基于保角变换的连续介质偏移成像
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摘要
用偏移成像方法对速度各向异性介质进行成像时,存在水平同相轴及大倾角界面畸变的缺陷.本文采用基于保角变换的偏移成像方法对畸变缺陷进行校正.首先,利用保角变换法可将不规则边界的单连通区域转变成规则边界的原理,将规则边界的连续介质场转变成不规则边界的均匀介质场,使该均匀介质场更适应现有Stolt等偏移方法对速度场的要求;其次,对改变了区域的模型地震记录进行常规的偏移成像处理;再利用推导出的反变换公式对成像结果进行反变换,得出模型的真实偏移成像结果.文章对合成模型进行了试算,并将试算结果与模型进行了比较.
In this article we studied the forward modeling of the medium which was continuous complex.In the first step,through using the formula of the conformal transformation,a continuous medium with regulation boundary in original area could be transformed to a homogeneous medium with anomalous boundary in complex area,so the new constant velocity field could be more adapt to the current Stolt migration's conditions.In the second step,the new model would be migrated by normal migration method.In the last step,the migration result in original area could be obtained by using inverse transform formula.The performance of the method is demonstrated on simple synthetic model.The migration result using this method is then compared with the model.
In this article we studied the forward modeling of the medium which was continuous complex.In the first step,through using the formula of the conformal transformation,a continuous medium with regulation boundary in original area could be transformed to a homogeneous medium with anomalous boundary in complex area,so the new constant velocity field could be more adapt to the current Stolt migration's conditions.In the second step,the new model would be migrated by normal migration method.In the last step,the migration result in original area could be obtained by using inverse transform formula.The performance of the method is demonstrated on simple synthetic model.The migration result using this method is then compared with the model.
引文
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[3]何际平,鲁烈琴,王红旗,冯心远,肖明图.复杂地区速度场建立与变速构造成图方法研究[J].地球物理学进展,2006,21(1):167~172.
[4]陈生昌,马在田.广义地震数据合成及其偏移成像[J].地球物理学报,2006,49(4):1144~1149.
[5]王红落,常旭,陈传仁.基于波动方程有限差分算法的接收函数正演与偏移[J].地球物理学报,2005,48(2):415~422.
[6]匡斌,王华忠,季玉新,马在田.任意复杂介质中主能量法地震波走时计算[J].地球物理学报,2005,48(2):394~398.
[7]张春城,周正欧.基于Stolt偏移的探地雷达合成孔径成像研究[J].电波科学学报,2004,19(3):316~320.
[8]Stolt.RH.Migration by Fourier transform[J].Geophysics,1978,43(1):23~48.
[9]Gazdag J.Wave equation migration with the phase shift meth-od[J].Geophysics,1978,43(1):176~185.
[10]Gazdag J,Sguazzero P.Migration of seismic data by phaseshift plus interpolation[J].Geophysics,1984,49(1):124~131.
[11]王祥春,刘学伟.变换坐标系下相移法起伏地表地震波场延拓[J].地球物理学进展,2005,20(3):677~680.
[12]张文生,张关泉,宋海斌.高精度混合法叠前深度偏移及其并行实现[J].地球物理学报,2001,44(4):542~551.
[13]吴信民.保角变换在位场转换中的应用[J].东华理工学院学报(自然科学版),1997,20(4):349~352.
[14]周海京,林为干,丁武,周传明.新型椭圆函数波导族的保角变换有限差分解法[J].电波科学学报,1999,14(2):121~128.
[15]杨秀夫,陈勉,刘希圣,蒋海军.保角变换法在水压裂缝缝内流场数值模拟中的应用研究[J].中国海上油气,2002,14(5):28~40.
[2]张致付,刘洪,陈景波,李幼铭.地震偏移的最优可分近似算法实现[J].地球物理学报,2005,48(6):1422~1427.
[3]何际平,鲁烈琴,王红旗,冯心远,肖明图.复杂地区速度场建立与变速构造成图方法研究[J].地球物理学进展,2006,21(1):167~172.
[4]陈生昌,马在田.广义地震数据合成及其偏移成像[J].地球物理学报,2006,49(4):1144~1149.
[5]王红落,常旭,陈传仁.基于波动方程有限差分算法的接收函数正演与偏移[J].地球物理学报,2005,48(2):415~422.
[6]匡斌,王华忠,季玉新,马在田.任意复杂介质中主能量法地震波走时计算[J].地球物理学报,2005,48(2):394~398.
[7]张春城,周正欧.基于Stolt偏移的探地雷达合成孔径成像研究[J].电波科学学报,2004,19(3):316~320.
[8]Stolt.RH.Migration by Fourier transform[J].Geophysics,1978,43(1):23~48.
[9]Gazdag J.Wave equation migration with the phase shift meth-od[J].Geophysics,1978,43(1):176~185.
[10]Gazdag J,Sguazzero P.Migration of seismic data by phaseshift plus interpolation[J].Geophysics,1984,49(1):124~131.
[11]王祥春,刘学伟.变换坐标系下相移法起伏地表地震波场延拓[J].地球物理学进展,2005,20(3):677~680.
[12]张文生,张关泉,宋海斌.高精度混合法叠前深度偏移及其并行实现[J].地球物理学报,2001,44(4):542~551.
[13]吴信民.保角变换在位场转换中的应用[J].东华理工学院学报(自然科学版),1997,20(4):349~352.
[14]周海京,林为干,丁武,周传明.新型椭圆函数波导族的保角变换有限差分解法[J].电波科学学报,1999,14(2):121~128.
[15]杨秀夫,陈勉,刘希圣,蒋海军.保角变换法在水压裂缝缝内流场数值模拟中的应用研究[J].中国海上油气,2002,14(5):28~40.
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