一阶弹性波交错网格时间高阶差分格式及稳定性分析
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摘要
弹性波模拟或逆时偏移时,对空间偏导数采用高阶差分格式可提高计算精度,但这种算法的稳定性条件过于严格,要求差分离散的时间步长必须足够小以确保算法稳定。在常规空间高阶差分格式的基础上,将速度(应力)对时间的高阶导数转化为不同精度的应力(速度)对空间的差分,得到了一种新的基于交错网格的时间高阶、空间高阶差分格式。通过对交错网格时间高阶差分格式稳定性的分析,认为该算法的稳定性条件较常规算法宽松,在弹性波场的求解过程中可以采用更大的时间步长。
During the elastic wave numerical simulation or reverse-time migration,using higher order difference scheme on spatial partial derivative can improve computational accuracy. But the stability condition of the algorithm is much too strict,it requires time step length of discrete differential should be small enough to ensure algorithm in stable. Based on traditional spatial higher order differential scheme,taking the higher order derivatives of velocity( stress) on time translate into differentials of stress( velocity) on space with different accuracy,acquired a new kind of higher order time,higher order space difference scheme based on staggered grid. Through the stability analysis of staggered grid higher order difference scheme has considered that the stability condition of the algorithm is more generous than that of traditional algorithm,thus in procedures for elastic wave field solution,larger time step length can be used.
During the elastic wave numerical simulation or reverse-time migration,using higher order difference scheme on spatial partial derivative can improve computational accuracy. But the stability condition of the algorithm is much too strict,it requires time step length of discrete differential should be small enough to ensure algorithm in stable. Based on traditional spatial higher order differential scheme,taking the higher order derivatives of velocity( stress) on time translate into differentials of stress( velocity) on space with different accuracy,acquired a new kind of higher order time,higher order space difference scheme based on staggered grid. Through the stability analysis of staggered grid higher order difference scheme has considered that the stability condition of the algorithm is more generous than that of traditional algorithm,thus in procedures for elastic wave field solution,larger time step length can be used.
引文
[1]Bai B,He B S,Li K R,Tang H G,Yang J J. Numerical simulation of seismic wavefields in TTI media using the rotated staggered-grid compact finite-difference scheme[J]. Earthquake Science,2018,31(02):75-82.
[2]张晶,何兵寿,张会星.含直立裂隙介质的弹性波动方程正演模拟[J].中国煤炭地质,2008(01):50-54.
[3]何兵寿,陈婷,王胜.任意广角方程逆时偏移的脉冲响应及模型试算[J].中国煤炭地质,2014(2):49-54.
[4]胡楠,何兵寿.三维各向同性介质矢量波场保幅分离方法[J].煤炭学报,2017(9).
[5]史才旺,何兵寿.基于炮采样的多尺度全波形反演[J]. Applied Geophysics,2018,15(02):261-270.
[6]李凯瑞,何兵寿,胡楠.基于一阶速度-胀缩-旋转方程的多分量联合逆时偏移[J].煤炭学报,2018,43(04):1072-1082.
[7]郭鹏,何兵寿,沈骥千.VTI介质弹性波波场分解的空间域算法[J].石油地球物理勘探,2013,48(4):567-575.
[8]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.
[9]李佳珂,张会星,白冰,等.TTI介质纯准P波一阶压力-速度方程及求解方法[J].中国煤炭地质,2018,30(07):72-78.
[10]陈可洋.高阶弹性波波动方程正演模拟及逆时偏移成像研究[D].黑龙江大庆:大庆石油学院,2009.
[11]常海明,何兵寿,杨佳佳,陈婷.逆时偏移中的归一化加权互相关成像条件及应用[J].中国煤炭地质,2014,26(01):51-55.
[12]刘学义,何兵寿.VTI介质中弹性波方程正演的一阶混合吸收边界[J].中国煤炭地质,2015,27(03):59-63.
[13]Igel H,Riollet B,Mora P. Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation[C]//1992 SEG Annual Meeting. Society of Exploration Geophysicists,1992.
[14]Virieux J. P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method[J]. Geophysics,1986,51(4):889-901.
[15]Levander A R. Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425-1436.
[16]裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2005,19(4):933-941.
[17]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.
[2]张晶,何兵寿,张会星.含直立裂隙介质的弹性波动方程正演模拟[J].中国煤炭地质,2008(01):50-54.
[3]何兵寿,陈婷,王胜.任意广角方程逆时偏移的脉冲响应及模型试算[J].中国煤炭地质,2014(2):49-54.
[4]胡楠,何兵寿.三维各向同性介质矢量波场保幅分离方法[J].煤炭学报,2017(9).
[5]史才旺,何兵寿.基于炮采样的多尺度全波形反演[J]. Applied Geophysics,2018,15(02):261-270.
[6]李凯瑞,何兵寿,胡楠.基于一阶速度-胀缩-旋转方程的多分量联合逆时偏移[J].煤炭学报,2018,43(04):1072-1082.
[7]郭鹏,何兵寿,沈骥千.VTI介质弹性波波场分解的空间域算法[J].石油地球物理勘探,2013,48(4):567-575.
[8]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.
[9]李佳珂,张会星,白冰,等.TTI介质纯准P波一阶压力-速度方程及求解方法[J].中国煤炭地质,2018,30(07):72-78.
[10]陈可洋.高阶弹性波波动方程正演模拟及逆时偏移成像研究[D].黑龙江大庆:大庆石油学院,2009.
[11]常海明,何兵寿,杨佳佳,陈婷.逆时偏移中的归一化加权互相关成像条件及应用[J].中国煤炭地质,2014,26(01):51-55.
[12]刘学义,何兵寿.VTI介质中弹性波方程正演的一阶混合吸收边界[J].中国煤炭地质,2015,27(03):59-63.
[13]Igel H,Riollet B,Mora P. Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation[C]//1992 SEG Annual Meeting. Society of Exploration Geophysicists,1992.
[14]Virieux J. P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method[J]. Geophysics,1986,51(4):889-901.
[15]Levander A R. Fourth-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425-1436.
[16]裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2005,19(4):933-941.
[17]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.