Modeling Full Seismogram Envelopes Using Radiative Transfer Theory with Born Scattering Coefficients

The equation of radiative transfer is used to model the transport of seismic energy in 2-D and 3-D acoustic random media. Monte-Carlo solutions of this equation using non-isotropic Born scattering coefficients are compared to three analytical solutions: Markov approximation, radiative transfer theory with isotropic scattering coefficients, and diffusion approximation. Additionally, we compare to finite differences solutions of the full wave equation in 2-D. We find a good correspondence of radiative transfer theory to Markov approximation for the case of multiple forward scattering. The comparison to radiative transfer theory with isotropic scattering coefficients, a model frequently used in data analysis, demonstrates that in the case of forward scattering the isotropic scattering model is not better than a diffusion approach. To compare radiative transfer theory with non-isotropic scattering coefficients to finite differences solutions of the full wave equation, the finite source duration and the bandpass filter process as well as the normalization of absolute amplitudes are explicitely taken into account. We find a good coincidence of both theories for scattering parameters, which are realistic for usual Earth crust. The theory correctly describes the unscattered direct wavefront, the envelope broadening caused by multiple forward scattering, as well as the late coda caused by multiple wide angle scattering. For strong scattering, which can be expected for very heterogeneous media such as strato volcanoes, the solutions of radiative transfer differ from the more complete solutions of the full wave equation.