Empirical Attenuation of Ground-Motion Spectral Amplitudes in Southeastern Canada and the Northeastern United States

A database of 1700 digital seismograms from 186 earthquakes of magnitude mN 2.5–5.6 that occurred in southeastern Canada and the northeastern United States from 1990 to 2003 was compiled. Maximum-likelihood regression analysis of the database was performed to determine a model for the attenuation of Fourier spectral amplitudes for the shear window, for the vertical and horizontal component of motion, for frequencies from 0.2 to 20 Hz. Fourier amplitudes follow a hinged trilinear attenuation model. Fourier spectral amplitudes decay as R 1.3 (where R is hypocentral distance) within 70 km of the source. There is a transition zone from 70 to 140 km as the direct waves are joined by strong postcritical reflections, where the attenuation is described as R ; spectral amplitudes actually increase with distance in this range for low frequencies. Beyond 140 km, the attenuation is well described by R , corresponding to geometric spreading in two dimensions. The associated model for the regional quality factor for frequencies greater than 1 Hz can be expressed as Q 893f . Q can be better modeled over a wider frequency range (0.2– 20 Hz) by a polynomial expression: log Q 3.052 0.393 log f 0.945 (log f ) 0.327 (log f ). The polynomial expression accommodates the observation that Q values are at a minimum (about 1000) near 1 Hz and rise at both lower and higher frequencies. Correction factors for the spectral amplitude model that describe the effects of focal depth on the amplitudes and their attenuation are developed using the subset of events with known focal depth. The attenuation model is similar to that determined from an earlier study with more limited data (Atkinson and Mereu, 1992), but the enlarged database indicates more rapid near-source amplitude decay and higher Q. The attenuation model is used to play back attenuation effects to determine the apparent source spectrum for each earthquake in the database and hence determine moment magnitude (M) and Brune stress drop. The events have moment magnitude in the range from 2.5 to 5. Stress drop increases with moment magnitude for events of M 4.3, then appears to attain a relatively constant level in the range from 100 to 200 bars for the larger events, as previously noted in Atkinson (1993b). The results of this study provide a useful framework for improving regional ground-motion relations in eastern North America. They further our understanding of attenuation in the region through analysis of an enlarged ground-motion database. In particular, the inclusion of the three-component broadband data gathered over the last decade allows extension of attenuation models to both horizontal and vertical components over a broad frequency range (0.2–20 Hz).