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以均质多面体为基础的模型在表示复杂地质源的位场中具有很大的灵活性。然而,这些物体现有的重、磁场表达式具有两个缺点。第一,物体表面必须简化为一组三角面,它使模拟程序的输入变得很不方便。第二,物体的每个面都必须旋转到一个特殊的位置,这就产生了大量的计算辅助操作。并使分析表达式难以解释。在本文中,将均质多面体产生的位场Pedersen傅里叶变换表达式改写成一个简单、坐标不变的形式。其结果表达式写成了由物体每个顶角的贡献之和。这种大为简化的形式用来作为模拟程序的基础,使该程序比现有的其它程序更直接且速度快得多。此外,该分析表达式对进一步探索多面体模型的反演方法也是有用的。
Homogeneous polyhedron-based models have great flexibility in locating complex geologic sources. However, the existing heavy and magnetic field expressions of these objects have two disadvantages. First, the surface of an object must be reduced to a set of triangular faces that make the input to the simulation program inconvenient. Second, each side of the object must be rotated to a special position, which produces a large number of computational aids. And make the analysis of expression difficult to explain. In this paper, the Pedersen Fourier Transform expression of the field generated by the homogeneous polyhedron is rewritten into a simple, coordinate-invariant form. The result expression is written as the sum of the contribution from each vertex of the object. This greatly simplified form is used as a basis for simulation programs, making the program more direct and much faster than other existing programs. In addition, this analytical expression is also useful for further exploration of the inversion method of polyhedron models.