Electromagnetic FWI of 2-D Inhomogeneous Objects Straddling Multiple Planar Layers by Finite-Element Boundary Integral and Levenberg–Marquardt Methods

This article extends the existing finite-element boundary integral (FEBI) method to account for electromagnetic (EM) scattering and inverse scattering from both isotropic and anisotropic 2-D inhomogeneous objects straddling multiple planar layers. In the forward scattering computation, the inhomogeneous scatterers placed across several layers are enclosed by a 1-D smooth boundary within which the finite element method (FEM) is implemented to solve for the 2-D EM field distribution. The integral equation (IE) is formulated on the 1-D boundary to form the radiation boundary condition (RBC) to truncate the FEM domain. The 2-D layered-medium dyadic Green’s functions (DGFs) used in the boundary IE to solve for the equivalent current and used in the scattering data equations to compute the scattered fields at the receiver array are evaluated for both the transverse electric (TE) and transverse magnetic (TM) modes. In the full-wave inversion (FWI) to reconstruct isotropic scatterer dielectric parameters in the TE mode and anisotropic scatterer dielectric parameters in the TM mode, we compute the first-order derivatives of the system mass matrix with respect to isotropic model parameters and the first-order derivatives of the system stiffness matrix with respect to anisotropic model parameters to assemble the sensitivity matrices for the TE mode and TM mode, respectively. Finally, the Levenberg-Marquardt (LM) method is used to iteratively call the FEBI forward solver to fulfill the reconstruction. Numerical experiments are carried out to show the computation efficiency and correctness of the forward scattering and FWI solvers.