The high-frequency shape of the earthquake spectrum strongly influences the amplitude of the peak ground acceleration and of the response spectrum at frequencies of 10 Hz and greater. A key parameter for the description of high-frequency ground motions is “kappa,” which is the decay slope of the Fourier spectrum of acceleration at near-source distances (Anderson and Hough, 1984; note Anderson and Hough originally referred to this parameter as kappa (0)). Kappa may be attributed to site effects (fmax; Hanks, 1982), source processes (Papageorgiou and Aki, 1983), or both.
Seismographic data place weak but significant constraints on kappa values. On average, there is no resolved kappa effect on spectra recorded at rock sites in eastern Canada, in the frequency range f ≦ 30 Hz. Four firm-soil sites in southwestern Ontario also show no kappa effect. An implied upper bound for kappa is 0.004 (or lower bound of 30 Hz for fmax). By contrast, source spectra from earthquakes in the Cascadia region, recorded on hard-rock sites in southwestern British Columbia (B.C.), appear to be well described by a kappa of 0.011 ± 0.002. The B.C. spectra are thus intermediate to the eastern case, with zero apparent kappa, and the typical California case, for which kappa is about 0.04.