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物探与化探  2020, Vol. 44 Issue (5): 1161-1171    DOI: 10.11720/wtyht.2020.0067
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
球坐标系密度界面反演方法及在华南大陆的应用
王祥1,2(), 郭良辉1
1.中国地质大学(北京) 地球物理与信息技术学院,北京 100083
2.中国地质调查局 昆明自然资源综合调查中心,云南 昆明 650000
Density interface inversion method in spherical coordinates and its application in the South China mainland
WANG Xiang1,2(), GUO Liang-Hui1
1.School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 100083, China
2.Kunming Natural Resources Comprehensive Survey Center of China Geological Survey, Kunming 650000, China
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摘要 

密度界面反演方法在油气勘探、推断区域构造、获取地壳结晶基底面、莫霍面起伏形态等方面具有重要意义。现有的密度界面反演方法大多基于笛卡尔坐标系统,当涉及到大区域乃至全球尺度的密度界面反演时,地球曲率的影响将不可忽视,需考虑基于球坐标系Tesseroid模型的密度界面反演方法。然而,受计算精度和效率制约,已有的基于Tesseroid模型的密度界面反演方法并不能很好地适用于地表重力观测数据的反演计算。笔者基于前人研究,给出了一种适用于地表观测数据的球坐标系密度界面反演方法。该方法首先将常规的球坐标系高斯—勒让德重力积分公式进行简化,提高了重力正演计算效率。随后,引入并改进了前人的自适应剖分方案,提高了重力正演计算精度。在此基础上,采用Cordell迭代优化算法,得到了适用于地表观测数据的球坐标系密度界面反演方法。通过模型数据试验,对本文球坐标系密度界面反演方法进行了验证。结果表明,笔者对高斯—勒让德积分公式加以改进和引入改进的自适应剖分方案后,很好地克服了计算精度和效率对地表观测重力计算的掣肘,并且,基于球坐标系的密度界面反演结果优于基于笛卡尔坐标系的密度界面反演结果。在华南大陆实际数据试验中,利用文中方法得到的华南大陆的莫霍面深度与前人得到的莫霍面深度具有较高的吻合度,莫霍面自西向东逐渐抬升,西部抬升剧烈,东部抬升平缓,沿武陵山—贵桂交界一带呈现明显的NNE向莫霍面梯级带,验证了文中方法的科学有效性。

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王祥
郭良辉
关键词 重力球坐标系密度界面反演Tesseroid华南大陆    
Abstract

The density interface inversion method has been playing an important role in the oil and gas exploration, regional structure inference studies as well as crustal crystal basement surface and Moho undulations researches. Most of the density interface inversion methods are generally based on the Cartesian coordinate system. When large regional or even global scale data are dealt with, the influence of earth curvature cannot be ignored, and the density interface inversion method based on Tesseroid model of spherical coordinate system needs to be considered. However, due to the limitations of calculation accuracy and efficiency, the existing density interface inversion method based on Tesseroid cannot be well applicable to the surface gravity observation data. In this paper, on the basis of previous studies, a density interface inversion method of spherical coordinate system suitable for surface observation data is proposed. Firstly, the gravity Gauss-Legendre integral formula in the spherical coordinate system is simplified to improve the forward calculation efficiency. Then, an optimized adaptive subdivision algorithm is introduced to enhance the calculation accuracy. According to the previous forward calculation and by using Cordell iterative optimization algorithm, the authors propose a density interface inversion method for the surface observation data in the spherical coordinate system. The proposed inversion method in this paper can be verified through the synthetic data test. The inversion results show that the proposed method can overcome the limitation of calculating precision and efficiency of the surface observation data. In addition, the inversion results based on spherical coordinate system are better than those based on cartesian coordinate system. Finally, tests on real data from South China mainland verify the feasibility of the presented methods. The results show that Moho depth rises gradually from the west to the east, with the western part uplifting dramatically and the eastern part uplifting gently. Between Wuling Mountain and Guizhou-Guangxi border, there is an obvious NNE-Moho step.

Key wordsgravity    spherical coordinate system    density interface inversion method    Tesseroid    South China mainland
收稿日期: 2020-02-17      出版日期: 2020-10-26
ZTFLH:  P631  
基金资助:国家自然科学基金面上项目(41774098)
作者简介: 王祥(1991-),男,中国地质调查局昆明自然资源综合调查中心助理工程师,主要研究方向为重磁数据处理和反演算法。Email: real_shuan_wang@163.com
引用本文:   
王祥, 郭良辉. 球坐标系密度界面反演方法及在华南大陆的应用[J]. 物探与化探, 2020, 44(5): 1161-1171.
WANG Xiang, GUO Liang-Hui. Density interface inversion method in spherical coordinates and its application in the South China mainland. Geophysical and Geochemical Exploration, 2020, 44(5): 1161-1171.
链接本文:  
http://www.wutanyuhuatan.com/CN/10.11720/wtyht.2020.0067      或      http://www.wutanyuhuatan.com/CN/Y2020/V44/I5/1161
Fig.1  Tesseroid单元体空间几何示意
Fig.2  Tesseroid单元体网格剖分示意
a—常规剖分的网格边长大小平均,LφLλ为Tesseroid单元体上表面纬度和经度方向上边长;b—自适应剖分方案的剖分采用的是在观测点近距离处小网格剖分,远距离处采用大网格剖分
Fig.3  正演计算模型剖面示意
Fig.4  Cordell迭代算法流程
Fig.5  球壳体模型示意
a—球壳内视;b—球壳侧视
Fig.6  不同网格大小下Taylor和2D-GLQ在不同观测高度处的重力异常计算值与理论异常值的对比
a—1°×1°;b—30'×30';c—15'×15';d—3'×3'
Fig.7  本文方法效率提升试验
a—,不同取值时,Er的十进对数值;b—不同的Er取值,时间耗费比例值T1/T2
Fig.8  理论模型正演
a—密度界面模型深度分布图;b—GQL-Plus计算的重力异常
Fig.9  各方法的理论模型反演对比试验
a—笛卡尔坐标系反演结果;b—基于二阶泰勒级数法正演的反演结果;c—基于本文2D-GLQ正演方法的反演结果;d、e、f—为图(a)、(b)、(c)反演结果与理论模型深度的平面差值;g—图(a)、(b)、(c)对角剖面与理论深度值对比;h—深度RMS随迭代次数的走势图;i—布格异常RMS随迭代次数的走势图
Fig.10  华南大陆实测数据试验
a—华南大陆重力异常滤波前异常;b—华南大陆重力异常低通滤波后区域异常;c—本文得到的华南大陆莫霍面;d—反演迭代收敛曲线;e—华南大陆莫霍面[39];f—c与e的莫霍面深度差值
[1] 孙德梅, 闵志. 三维密度界面反演的一个近似方法[J]. 物探与化探, 1984,8(2):89-98.
[1] Sun D M, Min Z. A technique for approximate inversion of three-dimensional density interface[J]. Geophysical and Geochemical Exploration, 1984,8(2):89-98.
[2] Cordell L, Henderson R G. Iterative three-dimensional solution of gravity anomaly data using a digital computer[J]. Geophysics, 1968,33(4):596-601.
doi: 10.1190/1.1439955
[3] Silva J B C. Interactive gravity inversion[J]. Geophysics, 2006: 1-9.
[4] Zhou X. Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction method[J]. Geophysical Prospecting, 2013,61(1):220-234.
doi: 10.1111/j.1365-2478.2011.01046.x
[5] Silva J B C, Santos D F, Gomes K P. Fast gravity inversion of basement relief[J]. Geophysics, 2014,79(5):79-91.
[6] 刘元龙, 王谦身. 用压缩质面法反演重力资料以估算地壳构造[J]. 地球物理学报, 1977,20(1):59-69.
[6] Liu Y L, Wang Q S. Inversion of gravity data by use of a method of “compressed mass plane” to estimate crustal structure[J]. Chinese J. Geophys. , 1977,20(1):59-69.
[7] 江为为, 周立宏, 肖敦清, 等. 东北地区重磁场与地壳结构特征[J]. 地球物理学进展, 2006,21(3):730-738.
[7] Jiang W W, Zhou L H, Xiao D Q, et al. The characteristics of crust structure and the gravity and magnetic fields in northeast region of China[J]. Progress in Geophysics, 2006,21(3):730-738.
[8] 胡立天, 郝天珧. 带控制点的三维密度界面反演方法[J]. 地球物理学进展, 2014,29(6):2498-2503.
doi: 10.6038/pg20140603
[8] Hu L T, Hao T Y. The inversion of three-dimensional density interface with control points[J]. Progress in Geophysics, 2014,29(6):2498-2503.
doi: 10.6038/pg20140603
[9] Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters[J]. Journal of the Society for Industrial and Applied Mathematics, 1963,11(2):431-441.
doi: 10.1137/0111030
[10] Chakravarthi V, Sastry S R. GUI based inversion code for automatic quantification of strike limited listric fault sources and regional gravity background from observed bouguer gravity anomalies[J]. Journal Geological Society of India, 2014,83:625-638.
[11] Mojica O F, Bassrei A. Regularization parameter selection in the 3D gravity inversion of the basement relief using GCV: A parallel approach[J]. Computers and Geosciences, 2015,82:205-213.
doi: 10.1016/j.cageo.2015.06.013
[12] 关小平. 利用Parker公式反演界面的一种有效方法[J]. 物探化探计算技术, 1991,13(3):236-242.
[12] Guan X P. An effective and simple approach of subsurface inversion using Parker’s equation[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1991,13(3):236-242.
[13] Parker R L. The rapid calculation of potential anomalies[J]. Geophysical Journal Royal Astronomical Society, 1972,37(3):447-455.
doi: 10.1111/j.1365-246X.1974.tb04096.x
[14] Oldenburg D W. The inversion and interpretation of gravity anomalies[J]. Geophysics, 1974,39:526-536.
doi: 10.1190/1.1440444
[15] Granser H. Three-dimensional interpretation of gravity data from sedimentary basins using an exponential density-depth function[J]. Geophysical Prospecting, 1987,35(9):1030-1041.
[16] Guspi F. Noniterative nonlinear gravity inversion[J]. Geophysics, 1993,58(7):935-940.
doi: 10.1190/1.1443484
[17] Santos D F, Silva J B C, Martins C M, et al. Efficient gravity inversion of discontinuous basement relief[J]. Geophysics, 2015,80(4):95-106.
[18] Shi L, Li Y H, Zhang E H. A new approach for density contrast interface inversion based on the parabolic density function in the frequency domain[J]. Journal of Applied Geophysics, 2015,116:1-9.
doi: 10.1016/j.jappgeo.2015.02.022
[19] Asgharzadeh M F, Von Frese R R B, Kim H R, et al. Spherical prism gravity effects by Gauss-Legendre quadrature integration[J]. Geophys. J. Int, 2007,169:1-11.
doi: 10.1111/gji.2007.169.issue-1
[20] Heck B, Seitz K. A comparison of the Tesseroid prism and pointmass approaches for mass reductions in gravity field modelling[J]. J. Geod., 2007,81(2):121-136.
doi: 10.1007/s00190-006-0094-0
[21] Roussel C, Verdun J, Cali J, et al. Complete gravity field of an ellipsoidal prism by Gauss-Legendre quadrature[J]. Geophys. J. Int., 2015,203:2220-2236.
doi: 10.1093/gji/ggv438
[22] Uieda L, Barbosa V C F, Braitenberg C. Tesseroids: Forward-modeling gravitational fields in spherical coordinates[J]. Geophysics, 2016: 41-48.
[23] Uieda L, Barbosa V C F. Fast nonlinear gravity inversion in spherical coordinates with application to the South American Moho[J]. Geophys. J. Int., 2017,208:162-176.
doi: 10.1093/gji/ggw390
[24] Anderson E G. The effect of topography on solutions of stokes' problem[M]. School of Surveying, University of New South Wales, Kensington, NSW, Australia, 1976.
[25] Liang Q, Chen C, Li Y. 3-Dinversion of gravity data in spherical coordinates with application to the GRAIL data[J]. J. Geophys. Res. Planets, 2014,119:1359-1373.
doi: 10.1002/2014JE004626
[26] Zhang Y, Wu Y L, Yan J G, et al. 3D inversion of full gravity gradient tensor data in spherical coordinate system using local north oriented frame[J]. Earth, Planets and Space, 2018,70(58):1-23.
doi: 10.1186/s40623-017-0766-4
[27] 梁青. 月球重力异常特征与三维密度成像研究:[D]. 武汉:中国地质大学(武汉), 2010.
[27] Liang Q. Gravity anomaly features and 3D density imaging of the moon: [D]. Wuhan:China University of Geosciences (Wuhan), 2010.
[28] Wild-Pfeiffer F. A comparison of different mass elements for use in gravity gradiometry[J]. J Geod., 2008,82:637-653.
doi: 10.1007/s00190-008-0219-8
[29] Grombein T, Seitz K, Heck B. Optimized formulas for the gravitational field of a Tesseroid[J]. J. Geodesy, 2013,87:645-660.
doi: 10.1007/s00190-013-0636-1
[30] Shen W B, Deng X L. Evaluation of the fourth-order tesseroid formula and new combination approach to precisely determine gravitational potential[J]. Stud. Geophys. Geod, 2016,60:1. (DOI: 10.1007/s11200-016-0402-y).
doi: 10.1007/s11200-015-0818-9
[31] Guo L H, Shi L, Meng X H, et al. Apparent magnetization mapping in the presence of strong remanent magnetization: The space-domain inversion approach[J]. Geophysics, 2015,81(2):J11-J24.
doi: 10.1190/geo2015-0082.1
[32] Li Z, Hao T, Xu Y, et al. An efficient and adaptive approach for modeling gravity effects in spherical coordinates[J]. Journal of Applied Geophysics, 2011,73(3):221-231.
doi: 10.1016/j.jappgeo.2011.01.004
[33] Bott M H P. The use of rapid digital computing methods for direct gravity interpretation of sedimentary basin[J]. Geophysical Journal Royal Astronomical Society, 1960,3:63-67.
doi: 10.1111/gji.1960.3.issue-1
[34] Heiskanen W A, Moritz H. Physical geodesy[M]. San Francisco:Freeman, 1967.
[35] Vaníček P, Novák P, Martinec Z. Geoid, topography, and the Bouguer plate or shell[J]. J. Geodesy, 2001,75:210-215.
doi: 10.1007/s001900100165
[36] Karcol R. Gravitational attraction and potential of spherical shell with radially dependent density[J]. Stud. Geophys. Geod., 2011,55:21-34.
doi: 10.1007/s11200-011-0002-9
[37] 舒良树. 华南构造演化的基本特征[J]. 地质通报, 2012,31(7):1035-1053.
[37] Shu L S. An analysis of principal features of tectonic evolution in South China Block[J]. Geological Bulletin of China, 2012,31(7):1035-1053.
[38] 张国伟, 郭安林, 王岳军, 等. 中国华南大陆构造与问题[J]. 中国科学:地球科学, 2013,43(10):1553-1582.
[38] Zhang G W, Guo A L, Wang Y J, et al. Tectonics of South China continent and its implications[J]. Science China: Earth Sciences, 2013,43(10):1553-1582.
[39] 郭良辉, 孟小红, 石磊, 等. 优化滤波方法及其在中国大陆布格重力异常数据处理中的应用[J]. 地球物理学报, 2012,55(12):4078-4088.
doi: 10.6038/j.issn.0001-5733.2012.12.020
[39] Guo L H, Meng X H, Shi L, et al. Preferential filtering method and its application to Bouguer gravity anomaly of Chinese continent[J]. Chinese J. Geophys. , 2012,55(12):4078-4088.
[40] Hilde T W C, Uyeda S, Kroenke L. Evolution of the western Pacific and its margin[J]. Tectonophysics, 1977,38:145-165.
doi: 10.1016/0040-1951(77)90205-0
[41] Smith A D. A plate model for Jurassic to recent intraplate volcanism in the Pacific Ocean basin[G]// Foulger G R, Jurdy D M. Plates, plumes, and planetary processes. Geol Soc Am (Spec Papers), 2007,430:471-495.
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