Multiple Isotropic Scattering Model Including P‐S Conversions For the Seismogram Envelope Formation

SUMMARY High‐frequency seismogram envelopes of local earthquakes are well characterized by the scattering nature of the randomly inhomogeneous lithosphere. In addition to direct P ‐ and S ‐wave phases, incoherent wave trains are found not only in the S coda but also between the P and S phases. This implies the importance of scattering with conversions between P and S . the contribution from scattering increases with increasing hypocentral distance or lapse time because of multiple scattering processes. the multiple scattering contribution has been extensively studied mathematically especially for the S coda by supposing isotropic scattering. Here, extending the isotropic scattering assumption for scattering in conversion between two different wave velocities, we formulate the multiple scattering process for spherical radiation from a point source and derive the space time distribution of the energy density in 3‐D space on the basis of energy transport theory. We confirm conservation of the total energy in the case of no intrinsic absorption, which assures the self‐consistency of the formulation. A hybrid method, combining the analytical solutions corresponding to single scattering and numerical calculations for multiple scattering with order greater than, or equal to, two, is proposed to synthesize the spacetime distribution of the energy density. Synthesized time traces give a good explanation of the rather smooth and gradual increase in amplitude of wave trains often observed between P and S phases and the larger amplitude of the S coda. the envelope characteristics, except for short time windows around the direct wave arrivals, are well characterized by multiple scattering irrespective of the change in source duration time.