Abstract
The transformation of the magnetization direction and the magnetic field component is one of the important methods in magnetic data processing and transformation, which can be conducted in both wavenumber and spatial domains. The transformation method in the wavenumber domain has simpler processing expression and higher processing efficiency than in the spatial domain; however, they are unstable at low latitude. In this paper, the conclusion that the sum is 0 of two vertical magnetic field components (magnetization inclinations are also perpendicular) in 2D is used for the 3D transformation of the magnetization direction and the magnetic field component. In addition, the transformation method at low latitudes based on vertical relationship (VMT) is proposed, which is an iterative algorithm that converts the transformation of the magnetization direction and the magnetic field component at the low latitude into the high latitude. This method restrains the instability of transformation of constant and variable magnetization direction and magnetic field components in low latitudes. The accuracy, stability, and practicality are verified from synthetic models and real data.
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References
Arkani-Hamed, J., 1988, Differential reduction-to-the-pole of regional magnetic anomalies: Geophysics, 53(12), 1592–1600.
Arkani-Hamed, J., 2007, Differential reduction to the pole: Revisited: Geophysics, 72(1), 13–20.
Baranov, V., and Naudy, H., 1957, Numerical calculation of the formula of reduction to the magnetic pole: Geophysics, 22(2), 358–383.
Bhattacharyya, B. K., 1965, Two-dimensional harmonic analysis as a tool for magnetic interpretation: Geophysics, 30(5), 829–857.
Chen, J., Gao, D. Z., Wen, N., et al, 2010, Characteristics of the geomagnetic field in the South China Sea: Progress in Geophys. (in Chinese), 2010, 25(2), 376–388.
Coopera, G. R. J., and Cowanb, D. R., 2005, Differential reduction to the pole: Computers & Geosciences, 31(8), 989–999.
Fang, Y. Y., Zhang, P. P., and Liu, H. J., 2006, Approaches to the interpretation of magnetic of ΔT anomalies in the low magnetic latitude area: Geophysical & Geochemical Exploration (in Chinese), 30(1), 49–54.
Guan, Z. N., 2005, Geomagnetic Field and Magnetic Exploration (in Chinese): Geological Publishing House, Beijing, 95.
Guo, Z. H., 1997, Application of equivalent source technique in the reduced to the pole of aeromagnetic prospecting within the low latitude area: BeiJing Geology (in Chinese), 8(2), 14–22.
Hansen, R. O., and Pawlowski, R. S., 1989, Reduction to the pole at low latitudes by wiener filtering: Geophysics, 54(12), 1607–1613.
Hao, M. C., Zhang, F. X., Tai, Z. H., et al, 2018, Reduction to the pole at low latitudes by using the Taylor series iterative method: Journal of Applied Geophysics, 159, 127–134.
Jing. L., Yang, Y. B., Chen, L., et al, 2017, An improved damping method for reduction to the pole of magnetic anomalies at low latitudes: Chinese J: Geophys. (in Chinese), 60(2), 843–850.
Keating, P., and Zerbo, L., 1996, An improved technique for reduction to the pole at low latitude: Geophysics, 61(1), 131–137.
Li, Q., Li, Q. C., and Jing, Y. H., 2014, The varying inclination method for magnetic reduction to the pole: Progress in Geophysics (in Chinese), 29(4), 1497–1502.
Li, X., 2008, Magnetic reduction-to-the-pole at low latitudes: Observations and considerations: The Leading Edge, 27(8), 990–1001.
Li, Y. G., Nabighian, M., and Oldenburg, D. W., 2014. Using an equivalent source with positivity for low-latitude reduction to the pole without striation: Geophysics, 79(6): 81–90.
Li, Y. G., and Oldenburg, D. W., 2001, Stable reduction to the pole at the magnetic equator: Geophysics, 66(2), 571–578.
Lin, X. X., and Wang, P., 2012, An improved method for reduction to the pole of magnetic at low latitude—the method for frequency conversion bidirectional damping factor: Chinese J. Geophys. (in Chinese), 55(10), 3477–3484.
Liu, W. M., and Zhou, X. M., 1998, The study of a new method of reduction to the magnetic pole in the low latitude region: World Geology (in Chinese), 17(1), 69–72.
Liu, X. H., and Zou, X. M., 1993, The theory of differential reduction to the pole of magnetic anomalies: Journal of ChangChun University of Earth Sciences (in Chinese), 23(1), 87–93.
Liu, Z. J., Zhang, Y. J., and Zhao, B. M., 2010, The application of the magnetic of reduction to the pole with zonation and differential inclinations to large-area aeromagnetic interpretation: Geophysical & geochemical exploration (in Chinese), 34(2), 222–224.
Luo, Y., and Xue, D. J., 2009, Stable reduction to the pole at low magnetic latitude by probability tomography: Chinese J. Geophys. (in Chinese), 52(7), 1907–1914.
Luo, Y., and Xue, D. J, 2010, Reduction to the pole at the geomagnetic equator: Chinese J. Geophys. (in Chinese), 53(12), 2998–3004.
Ma, T., Zhu, Y. J., Yang, Y., et al, 2020, Research on tectonic division in Jiaxie guyots based on gravity and magnetic anomalies: Geophysical and Geochemical Exploration, 44(4), 938–948.
Macleod, I. N., Jones, K., and Dai, T. F., 1993, 3-D analytic signal in the interpretation of total magnetic field data at low magnetic latitudes: Exploration Geophysics, 24(4), 679–688.
Mendonca, C. A., and Silva, J. B. C., 1993, A stable truncated series approximation of the reduction-to-the-pole operator: Geophysics, 58(8), 1084–1090.
Ribeiro, V. B., 2020, Recovering the total magnetization direction using a novel stable reduction to the pole filter (RTP): Journal of Applied Geophysics, 182, 104182.
Shi, L., Guo, L. H., Meng, X. H., et al, 2012, The modified pseudo inclination method for magnetic reduction to the pole at low latitudes: Chinese J. Geophys. (in Chinese), 55(5), 1775–1783.
Silva, J. B. C., 1986, Reduction to the pole as an inverse problem and its application to low-latitude anomalies: Geophysics, 51(2), 369–383.
Stewart, I. C. F., 2019, A simple approximation for low-latitude magnetic reduction-to-the-pole: Journal of Applied Geophysics, 166, 57–67.
Swain, C. J., 2000, Reduction-to the-pole of regional magnetic data with variable field direction, and its stabilization at low inclinations: Exploration Geophysics, 31(2), 078–083.
Wu, J. S., and Wang, J. L., 1992, Improving the effect of reducing magnetic anomaly to pole in low magnetic latitude area by using directional high cut filter: Oil Geophysical Prospecting (in Chinese), 27(5), 670–677.
Yao, C. L., and Guan, Z. N., 1997, Overcoming the difficulty of reduction to the pole at the low altitudes: Journal of Changchun University of Earth Sciences (in Chinese), 27(2), 178–181.
Yao, C. L., Guan, Z. N., Gao, D. Z., et al. 2003. Reduction to the pole of magnetic anomalies at low latitude with suppression filter. Chinese J. Geophys. (in Chinese), 46(5):690–696.
Yao, C. L., Huang, W. N., Zhang, Y. W., et al, 2004, Reduction to the pole at low latitude by direct damper filtering: Oil Geophysical Prospecting (in Chinese), 39(5), 600–606.
Yao, C. L., Li, H. W., Zhen, Y. M., et al, 2012, Research on iteration method using in potential field transformations: Chinese J. Geophys. (in Chinese), 55(6), 2062–2078.
Zeng, X. N., Li, X. H., Liu, Z. G., et al, 2016, Regularization method for reduction to the pole components transformation of magnetic anomaly at low latitudes, Geomatics and Information Science of Wuhan University (in Chinese), 41(3), 389–394.
Zhang, H. L., Marangoni, Y. R., Hu, X. Y., et al, 2014, NTRTP: a new reduction to the pole method at low latitudes via a nonlinear thresholding: Journal of Applied Geophysics, 111, 220–227.
Zhang, P. Q., and Zhao, Q. Y., 1996, Method of the magnetic direction transform of aeromagnetic anomalies with differential inclinations in low magnetic latitudes: Geophysical & geochemical exploration (in Chinese), 18(3), 207–214.
Zhang, Q., Zhang, Y. T., Li, Z. N., et al, 2018, An improved stable algorithm of the reduction to the pole at low latitude, Oil Geophysical Prospecting (in Chinese), 53(3), 606–616.
Zhang, X. L., 1994, The least mean-square error filtering reduction to the pole of magnetic anomalies: Geophysical & Geochemical Exploration (in Chinese), 19(3), 200–211.
Acknowledgments
The authors thank the reviewers for their comments and the editor for editing the paper. This study was supported by the subject “Study on the Comprehensive Processing and Interpretation Method and Software Development for Aerial Geophysics (No. 2017YFC0602202)” from National major Research and Development Project of China (No. 2017YFC0602200).
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He Tao is a Ph.D. candidate at Chang’an University. His research interests are gravity and magnetic theory methods and application research
Wang Wan-Yin, Professor, earned his Ph.D. in 2009 from the Chang’an University in Xi’an. He is currently teaching at Chang’an University. His research interests include the processing, inversion, and interpretation of gravity and magnetic potential fields.
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Tao, H., Sheng-Qing, X. & Wan-Yin, W. Three-dimensional transformation of magnetization direction and magnetic field component at low latitudes based on vertical relationship. Appl. Geophys. 19, 91–106 (2022). https://doi.org/10.1007/s11770-022-0928-4
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DOI: https://doi.org/10.1007/s11770-022-0928-4