Deep Learning-based Inverse Hessian Estimation in Multiscale Full Waveform Inversion

Full Waveform Inversion (FWI) is a powerful technique for high-resolution subsurface imaging, yet it remains limited by two major challenges: the computational cost of inverse Hessian estimation and convergence to local minima. To address these, we present a hybrid framework that integrates Deep Learning (DL) with a multiscale inversion strategy. A UNet-based convolutional neural network is trained to approximate the action of the inverse Hessian by mapping blurred gradients—generated through Born modeling—into smoother model updates. Embedding this learning-based preconditioning into a Gauss–Newton workflow accelerates convergence while preserving structural fidelity. Using the Marmousi-2 velocity model, we evaluate the method across three frequency scales (5, 10, and 25 Hz). Results demonstrate that the proposed GN-UNet recovers both large-scale structures and fine details more effectively than L-BFGS and Conjugate Gradient methods, while mitigating cycle-skipping through multiscale progression. Although runtime is modestly higher, GN-UNet achieves faster convergence and improved model reconstruction, highlighting its practical potential for robust seismic inversion. This work underscores the promise of DL-assisted inverse Hessian estimation in advancing FWI toward more accurate and efficient field applications.