EARTHQUAKE MECHANISMS FROM LINEAR-PROGRAMMING INVERSION OF SEISMIC-WAVE AMPLITUDE RATIOS

The amplitudes of radiated seismic waves contain far more information about earthquake source mechanisms than do first-motion polarities, bu t amplitudes are severely distorted by the effects of heterogeneity in the Earth. This distortion can be reduced greatly by using the ratios of amplitudes of appropriately chosen seismic phases, rather than sim ple amplitudes, but existing methods for inverting amplitude ratios ar e severely nonlinear and require computationally intensive searching m ethods to ensure that solutions are globally optimal. Searching method s are particularly costly if general (moment tensor) mechanisms are al lowed. Efficient linear-programming methods, which do not suffer from these problems, have previously been applied to inverting polarities a nd wave amplitudes. We extend these methods to amplitude ratios, in wh ich formulation on inequality constraint for an amplitude ratio takes the same mathematical form as a polarity observation. Three-component digital data for an earthquake at the Hengill-Grensdalur geothermal ar ea in southwestern Iceland illustrate the power of the method. Polarit ies of P, SH, and SV waves, unusually well distributed on the focal sp here, cannot distinguish between diverse mechanisms, including a doubl e couple. Amplitude ratios, on the other hand, clearly rule out the do uble-couple solution and require a large explosive isotropic component .