Finite-difference modeling of the monopole acoustic logs in a horizontally stratified porous formation

Abstract

Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biot's equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm.

Fast and slow flexural waves in a deviated borehole in homogeneous and layered anisotropic formations

“…To avoid reflections on the artificial boundaries of the computational region, the non‐splitting PML is employed as the absorbing boundary condition in the r ‐ and z ‐directions following the previous studies done by Wang & Tang (2003) and Guan et al . (2009).…”

3d Finite Difference Simulations of Acoustic Logs in Tilted Layered Porous Formations

“…Recently, Guan et al 7 numerically simulated the monopole logs in a symmetrical porous formation with horizontal layers using a 2D FDTD code. Yet no one, to the authors' knowledge, further investigated the sonic logging in a 3D heterogeneous case based on Biot's theory.…”

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