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 that rely purely on manually provided labels for supervision; however, their performances depend heavily on using large training data sets with corresponding velocity models. Because no physical laws are used in the training phase, it is usually challenging to generalize trained neural networks to a new data domain. To mitigate these issues, we have embedded a seismic forward modeling 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 modeling step. We verify the effectiveness of our approach through comprehensive experiments on synthetic data sets, where self-supervised learning outperforms the fully supervised approach, which accesses much more labeled data. The superior performance is even more significant when compared with a new data domain that has velocity models with faults and more geologic layers. Finally, in case of unknown and more complex data types, we develop a network-constrained full-waveform inversion (FWI) method. This method refines the initial prediction of the network by iteratively optimizing network parameters other than the velocity model, as found with the conventional FWI method, and demonstrates clear advantages in terms of interface and velocity accuracy. With these measures (self-supervised learning and network-constrained FWI), our physics-driven self-supervised learning system successfully mitigates issues such as the dependence on large labeled data sets, the absence of physical laws, and the difficulty in adapting to new data domains.