Traveltime tomography of crosshole radar data without ray tracing

We presented a least-squares traveltime inversion algorithm for crosshole ground-penetrating radar (GPR) direct-arrival data. The proposed scheme used the eikonal equation as traveltime functional and thus avoided tracing rays during inversion. The Jacobian matrix is constructed by a finite-difference approximation via the perturbation of slowness. The solutions were obtained by an iteratively linearized inversion approach. A smoothness-type regularization was implemented to stabilize the solutions. Traveltime calculations in forward modeling were performed by a finite-difference eikonal solver that allows modeling wavefronts. Matrix inversions were achieved by using conjugate gradient least-squares (CGLS) and LSQR algorithms. Broyden's method was used to accelerate the calculation of the Jacobian matrix when the number of model parameters was large. We tested the proposed method on three synthetic data sets and on a field data set from the Boise Hydrogeophysical Research Site (BHRS), Idaho; and we compared our model for the field data with the one obtained by a ray-tracing-based algorithm. This comparison indicated that the suggested inversion scheme was able to generate a solution as good as the one resulting from a conventional ray-based scheme. The synthetic data were obtained from simple to complex subsurface velocity distributions, including low- and high-velocity anomalies. Additionally, an image quality analysis was performed by calculating model covariance and model resolution matrices for one of the synthetic models having a complex subsurface structure and for the model resulting from the field data. All inversions were characterized by fast and stable convergence. Tests with noisy data sets indicated that the tomograms were relatively insensitive to noise in the data. It was also observed that the LSQR algorithm produced better results than the CGLS did in the tests with the synthetic models having complex subsurface structures. We considered the proposed technique to be an efficient traveltime inversion scheme for crosshole radar data. (C) 2010 Elsevier B.V. All rights reserved