Neural Network-Based Metamodel of synthetic seismograms: Application for uncertainty quantification

Abstract

We developed time and frequency domains neural network surrogate models of synthetic seismograms stemming from the resolution of the three-dimensional equation of motion. The surrogates predict the time or frequency-series knowing the input variables of the physical model. The surrogate models are used to quantify epistemic uncertainty in ground motion prediction through global sensitivity analysis. We first generate a dataset of time domain synthetic seismograms in a seven-dimensions uncertain space using the spectral-element method. To validate the surrogate model, we evaluate its ability to reproduce at least 80% of the bootstrap resamples. Additionally, the $R_2$ regression coefficient between the simulations generated by the spectral-element method code and those predicted by the neural network is 0.94 for the validation set, confirming the accuracy of the surrogate model. These surrogates allow fast predictions of velocity time-series or Fourier amplitude spectra where spectral-element simulations are not done (neural networks compute about 100,000 surrogates per second, while a single spectral-element simulation longs approximately 7 h on 48 cores). To quantify the uncertainty of the physical system under study, a global sensitivity analysis is undertaken to better understand how uncertain parameters affect the predicted state of the system. We present two sampling-based estimation methods, the so-called “pick-freeze” Sobol method and the Li and Mahadevan method, to quantify this uncertainty. The Sobol method requires approximately 500,000 simulations to achieve stability, whereas the Li and Mahadevan method requires only 30,000 simulations. Using the metamodel, both methods require only a few seconds to produce results, although the Li and Mahadevan method analyzes 10,000 simulations per second, compared to 3,000 for the Sobol method. The results indicate that the shear wave velocity in the physical system’s layer is the most influential parameter affecting the ground speed on the physical system. In contrast, at a reference station (without considering the geological properties of the physical system), the results show that the shear wave velocity in the first and third deep layers are the most influential parameters.