基于重力梯度张量曲率的边界识别
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摘要
重力梯度张量曲率目前广泛用于重力数据的处理和解释中.为了拓宽重力梯度张量曲率的应用,本文回顾了重力梯度张量曲率的定义,从等位面的曲率定义出发,讨论了正确计算曲率的测量参考系及局部旋转的相关理论,并以单个球体和棱柱体为例来说明曲率的正确计算方式.然后,在正确计算重力梯度张量曲率的基础上,将重力梯度张量曲率应用到重力数据的边界识别中,通过理论模型和实际数据详细分析和比较了各种曲率在重力边界识别中的应用效果.结果表明:基于等位面的局部旋转坐标系是各种曲率正确计算的先决条件,纠正了曲率计算的误区;在边界识别中,局部坐标系下所计算的高斯曲率进行边界识别能够较好的圈定地下地质体的边界.
Recently,the curvature of gravity gradient tensors is widely used in processing and interpretation of gravity data.In order to extend the application of this parameter,the local reference system based on the related theory of local rotation is discussed for the correct calculation of curvature using gravity vectors and gradient tensors.And a single sphere and prism as an example is taken to illustrate the correctness of this theory.Then,the correctly calculatedcurvature of gravity gradient tensors is applied to the edge detection of gravity data.Finally,using the synthetic models and real data,the application effect of various curvatures in edge detection was analyzed and discussed.The results show that the local rotation coordinate system based on the equipotential surface is a prerequisite for correct calculation of various curvatures,which corrects the misunderstanding in the calculation of the curvature.In the edge detection,the Gauss curvature calculated in the local coordinate system can better delineate the edge of the underground geological body.
Recently,the curvature of gravity gradient tensors is widely used in processing and interpretation of gravity data.In order to extend the application of this parameter,the local reference system based on the related theory of local rotation is discussed for the correct calculation of curvature using gravity vectors and gradient tensors.And a single sphere and prism as an example is taken to illustrate the correctness of this theory.Then,the correctly calculatedcurvature of gravity gradient tensors is applied to the edge detection of gravity data.Finally,using the synthetic models and real data,the application effect of various curvatures in edge detection was analyzed and discussed.The results show that the local rotation coordinate system based on the equipotential surface is a prerequisite for correct calculation of various curvatures,which corrects the misunderstanding in the calculation of the curvature.In the edge detection,the Gauss curvature calculated in the local coordinate system can better delineate the edge of the underground geological body.
引文
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Cevallos C.2014.Automatic generation of 3Dgeophysical models using curvatures derived from airborne gravity gradient data.Geophysics,79(5):G49-G58.
Cevallos C.2016.Interpreting the direction of the gravity gradient tensor eigenvectors:Their relation to curvature parameters of the gravity field.Geophysics,81(3):G49-G57.
Cevallos C,Kovac P,Lowe S J.2013.Application of curvatures to airborne gravity gradient data in oil exploration.Geophysics,78(4):G81-G88.
Chen C J,Ren Z Y,Pan K J,et al.2018.Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders.Geophysical Journal International,214(3):2115-2132.
Chowdhury P R,Cevallos C.2013.Geometric shapes derived from airborne gravity gradiometry data:New tools for the explorationist.The Leading Edge,32(12):1468-1474.
Dai W M,Huang D N,Li T L,et al.2018.The edge detection method and its application in the south China sea based on the gravity gradient structure tensor eigenvalue.Chinese Journal of Geophysics(in Chinese),61(6):2494-2507,doi:10.6038/cjg2018M0018.
Lee M,Morris W,Leblanc G,et al.2013.Curvature analysis to differentiate magnetic sources for geologic mapping.Geophysical Prospecting,61(S1):572-585.
Li J,Zhang X,Gong J Z,et al.2018.Signal-noise identification of magnetotelluric signals using fractal-entropy and clustering algorithm for targeted de-noising.Fractals,26(2):1840011.
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric signalnoise identification and separation based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007.
Li X.2015.Curvature of a geometric surface and curvature of gravity and magnetic anomalies.Geophysics,80(1):G15-G26.
Li Y G.2018.Understanding curvatures of the equipotential surface in gravity gradiometry.Geophysics,83(4):G35-G45.
Ning J S,Luo Z C,Chao D B.1996.The present situation on satellite gravity gradiometry and its vistas in the application of physical geodesy.Journal of Wuhan Technical University of Surveying and Mapping(in Chinese),21(4):309-314.
Pedersen L B,Rasmussen T M.1990.The gradient tensor of potential field anomalies;Some implications on data collection and data processing of maps.Geophysics,55(12):1558-1566.
Peng J Y.2016.Gravity anomaly derivative identification configuration application in Qiong Dongnan basin[Master′s thesis](in Chinese).Chengdu:Chengdu University of Technology.
Phillips J D,Hansen R O,Blakely R J.2007.The use of curvature in potential-field interpretation.Exploration Geophysics,38(2):111-119.
Qiao Z K.2017.The study on joint inversion of gravity and gravity gradient data and its application in Vinton Dome area[Master′s thesis](in Chinese).Changchun:Jilin University.
Ren Z Y,Chen C J,Pan K J,et al.2017a.Gravity anomalies of arbitrary 3Dpolyhedral bodies with horizontal and vertical mass contrasts.Surveys in Geophysics,38(2):479-502.
Ren Z Y,Tang J T,Kalscheuer T,et al.2017b.Fast 3-D largescale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method.Journal of Geophysical Research:Solid Earth,122(1):79-109.
Ren Z Y,Zhong Y Y,Chen C J,et al.2018.Gravity anomalies of arbitrary 3Dpolyhedral bodies with horizontal and vertical mass contrasts up to cubic order.Geophysics,83(1):G1-G13.
Slotnick M M.1932.Curvature of equipotential surfaces.AAPGBulletin,16(12):1250-1259.
Tang J T,Hu S G,Ren Z Y,et al.2017.Analytical formulas for underwater and aerial object localization by gravitational field and gravitational gradient tensor.IEEE Geoscience and Remote Sensing Letters,14(9):1557-1560.
Tang J T,Hu S G,Ren Z Y,et al.2018.Localization of multiple underwater objects with gravity field and gravity gradient tensor.IEEE Geoscience and Remote Sensing Letters,15(2):247-251.
Wang J,Meng X H,Li F.2015.Improved curvature gravity gradient tensor with principal component analysis and its application in edge detection of gravity data.Journal of Applied Geophysics,118:106-114.
Zhou W N,Du X J,Li J Y.2013.The limitation of curvature gravity gradient tensor for edge detection and a method for overcoming it.Journal of Applied Geophysics,98:237-242.
戴伟铭,黄大年,李桐林等.2018.基于重力梯度结构张量特征值斜导数边界识别方法及其在南海的应用.地球物理学报,61(6):2494-2507,doi:10.6038/cjg2018M0018.
宁津生,罗志才,晁定波.1996.卫星重力梯度测量的研究现状及其在物理大地测量中的应用前景.武汉测绘科技大学学报,21(4):309-314.
彭江英.2016.重力异常导数在琼东南盆地构造识别中的应用[硕士论文].成都:成都理工大学.
乔中坤.2017.重力及张量数据联合反演研究及在Vinton Dome地区的应用[硕士论文].长春:吉林大学.
Blakely R J.1995.Potential Theory in Gravity and Magnetic Applications.Cambridge:Cambridge University Press.
Cevallos C.2014.Automatic generation of 3Dgeophysical models using curvatures derived from airborne gravity gradient data.Geophysics,79(5):G49-G58.
Cevallos C.2016.Interpreting the direction of the gravity gradient tensor eigenvectors:Their relation to curvature parameters of the gravity field.Geophysics,81(3):G49-G57.
Cevallos C,Kovac P,Lowe S J.2013.Application of curvatures to airborne gravity gradient data in oil exploration.Geophysics,78(4):G81-G88.
Chen C J,Ren Z Y,Pan K J,et al.2018.Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders.Geophysical Journal International,214(3):2115-2132.
Chowdhury P R,Cevallos C.2013.Geometric shapes derived from airborne gravity gradiometry data:New tools for the explorationist.The Leading Edge,32(12):1468-1474.
Dai W M,Huang D N,Li T L,et al.2018.The edge detection method and its application in the south China sea based on the gravity gradient structure tensor eigenvalue.Chinese Journal of Geophysics(in Chinese),61(6):2494-2507,doi:10.6038/cjg2018M0018.
Lee M,Morris W,Leblanc G,et al.2013.Curvature analysis to differentiate magnetic sources for geologic mapping.Geophysical Prospecting,61(S1):572-585.
Li J,Zhang X,Gong J Z,et al.2018.Signal-noise identification of magnetotelluric signals using fractal-entropy and clustering algorithm for targeted de-noising.Fractals,26(2):1840011.
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric signalnoise identification and separation based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007.
Li X.2015.Curvature of a geometric surface and curvature of gravity and magnetic anomalies.Geophysics,80(1):G15-G26.
Li Y G.2018.Understanding curvatures of the equipotential surface in gravity gradiometry.Geophysics,83(4):G35-G45.
Ning J S,Luo Z C,Chao D B.1996.The present situation on satellite gravity gradiometry and its vistas in the application of physical geodesy.Journal of Wuhan Technical University of Surveying and Mapping(in Chinese),21(4):309-314.
Pedersen L B,Rasmussen T M.1990.The gradient tensor of potential field anomalies;Some implications on data collection and data processing of maps.Geophysics,55(12):1558-1566.
Peng J Y.2016.Gravity anomaly derivative identification configuration application in Qiong Dongnan basin[Master′s thesis](in Chinese).Chengdu:Chengdu University of Technology.
Phillips J D,Hansen R O,Blakely R J.2007.The use of curvature in potential-field interpretation.Exploration Geophysics,38(2):111-119.
Qiao Z K.2017.The study on joint inversion of gravity and gravity gradient data and its application in Vinton Dome area[Master′s thesis](in Chinese).Changchun:Jilin University.
Ren Z Y,Chen C J,Pan K J,et al.2017a.Gravity anomalies of arbitrary 3Dpolyhedral bodies with horizontal and vertical mass contrasts.Surveys in Geophysics,38(2):479-502.
Ren Z Y,Tang J T,Kalscheuer T,et al.2017b.Fast 3-D largescale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method.Journal of Geophysical Research:Solid Earth,122(1):79-109.
Ren Z Y,Zhong Y Y,Chen C J,et al.2018.Gravity anomalies of arbitrary 3Dpolyhedral bodies with horizontal and vertical mass contrasts up to cubic order.Geophysics,83(1):G1-G13.
Slotnick M M.1932.Curvature of equipotential surfaces.AAPGBulletin,16(12):1250-1259.
Tang J T,Hu S G,Ren Z Y,et al.2017.Analytical formulas for underwater and aerial object localization by gravitational field and gravitational gradient tensor.IEEE Geoscience and Remote Sensing Letters,14(9):1557-1560.
Tang J T,Hu S G,Ren Z Y,et al.2018.Localization of multiple underwater objects with gravity field and gravity gradient tensor.IEEE Geoscience and Remote Sensing Letters,15(2):247-251.
Wang J,Meng X H,Li F.2015.Improved curvature gravity gradient tensor with principal component analysis and its application in edge detection of gravity data.Journal of Applied Geophysics,118:106-114.
Zhou W N,Du X J,Li J Y.2013.The limitation of curvature gravity gradient tensor for edge detection and a method for overcoming it.Journal of Applied Geophysics,98:237-242.
戴伟铭,黄大年,李桐林等.2018.基于重力梯度结构张量特征值斜导数边界识别方法及其在南海的应用.地球物理学报,61(6):2494-2507,doi:10.6038/cjg2018M0018.
宁津生,罗志才,晁定波.1996.卫星重力梯度测量的研究现状及其在物理大地测量中的应用前景.武汉测绘科技大学学报,21(4):309-314.
彭江英.2016.重力异常导数在琼东南盆地构造识别中的应用[硕士论文].成都:成都理工大学.
乔中坤.2017.重力及张量数据联合反演研究及在Vinton Dome地区的应用[硕士论文].长春:吉林大学.
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