In Figure 2
we show an example of the processing steps for a peak acceleration map of the
magnitude 4.4 earthquake near Wrightwood, California (about 60 km northeast of
Los Angeles) which occurred on August 20, 1998.
First, peak ground motion parameters are recovered for each station and associated
with a particular earthquake origin time and epicenter (Fig. 2A).
In regions of sparse station spacing, ground motions are estimated
using magnitude-distance regressions from the strong motion ``centroid''
[Kanamori, 1993].
To determine the strong motion centroid, we apply empirically derived station
corrections and then fit the observed ground motions to find the best
equivalent point-source latitude, longitude, and magnitude [Kanamori, 1993].
We scan the parameter space to determine the global minimum
solution for location and magnitude, and then refine the solution using the method of least
squares. The magnitude is 
, and the station corrections are also calibrated to the
Wood-Anderson instrument response (natural period of about 0.8 sec).
These empirical station corrections are used only to compute the magnitude for
estimating ground motions; they are not further used in the processing.
Figure:
Steps in ShakeMap processing for the August 20, 1998 magnitude
4.4 Wrightwood earthquake. A) Shaded relief basemap showing epicenter (star) and
recordings stations (triangles). SB, LB, and PD denote locations of the cities San
Bernardino, Long Beach, and Palmdale, respectively.
B) Same as A) but with the addition of the centroid (open star) and
sites of estimated peak ground motions (circles).
C) Finely spaced grid (2.8 km, circles) and contours of peak acceleration
site-corrected to bedrock. D) Contours of site-corrected peak acceleration overlaid on
the QTM geology basemap (see text and Figure 1 for more details).
We create a coarse, uniformly spaced grid of 30-km spaced ``phantom'' stations. Peak ground motions are assigned to each coarse grid point using the [Joyner and Boore, 1981] distance attenuation relationship for ``rock sites'' and the magnitude of the centroid and its distance to each grid point. Peak response spectral values (0.3, 1.0, and 3.0 sec) are similarly estimated using [Boore et al., 1994]. However, as shown in Figure 2B, only those phantom stations further than 30 km from all TriNet stations are retained. Likewise, the peak values at the location of the centroid itself are only used if there are no nearby stations (<10 km). In Figure 2B, the epicenter is given by a filled star, the centroid is shown with an unfilled star, and the phantom stations at which ground motions are estimated are shown as circles. For this region, the TriNet station distribution is sufficiently dense that only 10 phantom stations are required on the scale of the map shown. All other predicted values in this case are superseded by recorded amplitudes. Out at greater distances, however, more phantom stations do contribute and they insure that the contour maps remain well-behaved and bounded at the edges.