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多面体磁异常表达式在二维磁数据拟合中具有重要作用,但已有的多面体磁异常表达式存在解析奇点,从而限制了其应用.本文基于磁荷面积分公式,对多面体磁异常表达式的奇点问题进行了讨论,指出了奇点存在的条件,并从磁荷面积分的基本表达式出发,推导出无奇点的多面体磁异常解析表达式.模型试验表明前人理论表达式存在奇点,并且随着多面体几何参数的变化奇点位置也随之改变,而本文推导出的表达式对于所有多面体模型均不存在奇点.另外,模型试验也说明对于斜面磁性层,本文推导的多面体模型相对于棱柱体模型其模拟真实模型的逼近程度更高、正演耗时更少,具有广泛应用前景.
The expression of polyhedron magnetic anomalies plays an important role in the fitting of two-dimensional magnetic data, but the existence of analytic singularities of the existing polyhedron magnetic anomalies has limited its application.In this paper, based on the magnetic charge area formula, The singularity problem is discussed, and the existence conditions of the singularity are pointed out. Based on the basic expression of magnetic charge area fraction, the analytical expression of the singularity polyhedron is deduced. The model test shows that the former theoretical expression The existence of singularities and the change of the singular points with the change of the geometrical parameters of the polyhedron, the expression derived in this paper does not have singular points for all the polyhedral models. In addition, the model test also shows that for the bevel magnetic layer, Compared with the prismatic model, the simulation model of the polyhedron model has a higher degree of approximation and consumes less time in forward modeling, so it has a wide range of application prospects.