基于预条件共扼残差法截断牛顿法的全波形反演

Full Waveform Inversion Based onPreconditioned Conjugate ResidualTruncated Newton Method

摘要: 全波形反演(FWI)是一个大规模的非线性不适定问题，其二阶梯度信息有着重要的作用，但牛顿型方法需要计算量和存储量巨大。本文基于共扼残差方法和信赖域全局化策略提出了一种高效的载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，从而提高反演精度，为了加速共扼残差法的收敛速度和计算效率，本文给出了预处理的共扼残差方法并给出了其相关性质。基于二维2004 BP模型和Sizsbee模型，验证了预处理共扼残差截断牛顿反演方法的有效性。数值结果表明预处理共辄残差截断牛顿法能充分利用二阶梯度信息，从而加速算法收敛速度和提高成像精度。

Abstract: Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem, and its second-order gradient information plays an important role. However, the implementa- tion of Newton-type method is expensive. In this paper, an efficient truncated Newton full waveform inversion method is proposed based on the conjugate residual method. The full waveform inversion method can make full use of the second-order gradient information of the target functional and improve the inversion accuracy. Aiming at the problem that the truncated Newton method depends on the initial value selection, this paper combines the trust region globalization strategy into the truncated Newton method. In order to accelerate the convergence rate of the conjugate residual method, the preprocessing operator is introduced in this paper. Based on the two-dimensional 2004 BP model and the Sigsbee model, the effectiveness of the preconditioned conju- gate residual truncated Newton inversion method is verified. The numerical results show that the preconditioned conjugate residual truncated Newton method can make full use of the second-order gradient information, thus accelerating the convergence speed of the algorithm and improving the imaging accuracy.