改进BISQ模型的双相介质地震波场数值模拟及频散校正
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摘要
从改进BISQ模型的双相介质所对应的速度-应力运动方程出发,构建2×2N阶交错网格有限差分模拟算法;同时,为压制模拟过程中的数值频散现象,采用通量校正传输(FCT)技术获得带FCT修正的交错网格有限差分模拟算法,对各向同性双相介质进行地震波场数值模拟。研究结果表明:(1)波场存在快纵波、慢纵波和横波等波场特征,并与模型的理论响应相符,说明交错网格模拟算法具有正确性和可行性;(2)采用FCT修正的交错网模拟算法能够有效压制数值频散,并保留真实的波场特征。
Based on first-order velocity?stress equations of reformulated BISQ theory in double-phase media,the simulation algorithm of the finite difference of 2-order time and 2N-order space staggered grids was constructed.Meanwhile,in order to suppress the numerical dispersion phenomenon during the process of the simulation,the flux-corrected transport(FCT) technique was discussed,and the algorithm of the finite difference of staggered grids was obtained,in which the FCT correcting was assembled.The algorithm was validated by simulating the wave-fields in isotropic double-phase media.The results show that: firstly,the existence of fast compressional wave,slow compressional wave and shear wave in wave-fields accords with the response of the model,which shows that the simulation algorithm of staggered grids is valid and practical.Secondly,with the use of algorithm of staggered grids which is corrected by FCT,dispersion can be effectively suppressed and the real wave-fields oscillation can be retained as well.
Based on first-order velocity?stress equations of reformulated BISQ theory in double-phase media,the simulation algorithm of the finite difference of 2-order time and 2N-order space staggered grids was constructed.Meanwhile,in order to suppress the numerical dispersion phenomenon during the process of the simulation,the flux-corrected transport(FCT) technique was discussed,and the algorithm of the finite difference of staggered grids was obtained,in which the FCT correcting was assembled.The algorithm was validated by simulating the wave-fields in isotropic double-phase media.The results show that: firstly,the existence of fast compressional wave,slow compressional wave and shear wave in wave-fields accords with the response of the model,which shows that the simulation algorithm of staggered grids is valid and practical.Secondly,with the use of algorithm of staggered grids which is corrected by FCT,dispersion can be effectively suppressed and the real wave-fields oscillation can be retained as well.
引文
[1]Biot M A.Theory of propagation of elastic waves in afluid-saturate porous solid,low-frequency range[J].J Acoust SocAmer,1956,28:168-178.
[2]Biot M A.Theory of propagation of elastic waves in afluid-saturate porous solid,higher-frequency range[J].J AcoustSoc Amer,1956,28:179-191.
[3]Dvorkin J,Nur A.Dynamic poroelasticity:A unified model withthe squirt and the Boit mechanisms[J].Geophysics,1993,58(4):524.
[4]Mamadou S.Acoustic wave propagation in saturated porousmedia:Reformulation of the Biot/Squirt flow theory[J].Journalof Applied Geophysics,2000,44(4):313-325.
[5]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场数值模拟[J].吉林大学学报:地球科学版,2003,33(2):217-196.MENG Qing-sheng,HE Qiao-deng,ZHU Jian-wei,et al.Seismic modeling in isotropic porous media based on BISQmodel[J].Journal of Jilin University:Earth Science Edition,2003,33(2):217-196.
[6]刘洋,李承楚,牟永光.任意偶数阶精度有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):275-284.LIU Yang,LI Cheng-chu,MOU Yong-guang.Finite-differencenumerical modeling of any even-order accuracy[J].OGP,1998,33(1):1-10.
[7]董良国,马在田,曹景忠,等.一阶弹性波动方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):853-861.DONG Liang-guo,MA Zai-tian,CAO Jing-zhong,et al.A studyon stability of the staggered-grid high-order difference method offirst-order elastic wave equation[J].Chinese Journal ofGeophysics,2000,43(6):853-861.
[8]Cerjan C,Kosloff D,Kosloff R,et al.A nonreflecting boundarycondition for discrete acoustic and elastic wave equation[J].Geohysics,1985,50(4):705.
[9]牟永光.储层地球物理学[M].北京:石油工业出版社,199627-38.MOU Yong-guang.Reservoir geophysics[M].Beijing:OilIndustry Press,1996:27-38.
[10]杨宽德,杨顶辉,王书强.基于Biot-Squirt方程的波场模拟[J].地球物理学报,2002,45(6):853-861.YANG Kuan-de,YANG Ding-hui,WANG Shu-qiang.Wave-field simulation based on the Biot-Squirt equation[J].ChineseJournal of Geophysics,2002,45(6):853-861.
[11]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略[J].地球物理学进展,2005,20(1):58-65.WU Guo-chen,WAN Hua-zhong.Analysis of numericaldispersion in wave-field simulation[J].Progress in Geophysics,2005,20(1):58-65.
[12]Dablain M A.The application of high differencing to the scalarwave equation[J].Geophysics,1985,51(1):54-66.
[13]XIAO Shao-ping.An FE-FCT method with implicit functions forthe study of shock wave propagation in solids[J].Wave Motion,2004,40:263-276.
[14]TONG Fei.Finite-difference modeling and depth-migration viaflux-corrected transport[J].SEG Expanded Abstracts 1993,12(5):1074-1077.
[15]Book D L,Boris J P,Hain K.Flux-corrected transport II:Generalization of the method[J].J Comput Phys,1975,18:248-283.
[2]Biot M A.Theory of propagation of elastic waves in afluid-saturate porous solid,higher-frequency range[J].J AcoustSoc Amer,1956,28:179-191.
[3]Dvorkin J,Nur A.Dynamic poroelasticity:A unified model withthe squirt and the Boit mechanisms[J].Geophysics,1993,58(4):524.
[4]Mamadou S.Acoustic wave propagation in saturated porousmedia:Reformulation of the Biot/Squirt flow theory[J].Journalof Applied Geophysics,2000,44(4):313-325.
[5]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场数值模拟[J].吉林大学学报:地球科学版,2003,33(2):217-196.MENG Qing-sheng,HE Qiao-deng,ZHU Jian-wei,et al.Seismic modeling in isotropic porous media based on BISQmodel[J].Journal of Jilin University:Earth Science Edition,2003,33(2):217-196.
[6]刘洋,李承楚,牟永光.任意偶数阶精度有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):275-284.LIU Yang,LI Cheng-chu,MOU Yong-guang.Finite-differencenumerical modeling of any even-order accuracy[J].OGP,1998,33(1):1-10.
[7]董良国,马在田,曹景忠,等.一阶弹性波动方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):853-861.DONG Liang-guo,MA Zai-tian,CAO Jing-zhong,et al.A studyon stability of the staggered-grid high-order difference method offirst-order elastic wave equation[J].Chinese Journal ofGeophysics,2000,43(6):853-861.
[8]Cerjan C,Kosloff D,Kosloff R,et al.A nonreflecting boundarycondition for discrete acoustic and elastic wave equation[J].Geohysics,1985,50(4):705.
[9]牟永光.储层地球物理学[M].北京:石油工业出版社,199627-38.MOU Yong-guang.Reservoir geophysics[M].Beijing:OilIndustry Press,1996:27-38.
[10]杨宽德,杨顶辉,王书强.基于Biot-Squirt方程的波场模拟[J].地球物理学报,2002,45(6):853-861.YANG Kuan-de,YANG Ding-hui,WANG Shu-qiang.Wave-field simulation based on the Biot-Squirt equation[J].ChineseJournal of Geophysics,2002,45(6):853-861.
[11]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略[J].地球物理学进展,2005,20(1):58-65.WU Guo-chen,WAN Hua-zhong.Analysis of numericaldispersion in wave-field simulation[J].Progress in Geophysics,2005,20(1):58-65.
[12]Dablain M A.The application of high differencing to the scalarwave equation[J].Geophysics,1985,51(1):54-66.
[13]XIAO Shao-ping.An FE-FCT method with implicit functions forthe study of shock wave propagation in solids[J].Wave Motion,2004,40:263-276.
[14]TONG Fei.Finite-difference modeling and depth-migration viaflux-corrected transport[J].SEG Expanded Abstracts 1993,12(5):1074-1077.
[15]Book D L,Boris J P,Hain K.Flux-corrected transport II:Generalization of the method[J].J Comput Phys,1975,18:248-283.
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