Abstract
Conference Title: 2014 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting Conference Start Date: 2014, July 6 Conference End Date: 2014, July 11 Conference Location: Memphis, TN, USA In a typical Logging While Drilling (LWD) application, several coils operating in the frequency range of few KHz to MHz are used as transmitters and receivers to characterize the earth formation. Electromagnetic modeling of such a low frequency system poses serious computational challenges. In the Method of Moment (MoM) formulation, contribution of vector potential to the total field becomes several orders of magnitude smaller than that of the scalar potential, thus making the resultant matrix highly ill-conditioned. Finite Difference Time Domain (FDTD) method, on the other hand, requires a very large number of time steps to capture the low frequency information. In this paper, we consider a layered-earth model and compute the electromagnetic field due to electrical and magnetic dipoles embedded in the formation. To address the low frequency problem in FDTD, we consider the source and the receiver dipoles to be infinitesimally small and aligned with the computational grid and modify the update equations accordingly. This approach reduces the time convergence of FDTD by two-to-three orders of magnitude, and also reduces the memory requirements by the same factor. Numerical results for the fields reflected from the layered interfaces are presented for multiple scenarios involving shale and sand zones.