Disaggregated Seismic Hazard and the Elastic Input Energy Spectrum: An Approach to Design Earthquake Selection
The design earthquake selection problem is fundamentally probabilistic. Disaggregation of a probabilistic model of the seismic hazard offers a rational and objective approach that can identify the most likely earthquake scenario(s) contributing to hazard. An ensemble of time series can be selected on the basis of the modal earthquakes derived from the disaggregation. This gives a useful time-domain realization of the seismic hazard, to the extent that a single motion parameter captures the important time-domain characteristics. A possible limitation to this approach arises because most currently available motion prediction models for peak ground motion or oscillator response are essentially independent of duration, and modal events derived using the peak motions for the analysis may not represent the optimal characterization of the hazard.
The elastic input energy spectrum is an alternative to the elastic response spectrum for these types of analyses. The input energy combines the elements of amplitude and duration into a single parameter description of the ground motion that can be readily incorporated into standard probabilistic seismic hazard analysis methodology. This use of the elastic input energy spectrum is examined. Regression analysis is performed using strong motion data from Western North America and consistent data processing procedures for both the absolute input energy equivalent velocity, (Vea), and the elastic pseudo-relative velocity response (PSV) in the frequency range 0.5 to 10 Hz. The results show that the two parameters can be successfully fit with identical functional forms. The dependence of Vea and PSV upon (NEHRP) site classification is virtually identical. The variance of Vea is uniformly less than that of PSV, indicating that Vea can be predicted with slightly less uncertainty as a function of magnitude, distance and site classification. The effects of site class are important at frequencies less than a few Hertz. The regression modeling does not resolve significant effects due to site class at frequencies greater than approximately 5 Hz.
Disaggregation of general seismic hazard models using Vea indicates that the modal magnitudes for the higher frequency oscillators tend to be larger, and vary less with oscillator frequency, than those derived using PSV. Insofar as the elastic input energy may be a better parameter for quantifying the damage potential of ground motion, its use in probabilistic seismic hazard analysis could provide an improved means for selecting earthquake scenarios and establishing design earthquakes for many types of engineering analyses.