大地电磁反演方法的数学分类

Mathematical classification of magnetotelluric inversion methods

大地电磁法(MT)经过50多年的发展,已经从一维反演步入到二维、三维反演阶段,如今大地电磁反演方法众多,但大多是利用目标函数梯度信息的线性化迭代类方法,并且基于相同的思想来改善反演问题的不适定性。本文简要介绍了MT反演中基本的正则化思想,根据几种主要的MT反演方法所采用的不同数值优化算法,对它们进行了数学上的分类,明确了其区别与联系,并对各种方法的主要优缺点进行了比较,最后探讨了MT反演的发展趋势。

During the past five decades,significant progress has been made in magnetotelluric(MT) method.Particularly the inversion techniques have been transformed from 1D into 2D,or even 3D.Nowadays there are numerous MT inversion methods,most of which belong to linearized,iterated approaches that make use of the gradient of the objective function,and almost all of these methods adopt strategies based on the same theory to handle the general ill-posedness of the inverse problem.This paper briefly introduces the basic idea of MT inversion,which is known as regularization theory.It then makes a mathematical classification of several main inversion methods according to the numerical optimization algorithms they employed so that the clear relationship among them can be acquired.In addition,their main merits and drawbacks are compared with each other.Finally,trends for MT inversion are considered.