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Certified By. A DISLOCATION APPROACH TO PLATE INTERACTION by RAYMON LEE BROWN, JR, B.S., University of Texas (1967) M.S., University of Hawaii (1969) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY August, 1975 Signature of Author . .,.-,...- .... , DepartmentCertified by.of ..-........Earth and& Planetary. _Sciences, * Thesis Supervisor Accepted by ................... ......... , ... * ..... Chairman, Departmental Committee on Graduate Students pEC 17 1975) ~~~~~~~~1WRa e i I 4, : 2 Abstract A Dislocation Approach to Plate Interaction by Raymon Lee Brown, Jr. Submitted to the Department of Earth and Planetary Sciences on August 25, 1975 in partial fulfillment of the requirements for the degree of Doctor of Philosophy A dislocation can be described in terms of a surface of discontinuity or the line which circumscribes this surface. We have applied the solutions of Yoffe (1960) and Comninou (1973) for an angular dislocation line to the problem of calculating the fields due to general polygonal dislocations. Next, anumerical method has been developed explicitly for finite sources (Finite Source Method or FSM) which allows the computation of fields from a dislocation that penetrates several layers of a layered half-space. The speed of the FSM allows the calculation of many models which are not econom- ically possible by other means. It is used here to model 3 earthquakes in layered media and plate bottom effects due to the interaction of lithospheric plates. Finally, the problem of the mutual interaction of lithospheric plates in relative motion has been posed in terms of dislocation theory (anti-dislocations). Dislocation models of various portions of the San Andreas fault in California are proposed and evaluated by comparing them with seismic and geodetic data, We find, for example, that fault creep near Hollister acts to obscure any locking at depth and that as much as 70% of the fault could be locked (down to 20 km) and still be consistent with the geodetic data, The models also suggest that the depth of locking (or non-slipping portion of the fault) varies from 10 to 80 km along the San Andreas, Under San Francisco the depth of locking appears to be 20 to 40 km while just north and south of this region the locking is from 10 to 15 km deep, Our models are also indicative of a more northerly component of motion for the Pacific with respect to the American plate than would be expected if the San Andreas were a simple strike-slip fault. South of Cholame the depth of locking begins a rapid increase and appears to lock to 80 km in the Tejon bend portion of the San Andreas. We are not able, however, to distinguish between an actual locking of the fault, capable of taking high stresses, or simply a low stress state. Thesis Supervisor: M. Nafi Toks6z Title: Professor of Geophysics 4 ACKNOWLEDGEMENTS This thesis represents the work of the author, but is, to a large extent, a reflection of the author's environment during the time in which the thesis was developed. I was encouraged to study the general subject of tectonic stresses in California by Professor M. Nafi Toks6z. Professor Keiiti Aki is responsible for teaching me philosophy and the fundamentals of dislocation theory (and introducing me to Maria Comninou). Don Weidner made me prove mathema- tically that dislocations could be used to model plate interaction. I miss the interaction I had with Don. Maria Comninou got me started with angular dislocations and helped considerably when I was programming her thesis. At one point in time the author wanted to eliminate the chapter on the numerical method for finite sources. This chapter would not have been completed had it not been for the firm encouragement of Professor M. Nafi Toks8z. I am appreciative of his help. Norm Brenner was instrumental in getting the author over the FFT hump at this stage of the thesis. Discussions with Raul Madariaga led to many of the results in Chapter II. Raul's availability for detailed discussions of complex problems make him an integral part of my M.I.T. experience. 5 Writing a west coast thesis on the east coast was made easier by the author's discussions with several west coast informants. Bill Ellsworth, Dave Hadley, and Gordon Stewart gave the author fault plane solutions (published and un- published) and their opinions of the tectonics of California. Bob Nason (U.S.G.S.) was extremely helpful with discussions on fault creep data and his impressions of what is driving the fault creep. Peter Molnar suggested some changes in Chapter IV and furnished additional insight into the tectonic history of California, Jim Savage (U.S.G.S.) read the whole thesis (and even checked some of the calculations). His interest in my thesis is deeply appreciated. Several people read my thesis in a rough form and helped me clarify certain points. I wish to thank Ken Anderson, Mike Chinnery, Mike Fehler, Tony Shakal, and Seth Stein for wading through a rough draft of the work presented. Seth Stein spent several hours going through the thesis and reviewing it with me. Donald Paul and I had several useful discussions on the discrete Fourier transform and Ken Anderson was always available (except on weekends) for programming assistance. During the initial stages of Chapter III Richard Buck helped with the drafting. The typing of this thesis was done by Dorothy Frank. Her patience and even temper made our association a pleasure. I cannot thank her enough for a job well done. 6 Moral support during the writing of the thesis came from Shamita Das. Although I have sacrificed a great deal for this thesis I feel that my wife, Merri, and our two daughters, Jennifer and Deborah, have given up far more, I hope that I can make it up to them. The research has been supported by the Advanced Research Projects Agency, monitored by the Air Force Office of Scientific Research under contracts F44620-71-C-0049 and F44620-75-C-0064, and by the Air Force Cambridge Research Laboratories, Air Force Systems Command under contract F19628-74-C-0072. 7 TABLE OF CONTENTS Abstract 2 Acknowledgements 4 Table of Contents 7 I. INTRODUCTION 1.1 Purpose and Scope of Thesis 10 1.2 History of Dislocation Theory 14 and its Application II. CONSTRUCTION OF FINITE DISLOCATION LOOPS VIA ANGULAR DISLOCATIONS 2.1 Introduction 20 2.2 Volterra Dislocations 21 2.3 Angular Dislocations 22 2.4 Dislocation Surfaces and Multi-Valuedness 24 2.5 Summary 32 Figures 34 III. FINITE DISLOCATIONS IN FLAT LAYERED MEDIA 3.1 Introduction 50 3.2 Finite Sources in Layered Media 3.2.1 A finite source numerical method 53 in three dimensions 3.2.2 Homogeneous solutions 56 3.2.3 Matrix approach to layered media 61 3.2.4 A finite source distributed 63 through several layers 3.3 Discussion and Application 8 3.3.1 Big numbers 68 3.3.2 Comparison with half-space solutions 71 3.3.3 Soft surface layer 76 3.3.4 Continental crustal models - vertical 80 faults 3.3.5 Oblique faults 83 3.3.6 A hard layer over a soft half-space 85 3.4 Conclusions 89 Figures 91 IV. A DISLOCATION APPROACH TO PLATE TECTONICS 4.1 Introduction 177 4.2 Anti-dislocation Models of Plate Interaction 178 4.3 Application to Plate Interaction 185 4.4 Hayward-Calaveras-San Andreas Fault Zone 4.4.1 Introduction 190 4.4.2 The SJB bend 191 4.4.3 Strain release of fault creep 204 4.4,4 Discussion 219 Tables 222 Figures 226 4.5 The Fort Tejon Bend and its Role in the Tectonics of Southern California 4.5.1 Introduction 271 4.5.2 Plate bottom effects 273 4.5.3 Models of the Tejon bend 277 4.5.4 Discussion 287 Figures 289 9 V. MODELS OF THE STRESS HISTORY OF CALIFORNIA 5.1 Introduction 342 5.2 Tectonic Model of California 343 5.3 California Earthquakes 351 5.4 Initial Conditions 355 5.5 Stress History of California 358 5.6 SJB-Cholame High Shear Zone 363 5.7 Conclusions 367 Tables 369 Figures 373 VI. SUMMARY OF THESIS 419 References 422 Appendix - The E matrix, its inverse, and the E' matrix 442 I 0 CHAPTER I INTRODUCTION 1.1 Purpose and Scope of Thesis For at least 5-25 million years the portion of land seaward of the San Andreas fault zone in California has been drifting northwestward with respect to the North American continent at an approximate rate of 3-5 cm/year. As the two land masses slide past one another, portions of their interface lock and internal stress builds up around these locked sections of the fault. The stress build up results eventually in the occurrence of an earthquake. The problem to be considered here is the quantitative description of the above mentioned stress accumulation and release. In particular, the main objectives of this thesis are: 1) the development and application of numerical techniques for computing the static fields of finite dislocations distributed throughout layered media; 2) the representation of the problem of plate interaction in terms of dislocation theory, and; 3) the application of the dislocation theory of plate interaction to specific regions of California. The computation of the stress accumulation due to lithos- pheric plate interaction is of importance because it yields (1) a quantitative discussion of the amount of locking and earthquake potential for various sections of the fault, 11 (2) a direct test of complex fault models and their effects upon local strain fields (rather than guessing, as is often the case), and (3) a more realistic model of earthquake.pre- stress than the usually assumed constant stress (and therefore stress drop).
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