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Efficient Numerical Simulation of Axisymmetric Electromagnetic Induction Data using a High-Order Generalized Extended Born Approximation

We develop a High-Order Generalized Extended Born Approximation (HoGEBA) for the numerical simulation of electromagnetic scattering due to rock formations that exhibit axial symmetry around a wellbore. The resulting equations are solved via 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. The 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 the HoGEBA is superior to that of the 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.