@Article{CiCP-10-695,
author = {},
title = {The Parameter Averaging Technique in Finite-Difference Modeling of Elastic Waves in Combined Structures with Solid, Fluid and Porous Subregions},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {3},
pages = {695--715},
abstract = {<p style="text-align: justify;">To finite-difference model elastic wave propagation in a combined structure
with solid, fluid and porous subregions, a set of modified Biot&#39;s equations are used,
which can be reduced to the governing equations in solids, fluids as well as fluid-saturated
porous media. Based on the modified Biot&#39;s equations, the field quantities
are finite-difference discretized into unified forms in the whole structure, including
those on any interface between the solid, fluid and porous subregions. For the discrete
equations on interfaces, however, the harmonic mean of shear modulus and the
arithmetic mean of the other parameters on both sides of the interfaces are used. These
parameter averaging equations are validated by deriving from the continuity conditions
on the interfaces. As an example of using the parameter averaging technique, a
2-D finite-difference scheme with a velocity-stress staggered grid in cylindrical coordinates
is implemented to simulate the acoustic logs in porous formations. The finite difference
simulations of the acoustic logging in a homogeneous formation agree well
with those obtained by the analytical method. The acoustic logs with mud cakes clinging
to the borehole well are simulated for investigating the effect of mud cake on the
acoustic logs. The acoustic logs with a varying radius borehole embedded in a horizontally
stratified formation are also simulated by using the proposed finite-difference
scheme.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.020810.161210a},
url = {http://global-sci.org/intro/article_detail/cicp/7457.html}
}