Multiple scattering of elastic waves from a continuous and heterogeneous region

In this paper, we develop an elastodynamic energy transport theory to form expressions for energy transmission through a heterogeneous continuum of large extent. A model of multiple scattering for a random elastic continuum is constructed by an iterative method based on single scattering by a thin heterogeneous layer or screen. This model is available both for strong scattering and for weak scattering, and both for common-type scattering (P-P and S-S) and for converted scattering (P-S and S-P), although here we assume high frequencies so that only forward scattering and common-type scattering are considered. Numerical results have been obtained in terms of the angular spectrum of the energy flux in successive orders of scattering. These results show that coda waves in seismograms mainly come from the scattering of S waves. They also indicate the limits within which first-order scattering can be used, and when, on the other hand, the scattered radiation is dominated by multiple scattering. The results are directly applicable to measurements of seismic energy flux in frequency-surface-wavenumber space.