A novel wavefield reconstruction inversion method using an approximated model-domain Hessian

Abstract

The Hessian matrix, though computationally expensive, plays a critical role in ensuring inversion accuracy and mitigating cross-talk in multi-parameter inversion. The well-known wavefield reconstruction inversion (WRI) or extended space full-waveform inversion can reduce nonlinearity and mitigate cycle skipping in traditional FWI. However, most implementations omit the Hessian. In this study, the Hessian—formulated as a function of measurement and theoretical covariance matrices—is incorporated into WRI within a Bayesian inference framework. Furthermore, the connections between the data- and model-domain Hessian equations are discussed, leading to a simplified calculation method for the extended source. Based on this approach, a new definition for the theoretical covariance matrix is proposed and validated through numerical tests, demonstrating its accuracy.

Keywords

Inversion / Bayesian inference / Theory covariance matrix

Funding

The study is supported by the Qingdao New Energy Shandong Laboratory Open Project under Grant QNESL OP202304.

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