Alternative cost function for full waveform inversion of GPR data

Abstract

Ground Penetrating Radar (GPR) is a geophysical method developed for subsurface imaging. The main components of a GPR system are the antenna, the control unit, and the encoder. The GPR system moves along the area of interest and a set of data, called radargram, is obtained. In a single-short offset GPR acquisition, the distance between the transmitter and receiver antennas is very short. The collected data over an area can be used to construct images of the dielectric permittivity and the electric conductivity of the subsurface, which allows identifying objects such as anti-personnel mines, pipes, people in an earthquake, fossils, among others. Full waveform inversion (FWI) of GPR data can be used to estimate such electromagnetic parameters based on the minimization of a misfit function. However, FWI of GPR data has several problems: cross-talk between parameters, the estimation of the amplitude and signature of the electromagnetic source, the presence of noise in the data, the non-uniqueness of the solution and the high computational cost. In this paper, an alternative cost function for FWI is proposed to mitigate the problem of the estimation of the amplitude of the electromagnetic source. We show that the proposed alternative cost function for FWI is more robust than traditional norm in noisy environments. The proposed cost function is tested over a synthetic model with complex structures called SEAM and over collected data in a region of Colombia. In order to deal with the high computational complexity of FWI, all the experiments are computed in a cluster of GPUs.