Source inversion of seismic waveforms: The Koyna, India, earthquakes of 13 September 1967

abstract The treatment of the seismic source inverse problem, when diverse forms of waveform data are available, is simple and elegant using a moment tensor formalism. If earth structure is known and its effects predictable in terms of vertically inhomogeneous elastic-layered models, then all types of wave phenomena (e.g., surface waves, body waves, leaky modes, etc.) for a purely deviatoric moment tensor point source may be represented by, at most, a sum of three Green9s functions. For an arbitrary symmetric moment tensor point source, one additional Green9s function is needed for the P - SV system. However elegant this formalism may be for posing the linear inverse problem, the major difficulties lie in earth structure unknowns and resultant nonlinearities in the Green9s functions which can cause significant trade-offs with source parameters. A hybrid inversion procedure is set up to gain insight into the probable unknowns in particular problems by incorporating both a linearized least-squares gradient method for the moment tensor or double couple, and smoothed time function parameters, and a nonlinear systematic trial-and-error search for moment tensor or double couple parameters for several assumptions of Green9s function. The inversion technique is applied to near-regional waveform data from a small earthquake associated with the Koyna Reservoir which occurred 13 September 1967, as the second in a group of three events with very similar waveshapes, but differing amplitudes. The magnitudes of the second and third events are smaller by −0.2 and −0.8 units, respectively, compared to the first. The absolute magnitude for the first event is poorly constrained but is estimated to be 4.0 to 4.5 rather than the previously published value of 5.5 to 6.0. From the similarity of waveshapes, all three events are inferred to have the same mechanism and occurred within about 2 km of the same hypocenter. The results from moment tensor and double couple inversions for event 2 data indicate that source depth was 5 km and that left-lateral faulting occurred on a plane with a strike of N20°E ± 5°, dip of 90° ± 15°, and a rake of 0° ± 35°. The inferred far-field time function is approximately 3 sec in duration, unusually long for the seismic moment of 9 × 10 22 dyne-cm, yielding a possible stress drop of about 0.05 bars. A fault map was constructed from LANDSAT image interpretation and shows a predominance of NNW to NNE striking faults in the Koyna area which is used to infer the appropriate nodal plane in the inversion results. These faults tend to define a broad en-echelon zone which parallels the Western Ghats in this area.

[1]  D. Helmberger Generalized ray theory for shear dislocations , 1974, Bulletin of the Seismological Society of America.

[2]  D. Jackson The use of a priori data to resolve non‐uniqueness in linear inversion , 1979 .

[3]  J. Brune Tectonic stress and the spectra of seismic shear waves from earthquakes , 1970 .

[4]  R. Athavale Induced seepage along a coastal parallel system of faults as a possible cause of the Koyna earthquakes , 1975 .

[5]  Charles A. Langston,et al.  The effect of planar dipping structure on source and receiver responses for constant ray parameter , 1977 .

[6]  Charles A. Langston,et al.  A body wave inversion of the Koyna, India, earthquake of December 10, 1967, and some implications for body wave focal mechanisms , 1976 .

[7]  L. Johnson,et al.  Source parameters of moderate size earthquakes and the importance of receiver crustal structure in interpreting observations of local earthquakes , 1977, Bulletin of the Seismological Society of America.

[8]  G. Mellman,et al.  Inversion of the body waves from the Borrego Mountain earthquake to the source mechanism , 1976, Bulletin of the Seismological Society of America.

[9]  Brian W. Stump,et al.  The determination of source properties by the linear inversion of seismograms , 1977, Bulletin of the Seismological Society of America.

[10]  D. L. Anderson,et al.  Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And , 1975 .

[11]  David C. Peters,et al.  Application of prediction analysis to hypocenter determination using a local array , 1972, Bulletin of the Seismological Society of America.

[12]  C. Langston A single‐station fault‐Plane solution method , 1979 .

[13]  R. Strelitz Moment tensor inversions and source models , 1978 .

[14]  J. Combs,et al.  Continued seismic activity at the Koyna reservoir site, India , 1976 .

[15]  D. Helmberger The crust-mantle transition in the Bering Sea , 1968 .

[16]  H. Narain Crustal Structure of the Indian Subcontinent , 1973 .

[17]  S. Guha,et al.  Case histories of some artificial crustal disturbances , 1974 .

[18]  O. Nuttli,et al.  Seismic wave attenuation and magnitude relations for eastern North America , 1973 .

[19]  R. Wiggins,et al.  The general linear inverse problem - Implication of surface waves and free oscillations for earth structure. , 1972 .

[20]  F. Gilbert Excitation of the Normal Modes of the Earth by Earthquake Sources , 1971 .

[21]  R. Geller Body force equivalents for stress-drop seismic sources , 1976, Bulletin of the Seismological Society of America.

[22]  L. J. Burdick,et al.  Modeling crustal structure through the use of converted phases in teleseismic body-wave forms , 1977, Bulletin of the Seismological Society of America.