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Physics-Driven Self-Supervised Learning System for Seismic Velocity Inversion

Seismic velocity inversion plays a vital role in various applied seismology processes. A series of deep learning methods have been developed which rely purely on manually provided labels for supervision; however, their performances depend heavily on the utilization of large training datasets with corresponding velocity models. Since no physical laws are utilized in the training phase, it is usually challenging to generalize trained neural networks to a new data domain. To mitigate these issues, we embed a seismic forward modelling step at the end of a network to remap the inversion result back to seismic data and thus train the neural network through self-supervised loss, i.e., the misfit between the network input and output. As a result, we eliminate the need for many labeled velocity models, and physical laws are introduced when back-propagating gradients through the seismic forward modelling step. We verify the effectiveness of the proposed approach through comprehensive experiments on synthetic datasets, where self-supervised learning outperforms the fully supervised approach which accesses to much more labeled data. The superior performance is even more significant when compared on a new data domain that has velocity models with faults and more geological layers. Finally, in case of unknown and more complex data types, we propose a network-constrained full waveform inversion method. This method refines the initial prediction of the network by iteratively optimizing network parameters other than the velocity model, as found with conventional full waveform inversion method, and demonstrates clear advantages in terms of interface and velocity accuracy. With these measures (self-supervised learning and network-constrained FWI), the proposed physics-driven self-supervised learning system successfully mitigates issues like the dependence on large labeled datasets, the absence of physical laws and the difficulty in adapting to new data domains.