Automated parameterization of velocity pulses in near‐fault ground motions

Abstract

Proper parameterization of near‐fault ground motions is of critical importance in earthquake engineering, and this process is traditionally performed by directly fitting an analytical pulse model to the original motion. Yet such a process is usually limited by the trial‐and‐error procedure, which is strongly dependent on the initial guesses and may converge to local rather than global minimums. In this study, we propose a progressive (step‐by‐step) iterative approach that can achieve a fully automated parameterization of the velocity pulse contained in near‐fault motions. Assuming that a velocity pulse can be characterized by a pulse model with four key parameters, the approach is conducted by iteratively matching the pulse model to the smoothed ground motion, and the parameterized pulse is analytically derived by best fitting to the smoothed motion not only in the time domain but also in the spectral domain. Specifically, the velocity time history of interest is initially smoothed by a moving average filter so that the low‐frequency content can be filtered out of the original motion, from which the pulse amplitude as well as its epoch is accordingly determined. The coherent velocity pulse is then progressively extracted by performing the nonlinear least‐square‐fitting of the pulse model to the filtered low‐frequency content, during which the remaining parameters, that is, the pulse period, the number of cycles and the phase of the pulse, are estimated successively. Finally, the above procedure is applied repeatedly to the original ground motion by changing an empirical factor controlling the extent of smoothing of the motion so that convergence to local minimums that frequently occurs in the trial‐and‐error procedure could be largely avoided, and best match of the spectrum of the extracted pulse to that of the original motion can be acquired. Fitting quality of the velocity pulses is examined by comparing with existing methods. Prospective applications of the proposed procedure include the stochastic simulations of near‐fault ground motions and parametric investigations of the influence of velocity pulses on various engineered structures.

Analysis of Near-Fault Ground Motions in the February 2023 Kahramanmaras, Türkiye, Earthquake Sequence

“…There have been a couple of studies (e.g., Hu et al, 2024;Ertuncay and Costa, 2024) analyzing the strong pulse-like features observed in the 2023 Türkiye earthquake sequence, of which the algorithm by Shahi and Baker (2014) was frequently used to identify if there are significant pulses contained in the velocity time histories. In this study, the approach newly proposed by Chang et al (2024a) is employed. Compared with previous studies (e.g., Baker, 2007;Shahi and Baker, 2014;Zhai et al, 2018;Chen et al, 2019;Feng et al, 2021;Tang et al, 2022;Zhao et al, 2023) that solely focused on the identification of pulse-like characteristics, the velocity pulses of interest observed in the 2023 Türkiye earthquake sequence are here not only quantitatively identified but are also fully parameterized.…”

“…Compared with previous studies (e.g., Baker, 2007;Shahi and Baker, 2014;Zhai et al, 2018;Chen et al, 2019;Feng et al, 2021;Tang et al, 2022;Zhao et al, 2023) that solely focused on the identification of pulse-like characteristics, the velocity pulses of interest observed in the 2023 Türkiye earthquake sequence are here not only quantitatively identified but are also fully parameterized. Specifically, four physical parameters for defining the waveform characteristics of the underlying pulses are determined using the approach in Chang et al (2024a). The parameterization of velocity pulses has various engineering applications, e.g., the stochastic simulations of near-fault ground motions (e.g., Yang and Zhou, 2015;Yadav and Gupta,2017;Dabaghi and Kiureghian, 2017) and the parametric investigations of the effects of velocity pulses on different structures (e.g., Kalkan and Kunnath, 2006;Rupakhety and Sigbjörnsson, 2011;Khoshnoudian and Ahmadi, 2013;Wu et al, 2014;Alonso-Rodríguez and Miranda, 2015).…”

“…To overcome the limitation of the trial-and-error procedure, Chang et al (2024a) proposed an indirect procedure by applying the Gabor wavelet (Gabor, 1946) to the fitting of a smoothed rather than the as-recorded ground motions. Specifically, the velocity time history of concern is initially smoothed by a moving average filter so that the low-frequency content can be filtered out of the original motion.…”

“…Figure 10A illustrates the velocity time histories as well as the extracted pulses of the ground motion '4632' shown in Figure 6. The extracted pulses and the EVP values are derived using the approach by Chang et al (2024a). The two components are rotated along 16 evenly spaced azimuths from 0  to 180  .…”

“…Specifically, the prediction model proposed by Zhao et al (2006) is applied to the 2023 Türkiye earthquake sequence, and it is shown that the PGA and Sa attenuation characteristics of not only the ordinary non-pulse-like ground motions but also the pulse-like ground motions can be reasonably captured using the Zhao et al (2006) model. Subsequently, a couple of ground motions with one-sided velocity pulses, possibly resulted from the fling-step effect, are observed in both the Mw7.8 and the Mw7.5 events; and permanent displacements, obtained by time integration of the velocity time histories, are estimated using the approach proposed in Chang et al (2024a). Finally, previous studies (e.g., Boore et al, 2006;Hong and Goda, 2007;Huang et al, 2008;Bradley and Baker, 2015) showed that pulse-like features can occur over a range of orientations, and the orientation with the maximum PGV could be used to determine the direction of the strongest pulse.…”