地震波初至旅行时计算策略
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摘要
以波前扩展法为基础,提出了适合强速度纵横向变化的有限差分法地震波初至旅行时外推策略,即在计算时采用二阶精度的有限差分法对程函方程进行了近似计算。在没有出现对负数开平方的情况下只计算三个可能的体波,当出现已知条件不满足或算法不稳定(如对负数开平方)的情况时就计算可能的3个首波和两个散射波,两种情况下都取其最小值作为地震初至旅行时。采用二分法的旅行时查找方法,完成了初至旅行时算法的改进。复杂模型试算结果表明,该方法提高了初至旅行时计算的精度和稳定性。
A strategy of seismic wave first break travel-time calculation with finite difference method was proposed on the basis of wavefront spread method.The strategy can adapt to the strongly lateral and/or vertical velocity variation media.The first break travel-times were calculated with the second order finite difference approximation in solving the eikonal equation.Without the circumstances of extracting the square roots of the negative number,only three probable body waves were calculated.Whether the given conditions are not satisfied or the algorithm is not stabilized(extracting the square root of the negative number),three probable body waves and two scattering waves must be calculated simultaneously.The minimization of travel-times was selected as the seismic wave first break travel-time in both cases listed above.The dichotomy was employed in looking for the location of wavefront point.Thus,the algorithm of first break travel-time calculation was improved.The method was applied successfully with a complicated model in the seismic wave first break travel-time calculation,which shows its high precision and stability.
A strategy of seismic wave first break travel-time calculation with finite difference method was proposed on the basis of wavefront spread method.The strategy can adapt to the strongly lateral and/or vertical velocity variation media.The first break travel-times were calculated with the second order finite difference approximation in solving the eikonal equation.Without the circumstances of extracting the square roots of the negative number,only three probable body waves were calculated.Whether the given conditions are not satisfied or the algorithm is not stabilized(extracting the square root of the negative number),three probable body waves and two scattering waves must be calculated simultaneously.The minimization of travel-times was selected as the seismic wave first break travel-time in both cases listed above.The dichotomy was employed in looking for the location of wavefront point.Thus,the algorithm of first break travel-time calculation was improved.The method was applied successfully with a complicated model in the seismic wave first break travel-time calculation,which shows its high precision and stability.
引文
[1]杜启振,刘莲莲,孙晶波.各向异性粘弹性孔隙介质地震波场伪谱法正演模拟[J].物理学报,2007,56(10):6143-6149.DU Qi-zhen,LIU Lian-lian,SUN Jing-bo.Numerical mod-eling of seismic wavefield in anisotropic viscoelastic por-ous medium with the pseudo-spectral method[J].ActaPhyisica Sinica,2007,56(10):6143-6149.
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[5]董渊,杨慧珠,杜启振.有限元-有限差分法二维波动逆时偏移初探[J].石油大学学报:自然科学版,2003,27(6):25-29.DONG Yuan,YANG Hui-zhu,DU Qi-zhen.Study on re-verse-time migration of two dimensional wave equationwith finite element-finite difference method[J].Journal ofUniversity of Petroleum,China(Edition of Natural Sci-ence),2003,27(6):25-29.
[6]VIDALE J E.Finite-difference calculation of traveltimes[J].Bull Seis Soc Amer,1988,78(6):2062-2076.
[7]QIN F,OLSEN K,LUO Y,et al.Finite-difference solu-tion of the eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.
[8]PODVIN P,LECOMTE I.Finite difference computationof traveltimes in very contrasted velocity model:a mas-sively parallel approach and its associated tools[J].Geo-phys J Int,1991,105(1):271-284.
[9]张霖斌,姚振兴,纪晨.地震初至波走时的有限差分计算[J].地球物理学进展,1996,11(4):47-52.ZHANG Lin-bin,YAO Zhen-xing,JI Chen.Finite differ-ence calculation of seismic first-arrival traveltime[J].Progress in Geophysics,1996,11(4):47-52.
[10]潘纪顺,张先康,赵成斌,等.二维复杂介质中地震波走时和射线的计算方法及其应用[J].地震研究,2006,29(3):245-250.PANJi-shun,ZHANG Xian-kang,ZHAO Cheng-bin,etal.Computation method of seismic wave travel times andrays in 2D complicated velocity models and its applica-tion[J].Journal of Seismological Research,2006,29(3):245-250.
[11]杨昊,孙建国,韩复兴.波前扩展有限差分地震波走时算法的C++语言描述[J].吉林大学学报:地球科学版,2006,37(3):615-619.YANG Hao,SUN Jian-guo,HAN Fu-xing.An C++language program implement of traveltime calculation ofexpanding wavefronts finite-difference method[J].Jour-nal of Jilin University(Earth Scince Edition),2006,37(3):615-619.
[2]裴正林.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报:自然科学版,2006,30(2):16-20.PEI Zheng-lin.A staggered-grid high order finite differ-ence method for modeling elastic wave equation in 3-Ddual phase anisotropic media[J].Journal of China Uni-versity of Petroleum(Edition of Natural Science),2006,30(2):16-20.
[3]王月英,孙成禹.弹性波动方程数值解的有限元并行算法[J].中国石油大学学报:自然科学版,2006,30(5):27-30.WANG Yue-ying,SUN Cheng-yu.Finite element parallelalgorithm for numerical solution of elastic wave equation[J].Journal of China University of Petroleum(Edition ofNatural Science),2006,30(5):27-30.
[4]王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):19-24.WANG Yong-gang,XING Wen-jun,XIE Wan-xue,et al.Study of absorbing boundary condition by perfectlymatched layer[J].Journal of China University of Petrole-um(Edition of Natural Science),2007,31(1):19-24.
[5]董渊,杨慧珠,杜启振.有限元-有限差分法二维波动逆时偏移初探[J].石油大学学报:自然科学版,2003,27(6):25-29.DONG Yuan,YANG Hui-zhu,DU Qi-zhen.Study on re-verse-time migration of two dimensional wave equationwith finite element-finite difference method[J].Journal ofUniversity of Petroleum,China(Edition of Natural Sci-ence),2003,27(6):25-29.
[6]VIDALE J E.Finite-difference calculation of traveltimes[J].Bull Seis Soc Amer,1988,78(6):2062-2076.
[7]QIN F,OLSEN K,LUO Y,et al.Finite-difference solu-tion of the eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.
[8]PODVIN P,LECOMTE I.Finite difference computationof traveltimes in very contrasted velocity model:a mas-sively parallel approach and its associated tools[J].Geo-phys J Int,1991,105(1):271-284.
[9]张霖斌,姚振兴,纪晨.地震初至波走时的有限差分计算[J].地球物理学进展,1996,11(4):47-52.ZHANG Lin-bin,YAO Zhen-xing,JI Chen.Finite differ-ence calculation of seismic first-arrival traveltime[J].Progress in Geophysics,1996,11(4):47-52.
[10]潘纪顺,张先康,赵成斌,等.二维复杂介质中地震波走时和射线的计算方法及其应用[J].地震研究,2006,29(3):245-250.PANJi-shun,ZHANG Xian-kang,ZHAO Cheng-bin,etal.Computation method of seismic wave travel times andrays in 2D complicated velocity models and its applica-tion[J].Journal of Seismological Research,2006,29(3):245-250.
[11]杨昊,孙建国,韩复兴.波前扩展有限差分地震波走时算法的C++语言描述[J].吉林大学学报:地球科学版,2006,37(3):615-619.YANG Hao,SUN Jian-guo,HAN Fu-xing.An C++language program implement of traveltime calculation ofexpanding wavefronts finite-difference method[J].Jour-nal of Jilin University(Earth Scince Edition),2006,37(3):615-619.
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