An iterative algorithm for calculating component ΔTPro from magnetic anomaly ΔT
HU Zhengwang1,2, DU Jinsong1,2,3, SUN Shida4, CHEN Chao1,2
1. Institute of Geophysics and Geomatics, China University of Geosciences(Wuhan), Wuhan, Hubei 430074, China; 2. Hubei Subsurface Multi-scale Imaging Key Laboratory, Wuhan, Hubei 430074, China; 3. State Key Laboratory of Geological Processes and Mineral Resources, Wuhan, Hubei 430074, China; 4. College of Exploration Technology and Engineering, Hebei GEO University, Shijiazhuang, Hebei 050031, China
Abstract:Total magnetic intensity anomaly(ΔT) is intrinsically different from the projected component (ΔTPro) of the magnetic vector anomaly(Ta) on the direction of the main field (T0), and this difference is very obvious in a highly magnetic environment. Traditionally, to simplify computation, ΔT is always treated as ΔTPro approximately. This may cause a large error in quantitative interpretation. This paper proposes an efficiently iterative algorithm for fast calculating ΔTPro from ΔT by utilizing the theoretical difference formula between ΔT and ΔTPro. First, the factors influencing the validity, convergence rate and calculating accuracy, and computational efficiency are analyzed successively by serial model tests. Then using field data, related problems which need to be paid attention and the difference between the results from our method and a traditional method are discussed. Both model and field applications have verified the reliability and stability of our method. Furthermore, compared with other methods, our method requires a little amount of computation and computer memory. It is effective and practical, and worth being promoted in the field application.
胡正旺, 杜劲松, 孙石达, 陈超. 基于磁异常ΔT计算投影分量ΔTPro的迭代算法[J]. 石油地球物理勘探, 2021, 56(3): 645-658.
HU Zhengwang, DU Jinsong, SUN Shida, CHEN Chao. An iterative algorithm for calculating component ΔTPro from magnetic anomaly ΔT. Oil Geophysical Prospecting, 2021, 56(3): 645-658.
管志宁,郝天珧,姚长利.21世纪重力与磁法勘探的展望[J].地球物理学进展, 2002, 17(2):237-244.GUAN Zhining, HAO Tianyao, YAO Changli. Prospect of gravity and magnetic exploration in the 21st century[J]. Progress in Geophysics, 2002, 17(2):237-244.
[2]
付丽华,曾诚,杨文采,等.用于地壳弧形构造信息提取的四阶谱矩分析[J].石油地球物理勘探, 2020, 55(4):923-930.FU Lihua, ZENG Cheng, YANG Wencai, et al. Fourth-order spectral moment analysis for extracting the information of crustal arc structures[J]. Oil Geophysical Prospecting, 2020, 55(4):923-930.
[3]
熊盛青,丁燕云,李占奎.西藏羌塘盆地的重磁场特征及地质意义[J].石油地球物理勘探, 2013, 48(6):999-1008.XIONG Shengqing, DING Yanyun, LI Zhankui. Gravity and magnetic field characteristics and their geological significance in the Qiangtang Basin, China[J]. Oil Geophysical Prospecting, 2013, 48(6):999-1008.
[4]
管志宁.地磁场与磁力勘探[M].北京:地质出版社, 2005.GUAN Zhining. Geomagnetic Field and Magnetic Exploration[M]. Geological Publishing House, Beijing, 2005.
[5]
Guo W, Dentith M, Bird R T, et al. Systematic error analysis of demagnetization and implications for magnetic interpretation[J]. Geophysics, 2001, 66(2):562-570.
[6]
Biedermann A R, McEnroe S A. Effects of magnetic anisotropy on total magnetic field anomalies[J]. Journal of Geophysical Research:Solid Earth, 2017, 122(11):8628-8644.
[7]
Clark D A. Methods for determining remanent and total magnetizations of magnetic sources:A review[J]. Exploration Geophysics, 2014, 45(4):271-304.
[8]
袁晓雨,姚长利,郑元满,等. 强磁性体ΔT异常计算的误差分析研究[J].地球物理学报, 2015, 58(12):4756-4765.YUAN Xiaoyu, YAO Changli, ZHENG Yuanman, et al. Error analysis of calculation of total field ano-maly due to highly magnetic bodies[J]. Chinese Journal of Geophysics, 2015, 58(12):4756-4765.
[9]
袁晓雨. 强磁异常ΔT的计算误差及高精度处理转换分析研究[D]. 北京:中国地质大学(北京), 2016.YUAN Xiaoyu. Research on Calculation Error and High-Precision Processing Conversion Analysis of Strong Magnetic Anomaly ΔT[D]. China University of Geosciences (Beijing), Beijing, 2016.
[10]
Blakely R J. Potential Theory in Gravity and Magne-tic Applications[M]. Cambridge University Press, Cambridge, 1995.
[11]
Hinze W J, von Frese R R B, Saad A H. Gravity and Magnetic Exploration:Principles, Practices, and Applications[M]. Cambridge University Press, Cambridge, 2013.
[12]
Zhen H X, Li Y Y, Yang Y S. Transformation from total-field magnetic anomaly to the projection of the anomalous vector onto the normal geomagnetic field based on an optimization method[J]. Geophysics, 2019, 84(5):J43-J55.
[13]
甄慧翔.基于优化算法的总场异常ΔT精确计算磁异常分量Tap方法[D]. 湖北武汉:中国地质大学(武汉), 2019.ZHEN Huixiang. Method for Accurately Calculating the Magnetic Anomaly Component Tap from ΔT Based on Optimization Algorithm[D]. China University of Geosciences (Wuhan), Wuhan, Hubei, 2019.
[14]
甄慧翔,杨宇山,李媛媛,等.基于L-BFGS反演算法的ΔT精确计算磁异常分量Tap方法[J]. 物探与化探, 2019, 43(3):598-607.ZHEN Huixiang, YANG Yushan, LI Yuanyuan, et al. Method for accurately calculating magnetic ano-maly component using ΔT based on L-BFGS inversion algorithm[J]. Geophysical and Geochemical Exploration, 2019, 43(3):598-607.
[15]
Sun S, Chen C, Liu Y. Constrained 3D inversion of magnetic data with structural orientation and borehole lithology:a case study in the Macheng iron deposit, Hebei, China[J]. Geophysics, 2019, 84(2):B121-B133.
[16]
孙石达,杜劲松,陈超,等.基于等效源的总强度磁异常非线性处理方法[J]. 地球物理学报, 2020, 63(1):351-361.SUN Shida, DU Jinsong, CHEN Chao, et al. Nonlinear equivalent source method for transformation and inversion of total-field magnetic anomaly[J]. Chinese Journal of Geophysics, 2020, 63(1):351-361.
[17]
Yang J, Liu S, Hu X. Inversion of high-amplitude magnetic total field anomaly:an application to the Mengku iron-ore deposit, northwest China[J]. Scientific Reports, 2020, doi:10.1038/s41598-020-68494-1.
[18]
Coleman C, Li Y. Quantifying the error level in computed magnetic amplitude data for 3D magnetization inversion[J]. Geophysics, 2018, 83(5):J75-J84.
[19]
Du J, Chen C, Lesur V, et al. Magnetic potential, vector and gradient tensor fields of a tesseroid in a geo-centric spherical coordinate system[J]. Geophysical Journal International, 2015, 201(3):1977-2007.
[20]
Tsay L J. The use of Fourier series method in upward continuation with new improvements[J]. Geophysical Prospecting, 1975, 23(1):28-41.
[21]
段本春,徐世浙.磁(重力)异常局部场与区域场分离处理中的扩边方法研究[J]. 物探化探计算技术, 1997, 19(4):298-304.DUAN Benchun, XU Shizhe. A study of the scheme of extending edge in the processing of separating local field from regional field for magnetic/gravity anomaly[J]. Computing Techniques for Geophysical and Geochemical Exploration, 1997, 19(4):298-304.
[22]
王万银,邱之云,刘金兰,等.位场数据处理中的最小曲率扩边和补空方法研究[J].地球物理学进展, 2009, 24(4):1327-1338.WANG Wanyin, QIU Zhiyun, LIU Jinlan, et al. The research to the extending edge and interpolation based on the minimum curvature method in potential field data processing[J]. Progress in Geophysics, 2009, 24(4):1327-1338.
[23]
蒋涛,李建成,党亚民,等.基于矩谐分析的区域重力场建模[J].中国科学:地球科学, 2014, 44(1):82-89.JIANG Tao, LI Jiancheng, DANG Yamin, et al. Regional gravity field modeling based on rectangular harmonic analysis[J]. Science China:Earth Sciences, 2014, 44(1):82-89.
[24]
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. Three-dimensional numerical simulation of the gravity ano-maly field in the space-wave number mixed domain[J]. Chinese Journal of Geophysics, 2020, 63(5):2107-2119.
[25]
周印明,戴世坤,李昆,等.基于样条插值的FFT及其在重磁场正演中的应用[J]. 石油地球物理勘探, 2020, 55(4):915-922, 930.ZHOU Yinming, DAI Shikun, LI Kun, et al. Cubic-spline-interpolation-based FFT and its application in forward modeling of gravity and magnetic fields[J]. Oil Geophysical Prospecting, 2020, 55(4):915-922, 930.
[26]
舒晴,张文志,周坚鑫,等.重力梯度张量分量转换处理误差研究[J].物探与化探, 2016, 40(1):111-116.SHU Qing, ZHANG Wenzhi, ZHOU Jianxin, et al. Error study on gravity gradient tensor components transformation[J]. Geophysical & Geochemical Exploration, 2016, 40(1):111-116.
[27]
Chai Y. Shift sampling theory of Fourier transform computation[J]. Science in China (Series E):Technological Sciences, 1997, 40(1):21-27.
[28]
Chai Y. A-E equation of potential field transformations in wavenumber domain and its application[J]. Applied Geophysics, 2009, 6(3):205-216.
[29]
柴玉璞,贾继军.偏移抽样理论在磁异常化极中的应用[J].石油地球物理勘探, 1998, 33(4):486-495.CHAI Yupu, JIA Jijun. Application of shift sampling theory to magnetic anomaly reduction-to-the-pole[J]. Oil Geophysical Prospecting, 1998, 33(4):486-495.
[30]
柴玉璞,万海珍.移样离散傅里叶变换在重磁勘探中的应用[J].石油地球物理勘探, 2020, 55(6):1358-1363.CHAI Yupu, WAN Haizhen. Shift sampling DFT(SFT) theory and its application in gravity and magnetic prospecting[J]. Oil Geophysical Prospecting, 2020, 55(6):1358-1363.
[31]
Fertner A. Computationally efficient methods for analysis and synthesis of real signal using FFT and IFFT[J]. IEEE Transaction on Signal Processing, 1999, 47(4):1061-1064.
[32]
Wu H, Niu X, Zhang L, et al. Geology and geochemistry of the Macheng Algoma-type banded iron-formation, North China Craton:Constraints on mi-neralization events and genesis of high-grade iron ores[J]. Journal of Asian Earth Sciences, 2015, 113:1179-1196.