Instantaneous physics-based ground motion maps using reduced-order models

Physics-based simulations of earthquake ground motion are useful to complement recorded ground motion data. However, the computational expense of realistic numerical simulations complicates their applicability to problems that need real-time solutions (e.g., earthquake early warning) or many solutions for diﬀerent earthquake sources, (e.g., probabilistic seismic hazard assessment). Here, we present a reduced-order model (ROM) that instantaneously generates peak ground velocity (PGV) maps. The predicted ground motions closely approximate high-resolution 3D seismic wave propagation simulation results up to 2 Hz that ordinarily require high-performance computing. We use the interpolated proper orthogonal decomposition technique, a type of surrogate modeling approach. We verify the ROM accuracy using simulations for ﬂat 1D layered and 3D velocity models that include topography. In both cases, the simulated PGV maps exhibit low-rank structure. We quantitatively compare four function approximators to ﬁnd the best-ﬁtting ROMs: radial basis function (RBF) interpolation, multilayer perceptron neural networks, random forests and k -nearest neighbors. We ﬁnd RBFs are the most accurate approximator, resulting in < 0 . 1 cm/s average PGV error when applied to an independent testing dataset. We apply the ROMs to predict PGV maps for 1 million diﬀerent focal mechanisms, in which the ROMs identify potentially damaging ground motions that might be overlooked when using only a few physics-based simulations. We also quantify correlations between focal mechanism, depth, and accuracy of the predicted PGV. Overall, the ROM approach demonstrates a new way to obtain physics-informed ground motion estimates on demand.