用超定方程求磁异常线性反演

A SOLUTION FOR MAGNETIC LINEAR INVERSION WITH THE AID OF OVER-DETERMINED SYSTEM OF EQUATIONS

对于二维和三维的磁异常反演问题,已有许多比较令人满意的方法,但有的也受一些条件的限制,例如初值的选择、计算繁杂等。文献[1]对国外的一些利用电算解重、磁反演问题的方法给了概括地评述。 通常,我们都是先对磁性体产生异常场这一过程做某些假设,同时估计一下磁性体的形状或根据异常求出磁性体的形状参数,并用简便的方法(例如特征点法等)很容易求得异常的反演。然而当异常复杂时(比如迭加异常以及非均匀磁化等),便不能直接使用这些方法。随着高速计算机的发展。

In this paper,the reasons that affect the precision in the solution of the magnetic linear inversion are analyzed and the problem as how to establish and solve a dictoried (over-determined) linear system of equations is discussed. In the case of knowing the observed magnetic anomaly the principles of dividing the terrian into smaller volume-units are presented. With the aid of the theoretical models, according to such an in-terpretated model, the stability of numerical solution can be raised. If the calculated value fits well to the observed value, then the destribution of the magnetic bodies within the earth's crust could be delineated. Finally, the effectiveness of this method was illustrated through inversing the magnetic anomaly with the values obeained in the field and through a comparison with other methods.