Geophysical diffraction tomography

Abstract

Regions of the earths subsurface to be imaged tomographically frequently exhibit large variations in refractive index so that the assumption of straight ray paths is invalid and often leads to inferior reconstructions. The use of curved raypaths in diffraction tomography, however, significantly complicates the reconstruction problem. We develop an algorithm for diffraction tomography which involves iterations on successive ray tracing and tomographic inversion. Singular value decomposition as well as conjugate gradients provide alternative approaches to the inversion step at each iteration. Each procedure can give good results but singular value decomposition can be costly to apply. In diffraction tomography, partial singular value decomposition using a very small number of singular values and singular vectors at each inversion step can yield very accurate reconstructions in a few iterations.