Simulation of ground motions with high frequency components obtained from Fourier neural operators

Seismic hazards analysis relies on accurate knowledge of ground motions arising from potential earthquakes to assess the risk of damage to buildings and infrastructure. It is necessary to perform ground motion simulations because recorded strong-motion data from specific combinations of earthquake magnitudes, epicentral distances, and site conditions are still limited. Physics-based simulations provide reliable ground motion estimates, but their application in practice is limited to frequency ranges f < 1Hz, largely due to limited computational resources and lack of information regarding earthquake sources and medium. While hybrid ground-motion computations combining deterministic low frequency components with stochastic high frequency components are often used,  their stochastic high frequency components fail to correctly account for source and path effects and lead to inconsistent building responses.

The large database of ground motion records from Japan lends itself to develop machine learning approaches to estimate high frequency ground motions. Applying state-of-the-art machine learning techniques, like Fourier neural operators (FNOs) and Generative Adversarial Networks (GANs), we estimate seismograms at higher frequencies from their low frequency counterparts. In our approach, the time and frequency properties of ground motions are estimated using two different FNO models. In the time domain, a relationship is established between normalised low pass filtered and broadband waveforms. Frequency domain analysis involves the learning of high frequency spectrum from low frequency spectrum. Finally, the time and frequency properties are combined to produce broadband ground motions. Source, site, and path aspects are naturally incorporated into the training process.

We use ground motion data collected between 1996 and 2020 at 18 stations in the Ibaraki province of Japan to train our models and validate them on different events (Mw 4 to 7) around Japan. Using goodness of fit measures (GOFs), we show that the resulting ground motions match the recorded observations with good to acceptable GOF values for most of the predictions. To enhance our predictions, we include uncertainty estimation by utilizing a conditioned GAN approach. Lastly, to demonstrate the practicality of the approach, we compute high frequency components for a physics based simulated hypothetical Mw 5.0 earthquake in Japan.