基于MINRES-QLP截断牛顿法的全波形反演

Truncated Newton Method Based on MINRES-QLP for Full Waveform Inversion

在全波形反演过程中,二阶梯度信息扮演着重要的作用.然而,由于其巨大的计算量和内存需求,限制了其在全波形反演问题中的应用.本文基于MINRES-QLP方法提出了一种高效的截断牛顿全波形反演方法.该全波形反演方法能够充分利用目标泛函的二阶梯度信息,提高反演精度.MINRES-QLP反演方法还能够利用Hessian阵负特征值信息,从而提高算法的重构分辨率和计算效率.针对Hessian阵计算难题,本文给出了一种矩阵向量相乘的快速算法.基于二维2004 BP模型,Sigsbee模型,验证了MINRES-QLP截断牛顿反演方法的有效性.数值结果表明MINRES-QLP截断牛顿法能充分利用二阶梯度信息和Hessian阵负特征值信息,从而加速算法收敛速度和提高成像精度.

Second-order derivative information plays an important role in full waveform inversion.However,its application in full waveform inversion is hindered by its huge computation and memory requirements.In this study,an efficient truncated Newton full waveform inversion method based on MINRES-QLP method is proposed.This full waveform inversion method can make full use of the second-order derivative information of the objective functional to improve the inversion accuracy.In addition,this MINRES-QLP truncated Newton method can also use the negative eigenvalue information of Hessian matrix to improve the inversion resolution and computational efficiency.For the computational challenge of the Hessian matrix,we present a fast matrix-vector product algorithm.Numerical experiments based on 2004 BP model and Sigsbee model are presented to show the performance of the MINRES-QLP truncated Newton method.Numerical results demonstrate that MINRES-QLP truncated Newton method can take advantage of the second-order derivative information and the negative eigenvalue information of Hessian matrix,accelerating the convergence speed of algorithm and improving the imaging accuracy.