Model Order Reduction for the Probabilistic Full-Waveform Seismic Inversion
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Full Waveform Inversion (FWI) is vital for high-resolution crustal imaging, which is crucial for exploring resources like critical minerals and geothermal energy. FWI involves solving a complex seismic forward problem, which is a multi-frequency, time-dependent hyperbolic partial differential equation in 3D. This is done using the spectral element method (SEM). However, the computational cost of solving this problem makes fully probabilistic inversions and global uncertainty quantification, driven by Markov Chain Monte Carlo (MCMC) techniques, impractical. To address this, Model Order Reduction (MOR) techniques are applied to reduce the computational time of the seismic wave propagation problem. Various strategies for implementing MOR within the FWI framework are tested. Initial results show that combining proper orthogonal decomposition and radial basis functions (POD-RBF) can create accurate surrogates for the forward problem. With a hybrid off-line-on-line training approach, MCMC-driven inversions could become feasible with moderate computational resources. This approach significantly reduces the calculation time of the seismic forward problem, making it possible to solve the FWI problem probabilistically and implement it in multi-observable joint inversions for exploring critical mineral systems and geothermal energy. However, maintaining the frequency characteristics of simulated wavefields in the time domain remains a significant challenge.