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

作　　者：Wei Guan Hengshan Hu 

机构地区：[1]Department of Astronautics and Mechanics,Harbin Institute of Technology,Postbox 344,92 West Dazhi Street,Harbin 150001,China

出　　处：《Communications in Computational Physics》2011年第8期695-715,共21页计算物理通讯（英文）

基　　金：supported by National Natural Science Foundation of China(40874062);Special Research Funds of Seismology in China(200808072);Natural Science Foundation of Heilongjiang Province of China(QC2010025);Research Fund for the Doctoral Program of Higher Education of China(20102302120024);Fundamental Research Funds for the Central Universities(HIT.NSRIF.2010071).

摘　　要：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 fluidsaturated 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 finitedifference 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.

关 键 词：FINITE-DIFFERENCE wave equation porous medium acoustic logging numerical simulation 

分 类 号：O17[理学—数学]