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), where N is the total,number of spatial discretization cells and C << 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.