A new constrained velocity tomography algorithm using geostatistical simulation

A new constrained velocity tomography algorithm is presented. This algorithm is based on slowness covariance modeling using experimental travel time covariance. Slowness and travel time covariances allow cokriging and simulation of slowness fields, between two boreholes, fitting the measured travel times. Cells with known velocities, for example the cells crossed by the holes, provide velocity constraints which are easily implemented. The proposed approach is compared to the classical LSQR algorithm using a synthetic model and real data collected for geotechnical evaluation in a karstic area. In each case, constrained and non-constrained LSQR, cokriging and simulation were performed. The tomographies on synthetic model 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 model increases the spatial resolution compared to LSQR. It is demonstrated that the method is robust with regard to an acceptable level of random noise on velocity constraints. The real data analysis shows that the proposed method gives very consistent results in regard to the drilling log information.