The hybrid extended Born approximation and CG-FFHT method for axisymmetric media

We develop the hybridization of the extended Born approximation (EBA) with spectral domain methods (CG-FFHT) for axisymmetric media. The hybrid method improves the efficiency of numerical solution of borehole induction problems in axisymmetric media in two ways. First, we use the FFHT to accelerate the EBA as a nonlinear approximation to induction problems, resulting in an algorithm with O(N log/sub 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-FPI-IT method to solve the problem accurately with few iterations. Numerical results confirm the accuracy and the efficiency of the hybrid method.