摘要
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. AT at all points in the source-flee 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.
已有的均匀磁化长方体磁场计算方法大都假设观测点位于上半无源空间,对于起伏地形条件而言,这些方法可能存在解析"奇点"。为此,本文基于地磁场基本理论,采用变量替换的积分方法,导出了改进的磁场表达式,详细讨论并有效解决了整个无源空间的所有奇点问题。相比前人的方法,其积分过程更自然、简单,最后的积分结果形式更加统一,并且不需要坐标变换即可求出无源区任意点处的磁场值,从而简化了正演过程。对比模型试验表明,新导出的磁场无解析"奇点"理论表达式是正确的,并能适应地形起伏的情况。
基金
supported by China Geological Survey Northeastern Tarim Aeromagnetic and Aerogravity comprehensive survey project(No.12120115039401)
