Effects of Caustics in Acoustic Inverse Scattering Experiments

摘要

Most inversion techniques described in the literature rely on the validity of raytracing, which breaks down in the presence of caustics. The linearized acoustic inverse problem with constant reference velocity is analyzed in order to quantify the effects of a caustic in a probing wavefront on the scattered signal. When the sound velocity is perturbed by a localized, unidirectional, high frequency inhomogeneity, the surprising result obtained is that the energy in the scattered field is spread out if the perturbation is located on the caustic. This spreading of energy allows the construction of an oscillatory integral representation of the scattered field, which has the same form, whether or not an incident caustic is present. On the other hand, a sequence of localized high frequency sound velocity perturbations is constructed such that the size of the scattered signal relative to the size of the inhomogeneity becomes arbitrarily large as the support of the perturbation approaches the caustic. In regions where there are no caustics, a general inverse operator is found for smoothly varying reference velocities. This operator is shown to be equivalent to an inverse operator constructed by Beylkin. (kr)