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. ΔT 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.
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