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Open-File Report 96-532

National Seismic Hazard Maps: Documentation June 1996

By Arthur Frankel, Charles Mueller, Theodore Barnhard, David Perkins, E.V. Leyendecker, Nancy Dickman, Stanley Hanson, and Margaret Hopper

Adaptive Weighting for CEUS

The interim hazard maps of the CEUS did not incorporate the background zones, because they can lower the hazard in some locations from that calculated from the historic seismicity alone. The June 1996 versions of the maps do include the background zones using a weighting scheme that can vary locally depending on the level of historic seismicity in that cell of the a-value grid. Spatially-varying weighting was suggested by Allin Cornell in the external review of the interim maps. Our "adaptive weighting" scheme avoids lowering the hazard in higher seismicity areas to raise the hazard in low seismicity areas. We implemented this by looping through the a-value grid and checking to see if the a-value for each cell from the historic seismicity was greater than the a-value from the background zone. For the CEUS the a-value from the historic seismicity was derived by weighting the rates from models 1, 2, and 3 by 0.5, 0.25, 0.25 respectively. If this weighted sum was greater than the rate from the appropriate background zone, then the rate for that cell was determined by weighting the rates from models 1-3 by 0.5, .25, .25 (i.e., historic seismicity only, no background zone). If the weighted sum from the historic seismicity was less than the rate of the background zone, then we used a weighting scheme of 0.4, 0.2, 0.2, 0.2 for models 1-4, respectively (including the background zone as model 4). This scheme does not make the rate for any cell lower than it would be from the historic seismicity (models 1-3). It also incorporates the background zones in areas of low historic seismicity. The total seismicity rate in the resulting a-value grid is only 10% larger than the observed rate of mb3's since 1976. We think this is not a major difference. Of course, this scheme produces substantially higher ground motions (in terms of percentage increase) in the seismically quiet areas, than was found in the interim maps. These values are still quite low in an absolute sense.

Figure 16 shows a hazard map derived from the a-value grid made with this adaptive weighting method, plus model 5. Note that areas of relatively high hazard have identical values between this map and the map using only historic seismicity plus model 5 (compare Figures 16 and 12; e.g., eastern Tennessee, northern New York state to Ottawa). Areas of lower hazard (e.g., Minnesota, Wisconsin, Florida, eastern Texas, southwestern Pennsylvania) now have higher values than in the case with just the historic seismicity. These areas have values equal to those in the map made with the background zone and the historic seismicity (compare Figures 16 and 14).

It is useful to compare the CEUS hazard curves made with adaptive weighting (Figure 2) with those in Figure 15 made with and without the background zones. For areas of higher hazard such as Memphis and New York City, the adaptive weighting hazard curves in Figure 2 are equivalent to those in Figure 15 made without the background zones. For areas of lower hazard such as St. Paul, the adaptive weighting hazard curve in Figure 2 is equivalent to the hazard curve in Figure 15 constructed with the background zone and the smoothed historic seismicity.

 

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