Tomography is an imaging technique to develop a representation of the internal features of material using a penetrating wave, such as an electromagnetic wave. The calculation method used is an example of an inverse problem, which is a system where the input and the output are known but the internal parameters are not. These parameters can be estimated by understanding the responses of a penetrating wave as it passes through the unknown media. A forward problem is just the opposite; the internal structure and input penetrating wave is known and the output is determined. For both forward and inverse problems, raytracing is needed to define the raypath through the medium and inversion techniques are used to minimize the error for a discretized matrix of material properties. To assess various inversion techniques for use in shallow karst conditions, three synthetic karst geology models, each with increasing complexity, were generated. Each model was analyzed using forward modeling techniques to compare the calculated tomograms from known geometry and material properties. Gaussian Raytracing with LSQR inversion technique performed the best. This technique, Gaussian Raytracing with LSQR, was then applied to an inversion problem; cross-borehole ground penetrating radar data was collected at a karst geology field site and tomograms were produced. The resulting tomography confirmed information detailed in the driller's logs and features between boreholes were identified. This confirmed that cross-borehole ground penetrating radar is an applicable technique for use in geotechnical site characterization activities in karst areas.