Machine learning approaches for solving subsurface inverse problems

Date

2023-07-28

Authors

Crocker, Jodie Amberly

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Abstract

A necessary component of geotechnical engineering design is the assessment of the physical properties of the subsurface, such as a site’s subsurface shear stiffness or shear-wave velocity (Vs). To obtain this information, various invasive and non-invasive methods may be used to perform seismic site characterization. Typically, non-invasive techniques, such as surface wave methods, are preferred due to being relatively inexpensive, quick, and easy to perform compared to invasive methods. Generally, surface wave methods involve three steps: (1) data acquisition; (2) data processing; and (3) inversion. While the first two steps are straightforward, the third step is particularly challenging due to the ill-posedness and non-uniqueness of the inverse problem. Additionally, traditional inversion may be time-consuming to perform, as it is computationally expensive and requires a high degree of domain expertise. Therefore, there has been a recent push to find non-traditional alternatives to performing inversion, particularly through the use of machine learning (ML) tools. These ML-driven tools, such as neural networks, allow users without domain expertise to quickly perform inversion, although care must be taken to ensure the tools adequately address the surface wave inverse problem. This dissertation discusses three possible ML-driven solutions to the inverse problem, beginning with a physics-aware convolutional neural network (CNN) that takes surface wave dispersion data as input and provides two-dimensional (2D) subsurface Vs profiles as output. To ensure the network learns the physical relationship between surface wave dispersion data and subsurface Vs, methods from the field of explainable artificial intelligence (XAI) are used during the network development process to perform hyperparameter tuning. Next, an ML-driven framework is presented that combines a CNN with a differentiable programming (DP) algorithm to provide one-dimensional (1D) velocity profile predictions. In this case, the CNN generates 1D velocity starting models for inversion. These velocity models are then passed through the DP algorithm, which uses a wave propagation simulator to solve the governing acoustic wave equation and perform inversion, leading to an optimized velocity profile. Finally, a comparison between a non-physical CNN and a simulation-based CNN is presented. The simulation-based CNN uses the previous DP algorithm as a layer to incorporate the physics of the acoustic wave equation into the network’s training process. This network takes 1D waveforms as input and provides 1D subsurface Vs profiles as output while ensuring the results are physically consistent.

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