Velocity analysis from common offset GPR data inversion: Theory and application to synthetic and real data

We implemented a procedure to estimate the electromagnetic (EM) velocity using common offset ground penetrating radar (GPR) data. The technique is based on the inversion of reflection amplitudes to compute the series of reflection coefficients used to estimate the velocity in each interpreted layer. The proposed method recursively calculates the incident angles at any interface, taking into account the offset between antennas, and needs as input, in addition to the picked amplitudes values, a reference amplitude for each analysed GPR trace and a velocity value for the first (shallowest) layer. The latter two parameters can be estimated directly from the available data or can be better constrained by further dedicated GPR acquisitions or by additional direct measurements. We critically evaluated the performances for both synthetic and real data acquired with different antenna frequencies and we demonstrated that the new method can be applied in several real situations. Despite the necessary approximations and simplifying hypotheses, the velocity values calculated for each layer are consistent with direct information and with cross-validations obtained considering profiles acquired using different antennas and various path directions. Tests of the method on synthetic and real data sets show that the errors in the calculated velocity fields are quite low and comparable with more demanding velocity analysis techniques. The obtained EM velocity field is crucial in many processing steps, such as, for example, true amplitude recovery, depth conversion and imaging, and provide essential information to characterize the subsurface materials.