Seismic wave propagation and inference using deep learning, numerical methods and wave physics

Seismic wave propagation, imaging, inversion, and uncertainty quantification rank amongst the computationally most demanding, and thus difficult problems in science and engineering. Numerous mathematical and algorithmic approaches have been developed for these problems at various levels of complexity, yet the computational burden is still cumbersome. For inversions, one typically requires access to the gradient of a measurement (misfit function) with respect to model parameters such as wavespeeds. The calculation of these Frechet derivatives bears the bulk cost of wave-based inverse problems. Moreover, the non-linearity and ill-posedness of the inverse problem lead to local minima in the solution, with little chance of full probabilistic posterior sampling. In summary, any potential computational speedup, especially for high frequencies, multi-physics and multi-scale problems is most welcome to obtain better characterization of the inverse problem and in turn, uncertainty quantification.

In this talk, we explore novel directions in which we utilize deep learning algorithms to alleviate some of these challenges. Not attempting to blindly re-learn the physics of wave propagation from scratch, we rather exploit existent knowledge and algorithms of wave propagation, reciprocity, by using full 4D simulated wavefields with their inherent smoothness as training. We show examples of accurately simulated seismic waves in complex media by deep networks, which can lead to a speedup compared to conventional forward modeling of a factor up to 100, as well as mapping low- to high-frequencies for any pre-defined model. This can open doors to model-space sampling and inference in a probabilistic context. Seismic inference can be conducted in many flavors, ranging from full Bayesian sampling to linear imaging and brute force model-space sampling. We will discuss this in the context of the approaches mentioned above, such as evaluating the inverse mapping in the deep network, directly calculating Frechet derivatives, learning high-frequency Frechet derivatives from low-frequency test data, and performing probabilistic model-space inference using such accelerated forward solutions.