Decay ofS‐Wave Amplitudes with Distance for Earthquakes in the Charlevoix, Quebec, Area: Effects of Radiation Pattern and Directivity

Abstract

Abstract The decay of the Fourier spectral amplitudes of S waves over distances of 10–80 km near Charlevoix, Quebec, was determined using waveforms from seven earthquakes with M N 3.3–5.4. The S ‐wave spectral amplitudes were corrected for site response and source amplitude by normalizing the coda‐wave spectrum at a fixed time after the origin time. The amplitude decay with distance was found to be less steep as the frequency increases from 1 to 14, contrary to what would be expected from anelastic and scattering attenuation for a point source with an isotropic radiation pattern. The decay at 14 Hz indicates that the geometrical spreading at distances less than 80 km is less steep than R −1.05 . The steeper distance decay of the low‐frequency spectrum appears to be an artifact of the radiation pattern and rupture directivity, which affect the low‐frequency amplitude more than the high frequency. Synthetic seismograms were made for a horizontally layered crust for the M w 4.6 Riviere du Loup earthquake and an M w 3.3 event. The decay with distance of the 1 Hz spectral amplitudes of the synthetics is similar to that observed for the Riviere du Loup earthquake, indicating that radiation pattern and rupture directivity are important factors in determining the attenuation with distance at 1 Hz. For the M w 3.3 earthquake, the distance decay of the 1 Hz spectral amplitudes was found to be sensitive to the focal mechanism. This study demonstrates that estimates of geometrical spreading made using 1 Hz amplitudes can be contaminated by radiation pattern and directivity effects and may not be applicable for constructing ground‐motion prediction equations for sources with other focal mechanisms and rupture behavior.