The dependence of PGA and PGV on distance and magnitude inferred from northern California ShakeMap data

We analyze peak ground velocity (PGV) and peak ground acceleration (PGA) data from 95 moderate (3.5 less than or equal to M < 5.5) and 9 large (5.5 less than or equal to M less than or equal to 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(-y)) 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.