Giovanni Angelo Meles

TL;DR: An iterative gradient method in which the steepest descent direction, used to update iteratively the permittivity and conductivity distributions in an optimal way, is found by cross-correlating the forward vector wavefield and the backward-propagated vectorial residual wavefield.

TL;DR: In this article, a new method of wavefield extrapolation based on inverse scattering theory produces accurate estimates of these subsurface scattered wavefields, while still using relatively little information about the Earth's properties.

Abstract: Cross‐hole radar tomography is a useful tool for mapping shallow subsurface electrical properties viz. dielectric permittivity and electrical conductivity. Common practice is to invert cross‐hole radar data with ray‐based tomographic algorithms using first arrival traveltimes and first cycle amplitudes. However, the resolution of conventional standard ray‐based inversion schemes for cross‐hole ground‐penetrating radar (GPR) is limited because only a fraction of the information contained in the radar data is used. The resolution can be improved significantly by using a full‐waveform inversion that considers the entire waveform, or significant parts thereof. A recently developed 2D time‐domain vectorial full‐waveform cross‐hole radar inversion code has been modified in the present study by allowing optimized acquisition setups that reduce the acquisition time and computational costs significantly. This is achieved by minimizing the number of transmitter points and maximizing the number of receiver positions. The improved algorithm was employed to invert cross‐hole GPR data acquired within a gravel aquifer (4–10 m depth) in the Thur valley, Switzerland. The simulated traces of the final model obtained by the full‐waveform inversion fit the observed traces very well in the lower part of the section and reasonably well in the upper part of the section. Compared to the ray‐based inversion, the results from the full‐waveform inversion show significantly higher resolution images. At either side, 2.5 m distance away from the cross‐hole plane, borehole logs were acquired. There is a good correspondence between the conductivity tomograms and the natural gamma logs at the boundary of the gravel layer and the underlying lacustrine clay deposits. Using existing petrophysical models, the inversion results and neutron‐neutron logs are converted to porosity. Without any additional calibration, the values obtained for the converted neutron‐neutron logs and permittivity results are very close and similar vertical variations can be observed. The full‐waveform inversion provides in both cases additional information about the subsurface. Due to the presence of the water table and associated refracted/reflected waves, the upper traces are not well fitted and the upper 2 m in the permittivity and conductivity tomograms are not reliably reconstructed because the unsaturated zone is not incorporated into the inversion domain.

TL;DR: In this paper, the up-and down-going Green's functions from virtual sources in the subsurface are reconstructed in convolutional interferometry by combining purely reflected, up and downgoing Green’s functions.

TL;DR: It is shown by means of several synthetic tests and theoretical considerations that local minima trapping can be avoided by starting the inversion with only the low frequency content of the data, and resolution associated with the high frequencies can be achieved by progressively expanding to wider bandwidths as the iterations proceed.