层状孔隙介质震电波场数值模拟高频不稳定性问题的解析处理方法(英文)
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摘要
自从发现震电现象以来,众多学者进行了相关研究.其中,Pride提出了一套描述流体饱和孔隙介质中震电波场的耦合与传播的宏观控制方程组,该方程组后来被广泛地应用到相关的震电研究中.Chen发展了一套广义反透射系数方法并将其应用到层状介质合成地震图的研究当中,该方法数值计算效率高并且可以处理带弯曲界面层状介质这种复杂模型.基于Pride的震电波场控制方程组,我们将Chen的广义反透射系数方法推广应用到层状孔隙介质中震电波场的数值模拟研究中,但是在数值计算过程中发现,当含源层的厚度相对于地震波波长较大时(即高频情况),会出现数值计算的不稳定,此即为高频不稳定性问题.针对高频不稳定性问题,一种自然的处理方法就是在原来的含源层中插入两个虚拟界面,构造出一个新的含源薄层,但是这会带来一些额外的计算量,此外,由于虚拟含源薄层的厚度是有限的,必须针对具体模型参数设定一个合适的厚度值.高频不稳定性问题同样存在于层状介质合成地震图的数值计算过程中,Chen提出了一种解析的处理方法,即在原含源层内引入一无限薄的虚拟含源薄层,通过解析的方法解决高频不稳定性问题,该方法不会降低计算效率且适用于任意参数模型.本文首先对层状孔隙介质中的震电波场数值计算公式进行分析,指出源项积分中的指数增长因子是导致高频不稳定性问题的根本原因;其次将Chen在合成地震图数值模拟研究中采用的解析处理方法推广到震电波场研究中,得到了适用于数值计算的公式;然后给出数值算例,并针对一个含源层过厚的模型,比较了自然处理方法和解析处理方法,两种方法得到的结果具有相当好的一致性,而解析处理方法计算效率更高,证实了本文给出的解析处理方法在解决层状孔隙介质震电波场数值模拟的高频不稳定性问题方面的有效性.
A new method of numerical simulation of seismoelectric wave-fields in multi-layered porous media has been developed by extending Chen's technique of computing synthetic seismograms to coupled seismic and electromagnetic waves.However, the existence of an exponential growth factor leads to numerical instability for high-frequencies.A natural regularization approach eliminating the high-frequency instability is to create a fictitious thin flat layer including the source point in the numerical calculation, which requires an adequate thickness of the fictitious source layer as well as some extra computation cost.In this article, an analytical regularization approach is developed to deal with the high-frequency instability problem in numerical simulations of seismoelectric wave-fields in multi-layered porous media.The results show that the analytical regularization approach is much more effective in solving the above high-frequency instability problem than the natural regularization approach.
A new method of numerical simulation of seismoelectric wave-fields in multi-layered porous media has been developed by extending Chen's technique of computing synthetic seismograms to coupled seismic and electromagnetic waves.However, the existence of an exponential growth factor leads to numerical instability for high-frequencies.A natural regularization approach eliminating the high-frequency instability is to create a fictitious thin flat layer including the source point in the numerical calculation, which requires an adequate thickness of the fictitious source layer as well as some extra computation cost.In this article, an analytical regularization approach is developed to deal with the high-frequency instability problem in numerical simulations of seismoelectric wave-fields in multi-layered porous media.The results show that the analytical regularization approach is much more effective in solving the above high-frequency instability problem than the natural regularization approach.
引文
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[5] Biot M A.Mechanics of deformation and acoustic propagation in porous media.J.Appl.Phys.,1962,33． 1482～1498
[6] Revil A,Leroy P.Governing equations for ionic transport in porous shales.J.Geophys.Res.,2004,109,B03208,doi:10． 1029/2006JB002755
[7] Revil A,Linde N.Chemico-electromechanical coupling in microporous media.J.Coll.Interf.Sci.,2006,302:682～694
[8] Thompson A H,Gist G A.Geophysical applications of electrokinetic conversion.The Leading Edge,1993,12:1169～1173
[9] Pride S R.Governing equations for the coupled electro-magnetics and acoustics of porous media.Phys.Rev.B,1994,50:15678～15696
[10] Pride S R,Haartsen M W.Electroseismic wave properties.J.Acoust.Soc.Am.,1996,100:1301～1315
[11] Haartsen M W,Pride S'R.Electroseismic waves from point sources in layered media.J.Geophys.Res.,1997,102:24745～24769
[12] Zhu Z,Haartsen M W,Toksoz M N.Experimental studies of seismoelectric conversions in fluid-saturated porous media.J.Geophys.Res.,2000,105:28055～28064
[13] Garambois S,Dietrich M.Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid-saturated stratified porous media.J.Geophys.Res.,2002,107,doi:10． 1029/2001JB000316
[14] Pride S R,Moreau F,Gavrilenko P.Mechanical and electrical response due to fluid-pressure equilibration following an earthquake.J.Geophys.Res.,2004,109,doi:10． 1029/2003JB002690
[15] Haines S S,and Pride S R.Seismoelectric numerical modeling on a grid.Geophysics,2006,71:N57～N65
[16] Chen X F.A systematic and efficient method for computing seismic normal modes in layered half-space.Geophys.J.Int.,1993,115:391～409
[17] Chen X F.Seismogram synthesis in multi-layered bali-space part Ⅰ.Theoretical formulations.Earthquake Research in China,1999,13:149～174
[18] Chen X F.Generation and propagation of seismic SH waves in multi-layered media with irregular interfaces.Advances in Geophysics,2007,48:191～264
[19] Ge Z,Chen X F.An Efficient Approach for Simulating Wave Propagation with the Boundary element Method in Multilayered Media with Irregular Interfaces.Bulletin of the Seismological Society of America,2008,98,doi:10． 1785/ 0120080920
[20] Ren H X,Huang Q H,Chen X F.A new numerical technique for simulating the coupled seismic and electromagnetic waves in layered porous media.Earthquake Science,2010,23(2) ,doi:10． 1007/s11589-009-0071-9
[21] Johnston M J S.Review of electric and magnetic fields accompanying seismic and volcanic activity.Surv.Geophys.,1997,18:441～475
[22] Huang Q H.One possible generation mechanism of co-seismic electric signals.Proc.JapanAcad.,2002,78:173～178
[23] Huang Q H.Controlled analogue experiments on propagation of seismic electromagnetic signals.Chinese Science Bulletin,2005,50:1956～1961
[24] Huang Q,Liu T.Earthquakes and tide response of geoelectric potential field at the Niijima station.Chinese J.Geophys.,2006,49:1745～1754
[25] Zhao G Z,Zhan Y,Wang L F et al.Electromagnetic anomaly before earthquakes measured by electromagnetic experiments.Earthquake Science,2009,22:395～402,doi:10． 1007/s 11589-009-0395-5
[26] Huang Q H,Ikeya M.Seismic electromagnetic signals(SEMS)explained by a simulation experiment using electromagnetic waves.Phys.Earth Planet.Inter.,1998,109(3-4) :107～114
[27] Huang Q H,Lin Y F.Selectivity of seismic electric signal(SES)of the 2000 Izu earthquake swarm:a 3D FEM numerical simulation model.Proc.Japan Acad.B,2010,86(3) :257～264,doi:10． 2183/pjab.86． 257
[2] Thompson R R.The seismic electric effect.Geophysics,1936,1:327～335
[3] Ivanov A G.Effect of electrization of earth layers by elastic waves passing through them.Dokl.Akad.Nauk SSSR,1939,24:42～45
[4] Frenkel J.On the theory of seismic and seismoelectric phenomena in a moist soil.J.Phys.,1944,8:230～241
[5] Biot M A.Mechanics of deformation and acoustic propagation in porous media.J.Appl.Phys.,1962,33． 1482～1498
[6] Revil A,Leroy P.Governing equations for ionic transport in porous shales.J.Geophys.Res.,2004,109,B03208,doi:10． 1029/2006JB002755
[7] Revil A,Linde N.Chemico-electromechanical coupling in microporous media.J.Coll.Interf.Sci.,2006,302:682～694
[8] Thompson A H,Gist G A.Geophysical applications of electrokinetic conversion.The Leading Edge,1993,12:1169～1173
[9] Pride S R.Governing equations for the coupled electro-magnetics and acoustics of porous media.Phys.Rev.B,1994,50:15678～15696
[10] Pride S R,Haartsen M W.Electroseismic wave properties.J.Acoust.Soc.Am.,1996,100:1301～1315
[11] Haartsen M W,Pride S'R.Electroseismic waves from point sources in layered media.J.Geophys.Res.,1997,102:24745～24769
[12] Zhu Z,Haartsen M W,Toksoz M N.Experimental studies of seismoelectric conversions in fluid-saturated porous media.J.Geophys.Res.,2000,105:28055～28064
[13] Garambois S,Dietrich M.Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid-saturated stratified porous media.J.Geophys.Res.,2002,107,doi:10． 1029/2001JB000316
[14] Pride S R,Moreau F,Gavrilenko P.Mechanical and electrical response due to fluid-pressure equilibration following an earthquake.J.Geophys.Res.,2004,109,doi:10． 1029/2003JB002690
[15] Haines S S,and Pride S R.Seismoelectric numerical modeling on a grid.Geophysics,2006,71:N57～N65
[16] Chen X F.A systematic and efficient method for computing seismic normal modes in layered half-space.Geophys.J.Int.,1993,115:391～409
[17] Chen X F.Seismogram synthesis in multi-layered bali-space part Ⅰ.Theoretical formulations.Earthquake Research in China,1999,13:149～174
[18] Chen X F.Generation and propagation of seismic SH waves in multi-layered media with irregular interfaces.Advances in Geophysics,2007,48:191～264
[19] Ge Z,Chen X F.An Efficient Approach for Simulating Wave Propagation with the Boundary element Method in Multilayered Media with Irregular Interfaces.Bulletin of the Seismological Society of America,2008,98,doi:10． 1785/ 0120080920
[20] Ren H X,Huang Q H,Chen X F.A new numerical technique for simulating the coupled seismic and electromagnetic waves in layered porous media.Earthquake Science,2010,23(2) ,doi:10． 1007/s11589-009-0071-9
[21] Johnston M J S.Review of electric and magnetic fields accompanying seismic and volcanic activity.Surv.Geophys.,1997,18:441～475
[22] Huang Q H.One possible generation mechanism of co-seismic electric signals.Proc.JapanAcad.,2002,78:173～178
[23] Huang Q H.Controlled analogue experiments on propagation of seismic electromagnetic signals.Chinese Science Bulletin,2005,50:1956～1961
[24] Huang Q,Liu T.Earthquakes and tide response of geoelectric potential field at the Niijima station.Chinese J.Geophys.,2006,49:1745～1754
[25] Zhao G Z,Zhan Y,Wang L F et al.Electromagnetic anomaly before earthquakes measured by electromagnetic experiments.Earthquake Science,2009,22:395～402,doi:10． 1007/s 11589-009-0395-5
[26] Huang Q H,Ikeya M.Seismic electromagnetic signals(SEMS)explained by a simulation experiment using electromagnetic waves.Phys.Earth Planet.Inter.,1998,109(3-4) :107～114
[27] Huang Q H,Lin Y F.Selectivity of seismic electric signal(SES)of the 2000 Izu earthquake swarm:a 3D FEM numerical simulation model.Proc.Japan Acad.B,2010,86(3) :257～264,doi:10． 2183/pjab.86． 257
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