Reflected wave modeling in heterogeneous acoustic media using the De Wolf approximation

A fast modeling method based on multiple-forescattering single-backscattering (MFSB) approximation, i.e. the De Wolf approximation for calculating reflected (or backscattered) wave fields in 3D heterogeneous acoustic media is introduced. The method is much faster than full wave finite difference or finite element methods. The formulation is especially suitable for the configuration of surface reflection surveying. When discontinuities in a medium are not very sharp or parameter perturbations of heterogeneities are not very strong, reverberations between heterogeneities or resonance scattering can be neglected. However, for large volume heterogeneous media or long propagation distances the accumulated effect of multiple forward scattering becomes very important for both forward modeling and inverse problems. In such cases, the Born approximation is not valid while the De Wolf approximation can be applied. After renormalizing the multiple scattering series of the Lipmann-Schwinger equation, a MFSB approximation for acoustic waves is derived and a fast dual-domain computation scheme is presented, in which the multi-screen one-way wave propagator is used. Finally numerical examples are given to demonstrate the validity of the method.