Abstract
An interferometric form of Fermat's principle and traveltime tomography is used to invert ground-penetrating radar (GPR) data for the subsurface velocity distribution. The input data consist of GPR traveltimes of reflections from two buried interfaces, A (reference) and B (target), where the data are excited and recorded by GPR antennas at the surface. Fermat's interferometric principle is then used to redatum the surface transmitters and receivers to interface A so the associated reflection traveltimes correspond to localized transit times between interfaces A and B. The overburden velocity model above interface A is not required. The result after tomographic inversion is a high-resolution estimate of the velocity between interfaces A and B that does not depend on the velocity model above interface A. A motivation for introducing interferometric traveltime tomography is that typical layer-stripping approaches will see the slowness error increase with depth as the layers are inverted. This suggests that near-surface statics errors are propagated and amplified with depth. In contrast, the interferometric traveltime tomography method largely eliminates statics errors by taking the difference between reflection events that emanate from neighboring layer interfaces. Slowness errors are not amplified with depth. However, the method is sensitive to the estimation accuracy for the geometry of the reference interface. Both synthetic and real field data are used successfully to validate the effectiveness of this interferometric technique.