接收函数曲波变换去噪与偏移成像
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摘要
增强接收函数偏移图像的垂向分辨率意味着提高参与叠加的接收函数的频率,但是采用高频接收函数通常伴随着对接收函数质量和参考速度模型的更高要求.通过叠加处理可去除部分接收函数中的随机噪声干扰,但同一台站的接收函数之间经常存在难以通过简单叠加消除的噪声信号.压制接收函数随机噪声的干扰可加强成像效果和提高图像分辨率,对推进叠加偏移成像质量的提高有重要的实际意义.本文利用在川西地区布设的31个流动台站所记录的远震波形数据,使用曲波变换去噪后信噪比增强的接收函数进行共转换点叠加(CCP),获得沿北纬31°线下方800km深度范围内速度间断面图像.研究结果表明:(1)对接收函数进行曲波变换去噪,可压制随机噪声,增强转换震相的追踪性,提高数据信噪比;(2)通过去噪处理,大幅提高接收函数用于偏移成像的主频率;(3)偏移结果确认了接收函数反演得到的松潘和川滇块体下方具有厚度约10～20km的过渡性Moho的认识;(4)上地幔过渡带的结果预示在龙门山断裂带以西的小范围内有可能存在下地壳或上地幔物质的拆沉.
Improving the vertical resolution of receiver function(RF)migration means to increase the high-frequency components of RFs based on high-quality data and more accurate reference velocity model.The randomly distributed noise in the high-frequency RFs could contaminate the migration imaging,some details of the images were blurred by extraneous phases.Therefore,noise suppression for RF data can greatly improve the resolution of RF migration.We selected RF data from 31 stations of the array along the profile of 31°N in the western Sichuan province.We used curvelet transform to denoise the data after the moveout correction,and obtained the structure of the crust and upper mantle in this area.The results show that:(1)Our method can significantly improve the signal-noise ratio of RF data.(2)The high-frequency components of the RF data have been well preserved during the denoising procedure.(3)Our migration results confirmed the existence of a 10～20 km Moho transition zone beneath the eastern margin of the Qinghai-Tibet Plateau.(4)The upper mantle image indicates the delamination of the lower crust or upper mantle to the west of the Longmenshan fault.
Improving the vertical resolution of receiver function(RF)migration means to increase the high-frequency components of RFs based on high-quality data and more accurate reference velocity model.The randomly distributed noise in the high-frequency RFs could contaminate the migration imaging,some details of the images were blurred by extraneous phases.Therefore,noise suppression for RF data can greatly improve the resolution of RF migration.We selected RF data from 31 stations of the array along the profile of 31°N in the western Sichuan province.We used curvelet transform to denoise the data after the moveout correction,and obtained the structure of the crust and upper mantle in this area.The results show that:(1)Our method can significantly improve the signal-noise ratio of RF data.(2)The high-frequency components of the RF data have been well preserved during the denoising procedure.(3)Our migration results confirmed the existence of a 10～20 km Moho transition zone beneath the eastern margin of the Qinghai-Tibet Plateau.(4)The upper mantle image indicates the delamination of the lower crust or upper mantle to the west of the Longmenshan fault.
引文
Ammon C J,Randall G E,Zandt G.1990.On the nonuniqueness of receiver function inversion.Journal of Geophysical Research:Solid Earth,95(B10):15303-15318.
Anderson D L.1989.Theory of the Earth.Boston:Blackwell Scientific Publication,366.
Bostock M G,Rondenay S.1999.Migration of scattered teleseismic body waves.Geophysical Journal International,137(3):732-746.
Cammarano F,Goes S,Vacher P,et al.2003.Inferring uppermantle temperatures from seismic velocities.Physics of the Earth and Planetary Interiors,138(3-4):197-222.
Candès E,Donoho D.2000.Curvelets-a surprisingly effective nonadaptive representation for objects with edges.∥Cohen A,Rabut C,Schumaker L eds.Curves and Surface Fitting:SaintMalo.Nashville:Vanderbilt University Press,105-120.
Candès E,Donoho D.2004.New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities.Communications on Pure and Applied Mathematics,57(2):219-266.
Candès E J,Romberg J,Tao T.2006.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on Information Theory,52(2):489-509.
Chen L,Wen L X,Zheng T Y.2005.A wave equation migration method for receiver function imaging:1.Theory.Journal of Geophysical Research:Solid Earth,110(B11):B11309,doi:10.1029/2005JB003665.
Dueker K G,Sheehan A F.1997.Mantle discontinuity structure from midpoint stacks of converted P to S waves across the Yellowstone hotspot track.Journal of Geophysical Research:Solid Earth,102(B4):8313-8327.
Guo B,Liu Q Y,Chen J H,et al.2009.Teleseismic P-wave tomography of the crust and upper mantle in Longmenshan area,west Sichuan.Chinese Journal of Geophysics(in Chinese),52(2):346-355.
Helffrich G.2000.Topography of the transition zone seismic discontinuities.Reviews of Geophysics,38(1):141-158,doi:10.1029/1999RG000060.
Herrmann F J,Verschuur E.2004.Curvelet-domain multiple elimination with sparseness constraints.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1333-1336.
Herrmann F J,B9niger U,Verschuur D J.2007.Non-linear primary-multiple separation with directional curvelet frames.Geophysical Journal International,170(2):781-799.
JuliàJ,Ammon C J,Herrmann R B,et al.2000.Joint inversion of receiver function and surface wave dispersion observations.Geophysical Journal International,143(1):99-112.
Kind R,Yuan X,Saul J,et al.2002.Seismic images of crust and upper mantle beneath Tibet:Evidence for Eurasian plate subduction.Science,298(5596):1219-1221.
Langston C A.1979.Structure under Mount Rainier,Washington,inferred from teleseismic body waves.Journal of Geophysical Research:Solid Earth,84(B9):4749-4762.
Lei J S,Zhao D P,Su J R,et al.2009.Fine seismic structure under the Longmenshan fault zone and the mechanism of the large Wenchuan earthquake.Chinese Journal of Geophysics(in Chinese),52(2):339-345.
Li C,Van Der Hilst R D.2010.Structure of the upper mantle and transition zone beneath Southeast Asia from traveltime tomography.Journal of Geophysical Research:Solid Earth,115(B7):B07308,doi:10.1029/2009JB006882.
Li Y,Yao H J,Liu Q Y,et al.2010.Phase velocity array tomography of Rayleigh waves in western Sichuan from ambient seismic noise.Chinese Journal of Geophysics(in Chinese),53(4):842-852,doi:10.3969/j.issn.0001-5733.2010.04.00.
Li Z C.2014.Research status and development trends for seismic migration technology.Oil Geophysical Prospecting(in Chinese),49(1):1-21.
Ligorría J P,Ammon C J.1999.Iterative deconvolution and receiverfunction estimation.Bulletin of the Seismological Society of America,89(5):1395-1400.
Liu Q Y,Kind R,Li S C.1996.Maximal likelihood estimation and nonlinear inversion of the complex receiver function spectrum ratio.Chinese Journal of Geophysics(Acta Geophysica Sinica)(in Chinese),39(4):500-511.
Liu Q Y,Kind R.2004.Multi-channel maximal likelihood deconvolution method for isolating 3-component teleseismic receiver function.Seismology and Geology(in Chinese),26(3):416-425.
Liu Q Y,Van Der Hilst R D,Li Y,et al.2014.Eastward expansion of the Tibetan plateau by crustal flow and strain partitioning across faults.Nature Geoscience,7(5):361-365,doi:10.1038/NGEO2130.
Liu X W,Liu H.2002.Status and progress on wave equation migration methods.Progress in Geophysics(in Chinese),17(4):582-591.
Liu Z,Tian X B,Gao R,et al.2017.New images of the crustal structure beneath eastern Tibet from a high-density seismic array.Earth and Planetary Science Letters,480:33-41.
Mancinelli N J,Fischer K M.2017.The spatial sensitivity of Sp converted waves-scattered-wave kernels and their applications to receiver-function migration and inversion.Geophysical Journal International,212(3):1722-1735.
Owens T J,Zandt G,Taylor S R.1984.Seismic evidence for an ancient rift beneath the Cumberland plateau,Tennessee:Adetailed analysis of broadband teleseismic Pwaveforms.Journal of Geophysical Research:Solid Earth,89(B9):7783-7795.
Qi S H,Liu Q Y,Chen J H,et al.2016.Attenuation of noise in receiver functions using curvelet transform.Chinese Journal of Geophysics(in Chinese),59(3):884-896,doi:10.6038/cjg20160311.
Robert,Zhu J,Vergne J,et al.2009.Crustal structures in the area of the 2008Sichuan earthquake from seismologic and gravimetric data.Tectonophysics,491(1-4):205-210.
Ryberg T,Weber M.2000.Receiver function arrays:A reflection seismic approach.Geophysical Journal International,141(1):1-11.
Sa L M,Yang W Y,Du Q Z,et al.2015.Past,present and future of seismic migration imaging.Oil Geophysical Prospecting(in Chinese),50(5):1016-1036.
Shang X F,De Hoop M V,Van Der Hilst R D.2012.Beyond receiver functions:Passive source reverse time migration and inverse scattering of converted waves.Geophysical Research Letters,39(15):L15308,doi:10.1029/2012GL052289.
Stehly L,Froment B,Campillo M,et al.2015.Monitoring seismic wave velocity changes associated with the MW7.9 Wenchuan earthquake:increasing the temporal resolution using curvelet filters.Geophysical Journal International,201(3):1939-1949.
Vinnik L P,Reigber C,Aleshin I M,et al.2004.Receiver function tomography of the central Tien Shan.Earth and Planetary Science Letters,225(1-2):131-146.
Wilson D,Aster R.2005.Seismic imaging of the crust and upper mantle using regularized joint receiver functions,frequencywave number filtering,and multimode Kirchhoff migration.Journal of Geophysical Research:Solid Earth,110(B5):B05305,doi:10.1029/2004JB003430.
Wu J P,Huang Y,Zhang T Z,et al.2009.Aftershock distribution of the MS8.0 Wenchuan earthquake and three dimensional P-wave velocity structure in and around source region.Chinese Journal of Geophysics(in Chinese),52(2):320-328.
Wu Q J,Tian X B,Zhang N L,et al.2003a.Receiver function estimated by maximum entropy deconvolution.Acta Seismologica Sinica(in Chinese),25(4):382-389.
Wu Q J,Tian X B,Zhang N L,et al.2003b.Receiver function estimated by wiener filtering.Earthquake Research in China(in Chinese),19(1):41-47.
Wu Q J,Li Y H,Zhang R Q,et al.2007.2DKirchhoff migration for receiver function.Chinese Journal of Geophysics(in Chinese),50(2):539-545.
Yuan X H,Ni J,Kind R,et al.1997.Lithospheric and upper mantle structure of southern Tibet from a seismological passive source experiment.Journal of Geophysical Research:Solid Earth,102(B12):27491-27500.
Yue H,Chen Y J,Sandvol E,et al.2012.Lithospheric and upper mantle structure of the northeastern Tibetan plateau.Journal of Geophysical Research:Solid Earth,117(B5):B05307,doi:10.1029/2011JB008545.
Zhang Z J,Wang Y H,Chen Y,et al.2009.Crustal structure across Longmenshan fault belt from passive source seismic profiling.Geophysical Research Letters,36(17):L17310,doi:10.1029/2009GL039580.
Zhang Z J,Yuan X H,Chen Y,et al.2010.Seismic signature of the collision between the east Tibetan escape flow and the Sichuan Basin.Earth and Planetary Science Letters,292(3-4):254-264,doi:10.1016/j.epsl.2010.01.046.
Zheng H S.2000.Study development of seismic migration.World Geology(in Chinese),19(4):392-396,401.
Zhu L P,Kanamori H.2000.Moho depth variation in southern California from teleseismic receiver functions.Journal of Geophysical Research:Solid Earth,105(2):2969-2980.
Zhu L P.2000.Crustal structure across the San Andreas fault,southern California from teleseismic converted waves.Earth and Planetary Science Letters,179(1):183-190.
郭飚,刘启元,陈九辉等.2009.川西龙门山及邻区地壳上地幔远震P波层析成像.地球物理学报,52(2):346-355.
雷建设,赵大鹏,苏金蓉等.2009.龙门山断裂带地壳精细结构与汶川地震发震机理.地球物理学报,52(2):339-345.
李昱,姚华建,刘启元等.2010.川西地区台阵环境噪声瑞利波相速度层析成像.地球物理学报,53(4):842-852,doi:10.3969/j.issn.0001-5733.2010.04.009.
李振春.2014.地震偏移成像技术研究现状与发展趋势.石油地球物理勘探,49(1):1-21.
刘启元,Kind R,李顺成.1996.接收函数复谱比的最大或然性估计及非线性反演.地球物理学报,39(4):500-511.
刘启元,Kind R.2004.分离三分量远震接收函数的多道最大或然性反褶积方法.地震地质,26(3):416-425.
刘喜武,刘洪.2002.波动方程地震偏移成像方法的现状与进展.地球物理学进展,17(4):582-591.
齐少华,刘启元,陈九辉等.2016.接收函数的曲波变换去噪.地球物理学报,59(3):884-896,doi:10.6038/cjg20160311.
撒利明,杨午阳,杜启振等.2015.地震偏移成像技术回顾与展望.石油地球物理勘探,50(5):1016-1036.
吴建平,黄媛,张天中等.2009.汶川MS8.0级地震余震分布及周边区域P波三维速度结构研究.地球物理学报,52(2):320-328.
吴庆举,田小波,张乃铃等.2003a.计算台站接收函数的最大熵谱反褶积方法.地震学报,25(4):382-389.
吴庆举,田小波,张乃铃等.2003b.用Wiener滤波方法提取台站接收函数.中国地震,9(1):41-47.
吴庆举,李永华,张瑞青等.2007.接收函数的克希霍夫2D偏移方法.地球物理学报,50(2):539-545.
郑海山.2000.地震偏移技术研究进展.世界地质,19(4):392-396,401.本文编辑何燕
Anderson D L.1989.Theory of the Earth.Boston:Blackwell Scientific Publication,366.
Bostock M G,Rondenay S.1999.Migration of scattered teleseismic body waves.Geophysical Journal International,137(3):732-746.
Cammarano F,Goes S,Vacher P,et al.2003.Inferring uppermantle temperatures from seismic velocities.Physics of the Earth and Planetary Interiors,138(3-4):197-222.
Candès E,Donoho D.2000.Curvelets-a surprisingly effective nonadaptive representation for objects with edges.∥Cohen A,Rabut C,Schumaker L eds.Curves and Surface Fitting:SaintMalo.Nashville:Vanderbilt University Press,105-120.
Candès E,Donoho D.2004.New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities.Communications on Pure and Applied Mathematics,57(2):219-266.
Candès E J,Romberg J,Tao T.2006.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on Information Theory,52(2):489-509.
Chen L,Wen L X,Zheng T Y.2005.A wave equation migration method for receiver function imaging:1.Theory.Journal of Geophysical Research:Solid Earth,110(B11):B11309,doi:10.1029/2005JB003665.
Dueker K G,Sheehan A F.1997.Mantle discontinuity structure from midpoint stacks of converted P to S waves across the Yellowstone hotspot track.Journal of Geophysical Research:Solid Earth,102(B4):8313-8327.
Guo B,Liu Q Y,Chen J H,et al.2009.Teleseismic P-wave tomography of the crust and upper mantle in Longmenshan area,west Sichuan.Chinese Journal of Geophysics(in Chinese),52(2):346-355.
Helffrich G.2000.Topography of the transition zone seismic discontinuities.Reviews of Geophysics,38(1):141-158,doi:10.1029/1999RG000060.
Herrmann F J,Verschuur E.2004.Curvelet-domain multiple elimination with sparseness constraints.∥74th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1333-1336.
Herrmann F J,B9niger U,Verschuur D J.2007.Non-linear primary-multiple separation with directional curvelet frames.Geophysical Journal International,170(2):781-799.
JuliàJ,Ammon C J,Herrmann R B,et al.2000.Joint inversion of receiver function and surface wave dispersion observations.Geophysical Journal International,143(1):99-112.
Kind R,Yuan X,Saul J,et al.2002.Seismic images of crust and upper mantle beneath Tibet:Evidence for Eurasian plate subduction.Science,298(5596):1219-1221.
Langston C A.1979.Structure under Mount Rainier,Washington,inferred from teleseismic body waves.Journal of Geophysical Research:Solid Earth,84(B9):4749-4762.
Lei J S,Zhao D P,Su J R,et al.2009.Fine seismic structure under the Longmenshan fault zone and the mechanism of the large Wenchuan earthquake.Chinese Journal of Geophysics(in Chinese),52(2):339-345.
Li C,Van Der Hilst R D.2010.Structure of the upper mantle and transition zone beneath Southeast Asia from traveltime tomography.Journal of Geophysical Research:Solid Earth,115(B7):B07308,doi:10.1029/2009JB006882.
Li Y,Yao H J,Liu Q Y,et al.2010.Phase velocity array tomography of Rayleigh waves in western Sichuan from ambient seismic noise.Chinese Journal of Geophysics(in Chinese),53(4):842-852,doi:10.3969/j.issn.0001-5733.2010.04.00.
Li Z C.2014.Research status and development trends for seismic migration technology.Oil Geophysical Prospecting(in Chinese),49(1):1-21.
Ligorría J P,Ammon C J.1999.Iterative deconvolution and receiverfunction estimation.Bulletin of the Seismological Society of America,89(5):1395-1400.
Liu Q Y,Kind R,Li S C.1996.Maximal likelihood estimation and nonlinear inversion of the complex receiver function spectrum ratio.Chinese Journal of Geophysics(Acta Geophysica Sinica)(in Chinese),39(4):500-511.
Liu Q Y,Kind R.2004.Multi-channel maximal likelihood deconvolution method for isolating 3-component teleseismic receiver function.Seismology and Geology(in Chinese),26(3):416-425.
Liu Q Y,Van Der Hilst R D,Li Y,et al.2014.Eastward expansion of the Tibetan plateau by crustal flow and strain partitioning across faults.Nature Geoscience,7(5):361-365,doi:10.1038/NGEO2130.
Liu X W,Liu H.2002.Status and progress on wave equation migration methods.Progress in Geophysics(in Chinese),17(4):582-591.
Liu Z,Tian X B,Gao R,et al.2017.New images of the crustal structure beneath eastern Tibet from a high-density seismic array.Earth and Planetary Science Letters,480:33-41.
Mancinelli N J,Fischer K M.2017.The spatial sensitivity of Sp converted waves-scattered-wave kernels and their applications to receiver-function migration and inversion.Geophysical Journal International,212(3):1722-1735.
Owens T J,Zandt G,Taylor S R.1984.Seismic evidence for an ancient rift beneath the Cumberland plateau,Tennessee:Adetailed analysis of broadband teleseismic Pwaveforms.Journal of Geophysical Research:Solid Earth,89(B9):7783-7795.
Qi S H,Liu Q Y,Chen J H,et al.2016.Attenuation of noise in receiver functions using curvelet transform.Chinese Journal of Geophysics(in Chinese),59(3):884-896,doi:10.6038/cjg20160311.
Robert,Zhu J,Vergne J,et al.2009.Crustal structures in the area of the 2008Sichuan earthquake from seismologic and gravimetric data.Tectonophysics,491(1-4):205-210.
Ryberg T,Weber M.2000.Receiver function arrays:A reflection seismic approach.Geophysical Journal International,141(1):1-11.
Sa L M,Yang W Y,Du Q Z,et al.2015.Past,present and future of seismic migration imaging.Oil Geophysical Prospecting(in Chinese),50(5):1016-1036.
Shang X F,De Hoop M V,Van Der Hilst R D.2012.Beyond receiver functions:Passive source reverse time migration and inverse scattering of converted waves.Geophysical Research Letters,39(15):L15308,doi:10.1029/2012GL052289.
Stehly L,Froment B,Campillo M,et al.2015.Monitoring seismic wave velocity changes associated with the MW7.9 Wenchuan earthquake:increasing the temporal resolution using curvelet filters.Geophysical Journal International,201(3):1939-1949.
Vinnik L P,Reigber C,Aleshin I M,et al.2004.Receiver function tomography of the central Tien Shan.Earth and Planetary Science Letters,225(1-2):131-146.
Wilson D,Aster R.2005.Seismic imaging of the crust and upper mantle using regularized joint receiver functions,frequencywave number filtering,and multimode Kirchhoff migration.Journal of Geophysical Research:Solid Earth,110(B5):B05305,doi:10.1029/2004JB003430.
Wu J P,Huang Y,Zhang T Z,et al.2009.Aftershock distribution of the MS8.0 Wenchuan earthquake and three dimensional P-wave velocity structure in and around source region.Chinese Journal of Geophysics(in Chinese),52(2):320-328.
Wu Q J,Tian X B,Zhang N L,et al.2003a.Receiver function estimated by maximum entropy deconvolution.Acta Seismologica Sinica(in Chinese),25(4):382-389.
Wu Q J,Tian X B,Zhang N L,et al.2003b.Receiver function estimated by wiener filtering.Earthquake Research in China(in Chinese),19(1):41-47.
Wu Q J,Li Y H,Zhang R Q,et al.2007.2DKirchhoff migration for receiver function.Chinese Journal of Geophysics(in Chinese),50(2):539-545.
Yuan X H,Ni J,Kind R,et al.1997.Lithospheric and upper mantle structure of southern Tibet from a seismological passive source experiment.Journal of Geophysical Research:Solid Earth,102(B12):27491-27500.
Yue H,Chen Y J,Sandvol E,et al.2012.Lithospheric and upper mantle structure of the northeastern Tibetan plateau.Journal of Geophysical Research:Solid Earth,117(B5):B05307,doi:10.1029/2011JB008545.
Zhang Z J,Wang Y H,Chen Y,et al.2009.Crustal structure across Longmenshan fault belt from passive source seismic profiling.Geophysical Research Letters,36(17):L17310,doi:10.1029/2009GL039580.
Zhang Z J,Yuan X H,Chen Y,et al.2010.Seismic signature of the collision between the east Tibetan escape flow and the Sichuan Basin.Earth and Planetary Science Letters,292(3-4):254-264,doi:10.1016/j.epsl.2010.01.046.
Zheng H S.2000.Study development of seismic migration.World Geology(in Chinese),19(4):392-396,401.
Zhu L P,Kanamori H.2000.Moho depth variation in southern California from teleseismic receiver functions.Journal of Geophysical Research:Solid Earth,105(2):2969-2980.
Zhu L P.2000.Crustal structure across the San Andreas fault,southern California from teleseismic converted waves.Earth and Planetary Science Letters,179(1):183-190.
郭飚,刘启元,陈九辉等.2009.川西龙门山及邻区地壳上地幔远震P波层析成像.地球物理学报,52(2):346-355.
雷建设,赵大鹏,苏金蓉等.2009.龙门山断裂带地壳精细结构与汶川地震发震机理.地球物理学报,52(2):339-345.
李昱,姚华建,刘启元等.2010.川西地区台阵环境噪声瑞利波相速度层析成像.地球物理学报,53(4):842-852,doi:10.3969/j.issn.0001-5733.2010.04.009.
李振春.2014.地震偏移成像技术研究现状与发展趋势.石油地球物理勘探,49(1):1-21.
刘启元,Kind R,李顺成.1996.接收函数复谱比的最大或然性估计及非线性反演.地球物理学报,39(4):500-511.
刘启元,Kind R.2004.分离三分量远震接收函数的多道最大或然性反褶积方法.地震地质,26(3):416-425.
刘喜武,刘洪.2002.波动方程地震偏移成像方法的现状与进展.地球物理学进展,17(4):582-591.
齐少华,刘启元,陈九辉等.2016.接收函数的曲波变换去噪.地球物理学报,59(3):884-896,doi:10.6038/cjg20160311.
撒利明,杨午阳,杜启振等.2015.地震偏移成像技术回顾与展望.石油地球物理勘探,50(5):1016-1036.
吴建平,黄媛,张天中等.2009.汶川MS8.0级地震余震分布及周边区域P波三维速度结构研究.地球物理学报,52(2):320-328.
吴庆举,田小波,张乃铃等.2003a.计算台站接收函数的最大熵谱反褶积方法.地震学报,25(4):382-389.
吴庆举,田小波,张乃铃等.2003b.用Wiener滤波方法提取台站接收函数.中国地震,9(1):41-47.
吴庆举,李永华,张瑞青等.2007.接收函数的克希霍夫2D偏移方法.地球物理学报,50(2):539-545.
郑海山.2000.地震偏移技术研究进展.世界地质,19(4):392-396,401.本文编辑何燕
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