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U.S. Geological Survey, Mail Stop 977, 345 Middlefield Road, Menlo Park, California 94025boore{at}samoa.wr.usgs.gov;joyner{at}samoa.wr.usgs.gov
Abstract
Seismic shear-wave velocity as a function of depth for generic rock sites has been estimated from borehole data and studies of crustal velocities, and these velocities have been used to compute frequency-dependent amplifications for zero attenuation for use in simulations of strong ground motion. We define a generic rock site as one whose velocity at shallow depths equals the average of those from the rock sites sampled by the borehole data. Most of the boreholes are in populated areas; for that reason, the rock sites sampled are of particular engineering significance. We consider two generic rock sites: rock, corresponding to the bulk of the borehole data, and very hard rock, such as is found in glaciated regions in large areas of eastern North America or in portions of western North America. The amplifications on rock sites can be in excess of 3.5 at high frequencies, in contrast to the amplifications of less than 1.2 on very hard rock sites. The consideration of unattenuated amplification alone is computationally convenient, but what matters for ground-motion estimation is the combined effect of amplification and attenuation. For reasonable values of the attenuation parameter 
0, the combined effect of attenuation and amplification for rock sites peaks between about 2 and 5 Hz with a maximum level of less than 1.8. The combined effect is about a factor of 1.5 at 1 Hz and is less than unity for frequencies in the range of 10 to 20 Hz (depending on 0).
Using these amplifications, we find provisional values of about 
= 70 bars and 0 = 0.035 sec for rock sites in western North America by fitting our empirically determined response spectra for an M 6.5 event to simulated values.
The borehole data yield shear velocities (
30) of 618 and 306 m/sec for "rock" and "soil" sites, respectively, when averaged over the upper 30 m. From this, we recommend that 30 equals 620 and 310 m/sec for applications requiring the average velocity for rock and soil sites in western North America.
By combining the amplifications for rock sites and the site factors obtained from our analysis of strong-motion data, we derive amplifications for sites with 30 = 520 m/sec (NEHRP class C, corresponding to a mix of rock and soil sites) and 30 = 310 and 255 m/sec (average soil and NEHRP class D sites, respectively). For the average soil site, the combined effect of amplification and attenuation exceeds a factor of 2.0 for frequencies between 0.4 and about 4 Hz, with a peak site effect of 2.4; the peak of the NEHRP class D site effect is 2.7.
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B. N. Margaris and D. M. Boore Determination of {Delta}{sigma} and {kappa}0 from response spectra of large earthquakes in Greece Bulletin of the Seismological Society of America, February 1, 1998; 88(1): 170 - 182. [Abstract] [PDF]
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