Machine learning based Pseudo-Dynamic rupture generator for geometric rough faults

Accurately predicting the intensity and variability of strong ground motions from future large earthquakes is crucial for seismic hazard analysis. While kinematic ground motion simulations are computationally efficient and can be conditioned to inferred source-inversion models of past events or ensemble statistics of rupture-model databases, they rely on predefined spatiotemporal evolution of slip. In contrast, dynamic rupture simulations solve for a physically self-consistent slip evolution under prescribed stress and friction laws on the fault, yet, they are still computationally expensive. A practical compromise, therefore, is a physics-compatible source model embedded in a kinematic approach (i.e., Guatteri et al., 2004), referred to as the Pseudo-Dynamic (PD) approach. Geologic features, such as small-scale fault roughness influence the rupture process, generating realistic high frequency radiation with  decay characteristics (Mai et al., 2017). Presently, most PD models are based on rupture simulations of planar faults (with the notable exception of Savran and Olsen, 2020). Additionally, these models rely on 1-point and 2-point statistics between source parameters, which may not adequately capture nonlinear relationships between kinematic rupture parameters. In this study, we develop a Machine Learning (ML) framework involving Fourier Neural operators (FNO) (Li et al ., 2020) to learn the interdependencies between earthquake source parameters. We train our model using 21 dynamic simulations of rough faults (15 for training, 6 for testing; all from Mai et al., 2017). Our generator initiates with a stochastic final slip (Mai and Beroza, 2002) and a slip-constrained hypocentre location (Mai et al., 2005). The local slip evolution is described by a regularized Yoffe source time function (STF) characterized by rupture onset time, slip, peak time and rise time. Dynamic rupture simulations show correlation between rupture speed and the gradient of fault roughness, with rupture deceleration in regions of positive roughness gradients, coinciding with fault areas of increased shear stress. Therefore, we establish rupture speed as a function of stress drop computed from 2D final slip and relate peak slip velocity to the estimated rupture speed. Assuming a Yoffe STF, we then compute rise time and the time of peak slip velocity, enabling a full spatiotemporal earthquake source characterization that accounts for dynamic rupture on rough faults. For the stochastic slip, we also demonstrate an approach to model roughness correlated with stress drop. Our PD rupture generator reproduces the mean and standard deviation of ground motion models for different intensity measures in simulations of M 6.0-7.0 strike slip scenarios. This outlines a new PD source modelling approach suitable for broadband physics-based probabilistic seismic hazard analysis.