Three-component seismogram envelope synthesis in randomly inhomogeneous semi-infinite media based on the single scattering approximation

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We present a method for synthesizing three-component seismogram envelopes of local earthquake in a randomly inhomogeneous semi-infinite medium. The method extends the single scattering model of Sato [Sato, H., 1984. Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. J. Geophys. Res. 89: 1221-1241.] by incorporating the effects of a free surface, frequency-dependent non-spherical radiation from a double-couple point source, and non-isotropic scattering including wave-type conversion. We synthesize seismogram envelopes-the root-mean-square (rms) amplitude of seismograms-at a receiver located on the free surface by dividing an inhomogeneous medium into many small cells and summing the energy of scattered waves from the cells on the isochronal scattering shells of different scattering modes for a given lapse time. Our main focus is the free surface effect, which alters the shape of isochronal scattering shells and the amplitudes of incident waves. Synthesizing three-component seismogram envelopes for different source-receiver configurations, we find that these effects on seismogram envelopes are not negligible and are pronounced at early S coda. P coda envelope shape is not very sensitive to free-surface incorporation because of dominant SP scattered waves which come from the source direction.

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