Gravity data inversion using high-order polynomial function of density contrast varying with depth
LIU Jie1, ZHANG Jianzhong1,2, JIANG Li1, WAN Li1, HU Jiashan3
1. Key Laboratory of Submarine Geosciences and Prospecting Techniques, Ministry of Education, College of Marine Geosciences, Ocean University of China, Qingdao, Shandong 266100, China; 2. Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266061, China; 3. Research Institute of Exploration and Production, Shengli Oilfield Branch Co., SINOPEC, Dongying, Shandong 257015, China
Abstract：The gravity inversion is one of the geophysical means for depicting the spatial distribution of mass bodies with density contrast.Conventional inversion methods directly invert density contrast values of each cell through both horizontal and vertical meshes.In this paper, complex density variations are approximated by polynomial functions, and a new method is proposed to determine density contrasts by inverting the coefficients of polynomial density functions.Different from the conventional inversion methods, this method can invert complex density contrasts without partitioning vertically cells.To some extent, it eases the contradiction between the quantity of mesh, memory occupancy, and inversion precision.Theoretical model tests show that polynomial coefficient inversion combined with multiple constraints can clearly highlight the position, scale and boundary information of local masses, and is superior to the conventional L2-norm inversion results.This proposed method is successfully applied to the identification of buried hills and sags in the Jiyang Depression.The boundaries of different lithologic bodies are roughly determined by density contrasts inverted, which makes up the gap of buried hill distributions showing on seismic sections.
刘洁, 张建中, 江丽, 万丽, 胡加山. 基于高阶多项式密度函数的重力反演[J]. 石油地球物理勘探, 2019, 54(3): 700-708.
LIU Jie, ZHANG Jianzhong, JIANG Li, WAN Li, HU Jiashan. Gravity data inversion using high-order polynomial function of density contrast varying with depth. Oil Geophysical Prospecting, 2019, 54(3): 700-708.
张建中.解重力反问题的边界元法[J].石油地球物理勘探, 1993, 28(5):603-613.ZHANG Jianzhong.Boundary element method for gravity inversion[J].Oil Geophysical Prospecting, 1993, 28(5):603-613.
[2]
谷文彬, 陈清礼, 王余泉, 等.饶阳凹陷虎8北潜山重力三维松约束反演[J].石油地球物理勘探, 2016, 51(6):1219-1226.GU Wenbin, CHEN Qingli, WANG Yuquan, et al.Part-constrained 3D gravity inversion for the Hubabei buried hill in Raoyang Sag[J].Oil Geophysical Prospecting, 2016, 51(6):1219-1226.
[3]
林宝泽, 肖锋, 王明常.二维重力数据径向反演及应用[J].石油地球物理勘探, 2018, 53(2):403-409.LIN Baoze, XIAO Feng, WANG Mingchang.2D gra-vity data radial inversion[J].Oil Geophysical Prospecting, 2018, 53(2):403-409.
[4]
张建中, 戴云, 钟本善.下辽河裂谷型断陷盆地基底的重力解释方法[J].物探化探计算技术, 1999, 21(3):252-256.ZHANG Jianzhong, DAI Yun, ZHONG Benshan.Gravitational method for determining the basement of Liaohe rifted basin[J].Computing Techniques for Geophysical & Geochemical Exploration, 1999, 21(3):252-256.
[5]
耿美霞, 杨庆节.应用RBF神经网络反演二维重力密度分布[J].石油地球物理勘探, 2013, 48(4):651-657.GENG Meixia, YANG Qingjie.2-D density inversion with the RBF neural network method[J].Oil Geophysical Prospecting, 2013, 48(4):651-657.
[6]
舒梦珵, 王彦飞.储层重力密度反演后验约束正则化方法[J].地球物理学报, 2015, 58(6):2079-2086.SHU Mengcheng, WANG Yanfei.The posterior constrained regularization method for reservoir density inversion[J].Chinese Journal of Geophysics, 2015, 58(6):2079-2086.
[7]
Li Y G, Oldenburg D W.3-D inversion of gravity data[J].Geophysics, 1998, 63(1):109-119.
[8]
Portniaguine O, Zhdanov M S.Focusing geophysical inversion images[J].Geophysics, 1999, 64(3):874-887.
[9]
Commer M.Three-dimensional gravity modelling and focusing inversion using rectangular meshes[J].Geophysical Prospecting, 2011, 59(5):966-979.
[10]
姚长利, 郝天珧, 管志宁, 等.重磁遗传算法三维反演中高速计算及有效存储方法技术[J].地球物理学报, 2003, 46(2), 252-258.YAO Changli, HAO Tianyao, GUAN Zhining, et al.High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms[J].Chinese Journal of Geophysics, 2003, 46(2):252-258.
[11]
姚长利, 郑元满, 张聿文.重磁异常三维物性反演随机子域法方法技术[J].地球物理学报, 2007, 50(5):1576-1583.YAO Changli, ZHENG Yuanman, ZHANG Yuwen.3-D gravity and magnetic inversion for physical properties using stochastic subspaces[J].Chinese Journal of Geo-physics, 2007, 50(5):1576-1583.
[12]
Chai Y, Hinze W J.Gravity inversion of an interface above which the density contrast varies exponentially with depth[J].Geophysics, 1988, 53(6):837-845.
[13]
Chakravarthi V, Sundararajan N.Ridge-regression algorithm for gravity inversion of fault structures with variable density[J].Geophysics, 2004, 69(6):1394-1404.
[14]
Chappell A, Kusznir N.An algorithm to calculate the gravity anomaly of sedimentary basins with exponential density-depth relationships[J].Geophysical Prospecting, 2008, 56(2):249-258.
[15]
张盛, 孟小红.约束变密度界面反演方法[J].地球物理学进展, 2013, 28(4):1714-1720.ZHANG Sheng, MENG Xiaohong.Constraint interface inversion with variable density model[J].Progress in Geophysics, 2013, 28(4):1714-1720.
[16]
商宇航, 邰振华, 秦涛.基于双曲线密度模型的频率域界面反演[J].石油地球物理勘探, 2018, 53(4):858-864.SHANG Yuhang, TAI Zhenhua, QIN Tao.Interface inversion in the frequency domain based on the hyper-bolic density model[J].Oil Geophysical Prospecting, 2018, 53(4):858-864.
[17]
Zhang J Z, Zhong B S, Zhou X X, et al.Gravity ano-malies of 2-D bodies with variable density contrast[J].Geophysics, 2001, 66(3):809-813.
[18]
Zhou X.Analytic solution of the gravity anomaly of irregular 2D masses with density contrast varying as a 2D polynomial function[J].Geophysics, 2010, 75(2):I11-I19.
[19]
Jiang L, Zhang J Z, Feng Z B.A versatile solution for the gravity anomaly of 3D prism-meshed bodies with depth-dependent density contrast[J].Geophysics, 2017, 82(4):G77-G86.
[20]
Zhang J Z, Jiang L.Analytical expressions for the gravitational vector field of a 3-D rectangular prism with density varying as an arbitrary-order polynomial function[J].Geophysical Journal International, 2017, 210(2):1176-1190.
[21]
Jiang L, Liu J, Zhang J Z, et al.Analytic expressions for the gravity gradient tensor of 3D prisms with depth-dependent density[J].Surveys in Geophysics, 2018, 39(3):337-363.
[22]
张建中, 周熙襄, 王克斌.密度随深度变化的二度体重力正演公式[J].石油地球物理勘探, 2000, 35(2):202-207.ZHANG Jianzhong, ZHOU Xixiang, WANG Kebin.2-D gravity forward formula showing density variation with depth[J].Oil Geophysical Prospecting, 2000, 35(2):202-207.
[23]
李丕龙, 张善文, 王永诗, 等.断陷盆地多样性潜山成因及成藏研究——以济阳坳陷为例[J].石油学报, 2004, 25(3):28-31.LI Peilong, ZHANG Shanwen, WANG Yongshi, et al.Multiplex buried-hill genesis and pool-forming in rift-ed basin[J].Acta Petrolei Sinica, 2004, 25(3):28-31.
[24]
胡加山, 胡贤根, 崔世凌.东营凹陷典型剖面重磁电震综合解释方法研究[J].石油物探, 2009, 48(4):401-406.HU Jiashan, HU Xian'gen, CUI Shiling.Gravity-magnetic-electric-seismic integrated interpretation method for typical profile of Dongying Sag[J].Geophysical Prospecting for Petroleum, 2009, 48(4):401-406.
