Applications of the BCGS-FFT method to 3-D induction well logging problems

Electromagnetic induction logging is one of the most important measurements in borehole characterization of an oil reservoir. With the ever increasing number of deviated and horizontal wells aiming for improved hydrocarbon production, simulation of induction well logging in realistic three-dimensional (3-D) environments has become an important subject of research. In this paper, we investigate a fast spectral-domain solver for the second-kind integral equation arising from Maxwell´s equations for 3-D induction logging. We combine an iterative stabilized biconjugate-gradient (BiCGSTAB) technique with a fast Fourier transform (FFT) algorithm (BCGS-FFT method) to compute electromagnetic fields in 3-D inhomogeneous media at induction frequencies. The electric field integral equation is discretized through the use of the magnetic vector potential to weaken the singularity associated with the dyadic Green´s function. The computational time and computer memory requirements of this BCGS-FFT method are O(NlogN) and O(N), respectively, where N is the total number of unknowns.