Envelope Synthesis Based on the Radiative Transfer Theory: Multiple Scattering Models

Abstract

In Chapter 3, we found that the squared sum of incoherent S-waves that are singly scattered by distributed random heterogeneities can provide an adequate firstorder model of the MS envelope of S-wave seismograms. As lapse time increases, however, we expect that double, triple, and higher-order multiple scattering contribute more than the single scattering process, so we need a model that includes the effects of multiple scattering. Kopnichev [1977] and Gao et al. [1983] modeled multiple scattering effects by summing up higher order scattering terms as a simple extension of the single scattering model; however, their models do not conserve total energy.