An empirical model that relates Fourier amplitude density of ground acceleration (FA) of Lg waves of Canadian Shield earthquakes to magnitude and distance has been calibrated at discrete frequencies. Magnitude (mbLg) ranges from 2.8 to 5.2, epicentral distance (R) from 70 to 900 km, and frequency (f) from 0.6 to 20 Hz. The data base consists of the vertical component of Lg waves as recorded in digital format by the Eastern Canada Telemetered Network. A linear regression is applied to the logarithm of the following model: FA = kebmbLge−γRR−0.5, where k = (2πf)2c and c is a constant coefficient (related to the prototype Fourier amplitude density of ground displacement), b reflects the magnitude dependence, γ is the anelastic attenuation coefficient, and 0.5 is the geometric spreading factor of surface waves. The magnitude coefficient, b, varies from a maximum of 3.0 at 1 Hz to 1.8 at 20 Hz, a trend indicative of the decrease in corner frequency with increasing magnitude. The anelastic attenuation coefficient can be represented by a frequency dependence of the form γ = 0.001 f0.8(km−1), and the associated quality factor, Q, by Q = 900 f0.2. Empirical relations for FA predict spectral trends that are generally within a factor of two of the mean trend of actual spectra. Since Lg waves are the primary contributor to moderate ground motion (and felt sensations) in the magnitude and distance range specified above, empirical relations derived for FA are of relevance not only to seismologists, but also to earthquake engineers as well.

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