Simulation of borehole induction using the hybrid extended Born approximation and CG-FFHT method

We propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier Hankel transform (CG-FFHT) method to improve the efficiency of numerical solution of borehole induction problems in axisymmetric media. First, we use the FFHT to accelerate the EBA as a nonlinear approximation to induction problems, resulting in an algorithm with O(N log 2 N) arithmetic operations, where N is the number of unknowns in the problem. This improved EBA is accurate for most formations encountered. Then, for formations with extremely high contrasts, we utilize this improved EBA as a partial preconditioner in the CG-FFHT method to solve the problem accurately with few iterations. The seamless combination of these two approaches provides an automatic way toward the efficient and accurate modeling of induction measurements in axisymmetric media.