Attenuation, dispersion, and anisotropy by multiple scattering of transmitted waves through distributions of scatterers

Scattering of waves causes the coherent wave field to be attenuated and dispersed. These phenomena express the fact that the pulse loses coherence by which incoherent coda energy is created. First-order scattering theory violates the law of energy conservation and therefore cannot be used when the wave field is strongly distorted. An approximation is proposed which estimates the interaction between different scatterers by considering only multiple forward scattering interactions. Internal of a single scatterer all multiple interactions are maintained. This approximation can only be valid for the first part of the wave field and sufficiently weak scattering conditions. The heterogeneous medium can then be described as an effective medium that is a function of the scatterer density and forward scattering amplitude and the background medium. Simulations of the multiple scattering process with isotropic scatterers in two dimensions show that the discrepancies between the exact and approximate solution are small compared to the difference with the undisturbed wave field, even when the pulse is severely attenuated. Contrary to single scattering theory multiple scattering maintains the propagation of a stable and localized coherent wave. Apparently the nonlinear multiple scattering interactions cause a tendency for the coherent wave field to become insensitive to the specific scatterer distribution. © 1995 Acoustical Society of America.