Spatial variability of the directivity pulse periods observed during an earthquake

The ground velocity pulses generated by rupture directivity effects in the near-fault region can cause a large amount of damage to structures. Proper estimation of the period of such velocity pulses is of particular importance in characterizing near-fault seismic hazard and mitigating potential damage. We propose a simple equation to determine the pulse period as a function of the site location with respect to the fault rupture (defined by the hypocentral distance hypD, the closest distance to the rupture area clsD, and the length of the rupture area that breaks toward the site D) and some basic rupture properties (average rupture speed and average rise time). Our equation is first validated from a dataset of synthetic velocity time histories, deploying simulations of various strike-slip extended ruptures in a homogeneous medium. The analysis of the synthetic dataset confirms that the pulse period does not depend on the whole rupture area, but only on the parameter D. It also reveals that the pulse period is not sensitive to the level of slip heterogeneity on the fault plane. Our model is tested next on a real dataset build from the Next Generation Attenuation-West2 Project database, compiling 110 observations of velocity pulse periods from 10 strike-slip events and 6 non-strike-slip events. The standard deviation of the natural logarithm residuals between observations and predictions is similar to 0.5. Furthermore, the correlation coefficient between observations and predictions equals similar to 0.8, indicating that despite its simplicity, our model explains fairly well the spatial variability of the pulse periods