论文标题
关于WRI和FWI之间的连接：Hessian矩阵中非线性术语的分析
On the connection between WRI and FWI: Analysis of the nonlinear term in the Hessian matrix
论文作者
论文摘要
标准完整波形反演（FWI）的实现会带来困难，因为初始模型偏移了真实模型。提出了波场重建反转（WRI），以通过放松波动方程约束来减轻这些困难。在此摘要中，在FWI的Hessian矩阵中使用非线性术语，我们开发了一种新的近似Hessian作为增强的高斯 - 纽顿（AGN）Hessian，其中包括二阶导数信息。此外，我们在更新公式之间建立了一个紧密的联系，这是由于牛顿方法与AGN Hessian在FWI问题上的大致求解和WRI方法。我们的分析为基于牛顿的方法开发有效算法的有效算法开辟了新的观点，并强调了在Hessian Matrix中非线性术语的重要性，在大多数情况下，这在大多数情况下都被忽略了。
Implementation of the standard full waveform inversion (FWI) poses difficulties as the initial model offsets from the true model. The wavefield reconstruction inversion (WRI) was proposed to mitigate these difficulties by relaxing the wave-equation constraint. In this abstract, working on the nonlinear term in the Hessian matrix of FWI, we develop a new approximate Hessian as an Augmented Gauss-Newton (AGN) Hessian including second-order derivative information. Moreover, we establish an intimate connection between an updating formula which results from approximate solve of the Newton's method with the AGN Hessian on the FWI problem and the WRI method. Our analysis opens new perspectives for developing efficient algorithms for FWI based on the Newton's method and highlights the importance of the nonlinear term in the Hessian matrix, which is ignored in most cases.
