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 Green's functions. For an arbitrary symmetric moment tensor point source, one additional Green's 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 Green's 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 Green's 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 × 10²² 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.