Diffusion of seismic waves in layered media: boundary conditions and analytical solutions

Abstract

SUMMARY A new model for multiple scattering of seismic waves including a depth dependency of scattering strength is presented. The problem of a strongly scattering layer over a weakly scattering half-space is treated within the diffusion approach. A ‘surface resistivity’ boundary condition connecting the scattering layer to the scattering half-space is presented and an analytical solution in the frequency–wavenumber domain is given. For the limiting case of zero scattering in the half-space, the new analytical solution approaches the well-known diffusion solution for the scattering layer over a homogeneous half-space. A comparison to numerical solutions of the equation of radiative transfer demonstrates that the new model has a broad range of validity. It only fails, if the layer is thinner than its transport mean free path and additionally a large contrast in scattering strength between layer and half-space exists. As an application of the theory seismograms measured in an active seismic experiment at Merapi volcano (Indonesia) are presented. These seismograms show an apparent decrease of scattering strength with increasing source–receiver distance, which can be explained by a depth-dependent diffusivity.