GPR Full-Waveform Sensitivity and Resolution Analysis Using an FDTD Adjoint Method

Radar tomography is a useful technique for mapping the permittivity and conductivity distributions in the shallow subsurface. By exploiting the full radar waveforms, it is possible to improve resolution and, thus, image subwavelength features not resolvable using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of a final result, possibly limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal model resolution and information content analysis. We present a novel method for computing the sensitivity functions (Jacobian matrix) based on a time-domain adjoint method. Because the new scheme only computes the sensitivity values for the transmitter and receiver combinations that are used, it reduces the number of forward runs with respect to standard brute-force or other virtual-source schemes. The procedure has been implemented by using a standard finite-difference time-domain modeling method. A comparison between cumulative sensitivity (column sum of absolute values of the Jacobian) images, which is sometimes used in geoelectrical studies as a proxy for resolution in practical cases, and formal model resolution images is also presented. We show that the cumulative sensitivity supplies some valuable information about the image, but when possible, formal resolution analyses should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of an experiment and shows the extent of the unresolved model space.