Computationally Efficient Emulation of Spheroidal Elastic Deformation Sources Using Machine Learning Models: A Gaussian‐Process‐Based Approach

• Published in: Journal of geophysical research. Machine learning and computation Vol. 1; no. 3
• Main Authors: Anderson, Kyle R., Gu, Mengyang
• Format: Journal Article
• Language: English
• Published: 01.09.2024
• Subjects: crustal deformation; emulator; geodesy; spheroidal cavity; surrogate model; volcano deformation
• DOI: 10.1029/2024JH000161
• ISSN: 2993-5210

Elastic continuum mechanical models are widely used to compute deformations due to pressure changes in buried cavities, such as magma reservoirs. In general, analytical models are fast but can be inaccurate as they do not correctly satisfy boundary conditions for many geometries, while numerical models are slow and may require specialized expertise and software. To overcome these limitations, we trained supervised machine learning emulators (model surrogates) based on parallel partial Gaussian processes which predict the output of a finite element numerical model with high fidelity but >1,000× greater computational efficiency. The emulators are based on generalized nondimensional forms of governing equations for finite non‐dipping spheroidal cavities in elastic halfspaces. Either cavity volume change or uniform pressure change boundary conditions can be specified, and the models predict both surface displacements and cavity (pore) compressibility. Because of their computational efficiency, using the emulators as numerical model surrogates can greatly accelerate data inversion algorithms such as those employing Bayesian Markov chain Monte Carlo sampling. The emulators also permit a comprehensive evaluation of how displacements and cavity compressibility vary with geometry and material properties, revealing the limitations of analytical models. Our open‐source emulator code can be utilized without finite element software, is suitable for a wide range of cavity geometries and depths, includes an estimate of uncertainties associated with emulation, and can be used to train new emulators for different source geometries. Plain Language Summary Mathematical models are widely used to calculate how an elastic material deforms due to pressure changes in a buried spheroidal cavity. These models have wide application to fields such as volcanology, where they can be used to understand the way the surface of the Earth deforms due to changes in buried magma reservoirs. Some models use relatively straightforward mathematical relations; these can generally make predictions quickly but can become highly inaccurate for some cavity geometries. Other models require sophisticated numerical techniques implemented in computers, but these are generally slow to run and may require specialized expertise or software. Here we use machine learning techniques to train a surrogate model (emulator) based on thousands of numerical computer simulations that can overcome these limitations. The emulator makes predictions that are both fast and accurate and can be applied to a wide range of problems. Key Points A machine learning algorithm based on Gaussian processes can be used to accurately predict (emulate) elastic deformation model output We emulate compressibility and surface displacements for pressure and volume changes in vertical spheroidal elastic cavities The emulators closely reproduce finite element model output but are orders of magnitude faster to run