Study of seismogram envelopes based on the energy transport theory
High-frequency seismograms of local earthquakes are considered to consist of incoherent body waves scattered by random inhomogeneities in the earth medium. Representing the random inhomogeneities by distributed point-like scatterers, we describe the multiple scattering process on the basis of energy transport theory. First, assuming isotropic scattering including conversions between P and S waves, we study the propagation of energy density for spherical radiation from a point source. Synthesized time traces give a good explanation of rather smooth amplitude of wave trains often observed between P and S phases and larger amplitudes of S coda. Second, by introducing a concept of directional distribution of energy density, we study the contribution of non-isotropic scattering to the S coda excitation. In addition to the Fourier transformation in space and the Laplace transformation in time, we use a spherical harmonic series expansion in solid angle. Then, the energy transport equation can be written as simultaneous linear equations, where Wigner 3 — j symbols appear. The numerical simulation for a case with strong forward scattering well explains the observed uniform distribution of S coda energy around the source at large lapse times.
KeywordsCoda Wave Isotropic Scattering Random Inhomogeneity Normalize Energy Density Spherical Harmonic Series
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