MATLAB-based finite difference frequency domain modeling and its inversion for subsurface sensing

Abstract

This dissertation focuses on the application of finite difference frequency domain method at propagation and scattering in lossy, inhomogeneous media for forward and inverse electromagnetic problems. The research is roughly split into two parts. The first part develops the forward modeling referred as MATLAB-based FDFD method for the electrical field distribution in the inhomogeneous media for subsurface sensing. The suggested approach for solving the sparse and large matrix equation is one of the Krylov subspace iterative methods: Parameter-tuned Loose-General Minimum Residue (P-LGMRES) method which speed up computation without extra memory requirement relative to LGMRES method. The Matlab-based FDFD model has been validated by theoretical analysis and numerical experiments, and its accuracy has been compared to other models used in the literature. The highlight of this forward modeling is its ability to handle the complicated inhomogeneous media with easy implementation, which is essential to subsurface sensing such as breast tumor detection since body tissues are always heterogeneous. The forward modeling serves to estimate field distribution and for error analysis, the function of inverse modeling is to detect and reconstruct objects based on measured data. The traditional inversion algorithm more or less depends on the Green Function which is difficult to derive for complicated geometry. The FDFD-based inversion algorithm developed in this study avoids having to calculate the Green Function by utilizing the matrix equation characteristic to construct relation between any two points of interest in the inverse problem. This algorithm is examined by the traditional Green function-based Born Approximation (GFBA) inversion model and other numerical experiments such as the objects detection in half space and the breast tumor detection. The algorithm's good performance suggests that FDFD-based inversion technique is a promising technique for location and detection of the subsurface objects without extensive calculation of complicated Green functions with reasonable computational time.