Physics-guided deep learning for seismic inversion with hybrid training and uncertainty analysis

ABSTRACT The determination of subsurface elastic property models is crucial in quantitative seismic data processing and interpretation. This problem is commonly solved by deterministic physical methods, such as tomography or full-waveform inversion. However, these methods are entirely local and require accurate initial models. Deep learning represents a plausible class of methods for seismic inversion, which may avoid some of the issues of purely descent-based approaches. However, any generic deep learning network capable of relating each elastic property cell value to each sample in a seismic data set would require a very large number of degrees of freedom. Two approaches might be taken to train such a network: first, by invoking a massive and exhaustive training data set and, second, by working to reduce the degrees of freedom by enforcing physical constraints on the model-data relationship. The second approach is referred to as “physics-guiding.” Based on recent progress in wave theory-designed (i.e., physics-based) networks, we have developed a hybrid network design, involving deterministic, physics-based modeling and data-driven deep learning components. From an optimization standpoint, a data-driven model misfit (i.e., standard deep learning) and now a physics-guided data residual (i.e., a wave propagation network) are simultaneously minimized during the training of the network. An experiment is carried out to analyze the trade-off between two types of losses. Synthetic velocity building is used to examine the potential of hybrid training. Comparisons demonstrate that, given the same training data set, the hybrid-trained network outperforms the traditional fully data-driven network. In addition, we perform a comprehensive error analysis to quantitatively compare the fully data-driven and hybrid physics-guided approaches. The network is applied to the SEG salt model data, and the uncertainty is analyzed, to further examine the benefits of hybrid training.