A unified probabilistic assessment of multiple ground-motion intensity measures in seismic hazard analysis based on Fourier amplitude spectra

Different ground-motion intensity measures capture unique aspects of seismic motion, all of which play vital roles in probability seismic hazard analysis (PSHA), depending on the objectives under consideration and the design or analysis methods employed. Within the current PSHA framework, performing probability assessments for multiple intensity measures to obtain their seismic hazard curves typically requires multiple ground motion prediction equations (GMPEs) for each intensity measure. While GMPEs for some intensity measures can be approximated from existing ones through modifications, many still need to be developed through regression analyses of extensive earthquake data. However, besides the laborious task of constructing multiple GMPEs, recent studies have also pointed out the difficulty in directly constraining the scaling of these intensity measures within GMPEs using seismological theory. To address these challenges, this study proposes a more efficient, physically reasonable, and internally consistent framework for probabilistically analyzing multiple intensity measures. Firstly, to avoid the effort of constructing multiple GMPEs, this study exclusively adopts the GMPE of the Fourier amplitude spectrum (FAS) coupled with a ground-motion duration model. Subsequently, multiple intensity measures are simultaneously estimated based on theoretical relationships between FAS with each intensity measure. In addition, given that Fourier spectra are more closely related to the physics of wave propagation, the scaling of FAS in GMPE is easier to constrain using seismological theory. Furthermore, the moment method, in conjunction with Latin hypercube sampling, is applied to calculate the exceedance probability for each intensity measure, thereby obtaining corresponding seismic hazard curves. Finally, a numerical example was conducted to verify the proposed framework.