A Non-linear GPR Tomographic Inversion Algorithm Based on Iterated Cokriging and Conditional Simulations

Abstract

A new constrained velocity tomography algorithm based on ray approximation is presented. This algorithm is based on slowness covariance modeling using experimental travel time covariance. The computed covariances, the measured travel times and additional slowness values allow cokriging and conditional simulation. Among several realizations, the one that minimized the L1 norm is chosen as the best velocity field. In the proposed method the raypaths must be known. Starting with a homogeneous velocity field, an iterated solution is computed updating the raypaths applying Snell-Descartes' law on the best velocity field after each iteration. First, the advantage of an iterated solution is presented. Then, the proposed approach is compared to a classical LSQR algorithm using a synthetic model and real data collected for geotechnical evaluation in a karstic area. The tomographies on synthetic models show that geostatistical methods provide comparable to or better results than LSQR. For both methods, additional velocity constraints reduce uncertainty and improve spatial resolution of the inverted velocity field. Also, the simulation on synthetic models increases the spatial resolution compared to LSQR. The real data analysis shows that the proposed method gives very consistent results with respect to the drilling log information.