基于BISQ模型双相各向同性介质弹性波传播的频率-空间域有限差分模拟

Wave propagation in two-phase isotropic medium based on BISQ madel in frequency-space domain

BISQ模型同时包含了合流体孔隙介质中Biot流动和喷射流动两种重要的力学机制.基于BISQ模型的双相各向同性介质弹性波波动方程是一个复变系数偏微分方程组.本文率先建立了该方程的25点频率-空间域有限差分数值解法,在理想相界和黏滞相界情况下,对Biot流动和喷射流动共同作用下的双相各向同性介质中的波传播进行了数值模拟,通过与仅受Biot流动作用下的波场模拟结果的对比,分析了两种机制耦合作用对弹性波传播的影响.同时,本文也研究了波在双层双相各向同性介质分界面处的反射和透射特征.数值模拟结果表明:在Biot流动和喷射流动耦合作用下,双相介质中传播的快P波的速度和振幅都小于仅考虑Biot流动的双相介质中的快P波,且慢P波的衰减也更为强烈,而S波的波速和振幅则无明显差异.这表明局部喷射流动对P波的衰减和频散具有重要影响,而对S波的影响较小;慢P波的强烈衰减使得其在波场快照中无法被观测到,双层双相介质中的波传播现象类似于单相介质的情况.同时本文的研究结果也表明,频率-空间域有限差分法在基于BISQ模型的双相介质中波传播数值模拟中的正确性和有效性,为开展孔隙弹性介质全波形反演问题的研究提供了研究基础.

BISQ modelcontainstwo importantmechanisms,Biotflow and squirt-flowcontainingfluidin porous medium.Waveequations for two-phaseisotropicmediumbased on BISQ modelarecomplexpartial differential equationswith variable coefficients.In this article,25-point frequency-space domain finite difference numerical solution was established for the first time.For the ideal and viscous fluidtwocases,wave propagation numerical simulation in isotropic media under the action of Biotflow and squirt-flow was investigated,compared and analyzed with the results only under the action of Biot-flow.Meanwhile,the paperalsostudiedwavesat the interfacereflection and transmissioncharacteristics in a two-layertow-phaseisotropicmedia.The numerical resultsshow that：In the Biot-flowand squirtflowcoupling,the two-phasemediafastP-wavepropagationvelocityandamplitudeare smaller thanthatonlyconsidering theBiotflow,and slowP-waveattenuationmoreintense.But the Swavepropagationvelocityand amplitude of the two cases arenot significantly different.These indicate thatthelocalsquirt-flow on theP-waveattenuation and dispersionhas an important influenceandhas little effectontheS-wave;thestrongattenuation of slow P-wavemakesitselfunobserved,two-layertow-phasemediumwavepropagation phenomenaissimilartothecaseof singlephasemedium.Whilethisstudyalso showed thatthe modeling method hasthecorrectness and validity and may also be applied in full waveform inversion for seismic waves in porous media.