A surrogate model of elastic wave propagation to quantify uncertainties in seismic hazard analysis

The propagation of seismic waves in the ground is subject to many sources of uncertainties, ranging from the uncertain activity of geological faults to the incomplete knowledge of mechanical properties inside the Earth's crust. To properly assess seismic hazard, it then becomes essential to quantify how uncertainties influence the intensity of ground motion generated by earthquakes.In areas with low-to-moderate seismicity, like most regions in metropolitan France, seismic records are too sparse to evaluate ground motion uncertainties. In this situation, numerical simulations are the only option to estimate ground motion intensity, but their high computational costs prevent most uncertainty analyses. In this thesis, we design a surrogate model that can replace the numerical solver by drastically reducing the computational costs while preserving its flexibility and a satisfying accuracy.We first illustrate the influence of geological heterogeneities on ground motion intensity in the context of the Mw4.9 Le Teil earthquake (Ardèche, France, 2019). Heterogeneities are added to a regional geological model in the form of random fields, and we show that it generates more realistic ground motion. However, heterogeneities also lead to a large variability between samples.To study this variability systematically, we build a database of 30,000 heterogeneous 3D geological models, and inside each geology, seismic waves are propagated from a random source using the spectral element code SEM3D. The database is then used to train a surrogate model in a purely data-driven framework.To design the surrogate model, we propose an extension of the Fourier Neural Operator called the Multiple Input Fourier Neural Operator (MIFNO). The MIFNO takes as inputs a 3D geology and a vector of source parameters to predict 3D ground motion. Ground motion is a time-dependent surface wavefield, but we do not need any time iteration thanks to a depth-to-time conversion. We characterize the MIFNO prediction error and explore the MIFNO generalization ability to out-of-distribution data.We finally take advantage of transfer learning to further improve the MIFNO accuracy in the context of the Le Teil earthquake. With this fine-tuned surrogate model, we obtain statistical distributions of several quantities of interest in seismic hazard assessment. They are coherent with numerical simulations and provide confidence intervals that were out of reach with existing methods.