A uniform risk functional (e.g., Fourier spectrum, response spectrum, duration, etc.) is defined so that the probability that it is exceeded by some earthquake during a selected period of time is independent of the frequency of the seismic waves. Such a functional is derived by an independent calculation, at each frequency, for the probability that the quantity being considered will be exceeded. Different aspects of the seismicity can control the amplitude of a uniform risk functional in different frequency ranges, and a uniform risk functional does not necessarily describe the strong shaking from any single earthquake.

To be useful for calculating uniform risk functionals, a scaling relationship must provide an independent estimate of amplitudes of the functional in several frequency bands. The scaling relationship of Trifunac (1976) for Fourier spectra satisfies this requirement and further describes the distribution of spectral amplitudes about the mean trend; here, it is applied to find uniform risk Fourier amplitude spectra. In an application to finding the uniform risk spectra at a realistic site, this method is quite sensitive to the description of seismicity. Distinct models of seismicity, all consistent with our current level of knowledge of an area, can give significantly different risk estimates.

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