基于L_p范数正则化的V字型密度界面重力反演
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摘要
V字型密度界面是一类常见的密度界面,如海沟、半地堑以及俯冲带之下的莫霍面,利用重力数据刻画此类密度界面形态对于区域构造研究、油气勘探以及物理海洋学等都具有重要意义.本文首先建立了Lp-范数形式的模型约束函数,并利用正则化原理将其与重力数据误差函数和已知深度约束函数结合形成V字型密度界面反演的目标函数,推导了目标函数的梯度表达式,并以非线性共轭梯度法为核心给出了反演流程.二维简单模型试算结果表明p=5时该方法能准确地刻画V字型密度界面起伏特征,且亦能准确地应用于二维复杂密度界面和三维界面的反演.最后将反演方法应用于挑战者深渊及邻区的实际资料处理之中,利用研究区海底地形数据和沉积层厚度数据对自由空间重力异常逐层剥离而得到莫霍面引起的重力异常,用本文方法对此重力异常进行反演,结果呈现了板块俯冲作用引起的V字型莫霍面起伏特征.
The V-shaped density interface is commonly seen such as the ocean trench,half-graben,and the Moho beneath a subduction zone.Delineating the relief of these V-shaped density interfaces is of significance in regional tectonic research,physical oceanography and oil and gas exploration.Among inversion methods of the density interface,the regularization approach,which applies prior information,can guarantee the inversion result to fit the known depth of the interface to be estimated.It can also control the shape of the interface via the model constraint function in the regularization item,making the inversion result agree with the real geologic feature.We have designed a model constraint function in the form of Lp-norm and then integrated it with the gravity data misfit function and the known depth constraint function to establish an objective function for V-shaped density interface inversion.Subsequently,we have derived the gradient of the objective functionand built the inversion process taking the nonlinear conjugate gradient algorithm as the core.The effect of our proposed inversion method is related to the value of p.The test results conducted with a two-dimensional simple model show that the method can be used to accurately estimate the V-shaped density interface relief when p=5,and the correctness of the proposed method is further confirmed by a two-dimensional V-shaped density interface with complex shape.The test results of a three-dimensional V-shaped density interface show that our proposed method is also appropriate for three-dimensional inversion.At the end of this article,the inversion method is tested with real gravity data of the Challenger Deep and adjacent regions.The gravity anomalies caused by the Moho were calculated by removing extra gravity effects layer by layer from the freeair gravity anomalies under the constraint of the submarine topography and sedimentary thickness data in this area.Inversion of these gravity anomalies using our proposed method shows that the method is able to delineate the relief of a V-shaped Moho under a subduction zone.The estimated depth of the Moho beneath the Challenger Deep ranges 18 km to 20 km,while the depth at the edge of the western Pacific Ocean is 8 km to 12 km,which,to some extent,suggests crustal complexity in the study area.Furthermore,a large inclination of the Pacific subduction slab is inferred from the locations of the maximum of the submarine topography and Moho depth in this area,indicating a relatively slow convergence between the Pacific and Philippine plates.
The V-shaped density interface is commonly seen such as the ocean trench,half-graben,and the Moho beneath a subduction zone.Delineating the relief of these V-shaped density interfaces is of significance in regional tectonic research,physical oceanography and oil and gas exploration.Among inversion methods of the density interface,the regularization approach,which applies prior information,can guarantee the inversion result to fit the known depth of the interface to be estimated.It can also control the shape of the interface via the model constraint function in the regularization item,making the inversion result agree with the real geologic feature.We have designed a model constraint function in the form of Lp-norm and then integrated it with the gravity data misfit function and the known depth constraint function to establish an objective function for V-shaped density interface inversion.Subsequently,we have derived the gradient of the objective functionand built the inversion process taking the nonlinear conjugate gradient algorithm as the core.The effect of our proposed inversion method is related to the value of p.The test results conducted with a two-dimensional simple model show that the method can be used to accurately estimate the V-shaped density interface relief when p=5,and the correctness of the proposed method is further confirmed by a two-dimensional V-shaped density interface with complex shape.The test results of a three-dimensional V-shaped density interface show that our proposed method is also appropriate for three-dimensional inversion.At the end of this article,the inversion method is tested with real gravity data of the Challenger Deep and adjacent regions.The gravity anomalies caused by the Moho were calculated by removing extra gravity effects layer by layer from the freeair gravity anomalies under the constraint of the submarine topography and sedimentary thickness data in this area.Inversion of these gravity anomalies using our proposed method shows that the method is able to delineate the relief of a V-shaped Moho under a subduction zone.The estimated depth of the Moho beneath the Challenger Deep ranges 18 km to 20 km,while the depth at the edge of the western Pacific Ocean is 8 km to 12 km,which,to some extent,suggests crustal complexity in the study area.Furthermore,a large inclination of the Pacific subduction slab is inferred from the locations of the maximum of the submarine topography and Moho depth in this area,indicating a relatively slow convergence between the Pacific and Philippine plates.
引文
Barbosa V C F,Silva J B C,Medeiros W E.1997.Gravity inversion of basement relief using approximate equality constraints on depths.Geophysics,62(6):1745-1757,doi:10.1190/1.1444275.
Barbosa V C F,Silva J B C,Medeiros W E.1999.Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth.Geophysics,64(5):1429-1437,doi:10.1190/1.1444647.
Bott M H P.1960.The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins.Geophys.J.Roy.Astr.Soc.,3(1):63-67,doi:10.1111/j.1365-246X.1960.tb00065.x.
Chakravarthi V,Sundararajan N.2004.Automatic 3-D gravity modeling of sedimentary basins with density contrast varying parabolically with depth.Comput.Geosci.,30(6):601-607,doi:10.1016/j.cageo.2004.03.014.
Chakravarthi V,Sundararajan N.2007a.INV2P5DSB-A code for gravity inversion of 2.5-D sedimentary basins using depth dependent density.Comput.Geosci.,33(4):449-456,doi:10.1016/j.cageo.2006.06.010.
Chakravarthi V,Sundararajan N.2007b.3Dgravity inversion of basement relief-A depth-dependent density approach.Geophysics,72(2):123-132,doi:10.1190/1.2431634.
Chakravarthi V,Kumar M P,Ramamma B,et al.2016.Automatic gravity modeling of sedimentary basins by means of polygonal source geometry and exponential density contrast variation:Two space domain based algorithms.J.Appl.Geophys.,124:54-61,doi:10.1016/j.jappgeo.2015.11.007.
Cordell L,Henderson R G.1968.Iterative three-dimensional solution of gravity anomaly data using a digital computer.Geophysics,33(4):596-601,doi:10.1190/1.1439955.
Ekblom H.1973.Calculation of linear best Lp-approximations.BITNumerical Mathematics,13(3):292-300,doi:10.1007/BF01951940.
Feng J,Meng X H,Chen Z X,et al.2014.The investigation and application of three-dimensional density interface.Chinese J.Geophys.(in Chinese),57(1):287-294,doi:10.6038/cjg20140124.
Feng R,Yan H F,Zhang R S.1986.The rapid inversion of 3-Dpotential field and program design.Acta Geologica Sinica(in Chinese),60(4):390-403.
Feng X L,Wang W Y,Liu F Q,et al.2014.2Dgravity inversion of basement relief of rift basin based on a dual interface model.Chinese J.Geophys.(in Chinese),57(6):1934-1945,doi:10.6038/cjg20140624.
Feng X L.2016.Study on the 3D gravity inversion of density interface relief in spatial domain[Ph.D.thesis](in Chinese).Xi′an:Chang′an University.
Fujioka K,Okino K,Kanamatsu T,et al.2002.Morphology and origin of the Challenger Deep in the Southern Mariana Trench.Geophys.Res.Lett.,29(10):1372,doi:10.1029/2001GL013595.
Gvirtzman Z,Stern R J.2004.Bathymetry of Mariana trench-arc system and formation of the Challenger Deep as a consequence of weak plate coupling.Tectonics,23(2):TC2011,doi:10.1029/2003TC001581.
Hall R.2002.Cenozoic geological and plate tectonic evolution of SEAsia and the SW Pacific:Computer-based reconstructions,model and animations.Journal of Asian Earth Sciences,20(4):353-431,doi:10.1016/S1367-9120(01)00069-4.
Hu L T,Hao T Y,Xing J,et al.2016.The Moho depth in the China Sea-West Pacific and its geological implications.Chinese J.Geophys.(in Chinese),59(3):871-883,doi:10.6038/cjg20160310.
Huber P J.1964.Robust estimation of a location parameter.Ann.Math.Stat.,35(1):73-101.
Le珘ao J W D,Menezes P T L,Beltr珘ao J F,et al.1996.Gravity inversion of basement relief constrained by the knowledge of depth at isolated points.Geophysics,61(6):1702-1714,doi:10.1190/1.1444088.
Lima W A,Martins C M,Silva J B C,et al.2011.Total variation regularization for depth-to-basement estimate:Part 2-Physicogeologic meaning and comparisons with previous inversion methods.Geophysics,76(1):113-120,doi:10.1190/1.3524547.
Lin Z M,Yang M.1985.A computer method for gravity interpretation of two-dimensional density contrast interface with some known depths.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),28(3):311-321.
Liu F L,Qu J.2013.Seafloor topography and bathymetric survey of the Challenger Deep of Mariana Trench.Marine Geology Frontiers(in Chinese),29(4):7-11,doi:10.16028/j.1009-2722.2013.04.009.
Liu X,Li S Z,Zhao S J,et al.2017.Structure of the Mariana subduction system.Earth Science Frontiers(in Chinese),24(4):329-340,doi:10.13745/j.esf.yx.2017-3-16.
Liu Y L,Zheng J C,Wu C Z.1987.Inversion of the three dimensional density discontinuity by use of a method of“compressed mass plane coefficient”based on the gravity data.Chinese J.Geophys.(in Chinese),30(2):186-196.
Luyendyk B P.1970.Dips of downgoing lithospheric plates beneath island arcs.Geological Society of America Bulletin,81(11):3411-3416,doi:10.1130/0016-7606(1970)81[3411:DODLPB]2.0.CO;2.
Martins C M,Barbosa V C F,Silva J B C.2010.Simultaneous 3Ddepth-to-basement and density-contrast estimates using gravity data and depth control at few points.Geophysics,75(3):121-128,doi:10.1190/1.3380225.
Martins C M,Lima W A,Barbosa V C F,et al.2011.Total variation regularization for depth-to-basement estimate:Part 1-Mathematical details and applications.Geophysics,76(1):I1-I12,doi:10.1190/1.3524286.
Nakanishi M,Hashimoto J.2011.A precise bathymetric map of the world′s deepest seafloor,Challenger Deep in the Mariana Trench.Mar.Geophys.Res.,32(4):455-463,doi:10.1007/s11001-011-9134-0.
Newman G A,Alumbaugh D L.2000.Three-dimensional magnetotelluric inversion using non-linear conjugate gradients.Geophys.J.Int.,140(2):410-424,doi:10.1046/j.1365-246x.2000.00007.x.
Oldenburg D W.1974.The inversion and interpretation of gravity anomalies.Geophysics,39(4):526-536,doi:10.1190/1.1440444.
Pallero J L G,Fernández-Martínez J L,Bonvalot S,et al.2015.Gravity inversion and uncertainty assessment of basement relief via particle swarm optimization.J.Appl.Geophys.,116:180-191,doi:10.1016/j.jappgeo.2015.03.008.
Pallero J L G,Fernández-Martínez J L,Bonvalot S,et al.2017.3Dgravity inversion and uncertainty assessment of basement relief via particle swarm optimization.J.Appl.Geophys.,139:338-350,doi:10.1016/j.jappgeo.2017.02.004.
Pilkington M,Crossley D J.1986.Determination of crustal interface topography from potential fields.Geophysics,51(6):1277-1284,doi:10.1190/1.1442180.
Polak E,Ribière G.1969.Note sur la convergence de méthodes de directions conjuguées.Revue Frans9aise d′Informatique et de Recherche Opérationnelle,16:35-43.
Prasanna H M I,Chen W,z H B.2013.High resolution local Moho determination using gravity inversion:A case study in Sri Lanka.Journal of Asian Earth Sciences,74:62-70,doi:10.1016/j.jseaes.2013.06.005.
Shin Y H,Choi K S,Xu H Z.2006.Three-dimensional forward and inverse models for gravity fields based on the Fast Fourier Transform.Comput.Geosci.,32(6):727-738,doi:10.1016/j.cageo.2005.10.002.
Silva J B C,Oliveira A S,Barbosa V C F.2010.Gravity inversion of 2Dbasement relief using entropic regularization.Geophysics,75(3):I29-I35,doi:10.1190/1.3374358.
Silva J B C,Santos D F,Gomes K P.2014.Fast gravity inversion of basement relief.Geophysics,79(5):G79-G91,doi:10.1190/geo2014-0024.1.
Smith W H F,Sandwell D T.1997.Global sea floor topography from satellite altimetry and ship depth soundings.Science,277(5334):1956-1962.
Sun J J,Li Y G.2014.Adaptive Lpinversion for simultaneous recovery of both blocky and smooth features in a geophysical model.Geophys.J.Int.,197(2):882-899,doi:10.1093/gji/ggu067.
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Barbosa V C F,Silva J B C,Medeiros W E.1999.Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth.Geophysics,64(5):1429-1437,doi:10.1190/1.1444647.
Bott M H P.1960.The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins.Geophys.J.Roy.Astr.Soc.,3(1):63-67,doi:10.1111/j.1365-246X.1960.tb00065.x.
Chakravarthi V,Sundararajan N.2004.Automatic 3-D gravity modeling of sedimentary basins with density contrast varying parabolically with depth.Comput.Geosci.,30(6):601-607,doi:10.1016/j.cageo.2004.03.014.
Chakravarthi V,Sundararajan N.2007a.INV2P5DSB-A code for gravity inversion of 2.5-D sedimentary basins using depth dependent density.Comput.Geosci.,33(4):449-456,doi:10.1016/j.cageo.2006.06.010.
Chakravarthi V,Sundararajan N.2007b.3Dgravity inversion of basement relief-A depth-dependent density approach.Geophysics,72(2):123-132,doi:10.1190/1.2431634.
Chakravarthi V,Kumar M P,Ramamma B,et al.2016.Automatic gravity modeling of sedimentary basins by means of polygonal source geometry and exponential density contrast variation:Two space domain based algorithms.J.Appl.Geophys.,124:54-61,doi:10.1016/j.jappgeo.2015.11.007.
Cordell L,Henderson R G.1968.Iterative three-dimensional solution of gravity anomaly data using a digital computer.Geophysics,33(4):596-601,doi:10.1190/1.1439955.
Ekblom H.1973.Calculation of linear best Lp-approximations.BITNumerical Mathematics,13(3):292-300,doi:10.1007/BF01951940.
Feng J,Meng X H,Chen Z X,et al.2014.The investigation and application of three-dimensional density interface.Chinese J.Geophys.(in Chinese),57(1):287-294,doi:10.6038/cjg20140124.
Feng R,Yan H F,Zhang R S.1986.The rapid inversion of 3-Dpotential field and program design.Acta Geologica Sinica(in Chinese),60(4):390-403.
Feng X L,Wang W Y,Liu F Q,et al.2014.2Dgravity inversion of basement relief of rift basin based on a dual interface model.Chinese J.Geophys.(in Chinese),57(6):1934-1945,doi:10.6038/cjg20140624.
Feng X L.2016.Study on the 3D gravity inversion of density interface relief in spatial domain[Ph.D.thesis](in Chinese).Xi′an:Chang′an University.
Fujioka K,Okino K,Kanamatsu T,et al.2002.Morphology and origin of the Challenger Deep in the Southern Mariana Trench.Geophys.Res.Lett.,29(10):1372,doi:10.1029/2001GL013595.
Gvirtzman Z,Stern R J.2004.Bathymetry of Mariana trench-arc system and formation of the Challenger Deep as a consequence of weak plate coupling.Tectonics,23(2):TC2011,doi:10.1029/2003TC001581.
Hall R.2002.Cenozoic geological and plate tectonic evolution of SEAsia and the SW Pacific:Computer-based reconstructions,model and animations.Journal of Asian Earth Sciences,20(4):353-431,doi:10.1016/S1367-9120(01)00069-4.
Hu L T,Hao T Y,Xing J,et al.2016.The Moho depth in the China Sea-West Pacific and its geological implications.Chinese J.Geophys.(in Chinese),59(3):871-883,doi:10.6038/cjg20160310.
Huber P J.1964.Robust estimation of a location parameter.Ann.Math.Stat.,35(1):73-101.
Le珘ao J W D,Menezes P T L,Beltr珘ao J F,et al.1996.Gravity inversion of basement relief constrained by the knowledge of depth at isolated points.Geophysics,61(6):1702-1714,doi:10.1190/1.1444088.
Lima W A,Martins C M,Silva J B C,et al.2011.Total variation regularization for depth-to-basement estimate:Part 2-Physicogeologic meaning and comparisons with previous inversion methods.Geophysics,76(1):113-120,doi:10.1190/1.3524547.
Lin Z M,Yang M.1985.A computer method for gravity interpretation of two-dimensional density contrast interface with some known depths.Chinese J.Geophys.(Acta Geophysica Sinica)(in Chinese),28(3):311-321.
Liu F L,Qu J.2013.Seafloor topography and bathymetric survey of the Challenger Deep of Mariana Trench.Marine Geology Frontiers(in Chinese),29(4):7-11,doi:10.16028/j.1009-2722.2013.04.009.
Liu X,Li S Z,Zhao S J,et al.2017.Structure of the Mariana subduction system.Earth Science Frontiers(in Chinese),24(4):329-340,doi:10.13745/j.esf.yx.2017-3-16.
Liu Y L,Zheng J C,Wu C Z.1987.Inversion of the three dimensional density discontinuity by use of a method of“compressed mass plane coefficient”based on the gravity data.Chinese J.Geophys.(in Chinese),30(2):186-196.
Luyendyk B P.1970.Dips of downgoing lithospheric plates beneath island arcs.Geological Society of America Bulletin,81(11):3411-3416,doi:10.1130/0016-7606(1970)81[3411:DODLPB]2.0.CO;2.
Martins C M,Barbosa V C F,Silva J B C.2010.Simultaneous 3Ddepth-to-basement and density-contrast estimates using gravity data and depth control at few points.Geophysics,75(3):121-128,doi:10.1190/1.3380225.
Martins C M,Lima W A,Barbosa V C F,et al.2011.Total variation regularization for depth-to-basement estimate:Part 1-Mathematical details and applications.Geophysics,76(1):I1-I12,doi:10.1190/1.3524286.
Nakanishi M,Hashimoto J.2011.A precise bathymetric map of the world′s deepest seafloor,Challenger Deep in the Mariana Trench.Mar.Geophys.Res.,32(4):455-463,doi:10.1007/s11001-011-9134-0.
Newman G A,Alumbaugh D L.2000.Three-dimensional magnetotelluric inversion using non-linear conjugate gradients.Geophys.J.Int.,140(2):410-424,doi:10.1046/j.1365-246x.2000.00007.x.
Oldenburg D W.1974.The inversion and interpretation of gravity anomalies.Geophysics,39(4):526-536,doi:10.1190/1.1440444.
Pallero J L G,Fernández-Martínez J L,Bonvalot S,et al.2015.Gravity inversion and uncertainty assessment of basement relief via particle swarm optimization.J.Appl.Geophys.,116:180-191,doi:10.1016/j.jappgeo.2015.03.008.
Pallero J L G,Fernández-Martínez J L,Bonvalot S,et al.2017.3Dgravity inversion and uncertainty assessment of basement relief via particle swarm optimization.J.Appl.Geophys.,139:338-350,doi:10.1016/j.jappgeo.2017.02.004.
Pilkington M,Crossley D J.1986.Determination of crustal interface topography from potential fields.Geophysics,51(6):1277-1284,doi:10.1190/1.1442180.
Polak E,Ribière G.1969.Note sur la convergence de méthodes de directions conjuguées.Revue Frans9aise d′Informatique et de Recherche Opérationnelle,16:35-43.
Prasanna H M I,Chen W,z H B.2013.High resolution local Moho determination using gravity inversion:A case study in Sri Lanka.Journal of Asian Earth Sciences,74:62-70,doi:10.1016/j.jseaes.2013.06.005.
Shin Y H,Choi K S,Xu H Z.2006.Three-dimensional forward and inverse models for gravity fields based on the Fast Fourier Transform.Comput.Geosci.,32(6):727-738,doi:10.1016/j.cageo.2005.10.002.
Silva J B C,Oliveira A S,Barbosa V C F.2010.Gravity inversion of 2Dbasement relief using entropic regularization.Geophysics,75(3):I29-I35,doi:10.1190/1.3374358.
Silva J B C,Santos D F,Gomes K P.2014.Fast gravity inversion of basement relief.Geophysics,79(5):G79-G91,doi:10.1190/geo2014-0024.1.
Smith W H F,Sandwell D T.1997.Global sea floor topography from satellite altimetry and ship depth soundings.Science,277(5334):1956-1962.
Sun J J,Li Y G.2014.Adaptive Lpinversion for simultaneous recovery of both blocky and smooth features in a geophysical model.Geophys.J.Int.,197(2):882-899,doi:10.1093/gji/ggu067.
Tikhonov A N,Arsenin V Y.1977.Solutions of Ill-Posed Problems.Washington DC:V.H.Winston&Sons.
Wang W Y,Pan Z S.1993.Fast solution of forward and inverse problems for gravity field in a dual interface model.Geophysical ProspectingforPetroleum(in Chinese),32(2):81-87.
Xing J,Hao T Y,Hu L T,et al.2016.Characteristics of the Japan and IBM subduction zones:Evidence from gravity and distribution of earthquake sources.Chinese J.Geophys.(in Chinese),59(1):116-140,doi:10.6038/cjg20160110.
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