关于用有限元法作磁法勘探正演计算的理论问题

本文提出用有限元法解磁法勘探的正问题,不再需要引入均匀磁化假定。 传统的正演计算方法是在均匀磁化的假定下建立的,它不能适应解释复杂磁异常的需要。近几年来,国外学者提出了用迭代方法作非均匀磁化条件下的正演计算,对形状比较简单的磁性体取得了较好的效果。但随着磁性体的形状变得比较复杂,计算所需时间很快增加,精度和稳定性也明显降低。以求能量函数极小的变分原理为依据,用有限元法作非均匀磁化条件下的正演计算,得到的磁位势函数满足磁性体内外的偏微分方程和全部界面条件（文中对此作了证明）。因此,这种方法可以研究各种复杂因素的影响,宜于计算非均匀磁化磁性体的有效磁化强度和磁异常。

ON THE THEORY USING THE FINITE ELEMENT METHOD TO SOLVE DIRECT PROBLEM OF MAGNETIC EXPLORATION

In this paper a finite element method for solving direct problem of magnetic exploration is proposed. Here the assumption of homogeneous magnetization is no longer required.In recent years, the problem of inhomogeneous magnetization is usually solved by iterative methods. These methods obtained good results for simple magnetic bodies. But. when the forms of the bodies become more complicated, the calculation time increases rapidly, and the accuracy and stability decreases. The finite element method is based on va-riational principle to minimize an energy function. The method can be applied to investigate the effects of various complicated factors, and to calculate the effective magnetization and magnetic anomalies of inhomogeneously magnetized bodies.