This study develops estimates for the attenuation of peak vertical ground motions using a conventional, least-squares regression model applied to unfiltered and bandpass-filtered ground-motion data. The input data are from 88 earthquakes (1.0 ≤ M ≤ 3.3; epicentral distance range 10 to 450 km) located along the Utah-Idaho border and propagating Sg and Lg waves southward to seismograph stations along the Wasatch front in north central Utah. The regression model includes parameters to account for geometric spreading, anelastic attenuation with a power-law-frequency dependence, source, size, and station site effects.

The maximum ground-motion amplitudes are derived from waves arriving about 3 sec, on the average, after the S-wave arrivals and are interpreted to be Sg in close (roughly 100 km or two crustal thicknesses) and Lg at greater distances. Accordingly, geometric spreading coefficients of 1.0 and 0.9 for body waves (Sg) and 0.83 (5/6) for higher-mode, Airy-phase surface waves (Lg) are chosen for testing. Similarly, a range of initial values of the power dependence of the attenuation (0.5 to 0.9) are also tested. The suite of estimates that result from regressing the amplitude data, while employing the family of fixed parameter values, leads to the following Q model: 
for 3 Hz ≤ f ≤ 10 Hz. These results are important to the estimation of the seismic hazard for the study area.

This pronounced level of attenuation, comparable to that found in California, has been reported in previous investigations of the study area using PSRV spectra, intensity attenuation and fall-off of Wood — Anderson seismogram amplitudes.

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