起伏地表二维声波方程地震波场延拓
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摘要
为了提高山地、沙漠、戈壁、黄土塬地区地震数据处理的效果,解决这些地区地表起伏变化对反射波地震波场的影响问题,提出将(x-z)域的曲网格映射成(ξ-η)域中的矩形网格的方法,推导出(ξ-η)域中的二维标量声波方程,并根据推导出来的波动方程采用逆时法将起伏地表上的地震波场在(ξ-η)域中向下延拓至一个水平面,从而校正地表起伏对地震波传播时间的影响.结果表明:对模型地震波场进行延拓计算,延拓前起伏表面上炮点位置处第1层的反射波旅行时间与延拓到平面上后该位置处第1层反射波的旅行时间差为59 ms,理论公式计算出的二者之差为61 ms,理论计算与实际延拓的结果相一致.在已知地表速度结构的前提下,该方法能够校正由于地表起伏变化对地震反射波造成的旅行时间的影响.
In order to eliminate the effect of surface topography on seismic data processing in mountains,deserts,gobis and loess tablelands,a method for transforming the curved grids of(x-z)-coordinate system into rectangular grids of(ξ-η)-coordinate system was presented and the 2-D acoustic wave equation in the(ξ-η)-coordinate system was derived.The wavefield on surface topography was downward continued to a flat datum using a reverse-time method in the transformed coordinate system.The results show that using the theoretical formula,on the shot's location of the model the first reflection wave's time difference between the point on topography and the corresponding point on the flat datum is 61 ms.And the time difference is 59 ms using the continuation method.The method is effective in correcting the propagation time of the seismic wave caused by the surface topography.
In order to eliminate the effect of surface topography on seismic data processing in mountains,deserts,gobis and loess tablelands,a method for transforming the curved grids of(x-z)-coordinate system into rectangular grids of(ξ-η)-coordinate system was presented and the 2-D acoustic wave equation in the(ξ-η)-coordinate system was derived.The wavefield on surface topography was downward continued to a flat datum using a reverse-time method in the transformed coordinate system.The results show that using the theoretical formula,on the shot's location of the model the first reflection wave's time difference between the point on topography and the corresponding point on the flat datum is 61 ms.And the time difference is 59 ms using the continuation method.The method is effective in correcting the propagation time of the seismic wave caused by the surface topography.
引文
[1]王祥春,刘学伟.起伏地表二维声波方程地震波场模拟与分析[J].石油地球物理勘探,2007,42(3):268-276.WANG Xiang-chun,LIU Xue-wei.Simulation and a-nalysis of seismic wavefield on relief surface by 2-D a-coustic wave equation[J].Oil Geophysical Prosec-ting,2007,42(3):268-276.
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[3]BERRYHILL J R.Wave-equation datuming[J].Ge-ophysics,1979,44(8):1329-1344.
[4]何樵登,熊维纲.应用地球物理教程:地震勘探[M].北京:地质出版社,1991:123-129.
[5]艾因双,郑天谕.波场延拓深度滤波方法[J].地球物理学报,1998,41(3):400-407.AI Yin-shuang,ZHENG Tian-yu.Wavefield contin-uation depth filtering[J].Chinese Journal of Geo-physics,1998,41(3):400-407.
[6]TESSMER E,KOSLOFF D,BEHLE A.Elasticwave propagation simulation in the presence of sur-face topography[J].Geophysics J Int,1992,108:621-632.
[7]FORNBERG B.The pseudospetral method:Accu-rate representation of interfaces in elastic wave calcu-lation[J].Geophysics,1998,53(5):625-637.
[8]NIELSEN P,IF F,BERG P,SKOVGAARD O.U-sing the pseudospectral technique on curved grids for2D acoustic forward modeling[J].Geophysical Pros-pecting,1994,42:321-341.
[9]HESTHOLM S,RUUD B.3-D finite-difference e-lastic wave modeling including surface topography[J].Geophysics,1998,63(2):613-622.
[10]HESTHOLM S,RUUD B.2D finite-difference e-lastic wave modeling including surface topograph[J].Geophysical Prospecting,1994,42:371-390.
[11]BEVC D.Flooding the topography;wave equationdatuming of land data with rugged acquisition to-pography[J].Geophysics,1997,62(5):1558-1569.
[2]BEASLEY C,LYNN W.The zero-velocity layer:Migration from irregular surfaces[J].Geophysics,1992,57(11):1435-1443.
[3]BERRYHILL J R.Wave-equation datuming[J].Ge-ophysics,1979,44(8):1329-1344.
[4]何樵登,熊维纲.应用地球物理教程:地震勘探[M].北京:地质出版社,1991:123-129.
[5]艾因双,郑天谕.波场延拓深度滤波方法[J].地球物理学报,1998,41(3):400-407.AI Yin-shuang,ZHENG Tian-yu.Wavefield contin-uation depth filtering[J].Chinese Journal of Geo-physics,1998,41(3):400-407.
[6]TESSMER E,KOSLOFF D,BEHLE A.Elasticwave propagation simulation in the presence of sur-face topography[J].Geophysics J Int,1992,108:621-632.
[7]FORNBERG B.The pseudospetral method:Accu-rate representation of interfaces in elastic wave calcu-lation[J].Geophysics,1998,53(5):625-637.
[8]NIELSEN P,IF F,BERG P,SKOVGAARD O.U-sing the pseudospectral technique on curved grids for2D acoustic forward modeling[J].Geophysical Pros-pecting,1994,42:321-341.
[9]HESTHOLM S,RUUD B.3-D finite-difference e-lastic wave modeling including surface topography[J].Geophysics,1998,63(2):613-622.
[10]HESTHOLM S,RUUD B.2D finite-difference e-lastic wave modeling including surface topograph[J].Geophysical Prospecting,1994,42:371-390.
[11]BEVC D.Flooding the topography;wave equationdatuming of land data with rugged acquisition to-pography[J].Geophysics,1997,62(5):1558-1569.
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