Skip Links

USGS - science for a changing world

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

Attenuation Relations for CEUS

The reference site condition used for the maps is specified to be the boundary between NEHRP classes B and C (Martin and Dobry, 1994), meaning it has an average shear-wave velocity of 760 m/sec in the top 30m. This corresponds to a typical "firm-rock" site for the western U.S. (see WUS attenuation section below), although many rock sites in the CEUS probably have much higher velocities. The basic motivation for using this reference site is that it corresponds to the average of sites classified as "rock" sites in WUS attenuation relations (see WUS attenuation section). In addition, we felt it would be less problematic to use this site condition for the CEUS than to use a soil condition. Most previously-published attenuation relations for the CEUS are based on a hard-rock site condition. It is less problematic to convert these to a firm-rock condition than to convert them to a soil site, since there would be less concern over possible non-linearity for the firm-rock site compared to the soil site. Participants of the ATC 35 workshop (Applied Technology Council) on the national maps (Sept. 1995) recommended a rock site reference, although the B/C boundary was not specified.

For the CEUS, we used two, equally-weighted, attenuation relations. Both sets of relations were derived by stochastic simulations and random vibration theory. First we used Toro et al. (1993) formula based on mblg. The attenuation relations were multiplied by frequency-dependent factors to convert them from hard-rock to firm-rock sites (see below and Appendix). We derived coefficients for 0.3 sec spectral response by interpolating the Toro et al. (1993) coefficients for 0.2 and 0.5 sec.

The second set of relations was derived by us for firm-rock sites (see Appendix). These relations were based on a Brune source model with a stress drop of 150 bars. The simulations contained frequency-dependent amplification factors derived from a hypothesized shear-wave velocity profile of a CEUS firm-rock site. We produced a series of tables of ground motions and response spectral values as a function of moment magnitude and distance (these tables are contained in the Appendix). In the hazard program, we calculate the hazard over increments of mblg. Each mblg value has an associated rate of earthquake occurrence. We convert the mblg to a moment magnitude using the empirical relation of Johnston (1994; we used the relation in this pre-print which differs slightly from that in the 1996 published version; we used M = 3.45-0.473mblg+0.145mblg2). Thus, the rate of occurrence is assigned to the converted value of moment magnitude. This allows us to use the attenuation tables based on moment magnitude. Note that the magnitude conversion is not needed for the Toro et al. (1993) relations, since they were based on mblg.

The magnitude conversion is needed when determining mblgmax values corresponding to Mmax values (moment magnitude). We used the Johnston (1994) conversion to find mblgmax's when using our new ground motion tables, to be consistent with the conversion used in the hazard code. We used the Boore and Atkinson (1987) conversion to find mblgmax's for Toro et al. (1993).

For the large events in model 5, we used the attenuation relations for moment magnitude from Toro et al. (1993) and our tables, with equal weights.

One key parameter was the site attenuation or kappa (t*) value. We chose a kappa value of 0.01. This is much lower than site kappas found for typical western U.S. rock sites. Our justification comes from work by Joe Fletcher using borehole recordings at Savannah River, SC of regional and local earthquakes. Fletcher determined kappa values for recordings made from a borehole sensor in bedrock and from a site at the top of the borehole on stiff soil. He found a difference of about 0.01, implying that the kappa of this soil site was about 0.01. Thus, we think this low value is reasonable to be used for a firm-rock site in the CEUS (see Appendix).

We also derived ratios between simulations using firm-rock site conditions and those using hard rock site conditions with the surface velocity and site kappa used by Toro et al. (1993). Values were found from the average ratios for M 5.0-5.6 and distances of 10-50 km. We used these average ratios as factors to adjust the Toro et al. (1993) hard-rock relations to firm-rock site conditions. We applied a factor of 1.52 for PGA, 1.76 for 0.2 sec spectral response, 1.72 for 0.3 sec spectral response and 1.34 for 1.0 sec spectral response. These factors were applied independently of magnitude and distance.

For CEUS hazard calculations for models 1-4 we assumed a source depth of 5.0 km when using our new ground motion tables. Since we have a minimum hypocentral distance of 10 km in these tables, the probabilistic ground motions are insensitive to the choice of source depth. In the hazard progam, when hypocentral distances are less than 10 km we set them to 10 km when using the tables. For the Toro et al. (1993) relations, we used the fictitious depths that they specify for each period, so that our choice of source depth was not applied. For M8.0 events in New Madrid and M7.3 events at Charleston, we used a source depth of 10 km when using our tables.

For both sets of ground motion relations, we used values of 0.75, 0.75, 0.75 and 0.80 for the natural logarithms of the standard deviation of PGA, 0.2 sec, 0.3 sec and 1.0 sec spectral responses, respectively. These values are similar to the aleatory standard deviations reported in Senior Seismic Hazard Analysis Committee (1996). All spectral response values shown in the maps correspond to 5% of critical damping.

For models 1-4 we used a maximum source-site distance of 500 km when calculating the hazard at each site. For model 5, we used a maximum source-site distance of 1000 km when calculating hazard at each site. On the 1.0 sec spectral maps, there are artifacts of the 1000 km maximum distance cut-off. On the 2% PE in 50 year map one can see some of the lowest contour levels about 1000 km from the New Madrid area. The M8.0 events at New Madrid still have a significant contribution to 1.0 sec hazard, even at 1000 km.

A cap in the MEDIAN ground motions was placed on the ground motions within the hazard code. We were concerned that the median ground motions of both the Toro et al. and our tables became very large (>2.5 g PGA) for distances of about 10 km for the M 8.0 events for New Madrid. We capped the median PGA's at 1.5 g. The median 0.3 and 0.2 sec values were capped at 3.75 g which was derived by multiplying the PGA cap by 2.5 (the WUS conversion factor). This only affected the PGA values for the 2% PE in 50 year maps for the area directly above the three fictitious faults for the New Madrid region (see below). It does not change any of the values at Memphis. Without the clipping, the 2%/50 year values were over 2g for this limited area over the New Madrid "faults". With the clipping, the values are about 1.5g. The capping did not significantly alter the 0.3 and 0.2 sec values in this area. The PGA and spectral response values did not change in the Charleston region from this capping. Note that the capping was for the median values only. The variability (sigma) of the ground motions was still maintained in the hazard code, so that values larger than the median were allowed. We felt that the capping recognizes that values derived from point source simulations are not as reliable for M8.0 earthquakes at close-in distances (< 20 km).

 

Part or all of this report is presented in Portable Document Format (PDF); the latest version of Adobe Reader or similar software is required to view it. Download the latest version of Adobe Reader, free of charge.

Accessibility FOIA Privacy Policies and Notices

Take Pride in America logo USA.gov logo U.S. Department of the Interior | U.S. Geological Survey
URL: http://pubsdata.usgs.gov/pubs/of/1996/532/CEUSatten.html
Page Contact Information: GS Pubs Web Contact
Page Last Modified: Wednesday, 07-Dec-2016 16:06:20 EST