Scattering and attenuation of elastic waves in random media

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.The coherent or average wave is assumed to be propagating in a homogeneous continuum characterized by a bulk complex wavenumber. This wavenumber depends on the frequency of the probing waves; and on the physical properties and the concentration of discrete scatterers, causing the effective medium to be dispersive. With the help of multiple scattering theory, we are able to analytically predict the attenuation of the transmitted wave intensity as well as the dispersion of the phase velocity. These two sets of data are valuable to the study of the inverse scattering problems in seismology. Some numerical results are presented and also compared, if possible, with experimental measurements.