Electromagnetic modeling of subsurface 3D structures

A 3D frequency domain electromagnetic numerical solution has been implemented for sensing buried structures in a lossy Earth. Because some structures contain metal, it is necessary to treat them as very good conductors residing in a complicated lossy Earth background. To model these scenarios and to avoid excessive gridding in the numerical solution, the authors assume the structures to be perfectly conducting, which forces the total electric field to zero within the conductor. This is accomplished by enforcing internal boundary conditions on the numerical grid. The numerical solution is based on a vector Helmholtz equation for the scattered electric fields, which is approximated using finite differences on a staggered grid. After finite differencing, a complex-symmetric matrix system of equations is assembled and preconditioned using Jacobi scaling before it is iteratively solved using the quasi-minimum residual (qmr) or bi-conjugate gradient (bicg) methods. For frequencies approaching the static limit (<10 kHz), the scheme incorporates a static-divergence correction to accelerate solution convergence. This is accomplished by enforcing the divergence of the scattering current within the Earth as well as the divergence of the scattered electric field in the air