地球物理资料非线性反演方法讲座(七)同伦反演法

同伦是代数拓扑学中的概念，同伦算法已应用于一些工程实际问题的求解。同伦方法的基本思想是：通过引入同伦参数，将原来复杂的非线性映射零点求解问题转化为跟踪同伦零点曲线问题，该同伦零点曲线的一端为已知值（给定的初始模型），另一端即为所求原映射的解。本讲座概要地介绍了同伦方法的基本原理，跟踪同伦曲线的具体算法，并给出了同伦方法在地震勘探波阻抗反演中的应用实例，最后归纳总结了同伦方法的特点及目前存在的不足。

Lecture on Non-Linear Inverse Methods in Geophysical Data(7) Homotopy Method

Homotopyis a concept of algebra topology,and homotopy algorithmhas been applied to solving the practical problems.The main spirit of the homotopyis that the original complicated problemis translatedintothe one of tracking homotopy zero curves which start with the knowninitial solutions and end withthe solutions of the object functions by adding homotopy parameter.This paper briefly introduces the homotopy theory and algorithm of tracking zero curves.At the same ti me,the paper gives the example of the i mpedance inversionin the seismic exploration.In the end,the advantages and disadvantages of the homotopy method are pointed out in this paper.