Simulation of broad-band ground motions with consistent long-period and short-period components using the Wasserstein interpolation of acceleration envelopes

Practical hybrid approaches for the simulation of broad-band ground motions often combine long-period and short-period waveforms synthesized by independent methods under different assumptions for different period ranges, which at times can lead to incompatible time histories and frequency properties. This study explores an approach that generates consistent broad-band waveforms using past observation records, under the assumption that long-period waveforms can be obtained from physics-based simulations. Specifically, acceleration envelopes and Fourier amplitude spectra are transformed from long-period to short-period using machine learning methods, and they are combined to produce a broad-band waveform. To effectively obtain the relationship of high-dimensional envelopes from limited amount of data, we (1) formulate the problem as the conversion of probability distributions, which enables the introduction of a metric known as the Wasserstein distance, and (2) embed pairs of long-period and short-period envelopes into a common latent space to improve the consistency of the entire waveform. An experimental application to a past earthquake demonstrates that the proposed method exhibits superior performance compared to existing methods as well as neural network approaches. In particular, the proposed method reproduces global properties in the time domain, which confirms the effectiveness of the embedding approach as well as the advantage of the Wasserstein distance as a measure of dissimilarity of the envelopes. This method serves as a novel machine learning approach that maintains consistency both in the time-domain and frequency-domain properties of waveforms.