Wavefield reconstruction inversion in the frequency domain of on-ground GPR data

Abstract

Full waveform inversion (FWI) is one of the most promising techniques for the quantitative characterization of the shallow subsurface of the Earth. However, the conventional FWI with the reduced approach is highly nonlinear, a challenging source of which is the cycle skipping. It would drive FWI to spurious local minima as soon as the initial model parameters are not accurate enough. By introducing a non-negative penalty term and a penalty parameter, wavefield reconstruction inversion (WRI) extends the search space of full waveform inversion, relaxes the requirement to satisfy exactly the wave equation at each iteration, and mitigates some of the problems related to poor start models, which leads to the cycle skipping phenomenon. Moreover, WRI breaks down FWI into two linear sub-problems and reconstruct the wavefield and estimate the model parameter in a loop and there is no need to update and store the wavefield. In this paper, we perform the model reconstruction of on-ground GPR using WRI in the frequency domain by inverting data of a limited number of frequency components, and compare the results of it with that of the conventional FWI. With a limited illumination of the subsurface, WRI with small penalty parameters has a positive performance.