On perfectly matched layer schemes in finite difference simulations of acoustic Logging‐While‐Drilling

Abstract

In the wave propagation simulation by finite difference time domain (FDTD), the perfectly matched layer (PML) is often applied to eliminate the reflection artifacts due to the truncation of the finite computational domain. In the acoustic Logging-While-Drilling (LWD) FDTD simulation, due to high impedance contrast between the drill collar and fluid in the borehole, the stability and efficiency of PML scheme is critical to simulate complicated wave modes accurately. In this paper, we compare four different PML implementations in FDTD in the acoustic LWD simulation, including splitting PML (SPML), Multi-axis PML (MPML), Non-splitting PML (NPML), and complex frequencyshifted PML (CFS-PML). The simulation indicates that NPML and CFS-PML can more efficiently absorb the guide wave reflection from the computational boundaries than SPML and MPML. For large simulation time, SPML, MPML and NPML are numerically instable. However, stability of MPML can be improved further to some extent. Among all, CFS-PML is the best choice for LWD modeling. The effects of CFS-PML parameters on the absorbing efficiency are investigated, including damping profile, frequency-shifted factor, scaling factor and PML thickness. For a typical LWD case, the best value for maximum of quadratic damping profile d0 is about 1. The optimal parameter space for the maximum value of linear frequency-shifted factor α0 and scaling factor β0 depends on the PML damping profile and thickness. If the PML thickness is 10 grids, the reflection residual can be reduced to less than 1%, using optimal CFS-PML parameters, while only about 0.5‰ reflection artifacts are observed for 20 grids PML buffer.