Application of perfectly matched layers to the transient modeling of subsurface EM problems

Abstract

Berenger's perfectly matched layers (PML) have been found to be very efficient as a material absorbing boundary condition (ABC) for finite‐difference time‐domain (FDTD) modeling of lossless media. In this paper, we apply the PML technique to truncate the simulation region of conductive media. Examples are given to show some possible applications of the PML technique to subsurface problems with lossy media. To apply the PML ABC for lossy media, we first modify the original 3-D Maxwell's equations to achieve PML at the boundaries of the simulation region. The modified equations are then solved by using a staggered grid with a central‐differencing scheme. A 3-D FDTD code has been written on the basis of our PML formulation to simulate the electromagnetic field responses of a dipole source in both lossless and lossy media. The code is first tested against analytical solutions for homogeneous media of different losses and then applied to some subsurface problems, such as a geological fault and a buried gas tank. Very interesting propagation and scattering phenomena are observed from the simulation results. Some analyses are also given to explain the physical phenomena of the calculated waveforms.