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U.S. Geological Survey
345 Middlefield Road
Menlo Park, California 94025
(J.B., H.B., J.L., L.S.)
Berkeley Seismological Laboratory
University of California, Berkeley
Berkeley, California 94720
(L.G., P.L.)
We analyze peak ground velocity (PGV) and peak ground acceleration (PGA)
data from 95 moderate (3.5 
M < 5.5) and 9 large (5.5 M 7.1)
earthquakes in northern California. The 95 moderate earthquakes occurred from
August 1998 through December 2002, and their peak motions were compiled and
mapped by ShakeMap. The nine large earthquakes include the M 6.2 Morgan Hill
earthquake in 1984, the M 6.9 Loma Prieta earthquake in 1989, and the M 7.1
Petrolia earthquake in 1992. For r > 100 km, the peak motions
attenuate more rapidly than a simple power law (that is,
r-
) can fit. Instead, we use an attenuation
function that combines a fixed power law (r-0.7) with a
fitted exponential dependence on distance, which is estimated as
exp(-0.0063r) and exp(-0.0073r) for PGV and PGA,
respectively, for moderate earthquakes. We regress log(PGV) and log(PGA) as
functions of distance and magnitude. We assume that the scaling of log(PGV)
and log(PGA) with magnitude can differ for moderate and large earthquakes, but
must be continuous. Because the frequencies that carry PGV and PGA can vary
with earthquake size for large earthquakes, the regression for large
earthquakes incorporates a magnitude dependence in the exponential attenuation
function. We fix the scaling break between moderate and large earthquakes at M
5.5; log(PGV) and log(PGA) scale as 1.06M and 1.00M, respectively, for
moderate earthquakes and 0.58M and 0.31M for large earthquakes.
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