Theoretical relations are developed for the attenuation of horizontal peak ground acceleration (PGA) and velocity (PGV) in Canada, with emphasis on eastern Canada. The theoretical basis is a composite of several approaches. At intermediate epicentral distances, results from random vibration theory (Hanks and McGuire, 1981; Boore, 1983), which can be used to describe PGA and PGV in terms of shear radiation implied by Brune's (1970) source model, are applied to Canadian earthquakes. Motions are extended into the near-source region using arguments concerning magnitude scaling (Joyner and Boore, 1981). At distances greater than two crustal thicknesses, ground motions are attributed largely to the Lg phase and are attenuated accordingly (Nuttli, 1982).
The resulting attenuation relations for PGA and PGV in eastern Canada are in excellent agreement with strong motion data from moderate eastern Canadian and Central United States earthquakes. Compared to empirical attenuation relationships based on Modified Mercalli Intensity, the theoretical model predicts a stronger dependence of peak ground motions on magnitude. In other respects (amplitude levels and distance decay), empirical and theoretical predictions are similar.
The model predicts that eastern events will have higher peak accelerations, but similar peak velocities, in comparison to their western counterparts of the same moment magnitude. This arises from the relative enrichment of eastern earthquakes in higher frequencies.