On the connection between WRI and FWI: Analysis of the nonlinear term in the Hessian matrix

TL;DR

This paper analyzes the nonlinear term in the Hessian matrix of full waveform inversion (FWI), proposing a new approximate Hessian that connects FWI and wavefield reconstruction inversion (WRI), and emphasizes the importance of nonlinear terms for efficient algorithms.

Contribution

It introduces an augmented Gauss-Newton Hessian including second-order derivatives and links FWI updates to WRI, highlighting the nonlinear Hessian term's significance.

Findings

Developed an approximate Hessian incorporating second-order derivatives.

Established a connection between FWI update formulas and WRI.

Highlighted the importance of the nonlinear Hessian term in FWI.

Abstract

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.