基于原始-对偶内点法寻优的地震数据稀疏反演方法

Primal-Dual method for optimization of sparse constraint seismic data inversion

针对波阻抗反演中反射系数的稀疏优化问题,本文提出了基于原始-对偶内点法[1]的最优化方法.将反射系数的反演问题描述为等价的不等式约束最优化问题,利用原始-对偶内点法实现最优求解.内点法分为内外两层循环,外循环使用逐步逼近(Sequential Unconstrained Minimization Technique,SUMT)的最优化方法,以对偶间隙(Duality Gap)作为停机准则,内循环为牛顿法解无约束最小化问题,利用预条件化后与LSQR分解方法提高了计算效率,经理论数据与实际资料验证,表明本文方法的有效性.

To improve the resolution and speed up the computing, a new method of deconvolution is proposed, which based on the Primal-Dual method for convex optimization. The object function minimizes the 11 norm of the reflectivities while trying to keep the convolution of them the same as the original data with some bias. With the Primal-Dual method, the minimization can be solved as an unconstrained minimization, which is part of the convex optimization. Two parts constitute the solving, one is the outer iterations, called Sequential Unconstrained Minimization Technique（SUMT）, stopping criterion of which is the Duality Gap; the other is the inner iterations looking for minimization under certain Duality Gap using Newton Method. Linear Equations need to be solved in the solving, and pre-conditioned LSQR is applied to so memory, CPU time can be saved, and high accuracy, quick convergence can be reached.