Abstract：
Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. ?T at all points in the source-free space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.
KUANG Xing-Tao,YANG Hai,ZHU Xiao-Ying et al. Singularity-free expression of magnetic field of cuboid under undulating terrain[J]. APPLIED GEOPHYSICS, 2016, 13(2): 238-248.
[1]
Bhattacharyya, B. K., 1964, Magnetic anomalies due to prism-shaped bodies with arbitrary polarization: Geophysics, 24(4), 517−531.
[2]
Bijendra, S., and Guptasarma, D., 2001, New method for fast computation of gravity and magnetic anomalies from arbitrary polyhedral: Geophysics, 66(2), 521−526.
[3]
Fregoso, E., and Gallardo, L., 2009, Cross-gradients joint 3D inversion with applications to gravity and magnetic data: Geophysics, 74(4), 31−42.
[4]
Goodacre, A. K., 1973, Some comments on the calculation of the gravitational and magnetic attraction of a homogeneous rectangular prism: Geophysical Prospecting, 21, 66−69
[5]
Guo, Z. H., Guan, Z. N., and Xiong, S. Q., 2004, Cuboid ?T and its gradient forward theoretical expressions without analytic odd points: Chinese J. Geophys. (in Chinese), 47(6), 1131−1138.
[6]
Kunaratnam, K., 1981, Simplified expressions for the magnetic anomalies due to vertical rectangular prisms: Geophysical Prospecting, 29, 883−890.
[7]
Li, Y. G., and Oldenburg, D. W., 1996, 3-D inversion of magnetic data: Geophysics, 61(2), 394−408.
[8]
Luo, Y., Wu, M. P., Wang, P., Duan, S. L., Liu, H. J., Wang, J. L., and An, Z. F., 2015, Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application: Applied Geophysics, 12(3), 283−291.
[9]
Pejman, S., Michel, C., and Denis, M., 2011, 3D stochastic inversion of magnetic data: Journal of Applied Geophysics, 73(4), 336−347.
[10]
Pilkington, M., 1999, 3-D magnetic imaging using conjugate gradient: Geophysics, 15(1), 1132−1142.
[11]
Portniaguine, O., and Zhdanov, M. S., 2002, 3-D magnetic inversion with data compressionand image focusing: Geophysics, 67(5), 1532−1541.
[12]
Rao, D. B., and Babu, N. R., 1991, A rapid methods for three dimensional modeling of magnetic anomalies: Geophysics, 56, 1729−1737.
2016, Vol. 13 
