Pseudo-full-waveform inversion of borehole GPR data using stochastic tomography

Electromagnetic full-waveform tomography is computer intensive and requires good knowledge of antenna characteristics and ground coupling. As a result, ground-penetrating-radar tomography usually uses only the first wavelet's arrival time and amplitude data. We propose to improve the classical approach by inverting multiple slowness and attenuation fields using stochastic tomography. To do so, we model the slowness and attenuation covariance functions to generate geostatistical simulations that are conditional to the arrival times, amplitudes, slowness, and attenuation observed along boreholes. We combine slowness and attenuation fields to compute conductivity and permittivity fields from which we model synthetic radar traces using a finite-difference timedomain full-waveform algorithm. Modeled traces that best match the measured ones correspond to the computed conductivity and permittivity fields that correlate best with the true physical properties of the ground. We apply the method to a synthetic example with known electric properties. We show that a combination of stochastic tomography and full-waveform modeling allows a better selection of permittivity fields close to the reference field, at a reasonable computing cost.