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Source, Scattering and Attenuation Effects on High SOURCE, SCATTERING AND ATTENUATION EFFECTS ON HIGH FREQUENCY SEISMIC vlAVES by BERNARD ALFRED CHOUET Electrical Engineer Federal Institute of Technology Lausanne, Switzerland (1968) S.M., Aeronautics and Astronautics, M.I.T. (1972) S.M., Earth and Planetary Sciences, M.I.T. (1973) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY Sept.ember, 1976 Signature of the Author Department: of Earth and Planetary Sciences, September 1976 Certified by ................................... Thesis Supervisor Accepted by ..............-.................... Chairman, Departmental Committee on Graduate Students ii SOURCE, SCATTERING AND ATTENUATION EFFECTS ON HIGH FREQUENCY SEISMIC WAVES by BERNARD ALFRED CHOUET Submitted to the Department of Earth and Planetary Sciences on August 12, 1976 in partial fulfillment of the requirements for the degree of Doctor of Philosophy ABSTRACT High frequency coda waves from small local earthquakes are interpreted as backscattering waves from numerous hete- rogeneities distributed uniformly in the earth's crust. Two extreme models of the wave medium that account for the ob- servations on the coda are proposed. In the first model we use a simple statistical approach and consider the back- scattering waves as a superposition of independent singly scattered wavelets. The basic assumption underlying this single backscattering model is that the scattering is a weak process so that the loss of seismic energy as well as the multiple scattering can be neglected. In the second model the seismic energy transfer is considered as a diffusion process. These two approaches lead to similar formulas that allow an accurate separation of the effect of earth- quake source from the effects of scattering and attenuation on the coda spectra. A marked difference was found in the scaling law of earthquake source spectra in various seismic regions of Ca- lifornia, Hawaii, and Japan, which may be attributed to the differences in inhomogeneity length and strength of the earth's crust. The apparent Q of coda waves in California and Japan is strongly frequency dependent with values in- iii creasing from 60-200 at 1.5 Hz to about 600-2000 at 24 Hz. The increase of the Q of coda with frequency is less pro- nounced in Hawaii, showing a roughly constant value of 250 below 6 Hz and about 450 near 20 Hz. These observations are interpreted as a combined effect of variation of the intrinsic Q with depth and frequency-dependent composition of coda waves described as follows. The turbidity coeffi- cient of the lithosphere required at 1.5 Hz to explain the observed coda as body wave scattering is orders of magnitude greater than previously known values such as those obtained by Aki (1973) and Capon (1974) under the Montana Lasa from amplitude and phase fluctuations of teleseismic P waves. From the high attenuation and turbidity obtained at this frequency we conclude that at around 1.5 Hz the coda is made of backscattering surface waves from heterogeneities in the shallow, low-Q lithosphere. The high Q observed for the coda at frequencies higher than 10 Hz, on the other hand, eliminates the possibility that these waves are back- scattering surface waves. We conclude that at these high frequencies the coda must be made of backscattering body waves from heterogeneities in the deep lithosphere. The sensitivity of the high frequency coda waves to changes in the medium structure is demonstrated in the data collected at Stone Canyon, California. The temporal change in behavior of the 24 Hz coda observed in this region is interpreted as being related mainly to an increase of the intrinsic Q in the shallow crust. Thesis Supervisor: Keiiti Aki Title: Professor of Geophysics iv ACKNOWLEDGEMENTS It was my privilege to have Keiiti Aki as my advisor. His enthusiasm, constant patience and penetrating physical insight made it a rewarding experience to work under his guidance. To him I wish to express my deepest gratitude. The field experiments were made possible only through the help of many people. Jerry Eaton, Jack Healy, and Dick Thompson of the U.S. Geological Survey helped with the operation at Stone Canyon. Bill Bakun kindly offered his data from Bickmore Canyon and Sam Stewart and Jim Ellis helped with the filtering of this data at the National Center for Earthquake Research in Menlo Park. Bob Tilling, Bob Koyanagi, Elliot Endo, George Kojima, Bill Francis, and the staff of the Hawaiian Volcano Observatory provided support for the experiment at Kilauea. Clarence Allen and Hiroo Kanamori of the California Institute of Technology, Harry Kues and Tom Werntz of the Los Angeles County Flood Control District, and James Vance of the U.S. Geological Survey assisted with the logistics and operation at San Fernando. George Keough of M.I.T. helped with the installation at the Wallace Geophysical Observatory. To all of them, I extend my warmest thanks. I am grateful to Masaru Tsujiura of Tokyo University for making the data from Tsukuba and Oishiyama available to me, and to Eystein Husebye for the coda record obtained at Norsar. The digitizing of the records was performed at Lincoln Laboratory. The permission to use the facilities is greatly acknowledged. I owe special thanks to my friends Michel Bouchon, Raoul Madariaga, Howard Patton and Ken Anderson with whom I had many beneficial discussions at various stages of this work. For her continuous encouragement and support, her refreshing presence and invaluable help with the preparation of the manuscript, the author wishes to express his sincere gratitude to his wife Danielle. This research was supported partially by the Energy Research and Development Agency under contract E(11-1)2534 and by the Advanced Research Project Agency, monitored by the Air Force Office of Scientific Research, under contract F44620-75-C-0064. TABLE OF CONTENT page CHAPTER 1 Introduction 1 CHAPTER 2 Interpretation of coda waves 5 2.1 Origin of the coda of local earthquakes 5 2.2 Two extreme models of coda waves 13 CHAPTER 3 Analysis of data 25 3.1 Earthquake selection 25 3.2 Data preparation 40 3.3 Data processing 42 3.4 Preliminary results 47 CHAPTER 4 Regional variation of the scaling law of earthquake source spectrum 73 4.1 Introduction 73 4.2 Source factors of coda 75 4.3 Construction of the scaling law 89 4.4 Discussion 112 CHAPTER 5 Quantitative discussion on the origin of coda waves 135 5.1 Introduction 135 5.2 Regional turbidities 135 5.3 Regional seismic attenuation properties of earth's crust 146 5.4 Temporal variation in the crustal structure near Stone Canyon 152 5.5 Concluding remarks 167 vii TABLE OF CONTENT (Continued) page CHAPTER 6 Conclusions 169 APPENDIX 171 REFERENCES 174 CHAPTER 1 Introduction High-frequency seismic waves are a fascinating tool for the study of the fine structure of the earth and the details of seismic sources. To extract the information carried by these waves, however, we must first be able to interpret their seismograms in terms of parameters of their physical models. A straightforward deterministic interpretation is difficult precisely because of the extreme sensitivity of these waves to details. Numerical approaches such as the finite difference and finite element methods may be used in special cases in which the model parameters for the earth medium are known and the computer cost is not a factor. This is, unfortunately, not the case in the usual study of local earthquakes. The above difficulties may be avoided by resorting to a statistical treatment of the heterogeneity of the earth medium. In other words, a small number of statistical parameters may be sufficient to characterize the medium for the interpretation of a certain aspect of the seismograms. There have been several attempts in recent years along this direction in earthquake seismology (Aki, 1969, 1973; Aki and Chouet, 1975; Takano, 1971; Haddon, 1972, 1975; Cleary and Haddon, 1972; King et al., 1973; Capon, 1974; Kopnichev, 1975; Husebye et al., 1976; Rautian and Khalturin, 1976) and explosion seismology (Wesley, 1965; Nicolayev, 1968, 1975; Nicolayev and Tregub, 1970; Levin and Robinson, 1969; Dunkin, 1969; Greenfield, 1971), as well as lunar seismology (Nakamura et al., 1970; Dainty et al., 1974a; Nakamura, 1976). The longer the waves travel, the greater the variety of heterogeneities they encounter. The later portions of a seismogram therefore may be considered as a result of some kind of averaging over many samples of heterogeneities, thus suggesting a statistical treatment in which a small number of parameters characterize the average properties of the heterogeneous medium. A few years ago Aki (1969) suggested that the seismic coda waves of local earthquakes are backscattering waves from numerous randomly distributed heterogeneities in the earth and may be treated by a statistical method. More recent studies by Scheimer and Landers (1974) and Aki and Chouet (1975), as well as the observational data accumulated in the past few years by this author and others in this country, Norway, Japan and the USSR seem to support the validity of Aki's model. The aim of this thesis is to study the high-frequency seismic coda in the range up to 25 Hz observed in the vicinity of small local earthquakes. We shall start, in Chapter 2, by presenting evidence to support the assumption that the coda waves are backscattering waves from randomly distributed heterogeneities. A method will then be described for the interpretation of the observed coda spectra on the basis of two extreme models of the wave medium. In the single back- scattering model the scattering is considered to be a weak process, and the loss of seismic energy by scattering is neglected. In the diffusion model the seismic energy transfer is considered as a diffusion process.
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