Fast Frequency-Domain Forward and Inverse Methods for Acoustic Scattering from Inhomogeneous Objects in Layered Media

The fast scattering and inverse scattering algorithms for acoustic wave propagation and scattering in a layered medium with buried objects are an important research topic, especially for large-scale geophysical applications and for target detection. There have been increasing efforts in the development of practical, accurate, and efficient means of imaging subsurface target anomalies. In this work, the acoustic scattering problem in layered media is formulated as a volume integral equation and is solved by the stabilized bi-conjugate gradient fast Fourier transform (BCGS-FFT) method. By splitting the layered medium Green’s function interacting with the induced source into a convolution and a correlation, the acoustic fields can be calculated efficiently by the FFT algorithm. This allows both the forward solution and inverse solution to be computed with only O(Nlog N) computation time per iteration, where N is the number of degrees of freedom. The inverse scattering is solved using a simultaneous multiple ...