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., Q ≫ 1) and thicknesses comparable with or smaller than the skin depth, the attenuation-compensated migration is stable.

Signal-to-Noise Ratio analysis for time-reversal based imaging techniques in bounded domains

“…Ambient noise measurements may be used as the primary recordings that are being time reversed, as in [16], but this is a slightly different problem than the one considered in this paper. Other types of difficulties that have been successfully treated by TR, include but are not limited to, media with random properties [17], multiple scattering in granular media [18], non-linear problems [19], multiple scatterer localization [20] and damping [21,22,23]. Consideration of damping is a critical issue in TR because it breaks the non-dissipation condition, necessary for time-reversibility of the wave equation.…”

Ultra‐Thick Paleoregolith Layer Detected by Lunar Penetrating Radar: Implication for Fast Regolith Formation Between 3.6 and 2.35 Ga

“…To further match the waveform of LPR reflections, we conducted a forward modeling of electromagnetic reflection waves using a series of relative permittivity models by finite‐difference method (Zhu et al., 2016). We adopt the trial‐error strategy to adjust the depth‐profile permittivity to minimize the data residuals between synthetics and observed waveforms.…”

A high-resolution weak-signal reconstruction method for electromagnetic wave modeling and reverse time migration of ground-penetrating radar data

“…Due to the similarity between the Electromagnetic wave and the seismic wave in kinematics and dynamics, RTM has been successfully implemented in processing GPR data to obtain the true depths and shapes of internal structures (Fisher et al, 1992;Leuschen and Plumb, 2001;Liu et al, 2014). However, the presence of electromagnetic wave attenuation distorts the phase and amplitude of the signal, and therefore degrades the image quality (Zhu et al, 2016). Attenuation in the ground can be highly variable and has a significant effect on the depth of penetration.…”