An unsupervised physics-constrained velocity inversion method based on spectral normalization adversarial learning

Summary Full waveform inversion (FWI) has significant potential to reconstruct the subsurface structure at high resolution, but it is a nonlinear and ill-posed problem. Traditional physics-based FWI methods that employ gradient-based optimization algorithms to minimize the discrepancy between observed and synthetic data face several challenges. The aforementioned methods are susceptible to becoming trapped in local minima as a result of cycle-skipping problems and require substantial computational resources, particularly with the increasing size and required resolution of seismic datasets. Nowadays many deep-learning methods are proposed to solve the above challenges. FWIGAN, a recently proposed unsupervised seismic velocity inversion method based on the Wasserstein generative adversarial network with gradient penalty (WGAN-GP), has demonstrated certain success in overcoming these challenges. However, FWIGAN enforces the Lipschitz constraint on the critic through a gradient penalty evaluated at dynamically sampled interpolation points between the observed and synthetic data. This strategy introduces additional computational and hyperparameter tuning costs. Motivated by these limitations, we introduce the spectral normalization into the FWIGAN framework, directly constraining the spectral norm of each network layer to control the Lipschitz behavior of the critic. It can enhance the stability of network training. The proposed method mitigates the dependence on having large labeled data and the pretraining of the network. The new scheme is applied to the Marmousi and Sigsbee models to verify its robust performance. The experimental results clearly indicate that our method outperforms common methods in terms of inversion accuracy.