Multi-scale ground penetrating radar full waveform inversion with hybrid Tikhonov and total-variation regularization for different geometric structure

Abstract

Full waveform inversion (FWI) is a high-resolution technique to estimate the parameters of dielectric permittivity (ϵ) and electrical conductivity (σ) and identify the structure of the subsurface for Ground Penetrating Radar (GPR) application. However, permittivity and conductivity parameters can be coupled in bi-parameter GPR inversion. This coupling effect leads to the crosstalk in the FWI result. To solve this problem, we propose a novel approach to use the multi-scale FWI with the hybrid regularization method, which combines Tikhonov and total-variation (TV) regularizers that simultaneously invert the ϵ and the σ parameters, which improve the inversion accuracy and reduce the crosstalk effect. The multi-scale strategy uses the Wiener filtering to process the GPR data in different frequency ranges. Then, the low frequencies signal updates the bottom part and subsequently increases the frequencies to invert for the shallow areas. The Tikhonov regularization stabilizes the reconstruction of the smoothly varying background part. In contrast, Total Variation (TV) regularization can recover the large contrasts associated with the LNAPL model. The new Tikhonov-TV (TT) regularization can mitigate the crosstalk caused by the parameter coupling effect. Numerical tests with typical GPR models demonstrate that the proposed multi-scale TT-FWI strategy can effectively eliminate the crosstalk and improve the reconstruction accuracy when the model parameters have a different structure.