Finite-Difference Method For Electromagnetic Logging In 3D Anisotropic Media

We consider the problem of computing the electromagnetic field in 3D anisotropic media for electromagnetic logging applications. The proposed finite-difference scheme for Maxwell equations has the following new features: coercivity, i.e., the complete discrete analogy of all continuous equations in every grid cell; a special conductivity averaging that does not require the grid to be small compared to layering or fractures; a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity. All these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3D geometries without sacrificing the accuracy. The problem is solved in both Cartesian and cylindrical coordinate systems. We use Spectral Lanczos Decomposition Method and its pre-conditioned modification as solvers. We present examples of modeling a triaxial induction tool response. Both metal and insulating tool details are included in the model.