|
|
|
| Three-dimensional inversion of gravity/magnetic anomalies based on curvelet compression and its applications |
| ZHANG Henglei1,2, GENG Meixia3, HU Xiangyun1,2 |
1. Key Laboratory of Geological Survey and Evaluation of Ministry of Education, China University of Geosciences (Wuhan), Wuhan, Hubei 430074, China;
2. School of Geophysics and Geomatics, China University of Geosciences (Wuhan), Wuhan, Hubei 430074, China;
3. Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates |
|
|
|
|
Abstract The three-dimensional(3D) inversion of gravity/magnetic anomalies plays an important role in constructing the 3D fine structure of underground space. However, the matrix of the kernel function in 3D inversion is large, and it requires huge computer memory, which limits its wide application. In order to reduce the memory required by the kernel function, a 3D inversion method of gravity/magnetic anomalies based on curvelet compression is proposed in this paper. In other words, through curvelet transform, the energy of the kernel matrix is mainly retained in a small part of sparse curvelet coefficients, which can achieve efficient compression inversion. Compared with wavelet transform, curvelet transform has superior signal sparse representation ability, so it can obtain higher compression accuracy under the same compression rate. In this paper, the application effects of wavelet compression and curvelet compression in the 3D inversion of gravity/magnetic anomalies are compared. Under the same calculation accuracy, curvelet compression can improve the kernel compression rate by 100% and reduce the memory requirement by 50%. In the model test, the kernel function has a size of(100×100)×(100×100×50), with a storage capacity of 37 GB in double precision, and the proposed method adopting a compression ratio of 4%(the kernel's memory is only 1.48 GB) obtains the inversion results similar to the wavelet compression adopting a compression ratio of 10%. The proposed method is applied to the 3D inversion of magnetic anomalies in the Galinge mining area in western China, in which the 3D magnetization model obtained from compression and inversion reveals the buried depth, spatial distribution, and magnetic strength of the ore body, which provides a reliable basis for later drilling verification, reserve evaluation, and concealed ore detection.
|
|
Received: 12 September 2022
|
|
|
|
|
|
| [1] |
郭培虹, 冯治汉, 王万银, 等. 北秦岭华阳川地区重磁三维反演及岩浆岩特征研究[J]. 物探与化探, 2021, 45(5):1217-1225.GUO Peihong, FENG Zhihan, WANG Wanyin, et al. Three-dimensional gravity and magnetic inversion of magmatic rocks in the Huayangchuan, North Qinling area[J]. Geophysical and Geochemical Exploration, 2021, 45(5):1217-1225.
|
| [2] |
胡斌, 贾正元, 张贵宾, 等. 青藏高原冈底斯带及邻区重磁三维反演及岩浆岩特征研究[J]. 地球物理学报, 2019, 62(4):1362-1376.HU Bin, JIA Zhengyuan, ZHANG Guibin, et al. Threedimensional inversion of gravity and magnetic data and its application in the study on the characteristics of magmatic rocks in the Gangdise belt and adjacent areas, Tibetan Plateau[J]. Chinese Journal of Geophysics, 2019, 62(4):1362-1376.
|
| [3] |
陈辉, 邓居智, 吕庆田, 等. 九瑞矿集区重磁三维约束反演及深部找矿意义[J]. 地球物理学报, 2015, 58(12):4478-4489.CHEN Hui, DENG Juzhi, LYU Qingtian, et al. Threedimensional inversion of gravity and magnetic data at Jiujiang-Ruichang district and metallogenic indication[J]. Chinese Journal of Geophysics, 2015, 58(12):4478-4489.
|
| [4] |
严加永, 吕庆田, 吴明安, 等. 安徽沙溪铜矿区域重磁三维反演与找矿启示[J]. 地质学报, 2014, 88(4):507-518.YAN Jiayong, LYU Qingtian, WU Ming'an, et al. Prospecting indicator of Anhui Shaxi porphyry copper deposit based on regional gravity and magnetic 3D inversion[J]. Acta Geologica Sinica, 2014, 88(4):507-518.
|
| [5] |
LI S, LI Y, MENG X. The 3D magnetic structure beneath the continental margin of the northeastern South China Sea[J]. Applied Geophysics, 2012, 9(3):237-246.
|
| [6] |
CAPPONI M, SAMPIETRO D, EBBING J, et al. Antarctica 3-D crustal structure investigation by means of the Bayesian gravity inversion:the Wilkes Land case study[J]. Geophysical Journal International, 2022, 229(3):2147-2161.
|
| [7] |
何庆禹, 郝天珧, 邢健, 等. 苏门答腊俯冲带地区壳内密度结构研究[J]. 地球物理学报, 2021, 64(2):569-581.HE Qingyu, HAO Tianyao, XING Jian, et al. Density structure of the crust in the subduction zone of Sumatra region[J]. Chinese Journal of Geophysics, 2021, 64(2):569-581.
|
| [8] |
刘代芹, 玄松柏, 王晓强, 等. 北天山地区近期重力场及地壳密度变化特征研究[J]. 大地测量与地球动力学, 2021, 41(5):459-465.LIU Daiqin, XUAN Songbai, WANG Xiaoqiang, et al. Study on the characteristics of recent gravity field and crustal density in North Tianshan area[J]. Journal of Geodesy and Geodynamics, 2021, 41(5):459-465.
|
| [9] |
徐伟民, 石磊, 陈石, 等. 华北地区重力场变化特征与孕震模型研究[J]. 地震学报, 2021, 43(4):441-452.XU Weimin, SHI Lei, CHEN Shi, et al. Gravity field characteristics and seismogenic model in North China[J]. Acta Seismologica Sinica, 2021, 43(4):441-452.
|
| [10] |
付广裕, 王振宇. 新疆精河6.6级地震周边地区密度构造、均衡异常以及岩石圈挠曲机理[J]. 地球物理学报, 2020, 63(6):2221-2229.FU Guangyu, WANG Zhenyu. Crustal structure, isostatic anomaly and flexure mechanism around the Jinghe MS6.6 earthquake in Xinjiang[J]. Chinese Journal of Geophysics, 2020, 63(6):2221-2229.
|
| [11] |
李海龙, 吴招才, 纪飞, 等. 南海北部地壳密度结构:基于约束三维重力反演[J]. 地球物理学报, 2020, 63(5):1894-1912.LI Hailong, WU Zhaocai, JI Fei, et al. Crustal density structure of the northern South China Sea from constrained 3-D gravity inversion[J]. Chinese Journal of Geophysics, 2020, 63(5):1894-1912.
|
| [12] |
张明辉, 申重阳, 吴桂桔, 等. 三河-平谷8.0级地震区浅层三维密度结构反演研究[J]. 大地测量与地球动力学, 2020, 40(11):1112-1117.ZHANG Minghui, SHEN Chongyang, WU Guijie, et al. Inversion of shallow three-dimensional density structure in Sanhe-Pinggu M8.0 earthquake area[J]. Journal of Geodesy and Geodynamics, 2020, 40(11):1112-1117.
|
| [13] |
GAO X, XIONG S, ZENG Z, et al. 3D inversion modeling of joint gravity and magnetic data based on a sinusoidal correlation constraint[J]. Applied Geophysics, 2019, 16(4):519-529.
|
| [14] |
孟小红, 刘国峰, 陈召曦, 等. 基于剩余异常相关成像的重磁物性反演方法[J]. 地球物理学报, 2012, 55(1):304-309.MENG Xiaohong, LIU Guofeng, CHEN Zhaoxi, et al. 3-D gravity and magnetic inversion for physical properties based on residual anomaly correlation[J]. Chinese Journal of Geophysics, 2012, 55(1):304-309.
|
| [15] |
郭良辉, 孟小红, 石磊. 磁异常ΔT三维相关成像[J]. 地球物理学报, 2010, 53(2):435-441.GUO Lianghui, MENG Xiaohong, SHI Lei. 3D correlation imaging for magnetic anomaly ΔT data[J]. Chinese Journal of Geophysics, 2010, 53(2):435-441.
|
| [16] |
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.
|
| [17] |
陈召曦, 孟小红, 刘国峰, 等. 基于GPU的任意三维复杂形体重磁异常快速计算[J]. 物探与化探, 2012, 36(1):117-121.CHEN Zhaoxi, MENG Xiaohong, LIU Guofeng, et al. The GPU-based parallel calculation of gravity and magnetic anomalies for 3D arbitrary bodies[J]. Geophysical and Geochemical Exploration, 2012, 36(1):117-121.
|
| [18] |
李泽林, 姚长利, 郑元满, 等. 数据空间磁异常模量三维反演[J]. 地球物理学报, 2015, 58(10):3804-3814.LI Zelin, YAO Changli, ZHENG Yuanman, et al. 3D data-space inversion of magnetic amplitude data[J]. Chinese Journal of Geophysics, 2015, 58(10):3804-3814.
|
| [19] |
戴世坤, 陈轻蕊, 李昆, 等. 重力异常场空间-波数混合域三维数值模拟[J]. 地球物理学报, 2020, 63(5):2107-2119.DAI Shikun, CHEN Qingrui, LI Kun, et al. Threedimensional numerical simulation of the gravity anomaly field in the space-wave number mixed domain[J]. Chinese Journal of Geophysics, 2020, 63(5):2107-2119.
|
| [20] |
袁洋, 崔益安, 陈波, 等. 基于BTTB矩阵的快速高精度三维磁场正演[J]. 地球物理学报, 2022, 65(3):1107-1124.YUAN Yang, CUI Yian, CHEN Bo, et al. Fast and high accuracy 3D magnetic anomaly forward modeling based on BTTB matrix[J]. Chinese Journal of Geophysics, 2022, 65(3):1107-1124.
|
| [21] |
LI Y, OLDENBURG D W. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method[J]. Geophysical Journal International, 2003, 152(2):251-265.
|
| [22] |
BRUUN C E, NIELSEN T B. Algorithms and Software for Large-scale Geophysical Reconstructions[D]. Technical University of Denmark, Kongens Lyngby, 2007.
|
| [23] |
彭国民, 刘展. 基于q-高斯分布和零阶最小熵正则化的三维重力聚焦反演[J]. 地球物理学报, 2022, 65(5):1866-1882.PENG Guomin, LIU Zhan. 3D focusing inversion of gravity data based on q-Gaussian distribution and zeroth-order minimum entropy regularization[J]. Chinese Journal of Geophysics, 2022, 65(5):1866-1882.
|
| [24] |
何浩源, 李桐林, 张镕哲, 等. 三维重力、重力梯度和大地电磁数据的平滑聚焦结构约束联合反演[J]. 地球物理学报, 2022, 65(5):1822-1838.HE Haoyuan, LI Tonglin, ZHANG Rongzhe, et al. Three-dimensional cross-gradient joint inversion of gravity, gravity gradient and magnetotelluric data based on smooth-focusing regularization method[J]. Chinese Journal of Geophysics, 2022, 65(5):1822-1838.
|
| [25] |
DARIJANI M, FARQUHARSON C G, LELIÈVRE P G. Joint and constrained inversion of magnetic and gravity data:a case history from the McArthur River area, Canada[J]. Geophysics, 2021, 86(2):B79-B95.
|
| [26] |
于会臻, 王金铎, 王千军. 基于密度模型稀疏表征的重力反演方法[J]. 地球物理学报, 2021, 64(3):1061-1073.YU Huizhen, WANG Jinduo, WANG Qianjun. Gravity inversion based on sparse representation of density model[J]. Chinese Journal of Geophysics, 2021, 64(3):1061-1073.
|
| [27] |
李芳, 王林飞, 何辉. 一种重力数据快速聚焦反演方法[J]. 地球物理学进展, 2021, 36(6):2486-2495.LI Fang, WANG Linfei, HE Hui. A fast method for focusing inversion of gravity data[J]. Progress in Geophysics, 2021, 36(6):2486-2495.
|
| [28] |
XU Z, WAN L, ZHDANOV M S. Focusing iterative migration of gravity gradiometry data acquired in the Nordkapp Basin, Barents Sea[J]. Geophysical Prospecting, 2020, 68(7):2292-2306.
|
| [29] |
XU Z, ZOU G, WEI Q, et al. Focusing joint inversion of gravity and magnetic data using a clustering stabilizer in a space of weighted parameters[J]. Geophysical Journal International, 2021, 224(2):1344-1359.
|
| [30] |
MARTIN R, GIRAUD J, OGARKO V, et al. Three-dimensional gravity anomaly data inversion in the Pyrenees using compressional seismic velocity model as structural similarity constraints[J]. Geophysical Journal International, 2021, 225(2):1063-1085.
|
| [31] |
HIGHTOWER E, GURNIS M, VAN AVENDONK H. A Bayesian 3-D linear gravity inversion for complex density distributions:application to the Puysegur subduction system[J]. Geophysical Journal International, 2020, 223(3):1899-1918.
|
| [32] |
TIAN Y, WANG Y. Inversion of the density structure of the lithosphere in the North China Craton from GOCE satellite gravity gradient data[J]. Earth, Planets and Space, 2018, 70(1):173.
|
| [33] |
MENG Z, LI F, XU X, et al. Fast inversion of gravity data using the symmetric successive over-relaxation (SSOR) preconditioned conjugate gradient algorithm[J]. Exploration Geophysics, 2017, 48(3):294-304.
|
| [34] |
WANG J, MENG X, LI F. A computationally efficient scheme for the inversion of large scale potential field data:application to synthetic and real data[J]. Computers & Geosciences, 2015, 85(Part A):102-111.
|
| [35] |
ELDOSOUKY A M, EL-QASSAS R A Y, POUR A B, et al. Integration of ASTER satellite imagery and 3D inversion of aeromagnetic data for deep mineral exploration[J]. Advances in Space Research, 2021, 68(9):3641-3662.
|
| [36] |
JORGENSEN M, ZHDANOV M S. Recovering magnetization of rock formations by jointly inverting airborne gravity gradiometry and total magnetic intensity data[J]. Minerals, 2021, 11(4):366.
|
| [37] |
JI F, LI F, GAO J Y, et al. 3-D density structure of the Ross Sea basins, West Antarctica from constrained gravity inversion and their tectonic implications[J]. Geophysical Journal International, 2018, 215(2):1241-1256.
|
| [38] |
LI Y, OLDENBURG D W. 3-D inversion of gravity data[J]. Geophysics, 1998, 63(1):109-119.
|
| [39] |
LI Y, OLDENBURG D W. 3-D inversion of magnetic data[J]. Geophysics, 1996, 61(2):394-408.
|
| [40] |
REZAIE M, MORADZADEH A, KALATEH A N. Fast 3D inversion of gravity data using solution space priorconditioned lanczos bidiagonalization[J]. Journal of Applied Geophysics, 2017, 136:42-50.
|
| [41] |
CANDÈS E J, DONOHO D L. Curvelets:a Surprisingly Effective Nonadaptive Representation for Objects with Edges[M]. Department of Statistics, Stanford University, Stanford, 1999.
|
| [42] |
苏扬, 殷长春, 刘云鹤, 等. 基于曲波变换的大地电磁二维稀疏正则化反演[J]. 地球物理学报, 2021, 64(1):314-326.SU Yang, YIN Changchun, LIU Yunhe, et al. 2D magnetotelluric sparse regularization inversion based on curvelet transform[J]. Chinese Journal of Geophysics, 2021, 64(1):314-326.
|
| [43] |
陈一方, 陈九辉, 郭飚, 等. 接收函数曲波变换去噪与偏移成像[J]. 地球物理学报, 2019, 62(6):2027-2037.CHEN Yifang, CHEN Jiuhui, GUO Biao, et al. Denoising the receiver function through curvelet transforming and migration imaging[J]. Chinese Journal of Geophysics, 2019, 62(6):2027-2037.
|
| [44] |
高玲琦, 殷长春, 王宁, 等. 基于曲波变换的航空电磁数据调平方法研究[J]. 地球物理学报, 2021, 64(5):1785-1796.GAO Lingqi, YIN Changchun, WANG Ning, et al. Leveling of airborne electromagnetic data based on Curvelet transform[J]. Chinese Journal of Geophysics, 2021, 64(5):1785-1796.
|
| [45] |
李继伟, 臧殿光, 刁永波, 等. 自适应相减和Curvelet变换组合压制面波[J]. 石油地球物理勘探, 2020, 55(5):1005-1015.LI Jiwei, ZANG Dianguang, DIAO Yongbo, et al. Combination of adaptive subtraction and Curvelet transform to suppress surface waves[J]. Oil Geophysical Prospecting, 2020, 55(5):1005-1015.
|
| [46] |
孙成禹, 刁俊才, 李文静. 基于曲波噪声估计的三维块匹配地震资料去噪[J]. 石油地球物理勘探, 2019, 54(6):1188-1194.SUN Chengyu, DIAO Juncai, LI Wenjing. 3D Block matching seismic data denoising based on Curvelet noise estimation[J]. Oil Geophysical Prospecting, 2019, 54(6):1188-1194.
|
| [47] |
余江奇, 曹思远, 陈红灵, 等. 改进阈值的Curvelet变换稀疏反褶积[J]. 石油地球物理勘探, 2017, 52(3):426-433.YU Jiangqi, CAO Siyuan, CHEN Hongling, et al. Sparse deconvolution based on Curvelet transform of improved threshold[J]. Oil Geophysical Prospecting, 2017, 52(3):426-433.
|
| [48] |
董烈乾, 李培明, 张奎, 等. 利用曲波变换预测多次波模型[J]. 石油地球物理勘探, 2015, 50(6):1098-1104.DONG Lieqian, LI Peiming, ZHANG Kui, et al. Multiple model prediction based on Curvelet transform[J]. Oil Geophysical Prospecting, 2015, 50(6):1098-1104.
|
| [49] |
张恒磊, 刘天佑, 李红巧. Curvelet域面波衰减方法研究[J]. 中南大学学报(自然科学版), 2011, 42(8):2372-2378.ZHANG Henglei, LIU Tianyou, LI Hongqiao. Attenuation of surface wave in Curvelet domain[J]. Journal of Central South University (Science and Technology), 2011, 42(8):2372-2378.
|
| [50] |
张恒磊, 刘天佑. 基于Curvelet域的位场多源数据融合方法[J]. 石油地球物理勘探, 2011, 46(4):648-653.ZHANG Henglei, LIU Tianyou. Potential field data fusion in Curvelet domain[J]. Oil Geophysical Prospecting, 2011, 46(4):648-653.
|
| [51] |
张恒磊, 刘天佑, 张云翠. 基于高阶相关的curvelet域和空间域的倾角扫描噪声压制方法[J]. 石油地球物理勘探, 2010, 45(2):208-214.ZHANG Henglei, LIU Tianyou, ZHANG Yuncui. High order correlation based dip angle scanning noise elimination method in Curvelet domain and space domain[J]. Oil Geophysical Prospecting, 2010, 45(2):208-214.
|
| [52] |
张恒磊, 张云翠, 宋双, 等. 基于Curvelet域的叠前地震资料去噪方法[J]. 石油地球物理勘探, 2008, 43(5):508-513.ZHANG Henglei, ZHANG Yuncui, SONG Shuang, et al. Curvelet domain-based prestack seismic data denoise method[J]. Oil Geophysical Prospecting, 2008, 43(5):508-513.
|
| [53] |
HUANG L, ZHANG H, SEKELANI S, et al. An improved Tilt-Euler deconvolution and its application on a Fe-polymetallic deposit[J]. Ore Geology Reviews, 2019, 114:103114.
|
| [54] |
ZHANG H, MARANGONI Y R, WU Z. Depth corrected edge detection of magnetic data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2019, 57(12):9626-9632.
|
|
|
|
2023, Vol. 58 
