均匀磁化直立长方体磁力三阶梯度张量无解析奇点正演计算公式研究  

Forward modeling formulae without analytic singularities for third-order magnetic gradient tensor of uniformly magnetized vertical cuboid

作　　者：王震 杜劲松[1,2,3] 钱博浩 袁常青 胡正旺 WANG Zhen;DU Jinsong;QIAN Bohao;YUAN Changqing;HU Zhengwang(School of Geophysics and Geomatics,China University of Geosciences,Wuhan,Hubei 430074,China;Hubei Subsurface Multiscale Imaging Key Laboratory,China University of Geosciences(Wuhan),Wuhan,Hubei 430074,China;State Key Laboratory of Geological Processes and Mineral Resources,China University of Geosciences(Wuhan),Wuhan,Hubei 430074,China)

机构地区：[1]中国地质大学(武汉)地球物理与空间信息学院,湖北武汉430074 [2]中国地质大学(武汉)地球内部多尺度成像湖北省重点实验室,湖北武汉430074 [3]中国地质大学(武汉)地质过程与矿产资源国家重点实验室,湖北武汉430074

出　　处：《石油地球物理勘探》2023年第3期728-739,共12页Oil Geophysical Prospecting

基　　金：国家自然科学基金面上项目“青藏高原三维岩石圈磁性结构及其地质意义”(42174090);地质过程与矿产资源国家重点实验室科技部专项“长江中下游矿集区及邻区深部结构探测”(MSFGPMR2022-4)联合资助。

摘　　要：均匀磁化直立长方体是磁力异常正演模拟与三维反演的最基本、最常用的一种场源模型,推导其正演计算解析公式具有重要的理论意义和实用价值。磁力三阶梯度张量是最近提出的一个新概念,可能是未来卫星与航空等磁测研究的一个重要发展方向。此外,多种磁力异常转换参量也涉及磁力三阶梯度张量的部分元素。因此,在前人研究基础上推导了均匀磁化直立长方体的磁力三阶梯度张量无解析奇点正演计算公式。首先验证了该公式的正确性,然后将其应用于总磁场强度异常一阶垂向导数的解析信号、磁力二阶梯度张量不变量的一阶导数、正则化磁源强度的一阶导数的计算。这些高精度、高效率的正演计算解析公式可为将来磁力三阶梯度张量勘探方法研究及基于磁力异常转换参量的解释方法研究奠定重要基础。As one of the most basic and most commonly used source models,the uniformly magnetized vertical cuboid is usually adopted for forward modeling and three-dimensional inversion of magnetic anomalies.Thus,its forward modeling formulae are of great importance both in theory and practice.The third-order magnetic gradient tensor(MGT)is a newly proposed concept and may be an important development direction of satellite magnetic and aeromagnetic surveys.Furthermore,many magnetic transforms for anomaly interpretation involve the forward modeling of several elements of the third-order MGT.Therefore,given the previous studies,the forward modeling formulae without analytic singularities for third-order MGT of the uniformly magnetized vertical cuboid are derived.Then,the correctness of the derived formulae is verified.Finally,the corresponding formulae are applied to the forward modeling of the analytic signal(AS)of the first-order vertical derivatives of total magnetic intensity(TMI)anomalies,first-order derivatives of the invariants of second-order MGT,and the first-order derivatives of normalized source strength(NSS).With high accuracy and high efficiency,the analytic formulae for forward modeling lay the foundation for future magnetic exploration utilizing the third-order MGT and the magnetic anomaly interpretation by magnetic transforms.

关 键 词：直立长方体 磁力三阶梯度张量 磁力异常 解析奇点 正演计算 

分 类 号：P631[天文地球—地质矿产勘探]