Self-Reinforced Deep Priors for Reparameterized Full Waveform Inversion

Full waveform inversion (FWI) has become a widely adopted technique for high-resolution subsurface imaging. However, its inherent strong nonlinearity often results in convergence toward local minima. Recently, deep image prior-based reparameterized FWI (DIP-FWI) has been proposed to alleviate the dependence on massive training data. By exploiting the spectral bias and implicit regularization in the neural network architecture, DIP-FWI can effectively avoid local minima and reconstruct more geologically plausible velocity models. Nevertheless, existing DIP-FWI typically use a fixed random input throughout the inversion process, which fails to utilize the mapping and correlation between the input and output of the network. Moreover, under complex geological conditions, the lack of informative prior in the input can exacerbate the ill-posedness of the inverse problem, leading to artifacts and unstable reconstructions. To address these limitations, we propose a self-reinforced DIP-FWI (SRDIP-FWI) framework, in which a steering algorithm alternately updates both the network parameters and the input at each iteration using feedback from the current network output. This design allows adaptive structural enhancement and improved regularization, thereby effectively mitigating the ill-posedness in FWI. Additionally, we analyze the spectral bias of the network in SRDIP-FWI and quantify its role in multiscale velocity model building. Synthetic tests and field land data application demonstrate that SRDIP-FWI achieves superior resolution, improved accuracy and greater depth penetration compared to multiscale FWI. More importantly, SRDIP-FWI eliminates the need for manual frequency-band selection and time-window picking, substantially simplifying the inversion workflow. Overall, the proposed method provides a novel, adaptive and robust framework for accurate subsurface velocity model reconstruction.

Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows

Full waveform inversion (FWI) is able to construct high-resolution subsurface models by iteratively minimizing discrepancies between observed and simulated seismic data. However, its implementation can be rather involved for complex wave equations, objective functions, or regularization. Recently, automatic differentiation (AD) has proven to be effective in simplifying solutions of various inverse problems, including FWI. In this study, we present an open-source AD-based FWI framework (ADFWI), which is designed to simplify the design, development, and evaluation of novel approaches in FWI with flexibility. The AD-based framework not only includes forword modeling and associated gradient computations for wave equations in various types of media from isotropic acoustic to vertically or horizontally transverse isotropic elastic, but also incorporates a suite of objective functions, regularization techniques, and optimization algorithms. By leveraging state-of-the-art AD, objective functions such as soft dynamic time warping and Wasserstein distance, which are difficult to apply in traditional FWI are also easily integrated into ADFWI. In addition, ADFWI is integrated with deep learning for implicit model reparameterization via neural networks, which not only introduces learned regularization but also allows rapid estimation of uncertainty through dropout. To manage high memory demands in large-scale inversion associated with AD, the proposed framework adopts strategies such as mini-batch and checkpointing. Through comprehensive evaluations, we demonstrate the novelty, practicality and robustness of ADFWI, which can be used to address challenges in FWI and as a workbench for prompt experiments and the development of new inversion strategies.