Time-step and Duration of Waveforms Influence on Ground Motion Simulation Validation

Karen M. Clark, Sajan K C, & Chukwuebuka C. Nweke

Published September 8, 2024, SCEC Contribution #13549, 2024 SCEC Annual Meeting Poster #184

When validating earthquake simulations, it is necessary to ensure that the frequency content of the simulation matches historical recordings. Fourier Amplitude Spectra (FAS) is commonly used for this comparison. FAS is a visualization of the intensity of the frequencies in a signal, and thus depends heavily on Fourier transformations. Fourier transformations are a process that converts a signal from the time domain to the frequency domain by decomposing it into a sum of sine and cosine waves. Fourier transformations make several assumptions, including the periodicity and infinite repetition of the signal, and depend on factors such as the sampling rate, signal content, and signal length. Historically, when computing FAS, the unaltered simulation output and the historical waveform are provided as inputs to the Fourier transformation. In most cases, the time step and duration of the waveform differ between the simulation and the historical recorded data. In this study, the impact of adjusting the time step and duration of the simulated and historical recordings to keep them the same in both waveforms is explored. It was found that decreasing the time step of a recording via linear interpolation (to achieve a higher sampling frequency) did not change the low-frequency content but expanded the high-frequency range represented by the FAS and often created fictitious frequencies in the high-frequency range. On the other hand, increasing the duration of a recording through zero-padding resulted in an increase in the low-frequency content resolution and range, and significantly decreased the Fourier amplitudes across the entire FAS. Since comparing the amplitudes is the primary purpose of computing FAS, linear interpolation may be unnecessary due to the addition of fictitious information and the limited change in Fourier amplitude. However, having uniform durations is critical for accurate comparison. Because FAS is one of the primary metrics used to determine the validity of earthquake simulations, it is imperative that it is consistent to avoid reaching misinformed conclusions about the simulations. Future work for this project will focus on determining whether it is best to zero-pad all recordings to a normalized duration or to trim the longer of the simulation and historical waveform for each station and event to match the length of whichever is shorter.

Key Words
Fourier Amplitude Spectra, Fourier Transformation, Simulation Validation

Citation
Clark, K. M., K C, S., & Nweke, C. C. (2024, 09). Time-step and Duration of Waveforms Influence on Ground Motion Simulation Validation. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Ground Motions (GM)