ﬂat slab) and intermediate angles of inclination. The models for subducting slabs at angles greater than 45o are not realistic, especially for the study area where relatively low angle (5o-20o) subduction is applicable.

2.3 Conclusions

Simple theoretical geological models were evaluated for their gravity and magnetic responses and provide the necessary backgound for signature recognition and interpretation of complex multi-altitude potential ﬁeld anomalies. The theoretical geological models also provide insights on the non-uniqueness of gravity and magnetic model solutions and the need to evaluate their geological feasibility by comparing the results with seismic, borehole and other geological and geophysical data.

Gravity and magnetic anomalies modeled at low altitudes exhibit amplitudes and frequencies that are attenuated at satellite altitudes to the point they may not be detected. Terrain gravity effects are more attenuated than root gravity effects from the surface to satellite altitudes. Thus, at altitudes that are large compared to the relief of the crustal terrain, FAGA provides an increasingly effective estimate of the crustal isostatic anomaly of isostatically disturbed terrain. At these altitudes, morever, the differences in the gravity responses of the various isostatic models (e.g., Airy, flexure,

Pratt) are quite similar. Thus, inversions of FAGA for isostatic mass diﬀerentials may implement the most convenient isostatic model which essentially complete generality.

32 Figure 2.10: Subduction zone modeling with 15o, 30o, 45o and 60o angles of inclination estimated at 20-km altitude at a 100-km station interval. (a) Geologic model. (b)FAGA and (c) corresponding TFMA.

33 CHAPTER 3

ISOSTATICALLY DISTURBED TERRAINS FROM SPECTRALLY CORRELATED FREE-AIR AND TERRAIN GRAVITY DATA

34 ABSTRACT

Recently revised models on global tectonics describe the convergence of the North

Andes, Nazca, Caribbean and South American Plates and their seismicity, volcanism, active faulting and extreme topography. The current plate boundaries of the area are mainly interpreted from volcanic and seismic datasets with variable conﬁdence levels. New insights on the isostatic state of the northwestern Andes Mountains can be obtained from the spectral analysis of recently available gravity and topography data.

Isostatically disturbed terrain produces free-air anomalies that are highly correlated with the gravity eﬀects of the terrain. Spectrally correlated the terrain gravity eﬀects

(TGE) and free air gravity anomalies (FAGA) of the Andes mountains conﬁrms that these mountains are isostatically disturbed. Strong negative terrain-correlated FAGA along western South America and the Greater and Lesser Antilles are consistent with anomalously deepened mantle displaced by subducting oceanic plates.

Inversion of the gravity anomalies reveals plate subduction systems with alternat- ing shallower and steeper subduction angles. The gravity modeling highlights crustal deformation from plate collision and subduction and other constraints on the tectonism of the plate boundary zones for the region.

3.1 Introduction

The tectonic setting of northwestern South America is poorly understood because of the complex interaction of numerous tectonic plates, and the scarce and incomplete

35 geologic mapping due to the dense vegetation cover and limited accessibility to re- mote areas. International scientiﬁc interest in the northwestern Andes Mountains is intense because it is the key to improve our understanding of the geological evolution of the backbone of the Americas and the Caribbean and related volcanic and seismic hazards. The ability of current physical models to predict neotectonic and other intra-plate lithospheric stresses and strain is limited because the structures and geometry of plate boundaries are largely hidden and poorly understood. However, the deployment of geodetic sensors including the GPS-derived ground velocities and high resolution topography has substantially improved the modeling of the lithosphere to analyze surface mass dynamics (Kellogg, et al., 1985).

In this chapter, spectral correlation theory (e.g., Leftwich, et al., 2005; von Frese and Tan, 1999) is applied to terrain and free-air gravity anomalies for new constraints on the boundary zones of the North Andes and Panama Microplates, and the Cocos,

Nazca, Caribbean and South American Plates. Normalization and local favorability indexes are implemented to facilitate the visualization and interpretation of gravity anomalies. This methodology has been applied and validated in other crustal studies such as East Asia (Tan and von Frese, 1997), Antarctica (von Frese et al., 1999), Green- land (Roman, 1999), Ohio (Kim et al., 2000), and Iceland (Leftwich, et al., 2005).

Isostatically disturbed terrain produces free-air anomalies that are highly correlated with the gravity eﬀects of the terrain. Spectrally correlating the terrain gravity eﬀects (TGE) and free-air gravity anomalies (FAGA) suggested that the Andes mountains are isostatically disturbed with an anomalous underlying crust-mantle interface

(MOHO). Strong negative terrain-correlated FAGA along western South America and

36 the Greater and Lesser Antilles are consistent with anomalously deepened mantle displaced by subducting oceanic plates. Crustal sections from inversion of gravity anomalies showed waves of shallowing and steeping subduction systems that are also supported by seismic data. However, gravity estimates regionally augment and extend the seismic estimates to highlight crustal deformation from plate collision and subduction in Northwestern South America. The gravity anomalies reveal a complex evolution for northwestern South America involving the accretion of an oceanic plateau with strong

Caribbean aﬃnities, obduction of the oceanic crust, over thrusting and strike-slip faulting. These tectonic characteristics are not readily accounted for by the conventional model of “Andean Type” orogenesis of the Central Andes (Liu, et al., 2002).

3.2 Spectrally correlated free-air and terrain gravity

The isostasy of northwestern South America was investigated considering the topography/bathymetry data from National Imagery and Mapping Agency (NIMA) from −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude. Surface and bathymetry elevations from the JGP95E terrain data base (Smith and Sandwell, 1994,

1997) were processed to produce the Digital Elevation Model (DEM) in Figure 3.1 for the water and rock terrain gravity components at 0.5o nodal spacing. Free-air gravity anomalies (FAGA) were estimated from the EGM96 spherical harmonic Earth Gravity

Model to degree and order 360 (Lemoine, et al., 1998) at 20 km altitude over the 32o x 32o area at 0.5o nodal spacing in Figure 3.2. The altitude of 20 km was chosen to help minimize the eﬀects of local density errors in the terrain gravity modeling (e.g.,

Leftwich et al., 2005).

37 Figure 3.1: Topography/bathymetry of northwestern South America with superposed regional tectonic features between −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

38 Figure 3.2: Free-air gravity anomalies (FAGA) at 20 km elevation for the study region (Lemoine, et al., 1998). Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

39 The terrain gravity eﬀects were modeled in spherical coordinates at 20 km altitude by Gauss-Legendre Quadrature integration in Figure 3.3 (von Frese, 1980). The terrain gravity modeling used densities of 2.8 gm/cm3 for the crust and 1.03 gm/cm3 for oceanic water.

Spectral correlation theory was used to analyze the co-registered FAGA and TGE for their anomaly correlations. Speciﬁcally, the Fourier transforms T and F of TGE and FAGA, respectively, were used to obtain their correlation spectrum (von Frese et al., 1997a, Kim, et al., 2000) given by:

" # F (k) |T (k)| CC(k) = cos(∆θk) = Re , (3.1) T (k) |F k)| where CC(k) is the correlation coeﬃcient between the kth wavenumber components

F(k) and T(k), and denotes taking the real parts of the wavenumber components.

Usually, CC(k) is evaluated from the cosine of the phase diﬀerence (∆θk) between the two kth wavenumber components.

Using the correlation spectrum between FAGA and TGE, spectral correlation ﬁlters were designed to extract terrain-correlated free-air gravity signals. Those wavenumber components showing intermediate to high positive (CCp(k) ≥ 0.3) and negative

(CCn(k) ≤ 0.3) correlations were identified. The cut off values for the correlation filter were determined to minimize correlative features between the terrain-decorrelated free- air and compensating terrain gravity components. Inversely transforming positively and negatively correlated free-air wavenumber components according to the selected cut off values yielded the terrain-correlated free air gravity anomalies (TCFAGA) in

Figure 3.4. The residual terrain-decorrelated free-air gravity anomalies (TDFAGA) in Figure 3.5 were calculated by subtracting TCFAGA from FAGA, so that

40 Figure 3.3: Terrain Gravity Eﬀects (TGE) at 20 km elevation for the study region by Gauss-Legendre quadrature integration. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

41 F AGA = T CF AGA + T DF AGA (3.2)

TCFAGA are explained by anomalies associated with the topography while TDFAGA include the gravity eﬀects of sources within the crust (i.e., local bodies) and the sub- crust.

Similarly, spectral correlation ﬁlters were used to extract FAGA-correlated TGE

(FCTGE) in Figure 3.6 and FAGA-decorrelated TGE (FDTGE) in Figure 3.7. The

FCTGE sharpen up the TGE components that may be isostatically disturbed, whereas the FDTGE involve relatively marginal amplitudes that appear to reﬂect mostly noise from data processing and other non-geological eﬀects.

3.3 Analysis of anomaly correlations

TCFAGA and FCTGE were normalized to facilitate recognizing the anomaly correlations between them (von Frese et al., 1997). To enhance the visual perception of the anomaly correlations, the following transformation was applied:

Ã ! xi − µX Zi(X) = σZ + µZ , (3.3) σX where µX and σX represent the values of the mean and standard deviation, respectively, of the signal X. The expression in parentheses standardizes the xi coeﬃcients to zero mean and unit standard deviation and is dimensionless. However, the values for mean

σZ and standard deviation of µZ of the normalized signal Z can be speciﬁed by the user to facilitate the visual analysis.

The transformations of TCFAGA and FCTGE used the normalization of σZ = 10 to facilitate plotting the two datasets with common plotting parameters (von Frese et al.,

42 Figure 3.4: Terrain-correlated FAGA (TCFAGA) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

43 Figure 3.5: Terrain-decorrelated FAGA (TDFAGA) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

44 Figure 3.6: FAGA-correlated TGE (FCTGE) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

45 Figure 3.7: FAGA-decorrelated TGE (FDTGE) at 20 km elevation for the study area. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

46 1997). Local favorability indices (Merriam and Sneath, 1966) were used to highlight the various anomaly correlations in the normalized TCFAGA and FCTGE. Positively correlated features were mapped out by summed local favorability indexes (SLFI) obtained by:

(zi(X)) − µZ ) (zi(Y ) − µZ ) SLF Ii = + , (3.4) σZ σZ

where Z(X) and Z(Y) were the normalized TCFAGA and FCTGE coefficients, respectively. The peak-to-peak correlations between the two data sets were mapped out by SLF Ii ≥ 8.7226 in Figure 3.8, whereas trough-to-trough correlations were mapped out by the coefficients satisfying SLF Ii ≤ 8.7226 in Figure 3.9. The SLFI coefficients brought out the positively or directly correlated features, while suppressing the negatively and null correlated features between TCFAGA and FCTGE.

To enhance the perception of inversely correlated features obtained from wavenum- bers with negative correlation coeﬃcients, the normalized and scaled datasets were subtracted cell by cell for diﬀerenced local favorability indexes (DLFI) by:

(zi(X)) − µZ ) (zi(Y ) − µZ ) DLF Ii = − (3.5) σZ σZ

Positive features in TCFAGA which were correlative with negative FCTGE features (peak-to-trough) were mapped out by DLFI ≥ 4.8904 in Figure 3.10, whereas negative TCFAGA that were correlative with positive FCTGE were mapped out by

DLFI ≤ −4.8904 in Figure 3.11. The DLFI coeﬃcients emphasized the inversely correlated features, while suppressing the positively and null correlated features between

TCFAGA and FCTGE. Table 3.1 summarizes the correlations between FAGA and

TGE and their correlated ﬁltered components.

47 Figure 3.8: Summed local favorability indices (SLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing TCFAGA-peak to FCTGE-peak correlations for SLFI ≥ 8.7226. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

48 Figure 3.9: Summed local favorability indices (SLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA-trough to FCTGE-trough correlations for SLFI ≤ −8.7226. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

49 CC TGE FCTGE FDTGE FAGA TCFAGA TDFAGA TGE 1 0.97 0.24 0.52 0.59 0 FCTGE 0.97 1 0 0.56 0.6 0.05 FDTGE 0.24 0 1 -0.09 0 -0.2 FAGA 0.52 0.56 -0.09 1 0.89 0.45 TCFAGA 0.59 0.6 0 0.89 1 0 TDFAGA 0 0.05 -0.2 0.45 0 1

Table 3.1: Correlation coeﬃcients (CC) between the gravity anomalies at 20 km altitude for the area from −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude in northwestern South America.

The increase in the CC between TCFAGA and TGE (CC= 0.59) relative to the CC between the raw FAGA and TGE (CC=0.52) facilitates the isostatic analysis of the tectonic features of the study area. However, the increase in the CC between TCFAGA and FCTGE (CC=0.6) with respect to the CC between TCFAGA and TGE (cc=0.59) is negligible and the physical meaning of FCTGE and FDTGE is obscured.

The CC between TDFAGA and FAGA (CC= 0.45) is signiﬁcant in showing the strong inﬂuence of the gridded data in the anomaly decomposition of FAGA in TCFAGA and TDFAGA. Therefore, further analysis of TDFAGA are required.

3.4 Discussion of results

Isostatically disturbed terrains have gravity eﬀects that directly correlate with

FAGA. The complementary TDFAGA reﬂect the eﬀects of lateral density variations in the crust, mantle and core, as well errors in the data and data processing.

50 Figure 3.10: Diﬀerenced local favorability indices (DLFI) between TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA-peak to FCTGE-trough associations for DLFI> 4.8904. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

51 Figure 3.11: Diﬀerenced local favorability indices (DLFI) for TCFAGA and FCTGE at 20 km elevation for the study region showing the TCFAGA-trough to FCTGE-peak associations for DLFI<- 4.8904. SNSM= Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

52 In the subsections below, the gravity eﬀects of the DTM and spectral correlations with free-air gravity anomalies are interpreted for constraints on the tectonic features of the study region.

3.4.1 Digital terrain model (DTM)

The DTM in Figure 3.1 presents major morphotectonic features that produce strong terrain gravity eﬀects in the gravity anomalies. The topography data are increasingly being integrated into the techniques to study plate boundary zones (Stein

& Freymueller, 2002). One approach is to use digital terrain models (DTM) showing the forms of mountain ranges, oceanic trenches, volcanic ridges and island arcs, and oceanic basins to constrain models of the processes that produced them. The DTM of northwestern South America suggests a complex tectonic setting with mountain building and uplift as a consequence of the plate convergences that have created the

North Andes Mountains, the Sierra Nevada of Santa Marta and the Cordillera Cen- tral Mountains. Flat low lands are associated with the stable cratonic terrains of the

Guiana Shield. Deep Paciﬁc Ocean trenches along the Peru - Ecuador - Colombia coastline and the Middle America Trench are associated with subduction zones. The

Puerto Rico Trench in the Caribbean is associated with the Caribbean − North Amer- ican subduction zone. The submarine Carnegie, Cocos and Malpelo volcanic ridges are associated with the Galapagos hot spot. The volcanic arc islands of the Lesser and

Greater Antilles reﬂect intensive geodynamics in the region, including high seismicity and volcanic activity.

3.4.2 Free-air gravity anomalies (FAGA)

The free air gravity anomalies in Figure 3.2 include the superposed gravity eﬀects of the terrain and subsurface gravity variations. The FAGA amplitudes are smaller than

53 the TGE amplitudes reﬂecting partial isostatic compensation of the terrain. However, the mean FAGA of 17 mGals indicates the mean terrain is isostatically disturbed.

The largest negative anomalies are over the subduction zones, whereas the strongest positive FAGA are over the Andes Mountains and Sierra Nevada of Santa Marta. Mod- erate positive and negative FAGA are distributed along the oceanic volcanic ridges,

Guiana Craton and oceanic plates. The positive correlation between TGE and FAGA

(CC = 0.52) reﬂects the predominant condition of isostatically disturbed terrain in the tectonically complex study region.

3.4.3 Terrain gravity eﬀects

The terrain gravity eﬀects (TGE) in Figure 3.3 produced by crust - air (2.8 gm/cm3) and crust - water (1.82 gm/cm3) interfaces are the highest density contrasts that can be deﬁned by the lithosphere. Therefore, the minimum and maximum

TGE values of -452.12 mGals and 285.02 mGals, respectively, are also the extreme values that we can expect FAGA to take on in a case of 0% isostatic compensation.

Negative TGE predominate (T GEmean = −51.21 mGals) and are stronger over the

Caribbean Sea than the Paciﬁc Ocean. Negative TGE overlie the Puerto Rico Trench,

Cayman Trough, and Colombian and Venezuelan Basins. The Beata Ridge, Lesser and

Greater Antilles have relatively positive TGE. In the Paciﬁc, negative TGE overlie the

Panama Basin and the Peru Trench, and positive TGE overlie the Carnegie, Cocos and Malpelo Ridges. At the continent, positive TGE reﬂect the presence of the mountainous Central America, Andes Mountains, Sierra Nevada of Santa Martha and the

Guiana Craton. Relatively negative anomalies are associated with the Vichada Plain and Amazon River Aulacogens.

54 3.4.4 Terrain-correlated free-air gravity anomalies

TCFAGA in Figure 3.4 have a more complex anomaly pattern than TGE infer- ring a wide range isostatic disturbances of the terrain. TCFAGA varies from -190.28 to

131.66 mGals, with a mean value of zero. Thus, the TCFAGA reﬂect both negative and positive disturbances of continental and oceanic features. Arcuate positive and negative

TCFAGA can be observed along the Greater and Lesser Antilles, along the Caribbean

- North American plate boundary. Volcanic activity and mountain building are associated with positive TCFAGA, whereas negative TCFAGA characterize trenches and troughs. Therefore, the subduction of the North American plate under the Caribbean

Plate is well mapped from the TCFAGA. Negative TCFAGA beneath the trenches are due to the negative density contrast (∼= - 0.37 gm/cm3) of the subducting oceanic slab into the mantle. Positive TCFAGA are explained by oceanic crustal thickening and the recently formed volcanic islands which are not fully compensated. The TCFAGA are smaller than TGE, suggesting partial isostatic compensation from the thickening of the oceanic crust into the mantle. Negative TCFAGA are located along the Colombian

- Venezuelan Basins and the Caribbean − North Andes subduction zone (Bird, 2003,

CASA, 1998). The low TCFAGA amplitudes suggests that this subduction is incipient with respect to the Caribbean - North American or Nazca - North Andes subduction zones. In Central America, the positive TCFAGA from Panama to Costa Rica (60-80 mGals) and from Nicaragua to Honduras (20-40 mGals) are less prominent than the

TCFAGA in the Andes (80-100 mGals) showing that Central America is relatively more fully compensated than the Andes Mountains. The converging plate boundary between the Panama and North Andes microplates proposed by Kellogg (1985) is not supported by the TCFAGA which shows no distinct anomaly between them.

55 At the Paciﬁc Ocean, negative TCFAGA clearly deﬁne the Middle America Trench.

Relatively positive TCFAGA are associated with the ﬂat slab subduction of the Cocos ridge under the Panama − Costa Rica Microplate. Negative TCFAGA along the western margin of South America vary from -10 to -60 mGals, being comparatively smaller in the Colombian Trench. These results reﬂect the lower angle of subduction of the

Nazca plate in contrast to the steeper angles of subduction and negative amplitudes at the Chilean - Peruvian subduction zone. Relative TCFAGA highs are associated with the ﬂat slab subduction of the Carnegie Ridge under the North Andes Microplate.

At the continent, positive TCFAGA at the Andes Mountains (90 to 130 mGals) show that these mountains are isostatically disturbed. A remarkable isolated positive

TCFAGA anomaly is located in northern Colombia, in the Sierra Nevada of Santa

Marta (130 mGals). Here, the highest elevations of northwestern South America have also the maximum TCFAGA, showing that these mountains, reaching elevations of

5800 m, are even less compensated than the Andes mountains suggesting that the

Sierra Nevada of Santa Marta has been intensively deformed and uplifted after the

Andean orogenesis.

It is not clear how these mountains were formed and why they occupy their present position. These mountains maybe are perhaps allochthonous tectonic blocks that were moved from the east along a left lateral fault (Dewey and Pindell, 1985). The TCFAGA also support this explanation, which implies that lateral stress caused crustal shortening and uplift of the Sierra Nevada of Santa Marta without signiﬁcant isostatic compensation.

TCFAGA at the Guiana Craton are close to zero suggesting nearly complete isostatic compensation. Local TCFAGA highs and lows may reﬂect the occurrence of lateral mass variations related to intrusive bodies without topographic expression (TGE

56 = 0). Here, the TCFAGA that are greater than the TGE give an example of overcompensated terrain. The negative TCFAGA along the Eastern Andes Mountains are associated with continent - continent convergence between the North Andes Microplate and the South American Plate with regional thrust faults dipping to the west and intensive compressional and transpressional deformation (Cediel et al., 2003). Therefore, the negative TCFAGA along the eastern cordilleran area appear to reﬂect the thickening of the continental crust with thick sedimentary sequences that are known to contain oil and gas deposits (Stein & Sella, 2002).

3.4.5 Terrain-decorrelated free-air gravity anomalies

The TDFAGA in Figure 3.5 are very poorly correlated with TGE (CC = −0.0575) and mostly show gridded patterns due likely to data processing noise. Thus, I do not consider the geological implications further for the TDFAGA.

3.4.6 TCFAGA and FCTGE anomaly correlations

Tectonic analysis of enhanced correlations between the TCFAGA and FCTGE are visualized better using summed local favorability indices with (SFLI ≥ 8.7226) in Figure 3.8. High amplitude peak-to-peak zones along the Andes Mountains over- lay mapped mineralized batholithic intrusions (INGEOMINAS, 1987). According to

Kerr, et al. (1997), subduction related batholiths and extrusive rocks found around the margin of the Caribbean - Colombian cretaceous igneous province are of two distinct events: one suite represents the pre-plateau, collision-related volcanism, whereas the other suite, which is slightly younger than the plateau, may be associated with subduction. Therefore, peak-to-peak zones along the western Cordillera may be associated with subduction, whereas peak-to-peak zones along the eastern Cordillera are associated with the pre-plateau collision suite of igneous rocks.

57 Intermediate amplitude peak-to-peak correlations at the Guiana Craton also indicate isolated topographic highs on relatively denser intrusive rocks of the cratonic basement. These inferred intrusions may be the source rocks of known gold and dia- mond placer deposits of the Guainia and Orinoco rivers (Romero et al., 1996).

The SLFI ≤ −8.7226 in Figure 3.9 show trough-to-trough correlations between

TCFAGA and FCTGE, respectively. They clearly mark the Puerto Rico, Colombian and Peruvian Trenches, while the Middle American Trench and the Paciﬁc Colombian

Trenches are relatively poorly deﬁned. The oceanic trenches are the most isostatically disturbed features in the area and also the most seismically active features. Of special interest are the intermediate trough-to-trough correlations of TCFAGA and FCTGE in the Colombian and Venezuela Basins. These areas are undergoing intensive exploration for oil and gas and have productive ﬁelds associated with delta deposits of the

Magdalena River, the major supplier of sediments to the Caribbean Sea. Therefore, the

SLFI anomaly correlations may mark strong prospective areas for locating sedimentary basins in the Caribbean plate.

The diﬀerenced local favorability indices with DLF I ≥ 4.8904 show TCFAGA-peak to FCTGE-trough correlations in Figure 3.10. They mark topographic depressions that are overcompensated by local denser bodies along the Lesser Antilles, Colombian basin, western and central ranges, Sierra Nevada of Santa Marta and at the North

American Plate. The TCFAGA-trough to FCTGE-peak correlations with DLF I ≤

4.8904 in Figure 3.11, on the other hand, show the distribution of low density zones along the eastern Andean Mountains, the upper Amazon River and lower Orinoco river. The negative DLFI zones mark mapped sedimentary basins including the upper, middle and lower Magdalena valley (UMV, MMV and LMV, respectively), and the

Orito, Llanos, Maracaibo, Guajira and Orinoco basins with known productive oil and

58 gas ﬁelds. Thus, The negative DLFI zone outlined at the upper Amazon river aulacogen may also infer a prospective sedimentary basin for oil and gas exploration.

3.5 Conclusions

The central parts of the Nazca, Cocos and Caribbean Plates are mostly in isostatic equilibrium with TCFAGA close to zero. This condition changes at the plate boundary zones and volcanic ridges. Positive TCFAGA are associated with the Malpelo, Cocos,

Carnegie and Beata Ridges. Thickening the oceanic crust by crustal roots into the mantle partially compensates for the TGE. In the case of the Malpelo Ridge, this volcanic range is partially compensated with a crustal root, in agreement with the model proposed by Watts (2001) for isostatic compensation of seamounts and oceanic islands. Depth to the MOHO estimated from gravity data is supported by seismic data

(Trummer, 2002). The Andes Mountains are isostatically disturbed. The Airy-type isostatic model is consistent with the thickening of the crust at the Andes Mountains, but lateral density variations between the oceanic and continental crusts must be involved to model TCFAGA. The Pratt-type isostatic model is not appropriate to model

TCFAGA of the Andean Mountains. This model can not account for the continental roots shown in the seismic data.

Locally positive TCFAGA anomalies in the Guiana Craton are associated with relatively denser intrusive bodies aﬀecting the host cratonic rocks. These intrusive bodies do not have a signiﬁcant surface expression and may be related to mass variations in the crust and upper mantle.

Compressional tectonics has played an important role in the mountain building of the North Andes Microplate as a consequence of the relative movements among Nazca,

South America and Caribbean Plates and Panama and North Andes Micro plates.

The shortening associated with plate motion, based on GPS data only accounts for

59 less than 50% of the mountain building (Lamb, 2004). Magmatic underplating and crustal doubling due to overthrusting may also contribute to the formation of the

Andes Mountains as inferred by the positive TCFAGA.

Considering that isostatic equilibrium is the ideal state that any uncompensated mass tends to reach through time, implies that any uncompensated mass of the North

Andes Mountains is under pressure to adjust vertically and horizontally to reach equilibrium. Therefore, a direct correlation is expected between disturbed and seismically active terrains whereas minimal seismic activity is expected for isostatically compensated terrains.

SLFI and DLFI enhance TCFAGA and FCTGE anomaly correlation, providing new criteria to locate areas for prospecting mineral and fossil fuel deposits.

60 CHAPTER 4

CRUSTAL THICKNESS AND DISCONTINUITY ESTIMATES

61 ABSTRACT

A new model for the crustal evolution of northwestern South America (−8oS to

23.5oN, −90oW to −58.5oW) was developed from gravityderived MOHO depth estimates and tectonic features interpreted from correlative geopotential anomalies and seismic data. Crustal thickness estimates provide important constraints on the distribution of volcanic and seismic hazards, and mineral and energy deposits. Gravity crustal thickness estimates are also useful for interpreting crustal magnetic anomalies and thermal gradients. Crustal thickness estimates were obtained by inversion of the compensated terrain gravity eﬀects (CTGE) and compared against theoretical Airy

MOHO and compiled seismic MOHO estimates.

Crustal thicknesses between 45 to 55 km at the continent are related to the presence of andesitic batholiths of economic interest. Major batholiths in the Central Andes, are related to gravity-inferred crustal thicknesses between 55 km to 60 km. Therefore, these results suggest that exploration of mineral deposits associated with batholithic intrusions in the Andes Mountains can be extended to crustal thicknesses from 45 km to 60 km.

Oceanic crustal thicknesses between 15 km to 20 km at the Caribbean are expected to have relatively low thermal gradients. These crustal thicknesses are ideal for hosting local oil and gas producing sedimentary basins that are associated with the delta deposits of the Magdalena and Orinoco Rivers.

62 New insights into the tectonic setting of northwestern South America are presented that establish the relationship between the crustal thickness variations and the distribution of magmatic bodies, active volcanoes, seismic hazards and economic mineral and energy deposits. They also show that the northwestern Andes are diﬀerent from the Central Andes Mountains that exhibit the typical “Andean subduction zone.”

4.1 Introduction

Terrain-correlated free-air anomalies can be compared with the gravity eﬀects of the terrain for estimating the relief of the crust-mantle boundary (MOHO) that non- gravity methods like seismic surveys image. Thus, new insights into crustal tectonic features and their evolution can result from the analysis of recently available gravity observations from satellite, airborne and surface survey.

Improved crustal thickness estimates are useful to advance understanding of the isostatic state of the Andes Mountains and the mapping of seismically active crustal discontinuities and plate boundary zones, the distribution of ore deposits and sedimentary basins for oil and gas exploration. This chapter presents the crustal thickness modeling for estimating the MOHO topography from the spectral correlation analysis of the free-air and terrain gravity eﬀects. Crustal discontinuities are also interpreted from the gravity anomalies on a 5 km x 5 km grid of the North Andes Microplate.

4.2 Crustal modeling

A new crustal thickness model for northwestern South America was developed using the compensated terrain gravity eﬀects (CTGE) in Figure 4.1 that resulted when the TGE (Figure 3.3) were subtracted from TCFAGA (Figure 3.4).The CTGE represent isostatically adjusted complete Bouguer anomalies that correspond to the gravity eﬀects of the terrain in isostatic equilibrium. This approach is feasible because

63 90% of the earth is in equilibrium with the mean global free-air gravity anomaly being zero (Heiskanen and Moritz, 1967). MOHO and related crustal thickness variations were modeled from the CTGE (Figure 4.1) by inversion as shown in Figure 4.2, assuming the constant nominal density contrast of 0.4 gm/cm3 of the mantle relative to the crust. This methodology has been successfully applied in studies of the mantle- crust interface for East Asia (Tan and von Frese, 1997), Antarctica (von Frese et al.,

1999), Greenland (Roman, 1999), Ohio (Kim et al., 2000), and Iceland and the North

Atlantic (Leftwich, et al., 2005, Leftwich, 2006).

Negative CTGE are located along the eastern Andes Mountains suggesting some degree of partial compensation and thickening of the crust. The CC between TCFAGA and CTGE is -0.3377 showing that most of the topography/bathymetry is isostatically disturbed.

Gravity MOHO estimates were compared against the seismic MOHO in Figure 4.3 compiled by Bassin et al. (2000). This model presents crustal thickness estimates on a 2ox2o grid was regridded to the 0.5o interval of the gravity MOHO.

4.3 Comparison with Airy MOHO estimates

The density compensation required for isostatic equilibrium from topographic load- ing is commonly assessed from the Airy compensation (Turcotte and Gerald, 2002) assuming constant densities of the crust (ρc) and mantle (ρm). The displacement d of the bottom of the crust in response to a crustal load of height h is:

ρ h d = c , (4.1) ρm − ρc where d and h are relative to the crust of constant thickness H. If the height of the topography is negative and covered by water, then

64 Figure 4.1: Compensated terrain gravity eﬀects (CTGE) at 20 km elevation for the study region obtained by subtracting TGE from TCFAGA. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western- Central ranges. This map was produced using the Albers equal-area conic projection.

65 Figure 4.2: Gravity MOHO obtained from the inversion of CTGE showing deep MOHO beneath the mountains and oceanic ridges. Map annotations include the amplitude range (AR) of (min; max) values, the amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

66 Figure 4.3: Seismic MOHO from the CRUST 2.0 model (Bassin et al., 2000) showing deeper MOHO below the mountains and oceanic ridges. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

67 " # ρ − ρ d = c w h (4.2) ρm − ρc

The Airy MOHO for northwestern South America was calculated (Figure 4.4)

3 3 3 assuming ρc = 2.8 gm/cm , ρm = 3.3 gm/cm , ρw = 1.03 gm/cm and H = 35 km.

This model shows the continental and oceanic crustal thickness variations, including the roots and anti-roots required to reach the isostatic compensation. The calculations used a crustal thickness (35 km) that corresponds to the mean seismic MOHO estimate.

Figure 4.5 gives the diﬀerences when the gravity MOHO is subtracted from the

Airy MOHO. The mean diﬀerence is -2.2 km. Crust-mantle density contrasts of 0.37 gm/cm3 at the oceans and 0.45 gm/cm3 at the continent were used for the Airy MOHO estimates, whereas 0.4 gm/cm3 was used for the gravity MOHO estimates, respectively.

4.4 Comparison with seismic MOHO estimates

Seismic MOHO estimates from the CRUST 2.0 model in Figure 4.3 were gath- ered from seismic experiments and averaged globally from similar geologic and tectonic settings (e.g., Archean, early Proterozoic, rifts etc.). These averages were used to infer MOHO depths in regions lacking seismic information (e.g., most of Africa, South

America). Bathymetry and topography data were compiled from ETOPO5. The global model is composed of 360 one dimensional proﬁles that were gridded at 2o x 2o.

The comparison of Figure 4.2 and Figure 4.3 shows that the seismic MOHO has lower resolution than the gravity MOHO. The seismic MOHO also shows a thinner oceanic crust and a thicker continental crust with deeper crustal roots beneath the

Andes Mountains.

The methodology applied in the CRUST 2.O model to average global seismic responses for similar geological and tectonic settings and assign these averages to regions

68 Figure 4.4: Airy MOHO obtained the hydrostatic equilibrium principle. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

69 Figure 4.5: MOHO diﬀerences by subtracting gravity MOHO from Airy MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

70 without seismic information is not effective for representing the tectonic features of northwestern South America. For example, the seismic and gravity Moho differences in Figure 4.6 are especially severe at the Cocos, Nazca, Malpelo and Beata oceanic volcanic ridges, the Guiana Craton, Puerto Rico Trench and Pacific Subduction zone.

The mean diﬀerence is -3.9 km which indicates that the seismic MOHO estimates do not take into account eﬀects related to thermal expansion and the resulting lower density of underplated mantle materials included in the gravity MOHO estimates.

The diﬀerences between the Airy and seismic MOHO estimates in Figure 4.7 are less severe as indicated by the mean value of 1.7 km. However, the diﬀerences are between 5 to 10 km at the oceanic ridges, the Greater and Lesser Antilles, the Sierra

Nevada of Santa Marta, and the northernmost Andes Mountains.

4.5 Crustal cross-sections

Airy, gravity and seismic MOHO proﬁles were constructed across the Paciﬁc subduction zone, the Caribbean subduction zone and the Caribbean plate from Central

America to the Lesser Antilles. In the sections below, these proﬁles are compared at the major tectonic features of the study area to investigate the veracity of the gravity

MOHO solutions.

4.5.1 Paciﬁc subduction zone - Andes Mountains - Guiana Craton

The proﬁle in Figure 4.8 was constructed along the 5oN latitude from −90oW to

−58.5oW longitudes. It includes the Cocos and Malpelo Ridges, the Paciﬁc subduction zone, the Andes Mountains and Guiana Craton. The correlation of the gravity

MOHO with the Airy MOHO is maximum(CC = 0.9701), but minimum with the seismic MOHO (CC = 0.8799) and somewhat higher (CC = 0.8936) between the Airy

71 Figure 4.6: MOHO diﬀerences by subtracting gravity MOHO from seismic MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

72 Figure 4.7: MOHO diﬀerences by subtracting the seismic MOHO from the Airy MOHO estimates. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

73 MOHO and the seismic MOHO. The three MOHO solutions are consistent with a thinner oceanic crust, low angle subducting slab, and thicker continental crust at the

Andes Mountains and an average thickness crust for the Guiana Craton. The differences between gravity and Airy MOHO solutions vary from 0 to 2.5 km at the Cocos and Malpelo Ridges and between 5 and 7.5 km at the continental roots of the An- des Mountains, reflecting partial isostatic compensation. The differences between the gravity and seismic MOHO estimates vary from 7.5 to 17.5 km at the volcanic ridges and from 2.5 to 5 km at the continental roots of the Andes Mountains, respectively, reflecting the reduced mantle density due to hotter than normal mantle at the ridge

(Leftwich et al., 2005).

4.5.2 Guiana Craton-Andes Mountains-Caribbean subduction zone

The proﬁle in Figure 4.9 was extracted from (OoN −78oW) to (23.5oN −75oW), across to the Caribbean - North Andes subduction zone . It includes the Guiana

Craton, the Venezuelan Andes, Caribbean subduction zone, Caribbean Plate, Greater

Antilles, Cayman Trough and North American Plate. The Gravity MOHO and Airy

MOHO are positively correlated (CC 0.9062) showing diﬀerences of 7.5 km at the

Venezuelan Andes mountains, 5 km at the Caribbean plate and 7 km at the Cayman

Trough. The gravity and seismic MOHO estimates are also poorly correlated (0.5348) with diﬀerences between 5 to 7.5 km at the Caribbean subduction zone and about 2 km at the Cayman Trough. The Airy and seismic MOHOs are likewise poorly correlated

(0.6464) with diﬀerences of 5 km at the Venezuelan Andes and 7 km at the Cayman

Trough.

74 Figure 4.8: Gravity, seismic and Airy MOHO estimates at 5oN latitude from −90o to −58.5o longitude. MOHO diﬀerences are greatest at the volcanic ridges and Andes Mountains.

75 Figure 4.9: Gravity, seismic and Airy MOHO estimates at the Guiana Craton and North Andes − Caribbean subduction zone along (OoN, −78oW) to (23.5oN, −75oW).

The three MOHO estimates show a thicker continental crust at the Andean Moun- tains. The North Andes - Caribbean subduction zone presents diﬀerent angles of inclination at each MOHO solution. The Caribbean-North America plate boundary zone is clearly marked by a symmetrical anomaly suggesting vertical inclination of the plate boundary in agreement with proposed tectonic models for the Caribbean Plate (Pin- dell, et al., 2006).

76 4.5.3 Middle American Trench - Caribbean Plate - North American Plate

The proﬁle in Figure 4.10 was constructed along (12.5oN, −90oW) to (16oN,

−58.5oW), across to the Middle American Trench and Caribbean-North America subduction zone. It includes The Middle American Trench, continental Central America, the Caribbean Plate and the Caribbean-North America subduction zone. The gravity and Airy MOHO estimates are positively correlated (CC = 0.9427) showing the largest diﬀerences only at the Central America-Caribbean plate boundary zone (5 km), and at the Caribbean-North American subduction zone (6 km). The gravity and seismic

MOHO estimates are also positively correlated (CC = 0.8774). There are diﬀerences as large as 5 km at the Caribbean-North American subduction zone and 4 km at the

Caribbean-Central America plate boundary zone, respectively. The Airy and seismic

MOHO estimates are positively correlated (CC = 0.8815) with diﬀerences as large as 5 km at the Caribbean plate. The three MOHO estimates show a thicker continental crust beneath Central America, a relatively thinner Caribbean oceanic crust, and thicker oceanic crust for the Lesser Antilles. The subduction zones are relatively poorly deﬁned in all the MOHO estimates. Figure 4.11 gives a more comprehensive crustal model of TCFAGA along 5oN latitude from −90o to −79oW, including the

Cocos and Malpelo Ridges of Figure 4.9. The Malpelo Ridge was studied by a high resolution seismic survey providing detailed MOHO estimates (Trummer, 2002). The modeling of TCFAGA was performed using GM-SYS and assigning density values of

1.03 gm/cm3 for sea water, 2.93 gm/cm3 for oceanic crust, and 3.3 gm/cm3 for the mantle. The model also included the presence of underplated material with the density of 3.0 gm/cm3 that was required to match observed and calculated TCFAGA.

The Gravity Moho is deeper beneath the Cocos and Malpelo Ridges reaching depths

77 Figure 4.10: Gravity, seismic and Airy MOHO estimates at the Caribbean − North American plates along (12.5oN, −90oW) , (16oN, −58.5oW).

78 Figure 4.11: Crustal proﬁle at 5oN latitude along −90oW to −79oW across the Cocos and Malpelo Ridges that is consistent with TCFAGA. Oceanic crustal thickening partially compensates TGE. The complete matching of observed and calculated gravity anomalies required the inclusion of underplated material that was less dense than the mantle.

of 20-25 km depth, and is positively correlated with the high resolution seismic MOHO of the Malpelo ridge (Trummer; 2002) in Figure 4.12, where an ophiolitic sequence overlaying an ultramaﬁc upper mantle was inferred. The mantle seismic velocities show variations from 4.0 to 4.8 km/s reﬂecting mantle anisotropy (Trummer,(2002).

The Cocos and Malpelo ridges are considered to be the tracks of the Galapagos hot spot, which is currently located beneath the Galapagos Archipelago (Trummer, 2002).

Therefore, the reduction in seismic velocities suggest the reduction of mantle density due to hotter than normal mantle at the ridge.

79 Figure 4.12: Two dimension P-wave velocity versus depth model across the Malpelo Ridge and Eastern Panama Basin showing an ophiolitic sequence with thinned oceanic crust and less dense underplated material in the upper mantle. The dashed line indicates a change in velocity gradient (Trummer, 2002).

80 The crustal features of the seven west-east oriented TCFAGA proﬁles in Figure 4.13 were inversely modeled using GM-SYS to estimate the angle of inclination along the

Paciﬁc subduction zone. The densities used were 2.85 gm/cm3 for continental crust,

2.93 gm/cm3 for oceanic crust and 3.3 gm/cm3 for the mantle. Subducting slabs with inclinations between 10o and 12o in profiles L1-L1’, L2-L2’, and L4-L4’ reflect relatively thinner subducting oceanic crust. The subducting slabs with an inclination < 10o (“flat slabs”) in profiles L3-L3’, L5-L5’, L6-L6’ and L7-L7’ are related to a relatively thicker subducting crust associated with the subduction of the Carnegie and Malpelo Ridges underneath the North Andes Microplate.

4.6 Crustal discontinuities of the North Andes Microplate

Gravity anomalies that require offsets or discontinuities may reflect the effects of tectonic lineaments that truncate the anomaly patterns. To interpret the TCFAGA gradient trends for crustal discontinuities, the digitizing tools from Oasis Montaj were used to infer major and local lineaments.

TCFAGA gradient trends in Figures 4.14 and 4.15 show the interpreted crustal discontinuities. The results clearly delineate the plate boundaries between the Caribbean-

North Andes, South American-North Andes and Caribbean-North American Plates.

However, the boundaries between the Caribbean-Costa Rica-Panama microplates are not well deﬁned. Plate boundaries at subduction zones tend to be better deﬁned than continent-continent collisional plate boundaries. The results locate the crustal discontinuities between the Eastern and Central Andean ranges and the crustal discontinuities limiting the Sierra Nevada of Santa Marta, delimiting various tectonic blocks in the

North Andes Microplate.

Figure 4.16 gives further crustal details from the inversion of two TCFAGA pro-

ﬁles oriented perpendicular to the North Andes Mountains. The TCFAGA inversions

81 Figure 4.13: Crustal profiles showing the different angles of subduction along the Nazca-North Andes plate boundary zone that are required to satisfy the TCFAGA. The TCFAGA map is also given in F igure 4.14. The TCFAGA map and crustal profiles were produced in Cartesian coordinates with origin (1’000.000 N, 1’000.000E) at the National Observatory of Bogota.

82 Figure 4.14: TCFAGA of northwestern South America at 20 km altitude and interpreted plate boundaries and intracrustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Ob- servatory of Bogota.

83 Figure 4.15: Plate boundaries and intracrustal discontinuities of northwestern South America interpreted from TCFAGA at 20 km altitude. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Ob- servatory of Bogota.

84 were obtained in Cartesian coordinates using GM-SYS capabilities. Proﬁle A-A’ shows how the continental crust varies from west to east. The MOHO estimates show two main continental roots below the western-central and eastern ranges reaching depths of 36 km and 47 km, respectively. The subducting oceanic slab with an initial inclination of 10o becomes steeper (15o to 20o) at 30 km depth. Proﬁle B-B’ shows a single continental root below the western-central ranges reaching a depth of 47 km.

The subducting oceanic slab is dipping 14oE.

Figures 4.17 and 4.18 show the surface free-air gravity anomalies and interpreted crustal discontinuities, respectively, in Cartesian coordinates. These maps were created using data reduction and processing procedures described in the Gravity National Net- work Catalog (IGAG, 1998) and classical geophysical textbooks (Telford, et al., 1994;

Keary Brooks, 1984). The randomly distributed point data data were interpolated at a 5 km x 5km grid using Geosoft Oasis Montaj. FAGA varies from -190 mGals to 131 mGals, with a mean zero value and standard deviation of 32 mGals. Crustal discontinuities inferred from FAGA at 20 km in Figures 4.14 and 4.15 are further detailed in surface FAGA including minor oﬀsets. Additional crustal discontinuities that were not readily detected at 20 km altitude are suggested in the surface FAGA to limit the regional tectonic blocks.

These new crustal discontinuities are associated with shallower structures, showing a regional trend oriented N20o − 30oE with a secondary trend oriented N 70o W that delimits elongated tectonic blocks of varying sizes. Major crustal discontinuities coincide with the limits of the tectonic realms proposed by Cediel et al. (2003) in

Figure 4.19. The crustal discontinuities interpreted from surface gravity anomalies reveal a complex pattern of rectangular tectonic blocks for the area.

The complete Bouguer anomalies at the surface in Figures 4.19 and 4.20 vary from -182 mGals to 249 mGals. Positive Bouguer anomalies are associated with the

85 Figure 4.16: Profiles (W-E) of the northern Andes Microplate showing the subducting oceanic slab under the continental crust as interpreted from TCFAGA at 20 km altitude. (a) Profile A-A: Two main continental roots were modeled below the west- central and eastern ranges, respectively. Smooth MOHO variations are observed below the Guiana Craton. (b) Profile B - B: A single continental root was modeled below the west-central ranges. No clear continental root below the incipient eastern range is evident and the MOHO below the Guiana Craton is relatively flat.

86 Figure 4.17: Surface FAGA and interpreted crustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the Na- tional Observatory of Bogota.

87 Figure 4.18: Plate boundaries and intracrustal discontinuities interpreted from surface FAGA. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota.

88 Figure 4.19: The tectonic realms and blocks of northwestern South America interpreted from geological and geophysical data (Cediel et al., 2003).

89 oceanic Caribbean and Nazca Plates. Intermediate positive anomalies are located at the Guiana Craton and Sierra Nevada of Santa Marta and remarkable negative Bouguer anomalies are found along the Andes Mountains. Relative to FAGA analysis, only a few of the discontinuities can be outlined in the Bouguer anomaly map.

4.7 Discussion

The Degree of isostatic imbalance is directly related to the magnitude of FAGA.

Removing TCFAGA from FAGA reduces the eﬀect of isostatic disturbances in the

TGE. Regional crustal thickness variations are supported by the gravity and seismic

MOHO estimates. The gravity MOHO estimates show higher resolution than the seismic MOHO estimates. Gravity components like CTGE, TGE and FAGA provide relatively continuous coverage for producing a 0.5o x 0.5o grid, while the seismic MOHO estimates were compiled from a 2o x 2o grid from the interpolation of sparse point depth solutions.

According to Watts (2001), local mass loads with wavelength less than 100 km

(∼= 1o in the spherical coordinates of the study area) are supported by the rigidity of the crust. Thus, our results which are based on a 0.5o array has limited resolution; therefore, the contribution of local body gravity eﬀects in the free-air gravity anomalies is minimal.

The gravity MOHO is shallower than the seismic MOHO of the continent and deeper than the seismic MOHO of the oceans. At the continent, seismic Moho estimates are systematically shallower (0 -12 km) than the gravity MOHO, suggesting that the mean density value assumed for the inverse modeling was higher, requiring less thickenning of the continental crust to match TCFAGA. At the oceans, seismic

MOHO estimates are systematically shallower 0 to 14 km systematically shallower than the gravity MOHO estimates.

90 Figure 4.20: Surface complete Bouguer anomalies and interpreted plate boundaries and intracrustal discontinuities. This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota.

91 Figure 4.21: Plate boundaries and intracrustal discontinuities interpreted from surface Bouguer anomalies. This map was produced in Cartesian coordinates referred to an origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota.

92 The advantage of using gravity data at 20 km altitude relies on enhancing the eﬀects of any regional disturbances of the terrain that may be related to the crust- mantle interface. Regional proﬁles of TCFAGA and gravity MOHO are useful for mapping the tectonic features of the oceanic and continental crust.

4.8 Conclusions

The tectonic analysis of northwestern South America shows a complex tectonic setting with regional crustal discontinuities that can be interpreted from satellite and surface gravity anomalies, and local discontinuities that can be only interpreted from the surface gravity anomalies.

The thickness of the continental crust varies from 35 km to 55 km and shows that the mountain ranges are partially compensated by continental roots. Thicker continental crust provides a better scenario for magmatic segregation of parental magmas generated at converging continental margins. Those magmas can be contaminated by the crust, forming mineralization of economic interest.

Major deposits of base and precious metals of the Andean Mountains are related to intermediate to felsic intrusions. Porphyry copper-molybdenum deposits coincide with

Mesozoic - Cenozoic orogenic belts and calc-alkaline volcanism (Guilbert and Park,

1997). The crustal thickness variations yield important constraints on the process of magma generation and the formation of ore deposits. Regions with crustal thickness between 50 km and 60 km are associated with the batholithic intrusions of economic interest in the Central Andes. In the North Andes Microplate, crustal thicknesses greater that about 45 km were identiﬁed as promising zones for locating batholiths of economic interest.

In any destructive plate margin environment (oceanic or continental) the nature and distribution of magmatic activity in the overriding plate is directly linked to

93 the geometry of the subducted slab (Wilson, 1989). The volumetric proportions of erupted rock types and geochemical characteristics likely are strongly correlated with the thickness and chemical characteristics of the crust through which the rising magmas travel.

Comparison of Figures 4.18 and 4.20 show that crustal discontinuities are more comprehensively deﬁned in TCFAGA anomalies than in the Bouguer anomalies. This can be explained by the fact that some crustal discontinuities also have topographic expression and thus they will be expressed in the TGE and TCFAGA.

The paciﬁc margin of the North Andes microplate shows varying angles of subduction which may control the shortening and the formation of the fold and thrust belt of the North Andes and its related magmatism.

The Caribbean margin of the North Andes microplate shows an incipient subduction of the Caribbean plate under the North Andes microplate.

94 CHAPTER 5

CRUSTAL MODELING FROM MAGNETIC DATA

95 ABSTRACT

A new crustal magnetic anomaly map for northwestern South America was produced from CHAMP observations using enhanced reduction procedures. Magnetic field effects due to crustal thickness variations were separated from magnetic components of the core field. Enhanced removal of external field variations and other non-lithospheric noise resulted from modeling ionospheric effects, spectral correlation filtering of neigh- boring tracks, and constructing a spectrum with improved signal-to-noise properties from the dusk and dawn maps.

The crustal magnetic anomaly map shows enhanced resolution of tectonic anomaly features to better constrain interpretations of the crustal geology. Additional constraints on the geological interpretation of magnetic data were developed by comparing them to corresponding ﬁrst vertical derivative of gravity anomalies using spectral correlation theory.

Positive magnetic anomalies and negative TCFAGA anomalies characterize the oceanic trenches at subduction zones. Positive TCFAGA and negative magnetic anomalies over the Andes Mountains may reﬂect thermally demagnetized crust. Negative magnetic and negative gravity anomalies tend to reﬂect thickened oceanic crust associated with non-magnetic sedimentary basins and geothermal variations.

96 5.1 Introduction

Terrestrial, marine, airborne and satellite CHAMP magnetic anomaly maps were analyzed and compared with the ﬁrst vertical derivative gravity anomalies and proposed plate boundary zones for northwestern South America. Accurate representation of the crustal magnetic map was necessary to better understand the crustal structures associated with the anomaly features. Satellite-derived magnetic anomalies (e.g.,

POGO, MAGSAT, CHAMP) for South America have shown good correlation with tectonic features (e.g., Longacre, 1981, Maus et al., 2002, Maus et al., 2003 Maus et al.,

2004, Lesur and Maus, 2005).

Regional variations of lithospheric magnetization are emphasized in the satellite magnetic anomalies. These variations can be interpreted for changes in crustal lithol- ogy, thermal properties, and thicknesses that result from the tectonic evolution of the lithosphere (von Frese et al., 1989). Therefore, analysis of satellite magnetic data can provide unique and important information on geology and tectonics of the lithosphere.

Four global crustal field models have been derived (MF1, MF2, MF3 and MF4) from the first four years of CHAMP data (Lesur and Maus, 2005). For each model, data were expanded to spherical harmonic degree and order 90. To estimate the crustal anomalies, the total field measurements were corrected for an internal field model to degree 15, an external field model to degree two, and the predicted magnetic field signatures for the eight main ocean tidal constituents. The remaining external field components were evaluated and removed on a track-by-track basis.

The CHAMP models were estimated from a subset of “magnetically quiet” data that were observed when the external ﬁeld activities were minimum. The resulting

MF models provided a good representation of the crustal ﬁeld down to an altitude of about 50 km at mid latitudes, but with reduced accuracy in the polar regions. Crustal

97 features came out signiﬁcantly sharper in the model MF3 (Maus, et al., 2004) than in previous models MF1 (Maus et al., 2002) and MF2 (Maus et al., 2003). Bands of magnetic anomalies along the subduction zones became visible for the ﬁrst time in the satellite observations.

The model MF4 (Lesur and Maus, 2005) was produced for representing the crustal magnetic field. That model was derived from almost 5 years of CHAMP measurements. The model was given as a spherical harmonic expansion of the scalar magnetic potential to degree 90. Coefficients 1 − 15 were set to zero, since these coefficients were taken to represent mostly the main magnetic field with its source in the Earth’s outer core. Relative to the model MF3, the model MF4 involved better calibrated CHAMP vector data, improved corrections for polar electro-jets and better elimination of data disturbed by ionospheric F-Region currents.

The above studies have provided mixed results regarding the degree that should be used to account for the core field. If the cut-off is too low, residual core field components might be left in the lithospheric anomaly field. Although, the remaining core field components may be small compared to those of the total core field, they are large relative to the crustal magnetic field components. On the other hand, if the cut-off is too high, substantial crustal components may be removed as core field components.

Clearly, the extraction of core ﬁeld components represents a signiﬁcant source of error in estimating lithospheric anomalies in regional magnetic observations.

In this study, an alternate approach for eﬀectively separating core and crustal ﬁeld components in the satellite magnetic data was applied using spectral correlation theory

(Tan, 1998; von Frese, et al., 1997a; von Frese et al., 1999). Spatially and temporally static crustal magnetic anomalies are contaminated by static core effects above spherical harmonic degree 12 and the dynamic, large amplitude external fields. Crustal thickness variations produce magnetic effects that spectrally overlap the core field

98 components (von Frese et al., 1999). Thus, we can use the correlation spectrum between the pseudo magnetic effects of the crustal thickness variations and the CHAMP core field components to separate the possible crustal thickness and core field effects in the CHAMP observations. Spectral correlation filters also can be used to separate the static crustal and dynamic external field components in the CHAMP data.

5.2 Core Field and external ﬁeld reductions

Figure 5.1 shows the intensity, inclination, and declination properties of the core

ﬁeld for study area at 400 km, from the International Geomagnetic Reference Field

(IGRF-10) obtained from NOAA (2006). Core ﬁeld intensities range from 21087 nT to 36475 nT, with magnetic declinations between −15o to 6.3o and magnetic inclinations from 0.75o to 53.79o. External ﬁelds vary typically from ±200 nT whereas the lithospheric anomalies are relatively weak, ranging commonly from ±20 nT. Hence, ignoring instrumental noise, the satellite magnetometer observation includes the core

ﬁeld component of roughly 98.5%, the external ﬁeld component of about 0.6%, and the lithospheric component of approximately 0.06%.

To obtain a crustal CHAMP magnetic anomaly map for the area (−8oS to 23.5oN,

−90oW to −58.5oW), an extended area (−10oS to 30oN, −100oW to −40oW) was considered to minimize edge effects in data processing. Efforts focused on isolating the external and core fields by wavenumber filtering correlation according to the procedures of Kim et al. (2005).

These procedures basically involved removing the IGRF10 up to degree 13 to eliminate the core effects from each orbital data track. A 2nd− order polynomial was removed from each orbital data profile to help account for the ionospheric field effects.

The passes were next sorted by local magnetic time into subsets of ascending and descending orbital datasets. The tracks were then correlation ﬁltered against each other

99 Figure 5.1: Core magnetic intensity (color), inclination (white contours) and declination (black contours) for northwestern South America from IGRF-10 (NOAA, 2006). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

100 to extract the static crustal components. The correlation ﬁltered tracks were gridded next by least squares collocation at 400 km altitude and the two maps were correlation

filtered against each other to suppress external field noise further. The correlation filtered maps were then subjected to spectral reconstruction to suppress track-line noise.

The resulting CHAMP total magnetic ﬁeld anomalies for the study region are shown in Figure 5.2

5.3 Diﬀerential Reduction to the Pole (DRTP)

To minimize spatial distortions between satellite magnetic anomalies and their geological sources caused by core field variations, the CHAMP crustal anomaly estimates in Figure 5.2 were differentially reduced to the pole (DRTP). Reducing the magnetic anomalies to vertical polarization enhances the ability to relate them to geologic features and helps to reduce ambiguities in interpretation. The DRTP operation re- calculates total magnetic intensity data as if the inducing magnetic field had a 90o inclination.

This procedure transforms dipolar magnetic anomalies to monopolar anomalies centered over their causative bodies which can simplify the interpretation of the data.

For this study, the reduction to the pole makes the simplifying assumption that the rocks in the survey area are all magnetized parallel to the Earth’s magnetic field. This is only true in the case of rocks with an induced magnetization so that remanent magnetization will not be correctly dealt with if the direction of remanence is different than the direction of the Earth’s magnetic field.

Lithospheric sources of satellite magnetic anomalies may have both inductive and remanent components of magnetization. These sources may be predominantly in the lower crust that is believed to be substantially more magnetized than the upper crust

101 Figure 5.2: CHAMP total magnetic ﬁeld anomalies (nT) at 400 km altitude for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

102 (Wasilewski and Mayhew, 1992). As crustal depth increases conditions for coherent regional magnetization are enhanced. Remanent and thermal overprints are diminished and viscous magnetization and initial susceptibility are enhanced with increasing temperature, especially within about 100oC - 150o C of the Curie point. The thickness of the crust aﬀected by this thermal regime may be 5 km to 20 km depending on the steepness of the geothermal gradient. Hence, deep magnetic sources are related to lateral variations of petrological factors or Curie isotherm topography. Viscous remanent magnetization of the lower crust is in-phase with the induced component. Thus, reducing the regional satellite magnetic anomalies from deep crustal sources to vertical polarization is warranted.

Remanently magnetized sources within the magnetically weaker upper crust produce high frequency signals which are substantially attenuated at satellite altitudes.

Hence, the errors in the DRTP estimates due to the upper crustal magnetic remanence is relatively small. In basins containing non-magnetic sediments, remanence is also not a problem. Close to the magnetic equator (≤ 10o declination), the DRTP procedures can become unstable. Errors in the DRTP transform usually appear as narrow anomalies elongated parallel to the declination of the Earth’s magnetic ﬁeld (Telford, et al.,

1994; Merrill et al., 1996), but appropriate stabilizing procedures can be implemented to mitigate the eﬀects (e.g., von Frese et al., 1988). Taking into account these consid- erations the CHAMP magnetic anomalies in Figure 5.2 were diﬀerentially reduced to the pole as shown in Figure 5.3.

The DRTP magnetic anomalies were obtained by the inversion of the total ﬁeld magnetic anomalies in Figure 5.2 for the magnetic susceptibilities on an equivalent source array of prisms making up the crust (von Frese et al., 1981; Kim et al., 2005).

Figure 5.4 gives the crustal susceptibilities that when evaluated under the inducing

103 Figure 5.3: Diﬀerentially reduce-to-pole CHAMP magnetic anomalies DRTP(TFMA) at 400 km for Northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

104 ﬁeld conditions of vertical inclination, zero declination and the constant intensity of

45000 nT yield the DRTP anomalies in Figure 5.3.

5.4 First vertical derivatives of FAGA (FVD(FAGA))

By Poisson’s theorem, the DRTP anomaly of a source that also represents a variation in density has the same spatial properties as the source’s ﬁrst vertical derivative gravity anomaly (e.g., von Frese et al., 1982). Thus, the DRTP magnetic anomalies can be correlated against the ﬁrst vertical derivative free-air gravity anomalies

(FVD(FAGA)) for additional insights on the crustal properties of the study region.

For this study, the FVD(FAGA) were computed numerically from the EGM96 coeﬃcients evaluated at 390 km and 410 km by

(F AGA − F AGA ) FVD(F AGA) = 390km 410km (5.1) 400km 20 km as shown in Figure 5.5. The polarity convention in Eq. 5.1 makes the sign of the

FVD(FAGA) estimate the same as the sign of the density contrast of the underlying source’s. For comparison, Figure 5.6 shows the FAGA at 400 km altitude.

5.5 Spectral correlations of CHAMP DRTP (TMFA) and FVD (FAGA) estimates

Spectral correlation analysis is applied to isolate gravity and magnetic anomaly correlations related to crustal thickness, petrological, and thermal variations. Gravity anomalies tend to be negative over thickened crust and positive over thinned crust, whereas magnetic anomalies tend to be inversely correlated with these gravity anomalies. Increased heat ﬂow in the crust also can produce inversely correlated geopotential

105 Figure 5.4: Crustal magnetic susceptibility values for northwestern South America calculated by linear inversion of DRTP CHAMP magnetic anomalies. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

106 Figure 5.5: First vertical derivative (FVD) of the free-air gravity anomalies (FAGA) at 400 km for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

107 Figure 5.6: Free-air gravity anomalies (FAGA) at 400 km elevation for northwestern South America. Map annotations include the amplitude range (AR) of (min; max) values and amplitude mean (AM) and standard deviation (SD). SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

108 CC FAGA) FVD(FAGA) TFMA DRTP FAGA 1 0.9101 -0.1264 0.361 FVD(FAGA) 09101 1 -0.00979 0.216 TFMA -0.1264 -0.0979 1 -0.0453 DRTP 0.1361 0.216 -0.0453 1

Table 5.1: Correlation coeﬃcients (CC) between the FAGA in Figure 5.6, FVI(FAGA) in Figure 5.5, CHAMP total ﬁeld magnetic anomalies (TFMA) in Figure 5.2 and the CHAMP DRTP TFMA in Figure 5.3 at 400 km altitude for northwestern South America from −8oS to 23.5oN latitude and from −90oW to −58.5oW longitude.

anomalies, that involve magnetic lows where the Curie isotherm is raised and gravity highs from the inflated crust. Petrological variations may result in positively correlated anomalies that broadly reflect the distribution of low-density and -magnetization felsic rocks or high-density and -magnetization mafic rocks.

Local favorability indices (LFI) were obtained between the CHAMP DRTP (TFMA) and FVD (FAGA). Figure 5.7 gives the SLFIs that highlight the peak-to-peak anomaly correlations, whereas the trough-to-trough associations are presented in Figure 5.8.

The DFLIs highlighting the FVD(FAGA) peak-to- DRTP (TFMA) trough and FVD(FAGA) trough-to-DRTP (TFMA) peak correlations are given in Figures 5.9 and 5.10, respectively. The geological implications of these LFIs are considered in section 5.7. The correlation coeﬃcients between the various regional gravity and magnetic data sets of this study area are given in Table 5.1.

5.6 Aeromagnetic anomalies of the North Andes Microplate

To facilitate the geological interpretation of satellite geopotential ﬁeld anomalies, regional aeromagnetic data were compiled from INGEOMINAS (1998). Figure 5.11

109 Figure 5.7: Peak-to-peak correlations between FVD(FAGA) and CHAMP DRTP (TFMA) at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

110 Figure 5.8: Trough-to-trough FVD(FAGA) and CHAMP DRTP (TFMA) at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

111 Figure 5.9: FVD(FAGA) peak-to- CHAMP DRTP (TFMA) trough correlations at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

112 Figure 5.10: FVD(FAGA) trough-to-CHAMP DRTP (TFMA) peak correlations at 400 km altitude for northwestern South America. SNSM = Sierra Nevada of Santa Martha, W-Mid = Western-Central ranges. This map was produced using the Albers equal-area conic projection.

113 shows these anomalies continued upward to 20 km for comparison with the EGM96 gravity anomalies of Figure 3.2.

Total magnetic ﬁeld anomalies vary from −123.6 nT to 110.8 nT, with a mean value of 3.86 nT and standard deviation of 26.27 nT. Although magnetic data coverage is poor in the Andes Mountains, the upward continued anomalies provide a geologically useful regional view of the main magnetic zones. Positive magnetic anomalies are associated with the Baudo volcanic arc, and the Sierra Nevada of Santa Martha, whereas linear trends of magnetic highs and lows characterize the Guiana Craton. Negative total magnetic ﬁeld anomalies characterize the Andes Mountains and local sedimentary basins. Only a few discontinuities seem to be outlined due to the low resolution of the data.

Negative magnetic anomalies along the Colombian Trench and Lesser Antilles re-

flect the Caribbean-North Andes plate boundary zone. The Pacific subduction along the Colombian trench does not appear to be well defined magnetically.

5.7 Discussion

The CHAMP magnetic observations were processed for crustal anomalies by removing possible contaminating core and external ﬁeld components. Deep crustal magnetic sources were revealed that are probably related to the MOHO and Curie isotherm topography and lateral petrological variations.

In general, crustal sources of satellite magnetic anomalies can have both inductive and remanent magnetizations. These sources are predominantly in the lower crust that is believed to be more magnetic than the upper crust and mantle (Wasilewski et al.,

1979; Wasilewski and Mayhew, 1982, 1992; Mayhew et al., 1985).

In Chapter 4, the crustal thickness estimates for the Andean Mountains revealed the need for additional continental roots between 5 km to 10 km on average to reach

114 Figure 5.11: Total magnetic ﬁeld anomalies at 20 km altitude for the North Andes Block with interpreted crustal discontinuities superposed (blue lines). This map was produced in Cartesian coordinates with the origin (1’000.000 N, 1’000.000 E) at the National Observatory of Bogota.

115 complete compensation. This “missed” root would have produced a strong positive magnetic anomaly from the lower crustal magnetic rocks. Therefore, a partial isostatic compensation also implies a partial magneto-isostatic compensation, where the magnetic ﬁeld associated with the isostatically disturbed crust has lower or higher intensity depending on whether the crust is over or under compensated by the mantle.

Positive DRTP magnetic anomalies in Figure 5.3 suggest enhanced magnetization for the crust along Central America, North of Cuba and Espa˜nola,The Vichada Plain and the Andes Mountains. Negative DRTP magnetic anomalies imply decreased magnetization for the crust in the Caribbean plate, northern Venezuela, Nazca and Cocos

Plates and the Amazon River Aulacogen.

The positive FVD(FAGA) estimates in Figure 5.5 suggest higher density crust in the Andean Mountains and Central America. Intensely negative FVD(FAGA) imply lower density crust along the Lesser and Greater Antilles related presumably to the eﬀects of the deep trench and subducting crustal slab displacing high density mantle.

The peak-to-peak correlations between FVD(FAGA) and CHAMP DRTP (TFMA) in Figure 5.7 reﬂect higher density and magnetization crust along Central America and the Andean Mountains. These areas show positive magnetic anomalies associated with a thicker continental crust that coincide with the positive FVD(FAGA) of the isostatically disturbed mountain ranges.

The trough-to-trough correlations in Figure 5.8 imply lower density and magnetization crust along the Lesser Antilles, the Caribbean-North American plate boundary and portions of the Ecuadorian Andes and the Guiana Craton. The lower density and magnetization can result from various sources such as sediment ﬁll, the depth of the oceanic trench in the Caribbean, and the possible presence of granitic intrusions with lower density and magnetization than the maﬁc host rocks.

116 The FVD(FAGA) peak-to DRTP (TFMA) trough correlations in Figure 5.9 re-

ﬂect higher density, lower magnetization crust in the Central Andes of Colombia and eastern Ecuador, Northern Venezuela and around the Cayman trough. Sources for these correlations include enhanced crustal heat ﬂow and anomalously thinned crust.

The FVD(FAGA) trough-to- DRTP (TFMA) peak correlations in Figure 5.10 suggest lower density higher magnetization crust along the Lesser and Greater Antilles

(north of Cuba) and the Middle American Trench related to the subducting crustal slab displacing higher density and lower (non magnetic) mantle. Features south of the

Carnegie ridge reﬂect lower density, higher magnetization, thickened oceanic crust.

The features at the Guiana Shield reﬂect lower density, higher magnetization sources associated with sedimentary basins or a tectonic graben.

The aeromagnetic data in Figure 5.11 show an arcuate positive anomaly along the western margin of the North Andes block associated with the presence of maﬁc rocks of oceanic aﬃnity. These results also show a highly magnetizated body in the eastern cordillera and the Guiana craton.

5.8 Conclusions

The CHAMP magnetic observations were processed for effective crustal components. The processing involved spectral correlation to suppress external magnetic magnetic field effects, and to separate the overlapping magnetic effects of the core and crustal thickness variations using the pseudo magnetic effects of the crustal thickness variations derived from the free-air and terrain gravity effects.

The CHAMP DRTP (TFMA) anomalies generally reﬂect the regional crustal features of Central America, the northwestern Andes and the Caribbean. Prominent magnetic minima overlie the thinned crust of marine basins. Low magnetic anomalies of the northern Andes Mountains may be related to demagnetizing eﬀects of the high

117 thermal gradients of the volcanic regions, as well as the non-magnetic sedimentary rocks of the Eastern Cordillera. Negative magnetic anomalies of the Guiana Craton at the Amazon River Aulacogen are diﬃcult to relate to known features of the crust.

However, they might reﬂect crustal thinning, enhanced heat ﬂow, and the presence of non-magnetic sedimentary basins.

Magnetic maxima that overlie the Central American continental crust, the Andean

Mountains at the latitude of the Carnegie Ridge and the Guiana Craton between the

Vichada Plain and Amazon River Aulacogen appear to reﬂect mostly enhanced crustal thickness eﬀects. The positive magnetic anomalies immediately northeast of Cuba and

The Espa˜nolaIslands also show relative thickening of the crust. The interpretation of these magnetic anomalies are mostly consistent with their correlative satellite altitude free-air gravity anomalies.

The aeromagnetic data of the North Andes provide limited coverage for constraining geological interpretations of the CHAMP crustal magnetic anomalies. However, they show a striking arc-shaped positive anomaly in the western margin of the North

Andes block that may represent the dismembered remnants of an oceanic plateau which formed the eastern Paciﬁc Ocean at 97-90 Ma (Kerr et al., 1997). Shortly after the plateau formed, its northern half was pushed between North and South America to form most of the Caribbean Plate.

As the southern part of the plateau approached the continental margin of northwestern South America, it was too buoyant to totally subduct and so its topmost parts accreted onto the continental margin (Kerr et al.,1997).

118 CHAPTER 6

CRUSTAL THICKNESS VARIATIONS AND SEISMICITY

119 ABSTRACT

Isostasy is the ideal state that any uncompensated mass seeks to achieve in time

(Turcotte and Schubert, 2002). Thus, any uncompensated mass of the northern Andes

Mountains is presumably under pressure to adjust within the Earth to its ideal state of isostatic equilibrium. These pressures interact with the relative motions between adjacent plates that give rise to earthquakes along the plate boundaries. By combining the gravity MOHO estimates and crustal discontinuities with historical and instrumental seismological catalogs it is possible to establish the correlation between isostatically disturbed terrains and seismicity.

The thinner and thicker crustal regions were mapped from the zero horizontal curvature of the crustal thickness estimates. These boundaries or edges of crustal thickness variations were compared to crustal discontinuities inferred from gravity and magnetic anomalies and the patterns of seismicity that have been catalogued for the last 363 years.

The seismicity is very intense along the Nazca-North Andes, Caribbean-North

American and North Andes-South American collision zones and associated with regional tectonic compressional stresses that is locally increased and/or diminished by compressional and tensional stress, respectively, due to crustal thickness variations.

High seismicity is also associated with the Nazca-Cocos diverging plate boundary whereas low seismicity is associated with the Panama-Nazca Transform Fault and the South American Plate.

120 6.1 Introduction

The increased number of seismological networks established during the last cen- tury led to the discovery that earthquakes are not randomly distributed, but tend to occur along well deﬁned earthquake belts (e.g., Shearer, 1999). These belts are largely concentrated along the margins of tectonic plates that shift slowly over geologic time.

The relative motions between adjacent plates give rise to earthquakes along the plate boundaries that include spreading oceanic ridges, converging subduction zones, collisional continental plate boundaries, and transform faults along which they shear past each other. For northwestern South America, the improvement in instrumentation and expansion of seismological networks has led to the production of relatively complete and accurate catalogs of earthquake locations and ground motions.

The response of ground during an earthquake is commonly attributed to elastic rebound theory whereby the low accumulation of shear stress at a point along a fault builds up until the elastic strength of the rock is exceeded and it fractures releasing energy to produce the earthquake (Reid, 1906 in Shearer, 1999). Crustal thickness variations also can contribute compressional stress where the crust is thinner than normal and tensional stress where it is thicker than normal (Artyushkov, 1973). Therefore, the crustal thickness estimates derived from gravity anomalies can be included in the analysis of earthquake behavior. For instance, areas where TCFAGA are excessively negative or positive are more prone to seismic activity than areas where the TCFAGA are closer to zero (Song and Simons, 2003).

This chapter analyzes and compares seismic data from the Advanced National Seis- mic System (ANSS) and the Red Sismologica Nacional de Colombia (RSNC) catalogs

121 with crustal thickness estimates from gravity anomalies from improved understanding of the large-scale dynamic models of earthquakes and tectonics. Gravity anomalies along trenches, continental converging margins, crustal discontinuities, mountain ranges and cratonic areas are compared with their seismic signatures from earthquake data collected over the last 363 years.

6.2 Zero Curvature of crustal thickness variation

The terrain-correlated free-air anomalies (TCFAGA) in Figure 3.4 mark regions of isostatically disturbed crustal features. For instance, the zero anomalies mark areas of crustal equilibrium so that the positive and negative anomalies reflect crust in compression and tension, respectively. In other words, positive and negative TCFAGA can mark crust that is isostatically too thin (under-compensated) or thick (over-compensated), respectively, and hence under pressure to equilibrate by the compressive in-flow or expansive out-flow of crustal material (e.g., Artyushkov, 1973). Thus these anomalies can reflect lithosphere in subsidence or uplift (e.g., Kim et al., 2000; von Frese et al., 1999a), or alternatively dynamic surface topography that is too high or too low, respectively, to be in isostatic equilibrium.

Figure 6.1 gives the crustal thickness variations for northwestern South Amer- ica obtained by adding the gravity MOHO estimates in Figure 4.2 to the DTM of

Figure 3.1.

The zero curvature contour in Figure 6.1 that estimates the edges of thickness variations was obtained using the tools in the Geosoft Oasis Montaj package (Appendix

B; Geosoft, 2006). The intervening yellow and blue regions of Figure 6.1 reﬂect the thicker and thinner crustal components, respectively.

122 6.3 Seismic data compilation

For comparison with the crustal thickness estimates, the regional seismic data of northwestern South America were compiled from the Advanced National Seismic Sys- tem catalog (ANSS; USGS, 2006). A more local study was also considered using the historic and instrumental seismic catalogs of the Red Sismologica Nacional of Colom- bia (RSNC; INGEOMINAS, 2006).

6.3.1 ANSS Catalog

The ANSS catalog is a world-wide earthquake catalog created by merging the master earthquake catalogs from contributing ANSS institutions and then removing duplicate solutions (USGS, 2006). The ANSS catalog currently consists of earthquake hypocenters, origin times, and magnitudes. The ANSS database was searched for data from 1966 to 2006 with Ritcher magnitudes M of 3-10.

The earthquake epicenters were converted from geographic to Cartesian coordinates in Figure 6.1 with the proportional symbols for Ritcher magnitudes given in the legend. Only those events with hypocenters from 0 to 60 km depths were considered in this study. The crustal discontinuities interpreted from TCFAGA in Figure 4.15 are also superposed in Figure 6.1.

The seismic events in Figure 6.1 are concentrated along the plate boundary zones of the Nazca, Caribbean, North American and South American Plates, the North

Andes, Panama and Costa Rica Microplates, the Cocos-Nazca spreading system, and the intraplate discontinuities. They are predominantly located in the thicker crustal sections and along the inferred edges of the thickness variations. However, the thicker

123 Figure 6.1: ANSS seismic catalog for 1966-2006 for three categories of earthquake magnitudes: M=3-4 (minor earthquakes), M= 4.1-5.5 (intermediate earthquakes), and M ≥ 5.5 to 10 (major earthquakes). Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. Yellow and blue zones correspond to thicker and thinner crust, respectively. This and succeeding ﬁgures were created using the capabilities of Oasis Montaj (Geosoft, 2006).

124 oceanic sections of the Nazca, Malpelo and Cocos Ridges in the Paciﬁc and the Beata

Ridge in the Caribbean are aseismic.

Comparatively few earthquakes are concentrated in the thinner crustal regions with relatively negative TCFAGA. The Guiana Craton and the interior of Nazca and

Caribbean oceanic Plates also lack signiﬁcant seismic events and are seismically quies- cent. To account for the intraplate earthquakes, gravity and magnetic anomalies that infer crustal discontinuities are useful to analyze deformation in the plate interior .

6.3.2 RSNC historical and instrumental seismic catalog

The RSNC catalog was created by merging the master earthquake catalogs from the

Observatorio Sismologico del Sur Occidente (OSSO), Centro Regional de Sismologia

Para America del Sur (CERESIS), Instituto Geoﬁsico de los Andes, Red Sismologica

Nacional and regional institutions of northwestern South America and the Caribbean

(INGEOMINAS, 2006). This catalog currently consists of earthquake epicenters, origin times, and magnitudes. The RSNC database compiled data from 1643 to 1991 for

Ritcher magnitudes from M ≥ 3.0 to M = 10.

The RSNC catalog contains an enormous number of events. Thus, the events were sorted by magnitude for the minor earthquakes (M = 3 to 4), moderate earthquakes

(M= 4.1 to 5.0), and strong earthquakes (M > 5.0) as shown in Figures 6.2, 6.3 and

6.4, respectively.

Minor and moderate seismic events in Figures 6.2 and 6.3, respectively, are concentrated along the Paciﬁc subduction zone and intracrustal discontinuities of the

North Andes Microplate. The concentration of events in the northern part of the eastern cordillera is known as the “Bucaramanga Nest.” Few events are recorded for the

Sierra Nevada of Santa Martha, Guiana Craton, and the northwestern ﬂat lands of

Colombia north of the Andes Mountains. At the continent, areas with thicker crust

125 Figure 6.2: RSNC historical seismic catalog for 1643-1991 of earthquakes with magnitudes from M=3.0 to 4.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

126 Figure 6.3: RSNC historical and instrumental seismic catalog for 1643-1991 of earthquakes with magnitudes from M=4.1 to 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

127 Figure 6.4: RSNC historical seismic catalog for 1643-1991 of earthquakes with magnitudes M > 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also display. The yellow and blue zones correspond to thicker and thinner crust, respectively.

128 are more seismically active, while areas of thinner crust are less seismically active. An exception is the Sierra Nevada of Santa Martha with a thick crust and low seismic activity.

Major earthquakes in Figure 6.4 are located along the converging Nazca-North

Andes and South America-North Andes continental boundaries. The major earthquakes are located further landward from the Paciﬁc subduction zone relative to the minor and intermediate earthquakes that are concentrated closer to the coastline. The few seismic events of the Guiana Craton are mostly localized along local crustal discontinuities and are not associated with crustal thickness variations.

6.3.3 Recent seismicity in the RSNC catalog

The RSNC started operating since 1992 and has amassed accurate instrumental information that consists of earthquake epicenters, hypocenters, origin times, and magnitudes. The epicenters were sorted by magnitude for minor events (M= 3 to

4) in Figure 6.5, moderate events (M= 4.1 to 5) in Figure 6.6, and major events

(M > 5.0) in Figure 6.7.

The minor and moderate earthquakes in Figures 6.5 and 6.6, respectively, deﬁne seismic corridors oriented along the major crustal discontinuities of the North Andes

Microplate. The Sierra Nevada of Santa Marta also shows more intensive seismic activity than previously recorded by the older data. Major earthquakes in Figure 6.7 are located along the major crustal discontinuities and plate boundary zones of the

North Andes Microplate. In general, seismic events are associated within thicker crust, and therefore can be associated with tensional stress. (Artyushkov, 1973).

Hypocenter depths from the modern RSNC were sorted into shallow earthquakes

(from 0 to 10 km) in Figure 6.8, intermediate earthquakes (10 km to 30 km) in

129 Figure 6.5: RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes from M=3.0 to 4.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

130 Figure 6.6: RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes from M=4.1 to 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

131 Figure 6.7: RSNC modern seismic catalog for 1992-2006 of earthquakes with magnitudes M > 5.0. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

132 Figure 6.9, deep earthquakes (30 km to 70 km) in Figure 6.10, and very deep earthquakes (70 km to 300 km) in Figure 6.11. The tendency of the deepening hypocenters to migrate landward of the Paciﬁc subduction zone is indicative of the oceanic plate subducting under the Andes at an angle that is less than vertical.

6.4 Discussion

Gravity and topography are related to seismic activity by the frictional behavior of plate boundary zones and crustal discontinuities. When two plates push against each other, friction between the plates builds up causing the plates to lock. The continued build up of tectonic stress also causes the plates to deform, creating variations in topography and gravity. In addition to deforming the plates, the rocks of the sticking point can break when the stress build up exceeds the breaking strength of the rocks.

The resulting strain released at the locking point produces the ground shaking of an earthquake. For northwestern South America, plate tectonic stress plays out notably in the ocean-continent, and ocean-ocean and continent-continent plate collision zones, and also along oceanic spreading ridges and transform faults. In the next subsections, these plate boundaries and associated earthquakes zones areas are analyzed further.

6.4.1 Ocean-continent collision zones

In Figures 6.1 to 6.11 the subduction of the Nazca plate under the North Andes microplate is clearly parallel to the the Andes Mountains. The collision caused the creation of the Andes Mountains by stacking thrust slices of crust. The lateral movement of these thrust slices in the welded continent has continued after the collision generating minor, moderate and major earthquakes with shallow, intermediate and deep hypocenter depths deﬁning seismic corridors that are oriented along the the subduction zone and the Andes Mountains. The general pattern of seismicity and focal

133 Figure 6.8: RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 0 km to 10 km. Crustal discontinuities interpreted from gravity anomalies and thezero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

134 Figure 6.9: RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 10 km to 30 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

135 Figure 6.10: RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths from 30 km to 70 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

136 Figure 6.11: RSNC modern seismic catalog for 1992-2006 of earthquakes with hypocenter depths to the hypocenter from 70 km to 300 km. Crustal discontinuities interpreted from gravity anomalies and the zero curvature contours of crustal thickness variations are also displayed. The yellow and blue zones correspond to thicker and thinner crust, respectively.

137 mechanism solutions of earthquakes are in accord with the easterly subduction of the

Nazca Plate beneath the Andes.

The intensive seismicity along the Middle American Trench (MAT) has a broad pattern reﬂecting the low angle of inclination of the subducting Nazca and Cocos plates under the Central American Continent. The seismicity along the Caribbean-North

Andes plate boundary is relatively low, with few minor (Figures 6.2, 6.5 and 6.8), moderate (Figures 6.3, 6.6 and 6.7), and major (Figure.6, 6.7 and 6.10) historical seismic events. This seismicity reﬂects the predominantly dextral lateral movement of the Caribbean Plate with respect to the North Andes Microplate and South American

Plate that may include minor subduction that is incipient when compared with the subduction of the Nazca Plate underneath the Andes Mountains.

6.4.2 Ocean-ocean collision zones

Figure 6.1 shows a broad arcuate seismic zone along the Lesser Antilles. A large number of events occurs along the Caribbean-North American plate boundary, which dips to the west away from the underthrusting oceanic plate. Shallow, intermediate and deep focus earthquakes occur at progressively greater distances from the site of underthrusting. The topographic expression of the trench in Figure 3.1 is largely obscured by thick sediment fill derived from the Orinoco River of Venezuela, but its presence is indicated by the belt of negative TCFAGA in Figure 3.4. The seismic events are located in thicker oceanic crust associated with the doubling of the collisional oceanic crust. Focal mechanism solutions of the Lesser Antilles reflect regional compressional stress. However, the relatively thicker oceanic crust reflects local tensional stress.

138 6.4.3 Continent-continent collision zones

The continent-continent collision boundary zone between the North Andes Mi- croplate and the South American plate in Figures 6.1 to 6.11 is characterized by intensive seismicity. Minor, moderate and major historical and recent seismic events in Figures 6.2 to 6.7 have occurred along the Llanos Front Fault. Shallow events in

Figure 6.8 can be associated with tensional stress of the sub-Andean thrust belt or fault zone, which is located on a relatively thicker continental crust that implies the local presence of additional tensional stress.

6.4.4 Oceanic spreading ridges

Minor and moderate earthquakes occur along the Galapagos spreading ridge and the Panama fracture zone in Figure 6.1. Focal mechanism solutions indicate regional tensional events associated with plate accretion and strike-slip events where the ridges are oﬀset by transform faults. However, the Panama fracture zone is located on relatively thinner oceanic crust that may be locally associated with compressional stress.

6.4.5 Transform faults

The Southern Panama Fault Zone constitutes a conservative plate boundary between the Nazca Plate and Panama Microplate where the plates are in tangential contact and are aﬀected by limited or no subduction or accretion. Therefore, events along this fracture are rare as shown in Figure 6.1.

6.4.6 Cratonic zone

The intraplate areas of the South American Plate are relatively aseismic. However, a few minor, moderate and major historical and recent seismic events in Figures 6.2 to 6.7 have occurred at shallow, intermediate, deep and very deep hypocenter depths

139 in Figures 6.8 to 6.11. These events are located along some of the crustal discontinuities interpreted from the surface FAGA in Figure 4.18 and the total magnetic ﬁeld anomalies at 20 km altitude in Figure 5.11. Their occurrence suggest the presence of continental sutures in the South American plate, with infrequently seismic activity. Although, these earthquakes are rare, they are important because they indicate the nature of directions of stress within the South American Plate. The instrumental seismic events in the above plate boundary zones are analyzed in the next section for their focal mechanisms.

6.5 Focal mechanism solutions

Figure 6.12 gives the compressional stress regime for the study region from stress inversions of the focal mechanisms of the instrumental earthquakes of northwestern

South America (Vargas et al., 2005), these solutions infer the type of faulting or focal mechanisms from the radiated seismic energy. The Costa Rica-Panama-North An- des converging margins show compressional stress oriented west-east, generating the relative movement of local tectonic blocks of the North Andes Microplate. Shallow earthquakes associated with the Paciﬁc subduction zone show compressional stress oriented NW-SE. Vectors of displacement and compressional stress in southwestern

Colombia are oriented west-east. The deep seismicity in the Bucaramanga nest reﬂects compressional stress oriented NNW - SSE, associated with the subducting Caribbean

Plate under the North Andes microplate. Complementary examples of global focal mechanisms for the study area can also be obtained from the Harvard Centroid Mo- ment Tensor catalog (CMT; Harvard, 2006). These results reﬂect the inversions of long-period body and surface waves for the source moment tensors and best-ﬁtting double-couple solutions.

140 Figure 6.12: Main stress axes determined by the Reches Method (Reches, 1983; Reches, 1987) from 94 focal mechanism solutions of the Central Moment tensor catalog (CMT) reported by Harvard University (CTM, Harvard, 2006) for the period 1976-2000 and event magnitudes M = 5.0 (Vargas et al., 2005).

141 6.6 Conclusions

Seismicity in northwestern South America is mainly restricted to the plate boundary zones of the Caribbean, North America, and South America Plates and the Panama,

Costa Rica and North Andes Microplates. Seismic corridors are oriented predominantly

SW-NW, showing their association with compressional stress generated by the convergence of the Nazca and South American plates and the shortening of the continental crust and mountain building of the Andes Mountains. The seismicity is extremely high along the northern margin of the Paciﬁc subduction zone.

The hypocenter depths show the tendency of the earthquakes to migrate from the coastline eastwards as the hypocenter depths increase, conﬁrming the eastward motion of the Nazca Plate under the North Andes Microplate.

The spatial distribution of earthquakes is consistent with crustal discontinuities interpreted from the gravity and magnetic anomalies. Seismic events are preferentially concentrated in zones of of relatively thicker continental crust. This crust is inherently under tension by virtue of its enhanced thickness, but it is also being subjected to overwhelming compression from plate subduction forces.

The analysis of the isostatic state of compensation from terrain and gravity anomalies of northwestern South America help to diﬀerentiate probable earthquake zones.

Integrating the local stress of the crustal thickness variations with regional tectonic stresses may help to predict local ground motions. The focal mechanisms reﬂect regional stress and more local stress from the thickness variations of the crust.

142 CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

143 Spectral correlation theory was used to investigate regional topographic, gravity and magnetic observations in spherical Earth coordinates for the crustal properties of northwestern South America. Moho depth estimates were modeled from the inversion of compensated terrain gravity eﬀects, which required accurate gravity models of the rock and water components of the terrain.

Gauss Legendre quadrature integration (GLQ) was used to model the gravity effects of the topography and bathymetry. The terrain gravity eﬀects (TGE) were spectrally correlated with free-air gravity anomalies (FAGA) obtaining terrain-correlated

(TCFAGA) and -decorrelated (TDFAGA) free-air gravity anomalies. The TCFAGA were removed from TGE to obtain the compensated TGE components (CTGE). The gravity eﬀects that annihilate the CTGE were assumed to be generated by the density contrast at the mantle - crust interface or MOHO. Therefore, the MOHO was estimated from the CTGE by inversion with the design matrix coeﬃcients modeled from

GLQ integration using the sparsely distributed seismic MOHO estimates.

Seismic studies have provided only limited point estimates of the MOHO and related crustal thickness variations. Thus, the more continuous gravity MOHO and crustal thickness estimates help to put the limited seismic point estimates into an effective regional context for enhanced tectonic analysis of northwestern South America.

Terrain-correlated free-air gravity anomalies include evidence of incomplete isostatic compensation of the crust that when combined with the gravity MOHO constrain the

MOHO uplift and subsidence required for isostatic equilibrium.

Crustal discontinuities inferred from gravity, magnetic and other geological and geophysical data of the North Andes Microplate were used to outline local tectonic blocks. These blocks showed varying isostatic compensating states and therefore varying isostatic adjustments that can be related to the variations in the seismic activity

144 of the area. Thus, these results are useful for characterizing crustal stress conditions and to interpret the historical and instrumental seismic catalogs of the study area.

The gravity MOHO and gravity and magnetic anomalies suggest a new model for the tectonic evolution of northwestern South America. The results are consistent with the tectonic style involving both rigid and non-rigid blocks. Where high-rigidity blocks are present, the style is dominated by overthrusting of the more rigid block. Where rigid blocks are largely absent, the style appears to be dominated by lower crustal ﬂow and continuous deformation. Within the North Andes Microplate, the rigid blocks appear to be separated by weaker areas which correlate with crustal discontinuities.

The near-zero FAGA of the Nazca, Cocos and Caribbean Plates suggests that they are almost completely compensated. The Cocos, Carnegie and Malpelo Oceanic Ridges in the Paciﬁc and the Beata Ridge in the Caribbean are associated with local positive TGE. The superposition of surface loads on the oceanic crust disturbs the local isostatic balance. TCFAGA of these volcanic ridges is lower in magnitude than their corresponding TGE suggesting partial isostatic compensation. Detailed analysis of the

Malpelo Ridge shows partial isostatic compensation by thickening the oceanic crust with underplated material of lower density than the mantle. The gravity MOHO estimates for the Malpelo ridge also support interpretations of detailed seismic refraction data (Trummer, 2002).

The large TCFAGA over the Andes Mountains (Andes Microplate) and the Sierra

Nevada of Santa Martha reveal them to be isostatically disturbed. The strong positive TCFAGA suggest the continental roots below these topographic features are not deep enough to annihilate the TGE. The Sierra Nevada of Santa Marta, rising above

5800 m just 42 km from the Caribbean coast is the world’s highest coastal peak. Its

TCFAGA of 121 mGals clearly suggests that it is out of isostatic balance. It is one of the most spectacular features of the northwestern South America. Topographically,

145 it is an isolated high, rising to glacier-capped peaks at nearly 5800 m elevation and surrounded by arid lowlands near sea level. In the Caribbean Sea, 85 km to the north, water depths exceed 3500 m, making the total topographic relief in excess of 9000 m.

The Sierra Nevada of Santa Marta and the Andes Mountains are clear examples of topographic highs supported by lateral stress.

The gravity MOHO of the Guiana Craton locally diﬀer from the regionally interpolated seismic Moho estimates. Local positive FAGA anomalies are associated with more dense intrusive bodies aﬀecting the host Paleozoic and Precambrian sequences.

These intrusive bodies do not have surface expressions and therefore are associated with lateral density variations within the continental crust.

An improved crustal CHAMP magnetic anomaly map at 400 km altitude was obtained using enhanced procedures for separating the external, core, and crustal components. To separate the overlapping eﬀects of the core ﬁeld and crustal thickness variations, the spherical harmonic expansion of IGRF10 was evaluated to degree 13.

Long wavelength features related to crustal thickness variations were extracted from the CHAMP data by correlating differentially reduced to pole magnetic anomalies with the pseudo magnetic anomalies of the crust that involved the first vertical derivative of the crustal thickness gravity effects.

Feature correlations between crustal gravity and magnetic anomaly estimates were isolated by the application of correlation ﬁlters in the wavenumber domains of the data sets. By normalization and summing local favorability indices, positively correlated features were resolved and visualized. Diﬀerencing the normalized local favorability indices yielded the negatively correlated features between gravity and magnetic anomalies. These correlation results further constrain the non-unique analysis of the lithospheric anomaly components from satellite magnetic data and gravity observations.

146 The gravity and magnetic anomalies of northwestern South America are consistent with a region that is not of typical “Andean Type” orogenesis. Compressional tectonics has played an important role in the mountain building of the North Andes as a consequence of the relative movements among the Nazca, South American and

Caribbean Plates and the Panama and North Andes Microplates. The crustal shortening associated with plate motion has produced relative movement of thrusting faults and crustal doubling.

The western margin of the continental crust provides clear testimony of the impor- tance of allochthonous terranes, with contrasting rock properties and driving mechanism that have generated crustal deformation, magmatism, uplift and sedimentation patterns. The Lesser and Greater Antilles represent the sites of subduction of the

North American Plate under the Caribbean Plate. The characteristic arcuate shape of the gravity anomalies are clear evidence of the doubling of the oceanic crustal thickness as indicated by the positive TCFAGA. Sediments forming the upper layer of the oceanic crust were scraped oﬀ the subducting plate as it descended and formed the accretionary wedges of fore-arc regions that generate the negative TCFAGA.

A volcanic arc developed an uplifted surface of Precambrian and Paleozoic rocks along much of the Paciﬁc margin of the Americas by late Triassic or early Jurassic

(Daziel, 1986) and volcanic activity has been essentially continuous to the present along diﬀerent segments of the plate margin.

The tectonic setting shows the progressive accretionary continental growth of northwestern South America, attaching oceanic terrains to the Guiana Craton and producing shortening of the crust by orogenic events from the late Paleozoic through Ceno- zoic. The tectonic model also includes dextral-oblique accretion of the allochthonous oceanic terrains along the Paciﬁc margin with strong Caribbean Plate aﬃnities ca- pable of obduction of oceanic crust, the northwest migration of the tectonic bocks to

147 the Caribbean Plate, and the overthrusting of tectonic blocks with various internal deformational styles. The geodynamic model is composed of highly oblique converging plates, accretion, and subduction of allochthonous oceanic crust as the main types of deformation.

Thus, accretion does not occur at the extreme northern and Southern Andes Moun- tains, where due to the absence of the Precambrian terrains, the unique tectonic setting facilitated the migration of the Caribbean and Scotia Oceanic Plates of Paciﬁc aﬃnity into the Atlantic Ocean. This lack of crustal accretion limited the longitudinal extend of the Andes Mountains.

The gravity and magnetic anomalies of the western margin of northwestern South

America indicate the migration of the Caribbean Plate. It seems to have a Paciﬁc provenance, with the trajectory from SW to NW along the western and northern margins of the North Andes Microplate, into the Caribbean.

The northwestern Andes involve isostatic disturbances and shortening of the continental crust that are consistent with horizontal compression maintaining vertical loads of uncompensated masses. These masses are under pressure to adjust spatially to greater levels of isostatic equilibrium and these adjustments generally tend to correlate with the seismicity variations of the study area.

The ANSS and RSNC historical and instrumental catalogs reveal the distinct concentrations of earthquakes along plate boundary zones and crustal discontinuities.

Shallow, intermediate, and deep earthquakes follow a pattern that infers the landward deepening of focal depths from the Paciﬁc subduction zone, indicating the inclination eastward of the subducting oceanic slab under the continent.

The results of this study show the power of crustal thickness variations to sustain regional topography. Areas with crustal thickness between 45 km and 55 km in the

148 North Andes mountains are associated with the presence of batholithic intrusions of economic interest for exploration for porphyry base, and precious metals.

Crustal thickness variations also are fundamental for the evaluation of hydrocarbon generation in oceanic basins and adjacent continental margins. Deﬁning the type of crust underlying an accretionary wedge is a fundamental constraint for estimating the heat ﬂow present in areas of exploration. This information can contribute signif- icantly in modeling the thermogenic generation of hydrocarbons, including areas of the subsurface known as “source kitchens, oil kitchen or gas kitchen” (Ceron, 2005;

Schlumberger, 2006) where the source rocks reach appropriate conditions of pressure and temperature to generate hydrocarbons. The anomalous thickened Caribbean Plate is overlain by thick sedimentary sequences that are favorable for the exploration of oil and gas deposits.

The interpretations and deductive processes presented here involved a judicious balance between the mathematical and geostatistical rigour of the geopotential data processing and the descriptive aspects of geological interpretation. Together they form a legitimate intellectual exercise which should contribute to the geologic knowledge of northwestern South America to help mitigate seismic and volcanic hazards and the risk factors in energy and mineral resource exploration ventures.

The integration of satellite, airborne and surface geopotential field data and future data from satellite missions like GOCE (Gravity field and steady-state ocean circulation explorer; ESA, 2006) and SWARM (The Earth’s magnetic field and environmental explorers; ESA, 2006) certainly will lead to new insights of the tectonic processes of northwestern South America. Additional recommendations for extending this research include:

To improve TGE estimates by assigning density values from available mapped lithological units instead of using a single density value.

149 To calculate and interpret the TCFAGA and CHAMP DRTP (TFMA) gradients to enhanced local crustal density and magnetic susceptibility variations.

To model the thermal structure of the study area from surface and borehole observations to support the interpretation of potential ﬁeld anomalies and stress modeling.

150 APPENDIX A

TWO DIMENSIONAL GRAVITY AND MAGNETIC ANOMALIES DUE TO A POLYGON BY GM-SYS

151 The methods used by GM-SYS to calculate the gravity and magnetic model response are based on the methods of Talwani et al, (1959), and Talwani and Heirtzler,

(1964), and make use of the algorithms described in Won and Bevis, (1987). Two and one-half-Dimensional calculations are based on Rasmussen and Pedersen, (1979).

The GM-SYS inversion routine utilizes a Marqardt inversion algorithm (Marqardt,

1963) to linearize and invert the calculations. GM-SYS uses an implementation of that algorithm for gravity and magnetics developed by the USGS and used in their computer program, SAKI (Webring, 1985).

GM-SYS uses a two-dimensional, flat-earth model for the gravity and magnetic calculations; that is, each structural unit or block extends to plus and minus infinity in the direction perpendicular to the profile. The earth is assumed to have topography but no curvature. The model also extends plus and minus 30,000 kilometers along the profile to eliminate edge-effects.

In GM-SYS, stations (points at which gravity or magnetic values are observed and calculated) should be outside of the source material (i.e., in an area of the model with a density, magnetization, and susceptibility equal to zero).

Won and Bevis(1987) present two algorithms for computing the gravitational and magnetic anomalies due to an n-sided polygon in a two-dimensional space.

Talwani et al, (1959), and Talwani and Heirtzler, (1964) presented a method for computing the gravitational attraction due to an n-sided polygon. Their algorithm has been used in computer programs for two-dimensional gravity modeling. because any

2-D body of arbitrary shape can be approximated by a polygon, and any 3-D density distribution can be modeled as an ensemble of juxtaposed constant-density polygons.

Won and Bevis (1987) modiﬁed algorithm for computing the gravitational acceleration due to a polygon, applying Poissons relation to expressions for gravitational acceleration. They derived a second algorithm for computing the magnetic anomaly due to

152 a polygon magnetized by an external ﬁeld. In this manner, the gravity and magnetic anomalies can be correctly determined for any point inside, outside, above, or below the polygon.

A.1 Gravity Anomaly due to a Polygon

Hubbert (1948) showed that the gravitational attraction due to a 2-D body can be expressed in terms of a line integral around its periphery. Talwani et al (1959) considered the case of an n-sided polygon and broke the line integral up into n contributions, each associated with a side of the polygon. Won and Bevis (1987) followed Talwani et al (1959) by placing the point at which the gravity anomaly is to be computed (i.e., the station) at the origin of the coordinate system and expressing the vertical and horizontal components of the gravity anomaly as:

Xn ∆gz = 2Gρ Zi (A.1) i=1 and

Xn ∆gx = 2Gρ Xi (A.2) i=1

th where Zi and Xi are line integrals along the i side of the polygon, G is the gravitational constant, and ρ is the density of the polygon. Talwani et al,(1959) derived expressions for Zi and Xi that make extensive references to trigonometric functions.

Grant and West (1965) reformulated the expression for Zi, by making more references to the vertex coordinates:

153 ³ ´ xi, zi = 1.n (A.3) i

And fewer references to angular quantities, and thus reduced the number of trigonometric expressions involved in the computation. Won and Bevis (1987) followed Grant and Wests approach producing a formula for Xi as well as Zi compacting the notation by eliminating i. Any two successive vertices were labeled 1 and 2, and each neigh- boring pair of vertices was treated as vertices 1 and 2 in turn. Thus the following algorithms were obtained:

h i r2 Z = A (θ1 − θ2) + Bln , (A.4) r1

h i r2 X = A (−θ1 − θ2) B + ln , (A.5) r1

(x2 − x1)(x1z2 − x2z1) A = 2 2 (A.6) (x2 − x1) + (z2 − z1)

z − z B = 2 1 (A.7) x2 − x1

2 2 2 r1 = x1 + z1, (A.8)

2 2 2 r2 = x2 + z2, (A.9)

154 The computation of (−θ1 − θ2) requires some care if the algorithm is to be valid for any local station. −θ1 and −θ2 are obtained using the relationship:

³ ´ −1 zj θj = tan (A.10) xj ∀j=1,2.

A.2 Magnetic Anomaly due to a Polygon

Talwani and Heirtzler (1964) introduced a method for computing the magnetic anomaly due to an inﬁnite polygonal cylinder. by combining the anomalies due to an ensemble of semiinﬁnite sills each of which was bounded by one of the polygons sides.

Alternatively, the magnetic anomaly due to an polygonal cylinder can be derived using

Poissons relation, from the previous expressions for the associated gravity anomaly.

Won and Bevis (1987) assumed that the magnetization of the cylinder was induced solely by the ambient earths magnetic ﬁeld. Then

kH δ ∆H = e ∆g (A.11) Gρ δα where

∆H = magnetic anomaly vector, ∆g = gravity anomaly vector, k = magnetic susceptibility of polygon, ρ = polygon density, He = ambient scalar earth magnetic ﬁeld strength, and α = direction of induced magnetization.

Unlike the gravity anomaly, the magnetic anomaly depends additionally on the strike of the cylinder,

Where:

155 I = Magnetic inclination, and β = The strike of the cylinder measured counterclockwise from magnetic north to the negative y-axis,

It can be shown that

∂ ∂ ∂ = sin I + sin β cos I (A.12) ∂α ∂z ∂x

From equation (A.10), vertical and horizontal components of the magnetic anomaly can be derived as

kH ∂ ∆H = e ∆g (A.13) z Gρ ∂α z

and

kH ∂ ∆H = e ∆g (A.14) x Gρ ∂α x

where expressions for gz and gx, are given by equations (A.1) and (A.2). Substitut- ing equations (A.l), (A.2), and (A.12) into equations (A.13) and (A.14), obtaining

³ ∂Z ∂Z ´ ∆H = 2kH sin I + sin β cos I , (A.15) z e ∂z ∂x

And

³ ∂X ∂X ´ ∆H = 2kH sin I + sin β cos I , (A.16) x e ∂z ∂x

156 Once ∆Hz and ∆Hx are known, the total ﬁeld scalar anomaly anomaly the total ﬁeld scalar anomaly ∆H may be computed by

∆H = ∆Hz sin I + ∆Hx sin β cos I. (A.17)

The derivatives in equations (a.15 and A.16) are

2 h i ∂Z (x2 − x1) z2 − z1 r2 = 2 (θ1 − θ2) + ln − P (A.18) ∂z R x2 − x1 r1

h i ∂Z −(x2 − x1)(z2 − z1) z2 − z1 r2 = 2 (θ1 − θ2) + ln + Q (A.19) ∂x R x2 − x1 r1

2 h i ∂X (x2 − x1) z2 − z1 r2 = 2 (θ1 − θ2) − ln + Q (A.20) ∂z R x2 − x1 r1

h i ∂Z (x2 − x1)(z2 − z1) z2 − z1 r2 = 2 (θ1 − θ2) − ln + P (A.21) ∂x R x2 − x1 r1

Where

2 2 2 R = (x2 − x1) + (z2 − z1) (A.22)

h i x1z2 − x2z1 x1(x2 − x1) − z1(z2 − z1) x2(x2 − x1) − z2(z2 − z1) P = 2 2 − 2 (A.23) R r1 r2

157 and

h i x1z2 − x2z1 x1(z2 − z1) + z1(x2 − x1) x2(z2 − z1) + z2(x2 − x1) Q = 2 2 − 2 (A.24) R r1 r2

Special cases 1 and 2 shown previously for the gravity problem also apply in the same way for the magnetic anomaly. In addition, a fourth case is as follows:

ifx1 = x2, then

∂Z = −P (A.25) ∂z

2 ∂Z −(z2 − z1) r2 = 2 ln + Q (A.26) ∂x R r1

∂X = Q (A.27) ∂z

∂X (z − z )2 = 2 1 (θ − θ ) + P (A.28) ∂x R2 1 2

Won and Bevis (1987) developed the FORTRAN subroutine m − poly computing the x-component, the z-component and the total anomalous magnetic field strength due to an infinite polygon cylinder magnetized by an external magnetic field. It was assumed that the cylinder strikes parallel to the y-axis in a right-handed coordinate system [x, y, z]. The vertical, horizontal and total field strength anomalies depend upon the relative locations of the polygon and station in the [x, y] plane, the magnetic susceptibility of the cylinder, the inclination of the Earth’s magnetic field,the

158 total field strength of the earth’s magnetic field, and the geomagnetic azimuth (strike) of the polygon. This quantity (β) is the angle from magnetic north to the negative x-axis measured in the horizontal plane. The angle is positive when measured counterclockwise from magnetic north. The x,y coordinates of the polygon’s vertices must be specified clockwise when the x,z plane is viewed toward the negative y-axis.

The routine computes the anomalies at any specific number of stations, and these stations may be specified in any sequence. In the event that the Earth’s magnetic field is vertical (Inclination = 90o), the strike (β) is undefined and irrelevant and can be set to any value. The algorithm does not include the effects of demagnetization (Grant and West, 1965) and thus it is not suited for modeling the anomalies due to bodies whose magnetic susceptibility exceeds 0.01 e.m.u. Magnetic susceptibility values must be assigned with care, even though magnetic susceptibility is a dimensionless quantity, it differs by a factor of 4π between the SI and emu system (kemu = 4πkSI ). H units are gammas. If the SI is used units are in NanoTeslas (nT). Spatial coordinates may be given in any unit of length, provided the unit chosen consistently.

The Fortran codes can be consulted in the journal of Geophysics, volume 52 No. 2 published by the Society of Exploration Geophysics (http://www.segdl.org/geophysics/).

159 APPENDIX B

FRACTIONAL VERTICAL DERIVATIVES

160 The use of vertical derivatives has been always a standard method of enhancing high frequency features in potential field data. Second order vertical derivatives were computed using convolution filters and Laplace’s equation (Sheriff, 1994).

∇2f = 0

Ã ! ∂2f ∂2f ∂2f ∂z2 = − ∂x2 + ∂y2 (B.1)

By Fourier ﬁltering it is possible to compute the nth order vertical derivatives by using the following relationship:

∂2f F( ) = kn.F(f) (B.2) ∂zn

Where F is the Fourier representation of the ﬁeld and K is the wavenumber or frequency. The derivation of equation 6.2 from spatial representation in equation 6.3 is based on Blakeley, (1955).

∂f f(x, y, z) − f(x, y, z − ∆z) = lim (B.3) ∂z ∆z→0 ∆z

Where f is the potential ﬁeld (or it’s derivative) and a z positive down sign convention implies that the data is upward continued an inﬁnitesimal distance and this is subtracted from the original data. The Simple for of equation 2 allows the use of non-integer values for n, providing fractional vertical derivatives which have an intermediate frequency content as compared to integer order vertical derivatives.

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