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The Parameter Averaging Technique in Finite-Difference Modeling of Elastic Waves in Combined Structures with Solid, Fluid and Porous Subregions

Published online by Cambridge University Press:  20 August 2015

Wei Guan  and
Hengshan Hu
Wei Guan*
Affiliation:
Department of Astronautics and Mechanics, Harbin Institute of Technology, Postbox 344, 92 West Dazhi Street, Harbin 150001, China
Hengshan Hu*
Affiliation:
Department of Astronautics and Mechanics, Harbin Institute of Technology, Postbox 344, 92 West Dazhi Street, Harbin 150001, China
*
Corresponding author.Email:gwllzh@tom.com
Email:wavehu@yahoo.com
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Abstract

To finite-difference model elastic wave propagation in a combined structure with solid, fluid and porous subregions, a set of modified Biot’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’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.

Keywords

76M2065M0676S0535L0586A15Finite-differencewave equationporous mediumacoustic loggingnumerical simulation
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 3 , September 2011 , pp. 695 - 715
Copyright
Copyright © Global Science Press Limited 2011

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