Hybrid synthesis of scalar wave envelopes in 2-D random Media having rich short wavelength spectra

[1] Wave trains in high-frequency seismograms of local earthquakes are mostly composed of incoherent waves that are scattered by distributed heterogeneities within the lithosphere. Their phase variations are very complex; however, their wave envelopes are systematic, frequency-dependent, and vary regionally. Stochastic approaches are superior to deterministic wave-theoretical approaches for modeling wave envelopes in random media. The time width of a wavelet is broadened with increasing travel distance mostly because of diffraction caused by the long-wavelength components of random velocity inhomogeneity. The Markov approximation for the parabolic wave equation is effective for the synthesis of envelopes for random media whose spectra are poor in short-wavelength components; however, we have to consider the contribution of large-angle nonisotropic scattering if the random media are rich in short-wavelength inhomogeneities. Multiple nonisotropic scattering can be reliably modeled as isotropic scattering by using an effective isotropic scattering coefficient given by the momentum transfer scattering coefficient, which is a reciprocal of the transport mean free path. It is mostly controlled by the short-wavelength spectra of random media. We propose a hybrid method for th