A fast integral equation solver for 3D induction well logging in formations with large conductivity contrasts

摘要

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three-dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre-corrected fast Fourier transform (pFFT)-accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation.