Seismogram Envelope Inversion Using a Multiple Isotropic Scattering Model: Application to Aftershocks of the 2001 Bhuj Earthquake

Abstract

We apply the energy transfer theory of 3D multiple isotropic scattering to analyze seismogram envelopes of the 2001 Bhuj earthquake of India. We synthesized the S -wave coda envelopes by using a numerical Monte Carlo method. Our model is described by total scattering coefficient g , intrinsic absorption coefficient b , spectral source energy S , and site factors Z . Isotropic source radiation and acoustic wave propagation were assumed. We inverted the observed coda envelopes of 10 aftershocks ( M L ≥4) using the grid search for g , least-squares inversion for b , and S between 1 and 24 Hz. Parameter g does not show significant frequency dependency and averages to 0.01 1/km. This corresponds to a mean free path of 100 km. Parameter b shows weak frequency dependency, increasing with frequency. Its value ranges from 0.02 1/sec to 0.05 1/sec. Consequently, the frequency dependency of intrinsic attenuation takes the power-law form of Qi ( f ) = 280 f 0.72. The source energy is largely consistent with the well-known ω 2-source model and the seismic moment is comparable to estimates using standard empirical relations between seismic moment and local magnitude. We also inverted the envelopes for site-amplification factors Z . The values of Z range from 0.5 to 1.75 with no clear frequency dependence, which is consistent with the geology of the region, as the stations were deployed on hard- rock sites.