Crosshole Radar Traveltime Tomographic Inversion using the Fast Marching Method and the Iteratively Linearized Scheme

Abstract

Traditional straight ray- and curved ray-based tomography algorithms need to perform ray tracing to calculate travel times and construct the Jacobi matrix. We present a crosshole radar traveltime tomography algorithm that is based on the fast marching method (FMM) and the iteratively linearized scheme. The travel time is calculated using FMM and the Jacobi matrix is constructed using finite difference approximation, thus the traveltime tomography is carried out without raytracing. We test the suggested method on three synthetic models. In model 1, three types of model parameter weighting matrices are considered. In model 2, both first- and second-order FMM are tested. In model 3, we analyze three types of matrix inversion methods. The synthetic data tests show that the reconstruction using the Laplace operator, second-order FMM and LSQR simultaneously achieve the best result. To test the reconstruction ability of the proposed scheme on a realistic geological structure, we apply the algorithm to a field data set from Guizhou. For comparison, two traveltime tomography algorithms based on straight ray and curved ray are used. The comparisons indicate that our scheme can obtain a solution as good as the one resulting from a curved ray-based traveltime tomography algorithm.