Non-singular calculation of geomagnetic vectors and geomagnetic gradient tensors

Liu, Xiaogang; Xu, Tianhe; Sun, Bijiao; Li, Xinxing; Wang, Yunpeng; Guan, Bin

doi:10.1002/essoar.10507459.1

Cited by 2 publications

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“…It has important applications in the fields of geomagnetic navigation background field construction, mineral resources development, seismogenic sources tracking, hidden tectonic and volcanic structures revealment, etc. (Beamish & White, 2011; De Ritis et al., 2010; Goodge & Finn, 2010; Hood, 2007; Liu et al., 2018, 2021; Minelli et al., 2016).…”

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confidence: 99%

Application of an Improved Calibration Flight Scheme in Aeromagnetic Interference Compensation

et al. 2022

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The aeromagnetic measurement technology, which can be implemented in areas difficult for ground magnetic measurement, such as desert, glacier, virgin forest and land-sea junction, is one of the most effective means to quickly and economically obtain high-precision geomagnetic data. It has important applications in the fields of geomagnetic navigation background field construction, mineral resources development, seismogenic sources tracking, hidden tectonic and volcanic structures revealment, etc.

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Section: Introductionmentioning

confidence: 99%

Application of an Improved Calibration Flight Scheme in Aeromagnetic Interference Compensation

et al. 2022

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“…Some previous efforts have solved the singularity problem of SHEs of gravitational field elements (Balmino et al, 1990;Bettadpur, 1995;Casotto & Fantino, 2007;Eshagh, 2008Eshagh, , 2009Eshagh & Sjöberg, 2009;Hotine & Morrison, 1969;Ilk, 1983;Liu et al, 2010Liu et al, , 2013Petrovskaya & Vershkov, 2006, 2008Wan, 2011;Zhu et al, 2017), whereas the same problem still exists in GVs and GGTs. The reason is that the gravitational field elements are expressed by fully normalized associated Legendre function (FNALF) (Chen et al, 2006;Fantino & Casotto, 2009;Fukushima, 2012aFukushima, , 2012bHirt et al, 2010;Jekeli & Lee, 2007;Liu et al, 2012;Pail et al, 2011;Pavlis et al, 2012;Rummel et al, 2011;Wan & Yu, 2013;Šprlák & Novák, 2017), while the GVs and GGTs are expressed by Schmidt semi-normalized associated Legendre function (SNALF) (Barraclough, 1974;Benton et al, 1982;Blakely, 1995;Chambodut et al, 2005;Du et al, 2015;Hemant & Maus, 2005;Huang et al, 2011;Kim et al, 2007;Kotsiaros & Olsen, 2012;Langel, 1987;Liu et al, 2019;Malin & Pocock, 1969;Quinn et ...…”

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Non‐Singular Calculation of Geomagnetic Vectors and Geomagnetic Gradient Tensors

Liu

Sun

et al. 2021

JGR Solid Earth

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Some spherical harmonic expressions of gravitational and geomagnetic field elements will become infinite when computation point approaches polar regions, as the sine function of the geocentric co‐latitude contained in the denominator tends to be zero. Currently, this singularity problem has been solved for gravitational field case, however, it remains unsolved for geomagnetic vectors (GVs) and geomagnetic gradient tensors (GGTs). Because the latter use Schmidt semi‐normalized associated Legendre function (SNALF), which is different from fully‐normalized associated Legendre function used in the former. To overcome this singularity problem, we derive new non‐singular expressions of the first‐ and second‐order derivatives of Schmidt SNALF (order m equals to 0 or 1), and the corresponding two kinds of spherical harmonic polynomials. When the non‐singular expressions are applied to the traditional formulae of GVs and GGTs, more practical expressions of GVs and GGTs with non‐singularity are formulated by refining the cases that the order m equals to 0, 1, 2 and other values. Furthermore, to provide flexible calculation strategies for Schmidt SNALF, we derive four kinds of recursive formulae, including the standard forward row recursion, the standard forward column recursion, the cross degree and order recursion, and the Belikov recursion. The standard formula to check the calculation accuracy of various recursive formulae of SNALF are also given. Besides, we demonstrate the effectiveness and reliability of the new derived non‐singular expressions of GVs and GGTs and analyze the computation speed and stability of the four recursive formulae by extensive numerical experiments.

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Non-singular calculation of geomagnetic vectors and geomagnetic gradient tensors

Cited by 2 publications

References 33 publications

Application of an Improved Calibration Flight Scheme in Aeromagnetic Interference Compensation

Application of an Improved Calibration Flight Scheme in Aeromagnetic Interference Compensation

Non‐Singular Calculation of Geomagnetic Vectors and Geomagnetic Gradient Tensors

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