Reverse time imaging of ground-penetrating radar and SH-seismic data including the effects of wave loss

Abstract

The presence of wave loss (velocity dispersion and attenuation in lossy media) degrades the resolution of migrated images by distorting the phase and amplitude of the signal. These effects have to be mitigated to improve resolution. We have developed a technique to perform reverse time migration of ground-penetrating radar and SH-seismic data in lossy media, suitable for engineering and seismic applications. The method is based on the solution of the transverse magnetic (TM) Maxwell equation, which in view of the acoustic-electromagnetic analogy, is mathematically equivalent to the SH-wave equation, where attenuation is described by the Maxwell mechanical model. Attenuation compensation is performed by reversing the sign of the diffusion term (first-order time derivative). In this manner, the TM equation has the same wave-velocity dependence with frequency (same velocity-dispersion behavior) but opposite attenuation, i.e., compensating for attenuation effects when back propagating. We have solved the equations numerically with a direct grid method by using the Fourier pseudospectral operator for computing the spatial derivatives, and we used an explicit staggered second-order finite-difference approximation for computing the time derivative. Four applications illustrated the potential of the algorithm. The migrated image by correcting for attenuation loss is able to improve the illumination of the target reflectors. This migration is found to be particularly useful to balance the overall image amplitude by illuminating shadow zones. Under the assumption of low-loss media (e.g., [Formula: see text]) and thicknesses comparable with or smaller than the skin depth, the attenuation-compensated migration is stable.