Multi-parameter Imaging by Finite Difference Frequency Domain Full Waveform Inversion of GPR Data: A Guide for Sedimentary Architecture Modeling

Abstract

The need for reconstruction of the distribution of physical properties like dielectric permittivity and electrical conductivity of shallow subsurface sedimentary architecture leads to the development of an optimum strategy of GPR data inversion. In this paper, we present finite difference frequency domain (FDFD) full waveform inversion (FWI) method to get high-resolution subsurface model using GPR data. FWI is an optimization technique which involves in search of the minima between recorded and predicted data. The inversion process includes the quasi-Newton method and simultaneous frequency sampling strategy of irregular sampling. The Hessian term in quasi-Newton algorithm is approximated using preconditioned-LBFGS consideration and the search directions are also optimized after following the Wolfe conditions. At the end of each iteration during inversion, permittivity and conductivity models were updated and became ready to be the initial model for the next iteration. The goals of this research were to develop a robust framework for sedimentary-GPR data inversion and to evaluate the efficacy of the novel grid strategy introduced by Layek and Sengupta (2021) proposed for FWI. This paper presents a comparative analysis between conventional and newly proposed technique from Layek and Sengupta (2021), supported by numerical experiments conducted through our own MATLAB programming. Numerical tests conducted on a benchmark from previously published article, established the fact that new grid formulation produces a faster converging rate and required less computation time. This approach demonstrates remarkable efficacy when applied to a comprehensive sedimentary model comprising a lossy medium.