Efficient Numerical Simulation of Axisymmetric Electromagnetic Induction Measurements Using a High-Order Generalized Extended Born Approximation

This paper develops a high-order generalized extended Born approximation (Ho-GEBA) for the numerical simulation of electromagnetic scattering due to rock formations that exhibit axial symmetry around a wellbore. The resulting equations of Ho-GEBA are solved with a numerical procedure that is as efficient as the extended Born approximation (EBA). With the acceleration of a fast Fourier transform, the operation count is proportional to$O(CN)$, whereNis the total number of spatial discretization cells and$Cll N$is a constant that depends on the number of discretization cells in the radial direction. Ho-GEBA remains accurate in the near-source scattering region and accounts for multiple scattering in the presence of large conductivity contrasts and relatively large frequencies. Numerical exercises conclusively indicate that the accuracy of Ho-GEBA is superior to that of EBA and the first-order Born approximation while maintaining the same level of algorithmic efficiency. These exercises are carried out on a variety of source–receiver configurations and frequencies typical of single-well borehole induction measurements.