Spatial variation of coda wave amplitude inmedia with a localized heterogeneous region

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Using an indirect boundary integralmethod, seismograms are computed for elastic mediawith localized heterogeneities. Models aretwo-dimensional homogeneous full spaces (P and SV waves) with many circular cavities asheterogeneities or scatterers. Heterogeneities arelocalized within a depth range, forming a relativelythin random layer. Seismograms are obtained forreceivers at depth 0 km (surface) and for severalfocal depths, with sources radiating S wavesisotropically. Seismograms are composed of thedirect S wave and all the possible scattered wavesby the heterogeneities, exhibiting late arrivals orcoda waves. The coda wave amplitude, or coda energylevel, and its duration vary for events withdifferent focal depths. As the focal depth increasesand the source gets closer to the layer of localizedheterogeneities, the coda level becomes small. Whenthe source is within the heterogeneous layer,however, the coda level becomes larger than for acase of the source either above or below theheterogeneous layer. This local enhancement of codatakes place clearly only in the frequency range forwhich the scattering is the most effective, that is,when the non-dimensional frequency kdtakes values from 2 to 3, where kis thewavenumber and dis the size of eachheterogeneity. Such enhancement of coda is notobserved when the density of cavities, or strengthof the heterogeneities, is reduced. Coda levelbecomes locally large for a source within theheterogeneous layer only in the case that theheterogeneities are strong enough to excite multiplyscattered waves, as compared with the singlyscattered ones. Robinson (1987) studied the temporalvariation of coda-duration magnitude relative toevent magnitude based on P and S wave amplitudesusing the seismic network of the Wellington, NewZealand, region. He found that coda-durationmagnitude relative to amplitude magnitude decreaseswith focal depth and becomes large locally forevents in the depth range from 65 and 75 km. Oursynthetic seismograms explain his results well,implying that there must be a region of localized,strong heterogeneity at depths around 70 km. Theeffective size of the heterogeneous region may be ofabout several kilometers because the observation wasperformed with 1 Hz seismometers. This localizedheterogeneous layer is probably associated with thesubducting Pacific plate underneath the Wellingtonregion.

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