Study of seismogram envelopes based on the energy transport theory

Abstract

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 WaveIsotropic ScatteringRandom InhomogeneityNormalize Energy DensitySpherical Harmonic SeriesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.