Inverse scattering from arbitrary two-dimensional objects in stratified environments via a Green's operator

An important problem in geophysics, medical imaging, and nondestructive imaging today is the construction of a practical, accurate, and efficient means of imaging geophysical anomalies, tumours, or material defects in layered media. This paper discusses such a method. The use of a ''stratified Green's function'' for the solution of the forward problem is detailed. This forward problem is then incorporated into an efficient and accurate inversion algorithm based on optimization. The method is nonperturbative, unlike diffraction tomography, which relies on linearization to make the problem tractable. In the inversion, a pair of Lippmann-Schwinger-like integral equations are solved simultaneously via the Galerkin procedure for the unknown total internal fields and speed distribution. The computational burden is high, but made manageable by utilizing BiConjugate gradients, fast fourier transforms, and ''sinc'' basis functions to speed up the solution of the forward problem. The size and contrasts for which the method converges are substantially beyond the Born or Rytov approximations, and other methods heretofore reported in the literature. The convolutional character of the layered Gr een's function, and thus numerical efficiency, is preserved by careful construction based on known reflection coefficients. (C) 1997 Acoustical Society of America.