Hybrid Electromagnetic Reconstruction of Multiple 2-D Subsurface Inhomogeneous Objects Based on FRTM and FEBI-LM Methods Enhanced by Domain Decomposition

This paper presents a hybrid method to reconstruct multiple 2-D inhomogeneous objects straddling multiple subsurface planar layers and segmented into multiple subdomains. In the forward electromagnetic scattering computation, the finite-element boundary integral (FEBI) method is employed to simultaneously solve for the total electric fields inside the multiple subdomains and the equivalent current on their boundaries which are connected with each other by the 2-D layered-medium dyadic Green’s functions. The scattered fields at the receiver array are then obtained by multiplying the boundary current with radiation matrices. The electromagnetic reconstruction is implemented in two steps. First, the frequency-domain reverse time migration (FRTM) combined with a level set of the indicator function and the K-means clustering is used to determine the approximate rectangular boundary for each full-wave inversion (FWI) subdomain. Second, the sensitivity matrix of the measured scattered electric fields with respect to the dielectric parameters inside all rectangular subdomains is assembled. The Levenberg-Marquardt (LM) method is then used to fulfill the multidomain electromagnetic FWI by iteratively calling the FEBI forward solver. Numerical experiments are carried out to compare the implementation cost and efficiency of the forward FEBI solver and the inverse FEBI-LM solver with and without domain decomposition.