Rayleigh wave tomography in the north-eastern margin of the Tibetan Plateau by way of training physics-informed neural networks

Machine learning is rapidly becoming ubiquitous in the Earth Sciences promising to provide scalable algorithms for data-mining, interpretation, and model building. Initially heralded for its ability to exclude complicated physics from data analysis, recent innovations seek to merge machine learning  solutions with conventional physics-based methods in order to enhance their capability

We present a novel eikonal tomography approach for Rayleigh wave phase velocity and azimuthal anisotropy based on the elliptical-anisotropic eikonal equation, by formulating the tomography problem as the training of a physics informed neural network (PINN). The PINN eikonal tomography (pinnET) neural network utilizes deep neural networks as universal function approximators and extracts traveltimes and medium properties during the optimization process. Whereas classical eikonal tomography uses a generic non-physics-based interpolation and regularization step to reconstruct traveltime surfaces, optimizing the network parameters in pinnET means solving a physics constrained traveltime surface reconstruction inversion, tackling measurement noise and resolving the underlying velocities that govern the physics. The fast and slow velocity and the anisotropic direction information can be directly evaluated from the trained medium property networks. Checkerboard tests indicate that the input velocity model can be well recovered by using this approach and synthetic data.

We demonstrate this approach by applying it to multi-frequency surface wave data from ChinArray phase II sampling the north-eastern Tibetan plateau. We are able to use much less data to achieve similar subsurface images because of the benefit of including the physics constraint while reconstructing the traveltime surfaces. We are able to obtain excellent results using only 10 sources.  Comparing results from pinnET with conventional eikonal tomography, we find good agreement with distinct low velocity structures beneath the Songpang-Ganzi block, Qilian and Western Qinling Orogen. Large phase velocity uncertainties occur in a small part of the southeastern Ordos Block, the western Songpan-Ganzi Block and the eastern Sichuan basin, which correspond to the reduced data coverage dependent on the selection of the 10 sources. We also verify the accuracy and reliability of the pinnET by choosing only one station as virtual source, the retrieved velocities show relatively good resolution which is much better than in conventional eikonal tomography using similar sized datasets. The method is memory efficient because compressing the traveltimes as outputs to a NN is a concept akin to compressed sensing and offers advantages over traditional anisotropic eikonal tomography or neural network approaches.