地震反演的一种算法

AN ALGORITH OF SEISMIC INVERSION

南京大学数学系

若地震信号是子波和反射系数的褶积。则地震反演问题可化为如下的l₁模极小化形式:min f(γ)=||γ||1,S·t·Aγ=b,其中A∈R_m^m×n,γ∈Rⁿ,b∈R^m,它是一种新型的l₁模反褶积。本文中的五个定理给出了解此问题的算法的理论基础。通过选取不同的下降方向和不同的步长因子,组成了几个不同的解此问题的下降算法。文章介绍了这些算法的详细步骤。

Assuming that signal is the convolution of wavelet and reflection coefficient, then the seismic inverse problem can be turned into the following minimal expression of L₁norm:min f(r)= ‖r‖where A∈R_m^m×n,γ∈Rⁿ,b∈R^m are the new type of L₁ norm deconvolution. In the paper, the solution of this problem and its theoretical basis for performing the algorithm are given from the five theorems. And by selecting different step-down directions and differ ent steplength factors, a couple of different step-down operations for solving this problem are made up. The procedures of applying the algorithm are elaborated.