AUTHOR=Sun Bingbing , Alkhalifah Tariq 

TITLE=ML-misfit: A neural network formulation of the misfit function for full-waveform inversion

JOURNAL=Frontiers in Earth Science

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2022.1011825

DOI=10.3389/feart.2022.1011825

ISSN=2296-6463

ABSTRACT=A robust misfit function is essential for mitigating cycle-skipping in full waveform inversion (FWI), leading to stable updates of the velocity model in this highly nonlinear optimization process. State of the art misfit functions, including matching filter or the optimal transport misfits, are all hand-crafted and developed with first principle. With the booming of artificial intelligence in geoscience, we propose to learn a robust misfit function for FWI, entitled ML-misfit, based on machine learning. Inspired by the recently introduced optimal transport of the matching filter objective function, we design a specific neural network architecture for the misfit function in a form to that allows for global comparison of the predicted and measured data. The proposed neural network architecture also guarantees that the resulting misfit is a pseudo-metric for efficient training. In the framework of meta-learning, we train the network by running FWI to invert for randomly generated velocity models and update the parameters of the neural network by minimizing a meta-loss, which is defined as the accumulated difference between the true and inverted velocity models. The learning and improvement of such an ML-misfit are automatic, and the resulting ML-misfit is data-adaptive. We first illustrate the basic principles behind the ML-misfit for learning a convex misfit function in the travel-time shifted signal example. Further, we train the neural network on 2D horizontally layered models, and apply the trained neural network to the Marmousi model, the resulting ML-misfit provides robust updating of the model and mitigates the cycle-skipping issue successfully.