高阶有限差分法管波传播数值模拟
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摘要
为正确认识流体充填钻孔中管波的传播规律,首先给出均匀各向同性介质中包含流体充填钻孔条件下的弹性波动力学方程和二阶速度-应力公式及差分格式的稳定性条件和边界条件;然后利用高阶交错网格有限差分法,结合典型模型,模拟了不同时刻管波的传播快照和复杂层状介质中管波的合成地震记录,并与实际管波地震记录进行了对比。结果表明:在地层分界面、溶洞的边界等波阻抗差异界面处,管波都会产生反射;反射管波的振幅、频率特征受界面两侧的岩石物理性质差异的影响;在理论合成记录中,反射管波与直达管波同相轴的交点与理论模型中地层分界面或异常体的边界一致。
Making use of the tube wave detection method to find geological disasters,such as karsts or corrosion cracks within a certain range around the borehole,is a new means of engineering geophysical survey.To better understand the tube wave propagation mechanism in fluid-filled boreholes,a staggered-grid finite-difference approach is applied to compute the wave propagation in homogeneous isotropic media including a fluid-filled borehole.Firstly,the wave motion equation was introduced,and the finite-difference solution was obtained with Taylor's series expansion,and then,the stability and absorption boundary conditions were discussed.Using a homogenous isotropic model,the snapshots were calculated under the non-borehole conditions and borehole conditions respectively.Two models were designed for the seismology,one was a three-layered model containing a hole filled with soil,and another was a practical model designed according to field data.Numerical simulation results showed that tube wave reflections existed on the interface of different impedance,such as formation interfaces and karst boundaries;the difference of physical properties of strata had an influence on the amplitude and the frequency of reflection waves;and in the synthesis record,the intersection of reflection tube waves and direct tube waves is consistent with the actual boundaries of formation or anomalous bodies designed in the theoretical model.
Making use of the tube wave detection method to find geological disasters,such as karsts or corrosion cracks within a certain range around the borehole,is a new means of engineering geophysical survey.To better understand the tube wave propagation mechanism in fluid-filled boreholes,a staggered-grid finite-difference approach is applied to compute the wave propagation in homogeneous isotropic media including a fluid-filled borehole.Firstly,the wave motion equation was introduced,and the finite-difference solution was obtained with Taylor's series expansion,and then,the stability and absorption boundary conditions were discussed.Using a homogenous isotropic model,the snapshots were calculated under the non-borehole conditions and borehole conditions respectively.Two models were designed for the seismology,one was a three-layered model containing a hole filled with soil,and another was a practical model designed according to field data.Numerical simulation results showed that tube wave reflections existed on the interface of different impedance,such as formation interfaces and karst boundaries;the difference of physical properties of strata had an influence on the amplitude and the frequency of reflection waves;and in the synthesis record,the intersection of reflection tube waves and direct tube waves is consistent with the actual boundaries of formation or anomalous bodies designed in the theoretical model.
引文
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[5]Bokov P M,Ionov A M.Tube-wave propagation in afluid-filled borehole generated by a single point forceapplied to the surrounding formation[J].Journal ofthe Acoustical Society of America,2002,112(6):2634-2644.
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[7]崔志文,刘金霞,王克协.井孔声波频散方程伪瑞利波的近似解析公式[J].吉林大学学报:地球科学版,2008,38(增刊1):113-116.CUI Zhi-wen,LIU Jin-xia,WANG Ke-xie.Approximate solutions for pseudo-rayleigh modes in afluid-filled borehole[J].Journal of Jilin University:Earth Science Edition,2008,38(Sup.1):113-116.
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[11]Medlin W L,Schmitt D P.Title fracture diagnosticswith tube-wave reflection logs[J].Journal ofPetroleum Technology,1984,46(3):239-248.
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[14]Nativ R,Adar E,Assaf L,et al.Characterization ofthe hydraulic properties of fractures in chalk[J].Ground Water,2003,41(4):532-543.
[15]李学文,郭金根,饶其荣.桩位岩溶探测新技术——管波探测法[J].工程地球物理学报,2005,2(2):129-133.LI Xue-wen,GUO Jin-gen,RAO Qi-rong.Tubewave detecting method[J].Chinese Journal ofEngineering Geophysics,2005,2(2):129-133.
[16]Cheng C H,Toksz M N.Elastic wave propagationin a fluid-filled borehole and synthetic acoustic logs[J].Geophysics,1981,46(7):1042-1053.
[17]Kurkijan A L.Theoretical far-field radiation fromlow-frequency horizontal acoustic point force in avertical borehole[J].Geophysics,1986,51(4):930-939.
[18]Tubman K M,Cheng C H,Toksz M N.Syntheticfull waveform acoustic logs in cased boreholes[J].Geophysics,1984,49(7):1051-1059.
[19]Schmitt D P,Bouchon N.Full-wave acoustic log-ging:synthetic micro-seismograms and frequency-wavenumber analysis[J].Geophysics,1985,50(11):1756-1778.
[20]Bouchon M.A numerical simulation of the acousticand elastic wave fields by a source on a fluid-filledborehole embedded in a layered medium[J].Geophysics,1993,58(4):475-481.
[21]Dong W,Bouchon M,Toksz M N.Borehole seismic-source radiation in layered isotropic and anisotropicmedia:boundary element modeling[J].Geophysics,1995,60(3):735-747.
[22]Stephen R A,Cardo-casas F,Cheng C H.Finite-difference synthetic acoustic logs[J].Geophysics,1985,50(10):1588-1609.
[23]Yoon K H,Mcmechan G A.3-D finite-differencemodeling of elastic waves in borehole environments[J].Geophysics,1992,57(6):793-804.
[24]Kostek S,Johnson D L,Randall C L.The intera-ctionof tube waves with borehole fractures,part I:numerical models[J].Geophysics,1998,63(3):800-808.
[25]Cheng A C H,Blanch J O.Numerical modeling ofelastic wave propagation in a fluid-filled borehole[J].Communications in Computational Physics,2008,3(1):33-51.
[26]侯安宁,何樵登,马在田.各向异性弹性波动交错网格高阶差分法的误差研究[J].长春科技大学学报,1995,25(4):446-451.HOU An-ning,HE Qiao-deng,MA Zai-tian.Astudy of the errors of elastic wave staggered-gridhigh-order difference method in anisotropic media[J].Journal of Changchun University of Science andTechnology,1995,25(4):446-451.
[27]Virieux J.P-SV wave propagation in heterogeneousmedia:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[28]Carcione J M,Herman G C,Kroode A P E.Seismicmodeling[J].Geophysics,2002,67(4):1304-1325.
[29]孟庆生,何樵登,朱建伟,等.基于BISQ模型双相各向同性介质中地震波数值模拟[J].吉林大学学报:地球科学版,2003,33(2):217-221.MENG Qing-sheng,HE Qiao-deng,ZHU Jian-wei,et al.Seismic modeling in isotropic porous mediabased on BISQ model[J].Journal of Jilin University:Earth Science Edition,2003,33(2):217-221.
[2]Chang S K,Liu H L,Johnson D L.Low-frequencytube waves in permeable rocks[J].Geophysics,1988,53(4):519-527.
[3]Norris A N.The speed of a tube wave[J].Journal ofthe Acoustical Society of America,1990,87(1):414-417.
[4]Norris A N,Sinha B K.Weak elastic anisotropy andthe tube wave[J].Geophysics,1993,58(8):1091-1098.
[5]Bokov P M,Ionov A M.Tube-wave propagation in afluid-filled borehole generated by a single point forceapplied to the surrounding formation[J].Journal ofthe Acoustical Society of America,2002,112(6):2634-2644.
[6]陈雪莲,王瑞甲.横向各向同性弹性地层井孔中模式波的探测深度[J].吉林大学学报:地球科学版,2008,38(3):502-507.CHEN Xue-lian,WANG Rui-jia.Investigating depthof mode waves in the borehole surrounded bytransversely isotropic elastic formation[J].Journal ofJilin University:Earth Science Edition,2008,38(3):502-507.
[7]崔志文,刘金霞,王克协.井孔声波频散方程伪瑞利波的近似解析公式[J].吉林大学学报:地球科学版,2008,38(增刊1):113-116.CUI Zhi-wen,LIU Jin-xia,WANG Ke-xie.Approximate solutions for pseudo-rayleigh modes in afluid-filled borehole[J].Journal of Jilin University:Earth Science Edition,2008,38(Sup.1):113-116.
[8]Hardage B A.An examination of tube wave noise invertical seismic profiling data[J].Geophysics,1981,46(6):892-903.
[9]Herman G C,Milliganz P A,Dong Qi-cheng,et al.Analysis and removal of multiply scattered tube waves[J].Geophysics,2000,65(3):745-754.
[10]Daley T M,Gritto R,Majer E L,et al.Tube-wavesuppression in single-well seismic acquisition[J].Geophysics,2003,68(3):863-869.
[11]Medlin W L,Schmitt D P.Title fracture diagnosticswith tube-wave reflection logs[J].Journal ofPetroleum Technology,1984,46(3):239-248.
[12]Medlin W L,Schmitt D P.利用管波反射测井诊断裂缝[J].郑永恒,译.国外测井技术,1994,9(6):25-41.Medlin W L,Schmitt D P.Fracture diagnostics withtube wave reflection logs[J].Translated by ZHENGYong-heng.Foreign Well Logging Technology,1994,9(6):25-41.
[13]Huang C F,Hunter J A.The tube-wave method ofestimating in-situ rock fracture permeability in fluid-filled boreholes[J].Geoexploration,1984,22(3/4):245-259.
[14]Nativ R,Adar E,Assaf L,et al.Characterization ofthe hydraulic properties of fractures in chalk[J].Ground Water,2003,41(4):532-543.
[15]李学文,郭金根,饶其荣.桩位岩溶探测新技术——管波探测法[J].工程地球物理学报,2005,2(2):129-133.LI Xue-wen,GUO Jin-gen,RAO Qi-rong.Tubewave detecting method[J].Chinese Journal ofEngineering Geophysics,2005,2(2):129-133.
[16]Cheng C H,Toksz M N.Elastic wave propagationin a fluid-filled borehole and synthetic acoustic logs[J].Geophysics,1981,46(7):1042-1053.
[17]Kurkijan A L.Theoretical far-field radiation fromlow-frequency horizontal acoustic point force in avertical borehole[J].Geophysics,1986,51(4):930-939.
[18]Tubman K M,Cheng C H,Toksz M N.Syntheticfull waveform acoustic logs in cased boreholes[J].Geophysics,1984,49(7):1051-1059.
[19]Schmitt D P,Bouchon N.Full-wave acoustic log-ging:synthetic micro-seismograms and frequency-wavenumber analysis[J].Geophysics,1985,50(11):1756-1778.
[20]Bouchon M.A numerical simulation of the acousticand elastic wave fields by a source on a fluid-filledborehole embedded in a layered medium[J].Geophysics,1993,58(4):475-481.
[21]Dong W,Bouchon M,Toksz M N.Borehole seismic-source radiation in layered isotropic and anisotropicmedia:boundary element modeling[J].Geophysics,1995,60(3):735-747.
[22]Stephen R A,Cardo-casas F,Cheng C H.Finite-difference synthetic acoustic logs[J].Geophysics,1985,50(10):1588-1609.
[23]Yoon K H,Mcmechan G A.3-D finite-differencemodeling of elastic waves in borehole environments[J].Geophysics,1992,57(6):793-804.
[24]Kostek S,Johnson D L,Randall C L.The intera-ctionof tube waves with borehole fractures,part I:numerical models[J].Geophysics,1998,63(3):800-808.
[25]Cheng A C H,Blanch J O.Numerical modeling ofelastic wave propagation in a fluid-filled borehole[J].Communications in Computational Physics,2008,3(1):33-51.
[26]侯安宁,何樵登,马在田.各向异性弹性波动交错网格高阶差分法的误差研究[J].长春科技大学学报,1995,25(4):446-451.HOU An-ning,HE Qiao-deng,MA Zai-tian.Astudy of the errors of elastic wave staggered-gridhigh-order difference method in anisotropic media[J].Journal of Changchun University of Science andTechnology,1995,25(4):446-451.
[27]Virieux J.P-SV wave propagation in heterogeneousmedia:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[28]Carcione J M,Herman G C,Kroode A P E.Seismicmodeling[J].Geophysics,2002,67(4):1304-1325.
[29]孟庆生,何樵登,朱建伟,等.基于BISQ模型双相各向同性介质中地震波数值模拟[J].吉林大学学报:地球科学版,2003,33(2):217-221.MENG Qing-sheng,HE Qiao-deng,ZHU Jian-wei,et al.Seismic modeling in isotropic porous mediabased on BISQ model[J].Journal of Jilin University:Earth Science Edition,2003,33(2):217-221.
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