Mathematical and Physical Characteristics of the Phase Spectrum of Earthquake Ground Motions

Abstract

This study presents a rigorous investigation into the mathematical and physical properties inherent in the Fourier phase spectrum of earthquake ground motions. This exploration includes a detailed examination of the probability distribution of phase angles and differences, elucidated through two novel numerical experiments utilizing the reduction ad absurdum approach. Moreover, the study scrutinizes the physical attributes of earthquake ground motion’s phase spectrum, employing the circular frequency-dependent phase derivative as a key analytical factor. In a novel approach, the research delves into the relationship between circular frequency-dependent phase derivatives and Fourier amplitudes, shedding light on essential connections within earthquake phenomena, particularly addressing non-stationarity. Expanding the scope, the study comprehensively examines the influence of source, propagation path, and site on both the phase spectrum and accelerogram. Employing the control variate technique facilitates this analysis, providing valuable insights into the underlying physical mechanisms governing earthquake wave behavior. The findings highlight the temporal properties of the phase spectrum, attributing its complexity to the temporal heterogeneity in energy release during the fault rupture and dispersion of earthquake waves. This novel approach not only enhances the understanding of earthquake dynamics, but also underscores the significance of considering temporal variations in earthquake events.