基于横向各向同性BISQ方程的弹性波传播数值模拟

英文篇名：NUMERICAL SIMULATION OF ELASTIC WAVE PROPA-GATION BASED ON THE TRANSVERSELY ISOTROPIC BISQ EQUATION
中文刊名：地震学报
英文刊名：Acta Seismologica Sinica
作者：杨宽德 ; 杨顶辉 ; 王书强
英文作者：Yang Kuande1 ; 2) Yang Dinghui1) Wang Shuqiang1) 1) Department of mathematical sciences ; Tsinghua University ; Beijing 100084 ; China 2) Mengzi Teacher's College ; Mengzi ; Yunnan 661100 ; China
中文关键词：BISQ方程 ; 波场模拟 ; 横向各向同性 ; 交错网格法
英文关键词：BISQ equation ; wave-fields simulation ; transversely isotropic medium ; staggered grid method
出版日期：2002-12-15
机构：清华大学数学科学系,清华大学数学科学系,清华大学数学科学系中国北京100084,蒙自师范高等专科学校中国云南蒙自市661100 ,中国北京100084 ,中国北京100084
年：2002
期：06
出版单位：地震学报

摘要

Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制. 近年来,利用同时处理这两种力学机制的BISQ(Biot-Squirt)模型,弹性波衰减和频散的问题已被广泛研究;然而基于BISQ方程的波场数值模拟尚未见到公开的报道.本文从BISQ方程出发,利用交错网格方法对横向各向同性孔隙介质中不同频率和相界情况,以及双层介质中的弹性波传播进行数值模拟,研究了在同时考虑两种流动机制作用情况下地震波和声波的传播特性及传播过程中出现的各种波动现象.
The Biot and squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, no numerical simulation based on the BISQ equation has been reported yet. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the staggered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occurred in the propagating process are investigated when the two mechanisms are considered simultaneously.

引文

①杨顶辉.1998.孔隙各向异性介质中基于BISQ模型的弹性波传播理论及有限元方法.石油大学博士后研究报告.
    杨顶辉,张中杰.2000.Biot和喷射流动耦合作用对各向异性弹性波的影响[J].科学通报,45(12):1333～1340
    BiotM A.1956.Theory of propagation of elastic waves in a fluid-saturated porous solid,I.Low-frequency range,II.Higher frequency range[J].J AcoustSocAmer,28:168～191
    BiotM A.1962.Mechanics of deformation and acoustic propagation in porous media[J].J ApplPhys,33(4):1482～1498
    ChengYuanfeng,YangDinghui,YangHuizhu.2002.Biot/Squirt model in viscoelastic porous media[J].ChinesePhysicsLetters,19(3):445～448
    DvorkinJ,NurA.1993.Dynamic poroelasticity:A unified model with the squirt and theBiot mechanisms[J].Geophysics,58:524～533
    FornbergB.1990.High-order finite differences and pseudo-spectral method on staggered grids[J].SIAM J NumerAnal,27(4):904～918
    MavkoG,NurA.1979.Wave attenuation in partially saturated rocks[J].Geophysics,44(2):161～178
    zdenvarT,McMechanG.1996.Cause and reduction of numerical artifacts in pseudo-spectral wave-field extrapolation[J].GeophysJ Int,126(3):819～828
    ParraJ O.1997.The transversely isotropic poroelastic wave equation including theBiot and the squirt mechanisms:Theory and application[J].Geophysics,62:309～318
    ParraJ O.2000.Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy[J].Geophysics,65(1):202~210
    YangDinghui,ZhangZhongjie.2002.Poroelastic wave equation including theBiot/Squirt mechanism and the solid/fluid coupling anisotropy[J].WaveMotion,35(3):223～245