First-Order Derivatives of Principal and Main Invariants of Magnetic Gradient Tensor of a Uniformly Magnetized Tesseroid and Spherical Shell

Deng, Xiao-Le1; Shen, Wen-Bin2,3; Yang, Meng4; Kuhn, Michael5,6; Ran, Jiangjun1

2022-03-01

10.1007/s10712-022-09697-1

SURVEYS IN GEOPHYSICS   影响因子和分区

0169-3298

1573-0956

Similar to the gravitational curvatures in the gravity field, the magnetic curvatures (i.e., third-order derivatives of the magnetic potential) have been recently proposed in the magnetic field. The components of the magnetic curvatures are all involved in the expressions for the first-order derivatives of invariants of the magnetic gradient tensor (MGT), whose physical meaning is the change rate of invariants of the MGT and their theoretical models have not yet been fully developed. In this contribution, the general expressions for the First-order derivatives of Principal and Main Invariants of the Magnetic Gradient Tensor (i.e., FPIMGT and FMIMGT) with combined components of the MGT and magnetic curvatures are presented. Specifically, the expressions for the FPIMGT and FMIMGT of a uniformly magnetized tesseroid and spherical shell are derived as examples for basic mass bodies in the spherical coordinate system in the spatial domain for the magnetic field modeling. The near zone and polar singularity problems are numerically investigated for these newly derived expressions. Numerical experiments show that the near zone problem has been found for the FPIMGT and principal invariants of the magnetic gradient tensor (PIMGT), whereas the polar singularity problem does not occur for the FPIMGT and PIMGT when using the Cartesian integral kernels for different heights and grid resolutions. This study shows that the calculation strategy by substituting the calculated values of the MGT and magnetic curvatures into the general formulae of the PIMGT and FPIMGT can provide proper numerical precision measured by relative approximation errors dependent on the computation point's height and latitude for the FPIMGT and PIMGT. For instance, using the grid size of 1 degrees x 1 degrees at a satellite height of 260 km, relative approximation errors in Log(10) scale have been reduced at a level lower than - 1 for the evaluation of the FPIMGT and PIMGT. The first-order derivatives of principal and main invariants of the MGT will be applied in related magnetic field studies (e.g., magnetic detection, inversion, location, position, characterization, navigation, and exploration) to present additional information (i.e., more detailed geophysical features in terms of change rates) compared to the principal and main invariants of the magnetic gradient tensor.

Magnetic field First-order derivatives of invariants of magnetic gradient tensor Magnetic curvatures Tesseroid Spherical shell

SCI ; EI

英语

第一 ; 通讯

China Postdoctoral Science Foundation[2021M691402] ; National Natural Science Foundation of China[42174096,41974094]

Geochemistry & Geophysics

Geochemistry & Geophysics

WOS:000770960500001

SPRINGER

20221211828336

Errors ; Magnetic fields ; Shells (structures) ; Spheres

Structural Members and Shapes:408.2 ; Magnetism: Basic Concepts and Phenomena:701.2 ; Algebra:921.1

GEOSCIENCES

Web of Science

1.Southern Univ Sci & Technol, Dept Earth & Space Sci, Shenzhen 518055, Peoples R China
2.Wuhan Univ, Sch Geodesy & Geomat, Wuhan 430079, Peoples R China
3.Wuhan Univ, State Key Lab Informat Engn Surveying Mapping & R, Wuhan 430079, Peoples R China
4.Sun Yat Sen Univ, Sch Geospatial Engn & Sci, Zhuhai 519082, Peoples R China
5.Curtin Univ, Sch Earth & Planetary Sci, Perth, WA, Australia
6.Curtin Univ, Western Australian Geodesy Grp, Perth, WA, Australia

Deng, Xiao-Le,Shen, Wen-Bin,Yang, Meng,et al. First-Order Derivatives of Principal and Main Invariants of Magnetic Gradient Tensor of a Uniformly Magnetized Tesseroid and Spherical Shell[J]. SURVEYS IN GEOPHYSICS,2022,43:1233-1262.

Deng, Xiao-Le,Shen, Wen-Bin,Yang, Meng,Kuhn, Michael,&Ran, Jiangjun.(2022).First-Order Derivatives of Principal and Main Invariants of Magnetic Gradient Tensor of a Uniformly Magnetized Tesseroid and Spherical Shell.SURVEYS IN GEOPHYSICS,43,1233-1262.

Deng, Xiao-Le,et al."First-Order Derivatives of Principal and Main Invariants of Magnetic Gradient Tensor of a Uniformly Magnetized Tesseroid and Spherical Shell".SURVEYS IN GEOPHYSICS 43(2022):1233-1262.