Transient modeling of subsurface EM problems using PML ABC

Abstract

Berenger’s perfectly matched layers (PML) has been found to be very efficient as a material absorbing boundary condition (ABC) for finite-difference time-domain (FDTD) modeling of lossy media as well as lossless media. In this paper, the PML technique is applied to truncate the simulation region for some typical subsurface problems which involve lossy media. To apply the PML ABC for lossy media, we first modify the original three-dimensional (3D) Maxwell’s equations to achieve perfectly matched layers at the boundaries of the simulation region. The modified equations are then solved by Yee’s staggered grid with central-differencing scheme. A 3D -FDTD code has been written based on 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, then applied to some subsurface problems such as a geological fault, or a buried gas tank. Very interesting propagation and scattering phenomena have been observed from the simulation results. Some analyses are also given to explain the physical phenomena of the calculated waveforms. Although all the problems solved are 3D simulations, our FDTD code solves them very easily because the PML ABC can truncate the simulation region efficiently. Only ten PML layers are needed outside the simulation region to reduce reflection to less than five percent. We view the new PML ABC for lossy media as an important contribution to the efficient and accurate FDTD modeling.