磁梯度张量系统目标探测技术研究进展

doi:10.12382/bgxb.2023.0964

摘要/Abstract

摘要：

磁梯度张量系统作为磁性目标全张量梯度探测的应用基础,以区域磁异常产生的磁梯度张量场为信息源,通过矢量磁传感器间的差分计算实现磁梯度张量分量测量。相较磁总场和矢量场探测设备,磁梯度张量系统具有分辨率高、信息量大、抗干扰能力强等优势,能获取目标更多的潜在物性信息,研究世界范围内基于磁梯度张量系统的目标探测技术进展,可为我国磁探测设备现代化信息化建设提供理论参考和技术支持。通过阐述现代磁法探测技术发展过程和阶段,对国内外研究团队设计搭建的基于超导效应和磁通门法两种类型的磁梯度张量系统及其应用进行了介绍和归纳,并针对磁梯度张量系统的校正补偿与降噪、磁性目标定位与识别等关键技术进行了前沿综述,展望了未来高精度磁梯度张量探测仪器的设计研发思路,对磁梯度张量探测各类关键技术目前存在的问题和发展趋势进行了总结。

关键词: 磁梯度张量系统, 磁性目标探测, 目标定位与识别, 磁通门传感器, 超导量子干涉仪

Abstract:

The magnetic gradient tensor system (MGTS) is the application basis for detecting the full tensor gradient field of magnetic target. Regional magnetic anomalies leads to a magnetic gradient tensor field, which MGTS uses as an information source to achieve the magnetic gradient tensor measurement through the differential calculation between vector magnetic sensors. Compared to the magnetic total field and vector field detection equipment, MGTS has high resolution, large information content, and strong anti-interference ability, which can obtain more potential physical property information of targets. The progress of target detection technology based on MGTSs worldwide is studied to provide theoretical reference and technical support for the modernization and informatization construction of magnetic detection equipment in China. The development process and stages of modern magnetic detection technology are elaborated, and then the two types of MGTSs based on superconducting technology and flux gate method, as well as their applications areintroduced and summarized. The calibration, compensation, noise reduction, magnetic target positioning and recognition technologies of MGTSs are reviewed. Finally, the design ideas for future high-precision magnetic gradient tensor detection instruments are prospected, and the current problems and development trends of various key technologies for magnetic gradient tensor detection are summarized.

Key words: magnetic gradient tensor system, magnetic target detection, target positioning and recognition, fluxgate sensor, superconducting quantum interference device

李青竹, 李晶, 李志宁, 石志勇, 文雪忠. 磁梯度张量系统目标探测技术研究进展[J]. 兵工学报, 2024, 45(12): 4205-4230.

LI Qingzhu, LI Jing, LI Zhining, SHI Zhiyong, WEN Xuezhong. Research Progress on Target Detection Technology of Magnetic Gradient Tensor System[J]. Acta Armamentarii, 2024, 45(12): 4205-4230.

图/表 20

表1 磁法探测技术发展阶段、测量张量阶次和磁测范围、仪器类型和功能[8]

Table 1 Development stages of magnetic detection technology, order and range of parameters, and instrument types and functions[8]

阶段	张量阶次	磁测范围	仪器类型	功能
1	0阶(标量)	磁总场	磁总场传感器	探测有无
2	0阶的梯度	磁总场;磁总场梯度	磁总场梯度仪	探测有无、定向、跟踪
3	1阶(矢量);1阶的梯度	磁总场;磁总场梯度;磁矢量场;磁矢量场梯度	磁矢量传感器;磁矢量梯度仪	探测有无、定向、跟踪、粗略定位
4	2阶及以上	前3阶段全部内容;磁梯度张量	磁梯度张量测量设备	探测有无、定向、跟踪、精确定位、反演、识别

表2 部分磁传感器理论上可达的响应频率、测量范围及分辨率[9,12]

Table 2 The theoretically achievable response frequency, measurement range and resolution of some magnetic sensors[9,12]

传感器类型	最高分辨率	最大测量范围	最高响应频率范围
磁感应线圈	100fT	±10⁴T	0.1mHz~1MHz
霍尔传感器	10nT	±20T	0~100MHz
磁阻传感器	100pT	0~100mT	0~100MHz
磁电传感器	1pT	±∞	0.1mHz~1kHz
质子磁强计	0.1nT	20~100μT	0~10Hz
光泵传感器	0.1pT	2μT ~1mT	0~10kHz
CPT磁力仪	1pT	0~1mT	0~100kHz
SQUID	5fT	±0.1mT	0~100MHz
磁通门传感器	10pT	±1mT	0~100kHz

图1 初代UUV-RTG系统[51]

Fig.1 First-generation UUV-RTG system[51]

图2 第2代UUV-RTG系统Bluefinl2[54]

Fig.2 Second-generation UUV-RTG system Bluefinl2[54]

图3 TMA阵列设计和初代STAR系统[52]

Fig.3 TMA array and the first-generation STAR system[52]

图4 改进型3-D STAR系统概念及其“STAR Cube” 改进结构[53]

Fig.4 3-D STAR system concept and its STAR Cube structure[53]

图5 用于未爆弹、地雷检测的单兵手持式便携STAR系统[55]

Fig.5 Man-portable STAR system for near-earth UXO and mine DLC[55]

图6 第1代正四面体型MGTS系统并进行自旋校准和试验场探测工作[58-59]

Fig.6 First-genrstion MGTS with regular tetrahedron and its rotation calibration and proving ground detection[58-59]

图7 第2代平面十字形MGTS系统用于未爆弹等目标多姿态二维网格测量

Fig.7 Second-generation planar-cross MGTS for multi- attitude 2D grid measurement of targets such as unexploded ordnance

图8 高温SQUID磁梯度张量系统GETMAG[65]

Fig.8 GETMAG, a high-temperature SQUID magnetic gradient tensor system[65]

图9 CSIRO研制的直角四面体型MGTS [66-67]

Fig.9 Right-angled tetrahedral MGTS developed by CSIRO[66-67]

图10 JESSY STAR和Air Bird系统

Fig.10 JESSY STAR and Air Bird systems

图11 轮式捷联SQUID磁梯度张量系统[73]

Fig.11 Ground-wheeled strapdown SQUID magnetic gradient tensor system[73]

图12 AUV水下未爆弹探测磁张量系统[41]

Fig.12 Magnetic gradient tensor system for AUV underwater UXO detection[41]

图13 S3MAG项目三角形MGTS用于AUV探测[40]

Fig.13 Triangle structure magnetic MGTS developed by S3MAG for AUV detection[40]

图14 十字形紧凑MGTS [75]

Fig.14 Cross-shaped compact magnetic gradient tensor system[75]

图15 带球形反馈线圈的紧凑型磁通门全张量磁梯度仪[15]

Fig.15 Compact fluxgate full tensor gradiometer with spherical feedback coil [15]

图16 平面十字形磁梯度张量系统与磁干扰补偿、温度补偿实验

Fig.16 Interference and temperature compensation experiments of magnetic gradient tensor system

图17 STAR Cube结构磁梯度张量系统[83]

Fig.17 Magnetic gradient tensor system of the STAR Cube structure[83]

图18 2阶和3阶MGTS

Fig.18 Second-and third-order MGTSs

参考文献 172

[1]	刘澜波, 钱荣毅. 探地雷达:浅表地球物理科学技术中的重要工具[J]. 地球物理学报, 2015, 58(8): 2606-2617. doi: 10.6038/cjg20150802
	LIU L B, QIAN R Y. Ground penetrating radar:a critical tool in near-surface geophysics[J]. Chinese Journal of Geophysics, 2015, 58(8): 2606-2617. (in Chinese)
[2]	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 Z N, HAO T Y, YAO C L. Prospect of gravity and magnetic exploration in the 21st century[J]. Progress in Geophysics, 2002, 17(2): 237-244. (in Chinese)
[3]	CHEN S D, ZHANG S, ZHU J, et al. Accurate measurement of characteristic response for unexploded ordnance with transient electromagnetic system[J]. IEEE Transactions on Instrumentation and Measurement, 2019, 69(4): 1728-1736.
[4]	张昌达. 关于磁异常探测的若干问题[J]. 工程地球物理学报, 2007, 4(6): 549-553.
	ZHANG C D. Some Problems Concerning the magnetic anomaly detection(MAD)[J]. Chinese Journal of Engineering Geophysics, 2007, 4(6): 549-553. (in Chinese)
[5]	WIGH M D, HANSEN T M, DOSSING A. Inference of unexploded ordnance (UXO) by probabilistic inversion of magnetic data[J]. Geophysical Journal International, 2020, 220(1): 37-58.
[6]	PAOLETTI V, BUGGI A, PASTEKA R. UXO detection by multiscale potential field methods[J]. Pure and Applied Geophysics, 2019, 176(10): 4363-4381. doi: 10.1007/s00024-019-02202-7
[7]	张朝阳, 刘济民, 杨林. 磁探潜关键技术现状及发展趋势[J]. 科学技术与工程, 2022, 22(1): 18-27.
	ZHANG C Y, LIU J M, YANG L. Situation and development trend of the key technology of magnetic submarine exploration[J]. Science Technology and Engineering, 2022, 22(1): 18-27. (in Chinese)
[8]	NERSESOV B A, AFANASYEV M S, KARABASHEVA E I. Magnetic ranging as a promising line of development of magnetometric tools for searching underwater objects[J]. Oceanology, 2015, 55(2): 306-310.
[9]	CARUSO M J, BRATLAND T, SMITH C H, et al. A new perspective on magnetic field sensing[J]. Sensors, 1998, 15(12): 34-47.
[10]	张昌达. 空磁力梯度张量测量——航空磁测技术的最新进展[J]. 工程地球物理学报, 2006, 3(5): 354-361.
	ZHANG C D. Airborne tensor magnetic gradiometry—The latest progress of airbone magnetometric technology[J]. Chinese Journal of Engineering Geophysics, 2006, 3(5): 354-361. (in Chinese)
[11]	李青竹, 李志宁, 张英堂, 等. 磁梯度张量系统发展及其误差校正研究现状[J]. 装甲兵工程学院学报, 2017, 31(6): 72-81.
	LI Q Z, LI Z N, ZHANG Y T, et al. Research progress of magnetic gradient tensor system and its error calibration[J]. Journal of Academy of Armored Force Engineering, 2017, 31(6): 72-81. (in Chinese)
[12]	YAVUZ E, ADNAN K, HAKAN C, et al. New magnetic measurement system for determining metal covered mines by detecting magnetic anomaly using a sensor network[J]. Indian Journal of Pure & Applied Physics, 2015, 53: 199-211.
[13]	CHWALA A, STOLZ R, ZAKOSARENKO V, et al. Full tensor SQUID gradiometer for airborne exploration[J]. ASEG Extended Abstracts, 2012, 2012(1): 1-4.
[14]	WANG M C, LIN J, YUE L G, et al. Compensation for mobile carrier magnetic interference in a SQUID-based full-tensor magnetic gradiometer using the flower pollination algorithm[J]. Measurement Science and Technology, 2021, 32(8): 085010.
[15]	SUI Y Y, LI G, WANG S L, et al. Compact fluxgate magnetic full-tensor gradiometer with spherical feedback coil[J]. Review of scientific instruments, 2014, 85(1): 014701.
[16]	YIN G, ZHANG Y T, FAN H B, et al. Linear calibration method of magnetic gradient tensor system[J]. Measurement, 2014, 56: 8-18.
[17]	石志勇, 李青竹, 李志宁. IVMD降噪下的磁梯度张量系统集成校准方法[J]. 陆军工程大学学报, 2022, 1(6): 1-10. doi: 10.12018/j.issn.2097-0730.20211219001
	SHI Z Y, LI Q Z, LI Z N. Integrated calibration method of magnetic gradient tensor system with IVMD noise reduction[J]. Journal of Army Engineering University of PLA, 2022, 1(6): 1-10. (in Chinese) doi: 10.12018/j.issn.2097-0730.20211219001
[18]	卞骁炜. 铯光泵磁力仪微弱信号检测技术研究[D]. 天津: 天津大学, 2017.
	BIAN X W. Study on optically pumped cesium magnetometer weak signal detection technology[D]. Tianjin:Tianjin University, 2017. (in Chinese)
[19]	OVERWAY D, CLEM T, BONO J, et al. Evaluation of the polatomic P-2000 laser pumped He-4 magnetometer/gradiometer[C]// Proceedings of the 2th OCEANS’02. Biloxi, MI, US: MTS/IEEE, 2002, 2: 952-960.
[20]	DILLON S. P-8A Poseidon multi mission maritime aircraft (P-8A):PMA-290[R]. Patuxent River, MD, US: Maritime Patrol and Reconnaissance Aircraft, 2015.
[21]	张振宇. 氦光泵磁测技术研究[D]. 长春: 吉林大学, 2012.
	ZHANG Z Y. Research on optically pumped heliummagnetic measurement technology[D]. Changchun: Jilin University, 2012. (in Chinese)
[22]	黄岩, 罗丁, 冯自成, 等. 无人直升机航磁测量系统集成及应用[J]. 物探与化探, 2019, 43(2):386-392.
	HUANG Y, LUO D, FENG Z C, et al. Unmanned helicopter aeromagnetic measurement system and its application[J]. Geophysical and Geochemical Exploration, 2019, 43(2): 386-392. (in Chinese)
[23]	ZHOU Z J, WANG C, MA M, et al. Research of control system model and design of digital controller for ⁴He optically pumped magnetometer (OPM)[J]. Journal of Computational & Theoretical Nanoscience, 2016, 13(1): 43-49.
[24]	HOOD P, MCCLURE D J. Gradient measurements in ground magnetic prospecting[J]. Geophysics, 1965, 30(3): 403-410.
[25]	NELSON J B. Calculation of the magnetic gradient tensor from total field gradient measurements and its application to geophysical interpretation[J]. Geophysics, 1988, 53(7): 957-966.
[26]	PHAM L T, OKSUM E, THANH D. Edge enhancement of potential field data using the logistic function and the total horizontal gradient[J]. Acta Geodaetica et Geophysica, 2019, 54(1): 143-155.
[27]	DOLL W E, GAMEY T J, BEARD L P, et al. Airborne vertical magnetic gradient for near-surface applications[J]. The Leading Edge, 2006, 25(1):50-53.
[28]	SHAHVERDI M, NAMAKI L, MONTAHAEI M, et al. Interpretation of magnetic data based on Tilt derivative methods and enhancement of total horizontal gradient, a case study: Zanjan Depression[J]. Journal of the earth and space physics, 2017, 43(1): 101-113.(in Farsi)
[29]	管志宁, 王继伦, 钱纪安, 等. 航磁梯度在矿产普查中的作用及有关问题讨论[C]// 1994年中国地球物理学会第十届学术年会论文集.长春:中国地球物理学会1994: 285.
	GUAN Z N, WANG J L, QIAN J A, et al. Discussion on the role and related issues of aeromagnetic gradient in mineral exploration[C]// Proceedings of the 10th Academic Annual Meeting of the Chinese Geophysical Society in 1994. Changchun:Chinese Geophysical Society, 1994:285. (in Chinese)
[30]	骆遥, 段树岭, 王金龙, 等. AGS-863航磁全轴梯度勘查系统关键性指标测试[J]. 物探与化探, 2011, 35(5): 620-625.
	LUO Y, DUAN S L, WANG J L, et al. Key indicators testing for AGS-863 three axis airborne magnetic gradiometer[J]. Geophysical and Geochemical Exploration, 2011, 35(5): 620-625. (in Chinese)
[31]	梁建, 庄道泽, 郭玉峰, 等. 利用航磁重复线测量内符合精度消除航磁梯度测量中的转向差[J]. 物探与化探, 2018, 42(3):576-582.
	LIANG J, ZHUANG D Z, GUO Y F, et al. Elimination of steering difference in aeromagnetic gradient measurement using internal accord accuracy for test repeat line in aeromagnetic survey[J]. Geophysical and Geochemical Exploration, 2018, 42(3): 576-582. (in Chinese)
[32]	KRAUSE H J, KREUTZBRUCK M V. Recent developments in SQUID NDE[J]. Physica C: Superconductivity, 2002, 368(1/2/3/4): 70-79.
[33]	DRUNG D, ABMANN C, BEYER J, et al. Highly sensitive and easy-to-use SQUID sensors[J]. IEEE Transactions on Applied Superconductivity, 2007, 17(2): 699-704.
[34]	MICHAEL M, HAN S, MYERS W R, et al. SQUID-detected microtesla MRI in the presence of metal[J]. Journal of Magnetic Resonance, 2006, 179(1): 146-151. pmid: 16310385
[35]	王宁, 金贻荣, 邓辉, 等. 基于高温超导量子干涉仪的超低场核磁共振成像研究[J]. 物理学报, 2012, 61(21): 196-203.
	WANG N, JIN Y R, DENG H, et al. Ultra-low field magnetic resonance imaging based on high Tc dc-SQUID[J]. Acta Physica Sinica, 2012, 61(21): 196-203. (in Chinese)
[36]	王永良. 超导量子干涉仪磁传感器电路关键技术研究[D]. 合肥: 中国科学技术大学, 2021.
	WANG Y L. Study on the circuit technologies of SQUID sensors for practical applications[D]. Hefei: University of Science and Technology of China, 2021. (in Chinese)
[37]	WYNN W M, FRAHM C P, CARROLL P J, et al. Advanced super-conducting gradiometer/magnetometer arrays and a novel signal processing technique[J]. IEEE Transactions on Magnetics, 1975, 11: 701-707.
[38]	SCHMIDT P W, CLARK D A. The magnetic gradient tensor: its properties and uses in source characterization[J]. The Leading Edge, 2006, 25(1): 75-78.
[39]	STOLZ R, ZAKOSARENKO V, SCHULZ M, et al. Magnetic full-tensor SQUID gradiometer system for geophysical applications[J]. Leading Edge, 2006, 25(2):178-180.
[40]	COCCHI L, CARMISCIANO C, PALANGIO P, et al. S3MAG-low magnetic noise AUV for multipurpose investigations[C]// Proceedings of OCEANS 2015-Genova. Genova, Italy: IEEE, 2015: 1-4.
[41]	PEI Y H, YEO H G, KANG X Y, et al. Magnetic gradiometer on an AUV for buried object detection[C]// Proceedings of OCEANS 2010 MTS/IEEE. Seattle, WA, US:IEEE, 2010: 1-8.
[42]	王君恒. 磁异常梯度张量理论反演与应用[D]. 武汉: 中国地质大学(武汉), 1990.
	WANG J H. Inversion and application of magnetic anomaly gradient tensor theory[D] Wuhan: China University of Geosciences (Wuhan), 1990. (in Chinese)
[43]	吴招才. 磁力梯度张量技术及其应用研究[D]. 武汉: 中国地质大学(武汉), 2008.
	WU Z C. Magnetic gradient tensor technology and its applications[D] Wuhan: China University of Geosciences (Wuhan), 2008. (in Chinese)
[44]	赵静. 高温超导磁梯度仪关键技术研究[D]. 长春: 吉林大学, 2011.
	ZHAO J. Study on technologies for HTS magnetic gradiometer[D] Changchun: Jilin University, 2011. (in Chinese)
[45]	李光. 基于磁通门的航空磁梯度张量系统研究[D]. 长春: 吉林大学, 2013.
	LI G. Study on airborne fluxgate magnetic tensor gradiometer[D] Changchun: Jilin University, 2013. (in Chinese)
[46]	LI Q Z, LI Z N, ZHANG Y T, et al. Integrated compensation and rotation alignment for three-axis magnetic sensors array[J]. IEEE Transactions on Magnetics, 2018, 54(10): 4001011.
[47]	郑东宁. 超导量子干涉器件[J]. 物理学报, 2021, 70(1): 170-183.
	ZHENG D L. Superconducting quantum interference devices[J]. Acta Physica Sinica, 2021, 70(1): 170-183. (in Chinese)
[48]	HARI R, SALMELIN R. Magnetoencephalography: from SQUIDs to neuroscience. neuroimage 20th anniversary special edition[J]. Neuroimage, 2012, 61(2): 386-396. doi: 10.1016/j.neuroimage.2011.11.074 pmid: 22166794
[49]	陈林, 李敬东, 唐跃进, 等. 超导量子干涉仪发展和应用现状[J]. 低温物理学报, 2005(增刊1):657-661.
	CHEN L, LI J D, TANG Y K, et al. Superconducting quantum Interferometers devices: applications and prospects perspectives[J]. Journal of Low Temperature Physics, 2005 (S1): 657-661. (in Chinese)
[50]	CLEM T R. Progress in magnetic sensor technology for sea mine detection[C]//Detection and Remediation Technologies for Mines and Minelike Targets II. Orlando, FL, US:SPIE, 1997, 3079: 354-371.
[51]	WYNN M, BONO J. Magnetic sensor operation onboard an AUV: magnetic noise issues and a linear systems approach to mitigation[C]// Proceedings of OCEANS’02 MTS/IEEE. Biloxi, MI, US: IEEE, 2002, 2: 985-993.
[52]	WIEGERT R, PRICE B, HYDER J. Magnetic anomaly sensing system for mine countermeasures using high mobility autonomous sensing platforms[C]// Proceedings of OCEANS’02 MTS/IEEE. Biloxi, MI, US: IEEE, 2002, 2: 937-944.
[53]	WIEGERT R, OESCHGER J. Generalized magnetic gradient contraction based method for detection, localization and discrimination of underwater mines and unexploded ordnance[C]// Proceedings of OCEANS 2005 MTS/IEEE. Washington, DC, US: IEEE, 2005: 1325-1332.
[54]	ALLEN G I, SULZBERGER G, BONO J T, et al. Initial evaluation of the new real-time tracking gradiometer designed for small unmanned underwater vehicles[C]// Proceedings of OCEANS 2005 MTS/IEEE. Washington, DC, US: IEEE, 2005: 1956-1962.
[55]	WIEGERT R F. Man-Portable magnetic scalar triangulation and ranging system for detection, localization and discrimination of UXO:MM-1511[R]. Washington, DC, US: SERDP, 2009.
[56]	BRACKEN R E, BROWN P J. Concepts and procedures required for successful reduction of tensor magnetic gradiometer data obtained from an unexploded ordnance detection demonstration at Yuma Proving Grounds, Arizona: 2006-1027[R]. Reston, VA, US: US Geological Survey, 2006.
[57]	BRACKEN R E, SMITH D V, BROWN P J. Calibrating a tensor magnetic gradiometer using spin data:2005-5045[R]. Reston, VA, US: US Geological Survey, 2005.
[58]	BROWN P J, BRACKEN R E, SMITH D V. A case study of magnetic gradient tensor invariants applied to the UXO problem[C]// SEG Technical Program Expanded Abstracts 2004. Online: Society of Exploration Geophysicists, 2004: 794-797.
[59]	SMITH D V, BRACKEN R E. Field experiments with the tensor magnetic gradiometer system for UXO surveys: a case history[C]// SEG Technical Program Expanded Abstracts 2004. Online: Society of Exploration Geophysicists, 2004: 806-809.
[60]	SMITH D V, PHILLIPS J D, HUTTON S R. Active tensor magnetic gradiometer system: MM-1514[R]. Washington, DC, US:SERDP, 2007.
[61]	WRIGHT D L, SMITH D V, ASCH T H, et al. On-time 3D time-domain EMI and tensor magnetic gradiometry for UXO detection and discrimination: MM-1328[R]. Washington, DC, US:SERDP, 2008.
[62]	GAMEY T J, STARR T, DOLL W E, et al. Initial design and testing of a full-tensor airborne SQUID magnetometer for detection of unexploded ordnance[C]// SEG Technical Program Expanded Abstracts 2004. Online: Society of Exploration Geophysicists, 2004:798-801.
[63]	BILLINGS S. Superconducting magnetic tensor gradiometer system for detection of underwater military munitions: MR-1661[R]. Washington, DC, US: SERDP, 2012.
[64]	KEENAN S T, CLARK D, BLAY K R, et al. Calibration and testing of a HTS tensor gradiometer for underwater UXO detection[C]//Proceedings of 2011 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices. Sydney, Australia:IEEE, 2011: 3-12.
[65]	SCHMIDT P, CLARK D, LESLIE K, et al. GETMAG-a SQUID magnetic tensor gradiometer for mineral and oil exploration[J]. Exploration Geophysics, 2004, 35(4): 297-305.
[66]	BILLINGS S, BLAY K, LESLIE K, et al. Precision geolocation of active electromagnetic sensors using stationary magnetic sensors: MM-1643[R]. Washington, DC, US:SERDP, 2009.
[67]	BLAY K, LESLIE K, TILBROOK D, et al. Precision geolocation of active electromagnetic sensors using stationary magnetic sensors[J]. ASEG Extended Abstracts, 2010, 2010(1): 1-4.
[68]	张昌达. 若干物探技术的最新进展[J]. 工程地球物理学报, 2012, 9(4):406-412.
	ZHANG C D. Developments of several geophysical methods[J]. Journal of Engineering Geophysics, 2012, 9(4): 406-412. (in Chinese)
[69]	FITZGERALD D J. Full tensor magnetic gradiometry[C]// Proceedings of Gravity Gradients for Exploration & Research SAGA 13th Biennial Conference. Kruger National Park, Mpumalanga, South Africa: Southern African Geophysical Association, 2013: 1-7.
[70]	ARGAST D, FITZGERALD D, HOLSTEIN H, et al. Compensation of the full magnetic tensor gradient signal[J]. ASEG Extended Abstracts, 2010, 2010(1): 1-4.
[71]	ZHDANOV M S, WILSON G A, POLOME L. 3D magnetization vector inversion for SQUID-based full tensor magnetic gradiometry[C]// Proceedings of 2012 SEG Annual Meeting.Las Vegas, NV, US: Society of Exploration Geophysicists, 2012.
[72]	STOLZ R, SCHULZ M, ZAKOSARENKO V, et al. Magnetic full tensor gradiometry[C]// Proceedings of the 11th SAGA Biennial Technical Meeting and Exhibition. Swaziland, South Africa: Southern African Geophysical Association, 2009: cp-241-00010.
[73]	LINZEN S, CHWALA A, SCHULTZE V, et al. A LTS-SQUID system for archaeological prospection and its practical test in Peru[J]. IEEE Transactions on Applied Superconductivity, 2007, 17(2): 750-755.
[74]	MEYER H G, HARTUNG K, LINZEN S, et al. Detection of buried magnetic objects by a SQUID Gradiometer system[J]. Proceedings of SPIE, 2009, 7303: 1-12.
[75]	JANOŠEK M, JAN V, ANTONIN P, et al. Compact full-tensor fluxgate gradiometer[J]. Journal of Electrical Engineering, 2015, 66(7/s): 146-148.
[76]	SCHMIDT A, DABAS M, SARRIS A. Dreaming of perfect data: Characterizing noise in archaeo-geophysical measurements[J]. Geosciences, 2020, 10(10): 382.
[77]	黄玉. 地磁场测量及水下磁定位技术研究[D]. 哈尔滨: 哈尔滨工程大学, 2011.
	HUANG Y. Geomagnetic field measurement and study on underwater magnetic localization technology[D]. Harbin:Harbin Engineering University, 2011. (in Chinese)
[78]	刘丽敏. 磁通门张量的结构设计、误差分析及水下目标探测[D]. 长春: 吉林大学, 2012.
	LIU L M. Configuration design, error analysis, and underwater target detection of fluxgate tensor magnetometer[D]. Changchun: Jilin University, 2012. (in Chinese)
[79]	PANG H F, LUO S T, ZHANG Q, et al. Calibration of a fluxgate magnetometer array and its application in magnetic object localization[J]. Measurement Science and Technology, 2013, 24(7): 075102.
[80]	WU Z T, WU Y X, HU X P, et al. Calibration of three-axis magnetometer using stretching particle swarm optimization algorithm[J]. IEEE Transactions on Instrumentation and Measurement, 2012, 62(2): 281-292.
[81]	PANG H F, PAN M C, WAN C B, et al. Integrated compensation of magnetometer array magnetic distortion field and improvement of magnetic object localization[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 52(9): 5670-5676.
[82]	PANG H F, CHEN D X, PAN M C, et al. Nonlinear temperature compensation of fluxgate magnetometers with a least-squares support vector machine[J]. Measurement Science and Technology, 2012, 23(2): 025008.
[83]	WANG C, QU X D, ZHANG X J, et al. A fast calibration method for magnetometer array and the application of ferromagnetic target localization[J]. IEEE Transactions on Instrumentation and Measurement, 2017, 66(7): 1743-1750.
[84]	李青竹, 李志宁, 张英堂, 等. 平面十字磁梯度张量系统的两步线性校正[J]. 仪器仪表学报, 2017, 38(9): 2232-2242.
	LI Q Z, LI Z N, ZHANG Y T, et al. Two step linear calibration of planar cross magnetic gradient Tensor system[J]. Chinese Journal of Scientific Instrument, 2017, 38(9): 2232-2242. (in Chinese)
[85]	LI Q Z, SHI Z Y, LI Z N, et al. Preferred configuration and detection limits estimation of magnetic gradient tensor system[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1010214.
[86]	李青竹, 石志勇, 李志宁, 等. 差分磁梯度张量测量极限估计[J]. 光学精密工程, 2022, 30(11):1325-1336.
	LI Q Z, SHI Z Y, LI Z N, et al. Estimation method for differential magnetic gradient tensor measurement limits[J]. Optics and Precision Engineering, 2022, 30(11): 1325-1336. (in Chinese)
[87]	LI Q Z, LI Z N, SHI Z Y, et al. Multi-Target magnetic positioning using SAFCM clustering and invariants-improved tilt angle[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5924015
[88]	LV J W, YU Z T, HUANG J L, et al. The compensation method of vehicle magnetic interference for the magnetic gradiometer[J]. Advances in Mathematical Physics, 2013, 2013(1): 523164.
[89]	SHEN M D, CHENG D F, AN Z F, et al. Geometry structure optimization of hexagonal pyramidal full tensor magnetic gradient probe[J]. IEEE Transactions on Magnetics, 2016, 52(9): 6100507.
[90]	QIU L Q, RONG L L, WU J, et al. Development of a squid-based airborne full tensor gradiometers for geophysical exploration[C]// SEG Technical Program Expanded Abstracts 2016. Online: Society of Exploration Geophysicists, 2016: 1652-1655.
[91]	WU J, XIE X M. The study of several key parameters in the design of airborne superconducting full tensor magnetic gradient measurement system[C]// SEG Technical Program Expanded Abstracts 2016. Online: Society of Exploration Geophysicists, 2016: 1588-1591.
[92]	庞鸿锋. 捷联式地磁矢量测量系统误差分析及校正补偿技术[D]. 长沙: 国防科学技术大学, 2015.
	PANG H F. Error analysis and calibration/ compensation method of strap-down geomagnetic vector measurement system[D]. Changsha: National University of Defense Science and Technology, 2015. (in Chinese)
[93]	王一凡. 面向机载地磁测量的磁干扰补偿技术研究[D]. 武汉: 华中科技大学, 2012.
	WANG Y F. A thesis submitted in partial fulfillment of the requirements for the degree of master of science[D]. Wuhan: Huazhong University of Science and Technology, 2012. (in Chinese)
[94]	PRIMDAHL F. Temperature compensation of fluxgate magnetometers[J]. IEEE transactions on magnetics, 1970, 6(4): 819-822.
[95]	李青竹, 李志宁, 张英堂, 等. 磁梯度张量系统传感器阵列的快速旋转校准[J]. 光学精密工程, 2018, 26(7): 1813-1826.
	LI Q Z, LI Z N, ZHANG Y T, et al. Fast rotation calibration of sensor array in magnetic gradient tensor system[J]. Optics and Precision Engineering, 2018, 26(7): 1813-1826. (in Chinese)
[96]	王婕, 郭子祺, 刘建英. 固定翼无人机航磁探测系统的磁补偿模型分析[J]. 航空学报, 2016, 37(11):3435-3443. doi: 10.7527/S1000-6893.2016.0059
	WANG J, GUO Z Q, LIU J Y. Analysis on magnetic compensation model of fixed-wing UAV aeromagnetic detection system[J] Acta Aeronautica et Astronautica Sinica, 2016, 37(11): 3435-3443. (in Chinese) doi: 10.7527/S1000-6893.2016.0059
[97]	张宁, 赵建扬, 林春生, 等. 直升机平台背景磁干扰小信号模型求解与补偿[J]. 电子学报, 2017, 45(1):83-88. doi: 10.3969/j.issn.0372-2112.2017.01.012
	ZHANG N, ZHAO J Y, LIN C S, et al. Helicopter platform background magnetic interference small signal model solving and compensation[J]. Acta Electronica Sinica, 2017, 45(1):83-88. (in Chinese) doi: 10.3969/j.issn.0372-2112.2017.01.012
[98]	MERAYO J M G, BRAUER P, PRIMDAHL F, et al. Scalar calibration of vector magnetometers[J]. Measurement Science and Technology, 2000, 11: 120-132.
[99]	PYLYANAINEN T. Automatic and adaptive calibration of 3D field sensors[J]. Applied mathematical modelling, 2007, 32: 575-587.
[100]	ALONSO R, SHUSTER M D. Centering and observability in attitude independent magnetometer bias determination[J]. The journal of the astronautical sciences, 2003, 51(2): 133-141.
[101]	李青竹, 李志宁, 张英堂, 等. 磁梯度张量系统的非线性集成矢量校正[J]. 武汉大学学报(信息科学版), 2019, 44(5): 714-722, 730.
	LI Q Z, LI Z N, ZHANG Y T, et al. Integrated vector calibration of magnetic gradient tensor system using nonlinear method[J]. Geomatics and Information Science of Wuhan University, 2019, 44(5):714-722, 730. (in Chinese)
[102]	王振雄, 张琦, 潘孟春, 等. 基于粒子群算法的地磁矢量测量系统一体化校正[J]. 中国测试, 2022, 48(6): 13-17, 25.
	WANG Z X, ZHANG Q, PAN M C, et al. Comprehensive calibration of geomagnetic vector measurement system based on PSO[J]. China Measurement & Test, 2022, 48(6): 13-17, 25. (in Chinese)
[103]	徐祥, 刘铭, 曹国灿, 等. 基于自适应参数估计的三轴磁传感器实时校正方法[J]. 中国惯性技术学报, 2019, 27(3): 384-389.
	XU X, LIU M, CAO G C, et al. Real-time calibration method for three-axis magnetometer based on adaptive parameter estimation[J]. Journal of Chinese Inertial Technology, 2019, 27(3): 384-389. (in Chinese)
[104]	罗静博, 陈浩, 赵苗, 等. 基于改进型入侵野草算法的三轴磁传感器非正交误差校正[J]. 兵工学报, 2019, 40(12): 2513-2518. doi: 10.3969/j.issn.1000-1093.2019.12.016
	LUO J B, CHEN H, ZHAO M, et al. Non-orthogonal error correction of three-axis magnetic sensor based on improved IWO algorithm[J]. Acta Armamentarii, 2019, 40(12): 2513-2518. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.12.016
[105]	高全明. 固定翼无人机航磁三分量系统误差校正与干扰补偿技术研究[D]. 长春: 吉林大学, 2020.
	GAO Q M. Research on system error calibration and interference compensation technology of aeromagnetic three-component survey based on fixed-wing UAV[D]. Changchun: Jilin University, 2020. (in Chinese)
[106]	CRASSIDIS J L, LAI K L. Real-time attitude-independent three-axis magnetometer calibration[J]. Journal of guidance of control and dynamics, 2005, 28: 115-120.
[107]	吴德会, 黄松岭, 赵伟. 基于FLANN 的三轴磁强计误差校正研究[J]. 仪器仪表学报, 2009, 30(3): 449-453.
	WU D H, HUANG S L, ZHAO W. Research correction of tri-axiamagnemeter based on FLANN[J]. Chinese Journal of Scientific Instrument, 2009, 30(3): 449-453. (in Chinese)
[108]	魏祎. 基于MEMS惯性传感器的磁力计校准技术研究[D]. 北京: 北京邮电大学, 2020.
	WEI W. Research on magnetometer calibration technology based on MEMS inertial sensors[D]. Beijing: Beijing University of Posts and Telecommunications, 2020. (in Chinese)
[109]	张海波, 翟晶晶, 李享, 等. 一种用于磁场复现和屏蔽的磁干扰主动补偿技术[J]. 宇航计测技术, 2021, 41(3):68-72.
	ZHANG H B, ZHAI J J, LI X, et al. An active compensation method of enviromental interference magnetic field for magnetic field reproduction and shielding[J]. Journal of Astronautic Metrology and Measurement, 2021, 41(3): 68-72. (in Chinese)
[110]	DAI J L, MENG L F, HUANG K, et al. Research on magnetic characteristics of small UAV for aeromagnetic measurement[J]. IOP Conference Series: Earth and Environmental Science, 2019, 310(3): 032068.
[111]	HAN Q, DOU Z J, TONG X J, et al. A modified Tolles-Lawson model robust to the errors of the three-axis strapdown magnetometer[J]. IEEE Geoscience and Remote Sensing Letters, 2017, 14(3): 334-338.
[112]	于振涛, 吕俊伟, 毕波, 等. 四面体磁梯度张量系统的载体磁干扰补偿方法[J]. 物理学报, 2014, 63(11): 110702.
	YU Z T, LÜ J W, BI B, et al. A vehicle magnetic noise compensation method for the tetrahedron magnetic gradiometer[J]. Acta Physica Sinica, 2014, 63(11): 110702. (in Chinese)
[113]	孙宇慧. 基于优化BP神经网络的磁补偿算法研究[D]. 哈尔滨: 哈尔滨工业大学, 2018.
	SUN Y H. Research on magnetic compensation Algorithm based on optimized BP neural network[D]. Harbin:Harbin Institute of Technology, 2018. (in Chinese)
[114]	吕辰, 张晓明, 檀杰, 等. 基于遗忘因子递推最小二乘的无人机在线磁补偿技术研究[J]. 传感技术学报, 2018, 31(2): 218-222.
	LV C, ZHANG X M, TAN J, et al. Research of on-line magnetic compensation technology for UAV based on forgetting factor and RLS[J]. Chinese Journal of Sensors and Actuators, 2018, 31(2): 218-222. (in Chinese)
[115]	于彩霞, 魏文博, 景建恩, 等. 希尔伯特-黄变换在海底大地电磁测深数据处理中的应用[J]. 地球物理学进展, 2010, 25(3): 1046-1056.
	YU C X, WEI W B, JING J E, et al. Application of Hilbert-Huang transformation to marine magnetotelluric sounding data processing[J]. Progress in Geophysics, 2010, 25(3): 1046-1056. (in Chinese)
[116]	KONSTANTIN D, DOMINIQUE Z. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62: 531-544.
[117]	李金朋, 任国全, 张英堂, 等. 改进二维变分模态分解的磁源分离[J]. 光学精密工程, 2020, 28(5):1200-1211.
	LI J P, REN G Q, ZHANG Y T, et al. Source separation based on improved two-dimensional variational mode decomposition[J]. Optics and Precision Engineering, 2020, 28(5):1200-1211. (in Chinese)
[118]	胡佃波, 焦磊明, 庞曦. 基于VMD的大地电磁信号去噪研究[J]. 能源与环保, 2020, 42(5): 72-77.
	HU D B, JIAO L M, PANG X. Research on denoising of magnetotelluric signal based on VMD[J]. China Energy and Environmental Protection, 2020, 42(5): 72-77. (in Chinese)
[119]	DEL N C, GRECO F, NAPOLI R, et al. Denoising gravity and geomagnetic signals from Etna volcano (Italy) using multivariate methods[J]. Nonlinear Processes in Geophysics, 2008, 15(5): 735-749.
[120]	谢凡, 滕云田, 徐平. 应用独立分量分析方法提取和剥离地磁观测中的轨道交通干扰[J]. 地球物理学进展, 2011, 26(5):1824-1831.
	XIE F, TENG Y T, XU P. Removal of EM interference generated by urban railway transit from geomagnetic observation by ICA method[J]. Progress in Geophysics, 2011, 26(5): 1824-1831. (in Chinese)
[121]	谢凡, 滕云田, 胡星星. 数学形态滤波在地磁数据干扰抑制中的应用[J]. 地球物理学进展, 2011, 26(1): 147-156.
	XIE F, TENG Y T, HU X X. Application of mathematical morphology-based filter in denoising geomagnetic data[J]. Progress in Geophysics, 2011, 26(1): 147-156. (in Chinese)
[122]	李季, 潘孟春, 唐莺, 等. 基于形态滤波和HHT的地磁信号分析与预处理[J]. 仪器仪表学报, 2012, 33(10):2175-2180.
	LI J, PAN M C, TANG Y, et al. Analysis and preprocessing of geomagnetic signals based on morphological filter and Hilbert-Huang transform[J]. Chinese Journal of Scientific Instrument, 2012, 33(10):2175-2180. (in Chinese)
[123]	陈海龙, 王长龙, 左宪章, 等. 磁记忆梯度张量测量信号预处理方法[J]. 系统工程与电子技术, 2017, 39(3): 488-493.
	CHEN H L, WANG C L, ZUO X Z, et al. Metal magnetic memory gradient tensor signal processing method[J]. Systems Engineering and Electronics, 2017, 39(3): 488-493. (in Chinese) doi: 10.3969/j.issn.1001-506X.2017.03.05
[124]	王海军, 邵宝武, 王海燕, 等. 基于数学形态学和Hough变换的高分辨率遥感影像道路提取[J]. 地理信息世界, 2018, 25(2):108-112.
	WANG H J, SHAO B W, WANG H Y, et al. Road extraction using high resolution remote sensing image based on mathematical morphology[J]. Geomatics World, 2018, 25(2):108-112. (in Chinese)
[125]	郑华林, 王超, 潘盛湖, 等. 基于EEMD和分层阈值的磁记忆信号降噪方法研究[J]. 工程设计学报, 2020, 27(4): 433-440.
	ZHENG H L, WANG C, PAN S H, et al. Research on noise reduction method of magnetic memory signal based on EEMD and layered threshold[J]. Chinese Journal of Engineering Design, 2020, 27(4): 433-440. (in Chinese)
[126]	张朝阳, 肖昌汉, 高俊吉, 等. 磁性物体磁偶极子模型适用性的试验研究[J]. 应用基础与工程科学学报, 2010, 18(5): 862-868.
	ZHANG C Y, XIAO C H, GAO J J, et al. Experiment research of magnetic dipole model applicability for a magnetic object[J]. Journal of Basic Science and Engineering, 2010, 18 (5): 862-868. (in Chinese)
[127]	FAN L M, KANG X Y, ZHENG Q, et al. A fast linear algorithm for magnetic dipole localization using total magnetic field gradient[J]. IEEE Sensors Journal, 2017, 18(3): 1032-1038.
[128]	贾文抖, 林春生, 孙玉绘, 等. 基于单个磁梯度计的磁目标定位方法研究[J]. 兵工学报, 2017, 38(8):1572-1577. doi: 10.3969/j.issn.1000-1093.2017.08.015
	JIA W D, LIN C S, SUN Y H, et al. Research on magnetic target location method based on a single magnetic gradiometer[J]. Acta Armamentarii, 2017, 38(8): 1572-1577. (in Chinese)
[129]	NARA T, SUZUKI S, ANDO S. A closed-form formula for magnetic dipole localization by measurement of its magnetic field and spatial gradients[J]. IEEE transactions on magnetics, 2006, 42(10): 3291-3293.
[130]	CLARK D A. Corrigendum to: New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength[J]. Exploration Geophysics, 2014, 45(4): 324-324.
[131]	LIU K, SUI Y Y, CHENG H, et al. Magnetic dipole moment determination using near-field magnetic gradient tensor data[J]. IEEE Geoscience and Remote Sensing Letters, 2020, 18(7): 1169-1173.
[132]	刘继昊, 李夕海, 曾小牛. 基于两点磁梯度张量的磁性目标在线定位方法[J]. 地球物理学报, 2017, 60(10): 3995-4004. doi: 10.6038/cjg20171026
	LIU J H, LI X H, ZENG X N. Online magnetic target location method based on the magnetic gradient tensor of two points[J]. Chinese Journal of Geophysics, 2017, 60(10): 3995-4004. (in Chinese)
[133]	李青竹, 李志宁, 张英堂, 等. 张量衍生不变关系下的磁源单点定位[J]. 光学精密工程, 2019, 27(8):1880-1893.
	LI Q Z, LI Z N, ZHANG Y T, et al. Magnetic source single-point positioning by tensor derivative invariant relations[J]. Optics and Precision Engineering, 2019, 27(8): 1880-1893. (in Chinese)
[134]	李青竹, 李志宁, 张英堂, 等. 基于二阶磁张量欧拉反褶积的磁源单点定位方法[J]. 石油地球物理勘探, 2019, 54(4): 915-924.
	LI Q Z, LI Z N, ZHANG Y T, et al. Magnetic source single-point positioning based on second-order magnetic tensor Euler deconvolution[J]. Oil Geophysical Prospecting, 2019, 54(4): 915-924. (in Chinese)
[135]	HANSEN R O, SIMMONDS M. Multiple-source Werner deconvolution[J]. Geophysics, 1993, 58(12): 1792-1800.
[136]	HANSEN R O. 3D multiple-source Werner deconvolution for magnetic data[J]. Geophysics, 2005, 70(5): L45-L51.
[137]	王林飞, 郭灿灿, 薛典军, 等. 磁梯度张量解析信号分析法及其在场源位置识别中的应用[J]. 地球物理学进展, 2016, 31(3):1164-1172.
	WANG L F, GUO C C, XUE D J, et al. Analytic signals of magnetic gradient tensor and their application to estimate source location[J]. Progress in Geophysics, 2016, 31(3): 1164-1172. (in Chinese)
[138]	李金朋, 张英堂, 范红波, 等. 基于磁传感器阵列的多磁源参数反演方法[J]. 仪器仪表学报, 2019, 40(10):28-37.
	LI J P, ZHANG Y T, FAN H B, et al. Multi-magnetic source parameter inversion method based on magnetic sensor array[J]. Chinese Journal of Scientific Instrument, 2019, 40(10):28-37. (in Chinese)
[139]	UGALDE H, MORRIS W A. Cluster analysis of Euler deconvolution solutions: new filtering techniques and geologic strike determination[J]. Geophysics, 2010, 75(3): L61-L70.
[140]	REN M, LIU P Y, WANG Z H, et al. A self-adaptive fuzzy c-means algorithm for determining the optimal number of clusters[J]. Computational Intelligence and Neuroscience, 2016, 2016: 2647389.
[141]	YIN G, ZHANG Y T, FAN H B, et al. Automatic detection of multiple UXO-like targets using magnetic anomaly inversion and self-adaptive fuzzy c-means clustering[J]. Exploration geophysics, 2017, 48(1): 67-75.
[142]	ZHOU Z J, ZHANG M, CHEN J F. A new multiple magnetic targets location method in 3D space[C]// SEG Technical Program Expanded Abstracts 2020. Online: Society of Exploration Geophysicists, 2020: 974-978.
[143]	李青竹, 李志宁, 石志勇, 等. AFCM聚类和张量不变量用于磁源多目标定位[J]. 光学精密工程, 2022, 30(20): 2523-2537.
	LI Q Z, LI Z N, SHI Z Y, et al. Multi-target magnetic positioning with the adaptive fuzzy c-means clustering and tensor invariants[J]. Optics and Precision Engineering, 2022, 30(20): 2523-2537. (in Chinese)
[144]	HELBIG K. Some integrals of magnetic anomalies and their relation to the parameters of the disturbing body[J]. Zeitschrift fur Geophysik, 1963, 29(2): 83-96.(in Germany)
[145]	SCHMIDT P W, CLARK D A. The calculation of magnetic components and moments from TMI: a case study from the Tuckers igneous complex, Queensland[J]. Exploration Geophysics, 1998, 29(4): 609-614.
[146]	PHILLIPS J D. Can we estimate total magnetization directions from aeromagnetic data using Helbig’s integrals?[J]. Earth, Planets and Space, 2005, 57(8): 681-689.
[147]	LI Q Z, LI Z N, SHI Z Y, et al. Application of Helbig integrals to magnetic gradient tensor multi-target detection[J]. Measurement, 2022, 200: 111612.
[148]	DAVIS K, LI Y, NABIGHIAN M. Automatic detection of UXO magnetic anomalies using extended Euler deconvolution[J]. Geophysics, 2010, 75(3): G13-G20.
[149]	SONG S, HU C, MENG M Q H. Multiple objects positioning and identification method based on magnetic localization system[J]. IEEE Transactions on Magnetics, 2016, 52(10): 9600204.
[150]	MILLER H G, SINGH V. Potential field tilt-a new concept for location of potential field sources[J]. Journal of Applied Geophysics, 1994, 32(2/3): 213-217
[151]	LI J P, ZHANG Y T, FAN H B, et al. Estimating the location of magnetic sources using magnetic gradient tensor data[J]. Exploration Geophysics, 2019, 50(6): 600-612.
[152]	GEROVSKA D, ARAUZO-BRAVO M J, STAVREV P. Determination of the parameters of compact ferro-metallic objects with transforms of magnitude magnetic anomalies[J]. Journal of Applied Geophysics, 2004, 55(3/4): 173-186.
[153]	BEIKI M, CLARK D A, AUSTIN J R, et al. Estimating source location using normalized magnetic source strength calculated from magnetic gradient tensor data[J]. Geophysics, 2012, 77(6): J23-J37.
[154]	马国庆, 李丽丽, 杜晓娟. 磁张量数据的边界识别和解释方法[J]. 石油地球物理勘探, 2012, 47(5): 815-821, 844, 682.
	MA G Q, LI L L, DU X J. Boundary detection and interpretation by magnetic gradient tensordata[J]. Oil Geophysical Prospecting, 2012, 47(5): 815-821, 844, 682. (in Chinese)
[155]	CLARK D A. New methods for interpretation of magnetic vector and gradient tensor data II: application to the Mount Leyshon anomaly, Queensland, Australia[J]. Exploration Geophysics, 2013, 44(2): 114-127.
[156]	ZHANG J H, MA W W, LIN J W, et al. Fault diagnosis approach for rotating machinery based on dynamic model and computational intelligence[J]. Measurement, 2015, 59: 73-87.
[157]	ZHENG J Y, FAN H B, YIN G, et al. A method of using geomagnetic anomaly to recognize objects based on HOG and 2D-AVMD[J]. AIP Advances, 2019, 9(7): 075015.
[158]	JAIN A K, DUIN R P W, MAO J. Statistical pattern recognition: a review[J]. IEEE Transactions on pattern analysis and machine intelligence, 2000, 22(1): 4-37.
[159]	HUANG G B, ZHU Q Y, SIEW C K. Extreme learning machine: theory and applications[J]. Neurocomputing, 2006, 70(1/2/3): 489-501.
[160]	SNYDSMAN W E, AMINZADEH F, WEIL C B. Pattern recognition in geophysical exploration[J]. Proceedings of SPIE, 1987, 768: 53-60.
[161]	RAICHE A. A pattern recognition approach to geophysical inversion using neural nets[J]. Geophysical Journal International, 1991, 105(3): 629-648.
[162]	ROSATI I, CARDARELLI E. Statistical pattern recognition technique to enhance anomalies in magnetic surveys[J]. Journal of Applied Geophysics, 1997, 37(2):55-66.
[163]	CARLOS C M, SEN M K, STOFFA P L. Artificial neural networks for parameter estimation in geophysics[J]. Geophysical Prospecting, 2000, 48(1): 21-47.
[164]	FERNANDEZ J P, BARROWES B, O’NEILL K, et al. Evaluation of SVM classification of metallic objects based on a magnetic-dipole representation[J]. Proceedings of SPIE, 2006, 6217: 621703.
[165]	TURLAPATY A C, ANANTHARAJ V G, YOUNAN N H. A pattern recognition based approach to consistency analysis of geophysical datasets[J]. Computers & Geosciences, 2010, 36(4): 464-476.
[166]	EHRET B. Pattern recognition of geophysical data[J]. Geoderma, 2010, 160(1): 111-125.
[167]	AL-GARNI M A. Interpretation of magnetic anomalies due to dipping dikes using neural network inversion[J]. Arabian Journal of Geosciences, 2015, 8(10): 8721-8729.
[168]	谢永茂. 基于模板匹配的局部磁异常识别方法[D]. 北京: 中国地质大学(北京), 2012.
	XIE Y M. Recognition of magnetic local anomaly based on template matching[D]. Beijing: China University of Geosciences (Beijing), 2012. (in Chinese)
[169]	李昌珑, 李宗超, 吕红山, 等. 基于三维图像模式识别的西藏东南部地震灾害损失风险评估[J]. 地球物理学报, 2019, 62(1):393-410.
	LI C L, LI Z C, LÜ H S, et al. Seismic disaster loss risk assessment for southeastern Tibet based on 3D image pattern recognition[J]. Chinese Journal of Geophysics, 2019, 62(1): 393-410. (in Chinese)
[170]	ZHENG J, FAN H, ZHANG Q, et al. Magnetic anomaly target recognition based on SVD and SVMs[J]. IEEE Transactions on Magnetics, 2019, 55(9): 6000708.
[171]	ZHOU Z J, ZHANG M, CHEN J F, et al. Detection and classification of multi-magnetic targets using mask-RCNN[J]. IEEE Access, 2020, 8: 187202-187207.
[172]	李青竹, 李志宁, 石志勇, 等. MGTS单航线测量用于磁性目标模式识别[J]. 光学精密工程, 2023, 31(6):872-891.
	LI Q Z, LI Z N, SHI Z Y, et al. Single heading-line survey of MGTS for magnetic target pattern recognition[J]. Optics and Precision Engineering, 2023, 31(6):872-891. (in Chinese)