Finite-difference Modeling of EM Fields Using Coupled Potentials In 3D Anisotropic Media: Application to Borehole Logging

We present a staggered finite-difference (FD) forward modeling algorithm of computing frequency-domain EM fields using coupled potentials in 3D inhomogeneous anisotropic media. This algorithm is based on the partial differential equations (PDE) for coupled vector and scalar potentials subject to the appropriate boundary conditions, which are approximated using central FD on a Yee’s staggered grid. After discretization, a complex matrix equation is assembled, and is iteratively solved using complex biconjugate gradient method with preconditioning such as SSOR and Jacobi preconditioners. For the homogeneous full space, 1D and 2D layered anisotropic formations, we compared the numerical results from our algorithm with analytical solutions, our own 2D coupled potential FD solutions and 3D direct field FD solutions, and found excellent agreements between them. We also discussed the influences on iterative convergence rate using different frequencies and conductivity contrasts. To illustrate practical applications of this new algorithm, we conducted some more complicated model simulations. All numerical examples show that the algorithm can efficiently simulate EM fields in 3D inhomogeneous anisotropic media with highly discontinuous anisotropic conductivities over a wide range of frequencies.