Parametric Closed-Form Formulation of Distinct Pulses in Strong Near-Field Ground Motions

Ground motions recorded in the near-fault zones exhibit unique physical characteristics different from far-field records. These differences are conspicuously evident in the configuration of accelerograms and their corresponding velocity-based as well as displacement-based time-histories. Particularly noteworthy are the variations observed in velocity time-histories, which require significant attention, especially in cases of intensive ground motions characterized by strong forward directivity effects. The presence of distinctive high-amplitude velocity pulses represents a vital aspect of these disparities. Numerous researchers have endeavored to develop closed-form formulas to accurately capture and explain these coherent pulses in velocity time-histories, as well as represent the medium to high-amplitude frequency domains of wave-type strong ground motions. These closed-form formulas have been prepared to provide mathematical expressions that can effectively model the unique features of strong near-fault ground motions. However, from the mathematical viewpoints achieving precise representations of the aforementioned pulses and the accompanying ground motion characteristics remains challenging. This paper aims to employ numerical modeling and analytical techniques to simulate the coherent velocity pulses, utilizing closed-form formulas and analytical approximations to closely replicate the features of the companion accelerograms accompanying the original earthquake records. Additionally, the calculation approach and processing of mathematical functions are concentrated on modeling and matching the companion parametric statements.