Two-dimensional traveltime tomography of crosshole ground penetrating radar (GPR) data

In this thesis, two different traveltime tomography methods, based on the functional description of traveltimes (Method 1) and ray tracing (Method 2), was compared by using both three synthetic and a field data set. The synthetic data sets were generated using the models with the various velocity distributions ranging from simple to complex. Only direct arrivals were considered during the inversion thus the head waves caused at air-ground interface were not taken into account. Traveltimes were obtained by a finite-difference solution of the eikonal equation and a finite difference time domain (FDTD) modeling of electromagnetic wave propagation.The proposed method in this thesis (Method 1) is based on a linearized least-squares inversion of traveltimes using Tikhonov regularization and conventional ray tracing is not a part of this scheme. In this method, the Jacobian matrix containing the partial derivatives of traveltimes with respect to the cell slowness was obtained by a finite-difference approach. Matrix inversions were implemented by iterative conjugate gradient algorithm. Smoothness-constrained regularization was used to stabilize the solutions, and Broyden's method was carried out to expedite the computation of the sensitivity matrix. In the second method based on the ray tracing, the velocity fields were updated by simultaneous iterative reconstruction method using both straight- and curved-ray approximations. The effects of the velocity cell size, initial model and noise on the solutions were also investigated for both inversion schemes. The velocity tomograms obtained from Method 1 were characterized by lower traveltime residuals, smaller Euclidean distances, and lower cell velocity errors. Furthermore, the convergence rate of the solutions from Method 1 was quicker than from the both approximations of Method 2. The zones with low velocity contrast in the test models were better imaged by both of the methods, but the Method 1 was more successful to image the zones with high-velocity contrast. Among the approximations of Method 2, the solutions obtained by using curved rays have generally produced better results. Based on these, the field data set was interpreted by the Method 1 and curved-ray based Method 2. Both algorithms successfully imaged the characteristic velocity anomalies in the model. It was shown that the suggested algorithm in this thesis study could be effectively used to interpret crosshole GPR data.