Study of seismogram envelopes based on scattering by random inhomogeneities in the lithosphere: a review

Abstract

Abstract Instead of the precise examination of individual phases in seismograms, we will focus on the relation between random inhomogeneities in the lithosphere and the systematic change in seismogram envelopes. Recent developments in the study of high-frequency seismogram envelopes are briefly reviewed. The smooth amplitude decay of coda envelopes of local earthquakes first attracted seismologists' interest in scattering and was investigated based on the single-scattering assumption with a uniform distribution of point-like scatterers. Subsequently, the importance of multiple scattering was recognized and theoretical models were introduced. As a bridge between conventional seismology and the scattering approach, a hybrid model in which a large impedance contrast plane was embedded in a scattering medium was proposed for the interpretation of a reflected S phase in the coda for shallow events around a volcanic front in Japan. Next, three-component seismogram envelopes of a small local earthquake were synthesized using the Born approximation in inhomogeneous media. The S coda is excited in all directions from the hypocenter. The P coda appears even in the nodal direction of the P-wave radiation mostly owing to SP scattering near the hypocenter. Both pseudo P and S phases appear even on the null axis. These synthetic seismogram envelopes are in harmony with characteristics of observed seismogram envelopes of local earthquakes. Scattering due to random inhomogeneities quantitatively explains the frequency dependence of S-wave attenuation. From the analysis of seismogram envelopes around direct S waves of earthquakes with intermediate hypocentral distances, it was recently found that the time lag of the maximum amplitude arrival from the S-wave onset increased and the envelope broadened with travel distance. Diffraction due to slowly varying velocity inhomogeneities is modeled using the parabolic approximation, and is used to explain the envelope around the S-wave arrival observed at intermediate distances. A nonlinear inversion of the full seismogram envelope is used for the evaluation of randomness. Thus, the analysis of seismogram envelopes offers us useful information on the randomly inhomogeneous structure of the lithosphere complementary to the array observation analysis of individual phases.