Multi-scale phase waveform inversion method of on-ground GPR data

Abstract

Full waveform inversion of ground penetrating radar (GPR) based on Maxwell’s equations can invert the permittivity and conductivity of the underground medium, and achieve quantitative interpretation of the target formation. Here, we present a GPR waveform inversion method based on the phase misfit function, and inverts the phase information in the GPR data. By analyzing the characteristics of phase transformation, the misfit function of PWI is given. The gradient is constructed by the convolution of the forward and reverse fields, and its gradient formula is derived. When the transmitting source and receiver of GPR are arranged on the ground, the waveform inversion can only use the scattered field to obtain the effective information of the underground medium, and the inversion will face a strong indetermination. The inversion is more dependent on the initial model than the cross-hole GPR waveform inversion, but non-destructive detection often lacks prior information. In order to solve this problem, this paper makes use of the characteristics of integral operation and formulates a multi-scale inversion strategy. In the iterative process of inversion, high integration times are preferentially used to restore long wavelength information. This can reduce the dependence of the waveform inversion on the initial model as much as possible, implement the waveform inversion method for on-ground GPR data, and verify it with two sets of synthetic data.