Jian Sun, Kristopher Innanen, Chao Huang

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 (FWI). 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; it has a growing record of providing solutions for general image processing tasks. However, any generic deep learning network capable of relating each elastic property cell value to each sample in a seismic dataset 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 dataset; second, by working to reduce the degrees of freedom by enforcing physical constraints on model-data relationship. The second approach is referred to as ``theory-guiding. Based on recent progress of wave theory-designed network, we propose a hybrid network design, involving both deterministic, physics-based modelling and data-driven deep learning components. From an optimization standpoint, both a data-driven model misfit (i.e., standard deep learning), and now a model-driven data misfit (i.e., a wave propagation network), are simultaneously minimized during the training of the network. We compare the prediction capability of this physics-guided network with that of a fully data-driven counterpart in a synthetic salt velocity model building problem. The results indicate that the fully data-driven neural network acts like a smooth global inversion method: it recovers a large amount of large scale structural information, including the location and approximate boundaries of salt bodies, and background trends, directly from raw seismograms. The physics guided component appears to act to enhance detail and to more highly resolve structures, including salt body boundaries, and interfaces of background layers.