Seismic geotechnical imaging using Full-Waveform Inversion and Physics-Informed Neural Networks

Abstract

Significant uncertainties in the characteristics of natural geomaterials limit the applicability of theoretical predictive models for real-life problems in geotechnical engineering. Over the past few decades, various geophysical techniques, based on the characteristics of seismic wave propagation in heterogenous geomaterials, have been used to reduce the epistemic part of these uncertainties. These techniques generally rely on sparse field seismic measurements on the ground surface, or within a borehole, to retrieve information on the subsurface layering and material properties. One of the major shortcomings of these approaches is their selectiveness in using only part of the recorded data (for example, using first-arrival times only). The full-waveform inversion (FWI) technique, on the other hand, utilizes the entire content of the seismic record to extract subsurface properties. This method, however, has not been attractive to the geoengineering community due to its high computational cost and involved formulation, both of which render FWI an abstract technique rather than a practical approach. In this study, we propose to use Physics-Informed Neural Networks (PINNs) to alleviate these two limitations and develop a robust, yet not complicated, inversion technique for geotechnical applications. Acting as a bridge between traditional physical models and data-driven neural networks, PINNs infuse the underlying physics into neural networks by adding the governing equations to the loss function. The resultant algorithm can train the model with fewer data points and better predict the response beyond the range of the training data set. PINNs can also be used to solve seismic inversion problems by defining unknown P- and S-wave velocities as trainable parameters. To demonstrate the effectiveness of the proposed approach, we apply it to the problem of 2D geotechnical subsurface characterization. We consolidate the governing geometric and material parameters into a set of normalized parameters, such as dimensionless frequency and normalized thickness. Then, we generate synthetic data using a Finite Volume forward solver of the Navier-Cauchy equation and use our FWI-PINNs approach to retrieve unknown normalized parameters. Lastly, we use actual seismic records at the Treasure Island Downhole Array site to investigate the performance of FWI-PINNs under realistic conditions. With the fast-growing advancements in GPU-based machine learning algorithms and their public availability and simplicity, we believe the proposed inversion method can turn into a fast, robust, and practical site characterization tool in the geotechnical engineering community.