- Ground-motion model is: where PGA is in m∕s2, ψ1 = 1.45 ± 0.24, ψ2 = 1.00 ± 0.01, ψ3 = 0.31 ± 0.09, η1 = 0.0073 ± 0.0003,
ρ = -0.30 ± 0.06, σe = 0.170 (inter-earthquake) and σr = 0.361 (intra-earthquake).
- Classify station into four classes using the NEHRP categories using geological maps:
- Rock. Amplification from category C 0.79.
- Soft rock or stiff soil. Amplification from category C 1.00.
- Soft soil. Amplification from category C 1.35.
- Bay mud. Amplification from category D 1.64.
The amplifications (from Boore et al. (1997)) are used to correct for site effects.
For some stations in the broadband Berkeley Digital Seismic Network, which are in seismic vaults and
mine adits and therefore have low site amplifications, use one-half the above site amplifications.
- Use data from August 1999 and December 2002 from the northern California ShakeMap set of data. Extend
set to larger earthquakes by adding data from nine previous large northern California earthquakes.
- Focal depths, 0.1 ≤ h ≤ 28..8km.
- Use hypocentral distance because this distance is available to ShakeMap immediately after an earthquake.
Note that this is a poor predictor of near-field ground motion from extended faults.
- Plot decay of PGA with distance for two moderate earthquakes (M = 4.9, M = 3.9) and find decay is
poorly fit by a power-law function of distance and that fitting such an equation who require PGA ∝ r-2,
which they believe is physically unrealistic for body-wave propagation.
- Find that PGAs flatten or even increase at large distances, which is believed to be due to noise. Hence use
a magnitude-dependent limit of rmax = 100(M - 2) ≤ 400km, determined by inspecting PGA and PGV
data for all events, to exclude problem data.
- Fit data from each event separately using log PGA = ψ - ηr - log g(r) + log sBJF. Find η varies between
four groups: events near Eureka triple junction, events within the Bay Area, events near San Juan Bautista
and those in the Sierras and the western Mojave desert.
- Use a numerical search to find the segmentation magnitude M′. Choose M′ = 5.5 as the segmentation
magnitude because it is the lowest segmentation magnitude within a broad minimum in the χ2 error for
- Fit magnitude-dependent part of the equation to the PGA values scaled to 10km and site class C.
- Note that the PGAs predicted are significantly higher than those given by equations derived by Joyner
and Boore (1981) and Boore et al. (1997) because of use of hypocentral rather than fault distance.
- Recompute site amplifications relative to category C as: for B 0.84 ± 0.03, for D 1.35 ± 0.05 and for E
2.17 ± 0.15.