基于算子优化的Fourier有限差分法保幅叠前深度偏移
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摘要
从声波方程的单程波分解出发,对传统波动方程叠前深度偏移的传播算子和边界条件进行优化,推导出基于优化算子的保幅边界条件和3个新偏移算子。通过应用新算子和边界条件,断层和倾斜层处的成像效果有明显改善,并且叠前深度偏移的质量也得到提高。模型试算和实际资料处理结果表明,使用优化的边界条件和偏移算子,能够提高横向速度变化情况下的成像精度。
Beginning the one way splitting of the acoustical wave equation,continuation operator and boundary condition based on traditional wave equation in the prestack depth migration were derived.Then the true-amplitude boundary condition and three new migration operators with the optimized operator were gotten.Through the new operators and boundary condition,the imaging effect in fault and inclined layers and the quality of the prestack depth migration were impoved.The model calculation and real data process results show that using the optimized boundary condition and migration operators can enhance the imaging precision even if the lateral velocity is variable.
Beginning the one way splitting of the acoustical wave equation,continuation operator and boundary condition based on traditional wave equation in the prestack depth migration were derived.Then the true-amplitude boundary condition and three new migration operators with the optimized operator were gotten.Through the new operators and boundary condition,the imaging effect in fault and inclined layers and the quality of the prestack depth migration were impoved.The model calculation and real data process results show that using the optimized boundary condition and migration operators can enhance the imaging precision even if the lateral velocity is variable.
引文
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[9]程玖兵,王华忠,马在田.带误差补偿的有限差分叠前深度偏移算法[J].石油地球物理勘探,2001,36(4):408-413.CHENG Jiu-bing,WANG Hua-zhong,MA Zai-tian.Fi-nite-difference pre-stack depth migration with errors com-pensation[J].Oil Geophysical Prospecting,2001,36(4):408-413.
[10]BLEISTEIN N.On the imaging of reflectors in the earth[J].Geophysics,1987,52(1):931-942.
[11]CAO J,WU R S.Study of the influence of propagatoramplitude correction on image amplitude using beamletpropagator with local WKBJ approximation[C/OL]//76th Annual International Meeting,SEG,New Orleans,USA,October 15-21,2006[2010-01-10].
[2]张关泉.波动方程的上行波和下行波的耦合方程组[J].应用数学报,1993,16(2):251-263.ZHANG Guan-quan.System of coupled equations for up-coming and downgoing waves[J].Acta MathematicaeApplicatae,1993,16(2):251-263.
[3]张宇.振幅保真的单程波方程偏移理论[J].地球物理学报,2006,49(5):1410-1430.ZHANG Yu.The theory of true amplitude one-way waveequation migration[J].Chinese Journal of Geophysics,2006,49(5):1410-1430.
[4]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究[J].地球物理学报,2004,47(3):509-513.CUI Xing-fu,ZHANG Guan-quan,WU Ya-li.True am-plitude seismic migration operator in 3-D heterogeneousmedium[J].Chinese Journal of Geophysics,2004,47(3):509-513.
[5]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1):268-276.LIU Ding-jin,YIN Xing-yao.A method of Fourier finite-difference preserved-amplitude prestack depth migration[J].Chinese Journal of Geophysics,2007,50(1):268-276.
[6]VIVAS F A,PESTANA R C.True-amplitude one-waywave equation migration in the mixed domain[J].Geo-physics,2010,75(5):199-209.
[7]YE Y M,LI Z C.Preserved amplitude migration basedon the one way wave equation in the angle domain[J],Applied Geophysics,2009,6(1):50-58.
[8]叶月明,李振春,仝兆岐,等.双复杂介质条件下频率空间域有限差分法保幅偏移[J].地球物理学报,2008,51(5):1511-1519.YE Yue-ming,LI Zhen-chun,TONG Zhao-qi,et al.Preserved-amplitude migration with dual-complexity[J].Chinese Journal of Geophysics,2008,51(5):1511-1519.
[9]程玖兵,王华忠,马在田.带误差补偿的有限差分叠前深度偏移算法[J].石油地球物理勘探,2001,36(4):408-413.CHENG Jiu-bing,WANG Hua-zhong,MA Zai-tian.Fi-nite-difference pre-stack depth migration with errors com-pensation[J].Oil Geophysical Prospecting,2001,36(4):408-413.
[10]BLEISTEIN N.On the imaging of reflectors in the earth[J].Geophysics,1987,52(1):931-942.
[11]CAO J,WU R S.Study of the influence of propagatoramplitude correction on image amplitude using beamletpropagator with local WKBJ approximation[C/OL]//76th Annual International Meeting,SEG,New Orleans,USA,October 15-21,2006[2010-01-10].
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