Scattering attenuation of elastic waves due to low-contrast inclusions

Seismic scattering attenuation due to random lithospheric heterogeneity has been theoretically modeled using two approaches. One approach is the Born approximation theory (BAT), which is primarily used to treat weak continuous heterogeneity, and the other approach is the Foldy approximation theory (FAT), which deals with sparsely distributed discrete inclusions. We apply the BAT to elastic wave scattering due to inclusions having low contrast with the matrix, and compare the results with those predicted by the FAT. We thus investigate the valid wavenumber range of the BAT based on a reasonable assumption that the inclusions are distributed so sparsely that the FAT is effectively correct for any wavenumber. For simplicity, we consider a specific type of round inclusion, which is either two- or three-dimensional and has a two-valued wave velocity and/or mass density. Both theories are confirmed to yield essentially equivalent results below a certain wavenumber limit, depending on the contrast. This is known as the Rayleigh-Gans scattering regime. Beyond the wavenumber limit, the BAT overestimates the attenuation for common-mode scattering due to wave-velocity contrast, but remains valid with respect to the attenuation for scattering due to mass-density contrast and/or conversion scattering. These conclusions are independent of the spatial dimensions of the media as well as the modes of the elastic waves (P or S). Some advantages of the BAT over the FAT for application to low-contrast inclusions are discussed.