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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

NEW MOTIONS FOR THIS APPLICATION

The ground motions new to this application were based on the random-vibration implementation of the stochastic model, with parameters described below. The results are in the form of tables of ground motion for a set of moment magnitudes and hypocentral distances; there are separate tables for the various ground-motion parameters (peak acceleration and response spectra with 5% critical damping). The tables used in the hazard maps are contained in Tables A1-A4. The input parameters for the stochastic model are given in Table A5, which is a listing of the input-parameter file. The meaning of the various parameters is explained in detail in Boore (1996). We discuss a few of these parameters here.

Source: The most important parameter affecting the source is the stress parameter. Atkinson finds that a single-corner-frequency spectrum with a stress parameter of 180 bars will fit the high-frequency spectral level data that she published in 1993 (Atkinson, personal communication, 1995, and Atkinson and Boore, 1996). Because of her data selection and her data reduction procedure, her stress parameter is appropriate for a hard-rock site with no near-surface amplification and a source shear velocity of 3.8 km/s. On the other hand, we think that hard-rock sites should have some amplification, and we have used a source shear velocity of 3.6 km/s. For this reason, we have modified her stress parameter to account for these two effects (note that later we discuss the further amplification for a firm-rock site). The decreased source shear velocity and the near-surface amplification will increase high-frequency spectral levels for a given stress parameter; for this reason, the stress parameter in our model must be reduced in order to preserve the high-frequency spectral levels (we are assuming that Atkinson's source model gave an adequate fit to the observed spectral levels). With amplification the new high-frequency spectral level (i.e., the spectral level above the corner frequency, but not at frequencies so high as to be affected by diminution effects such as kappa or fmax) would be about equal to A * stress(2/3)/beta, where the near-surface hard-rock amplification A is about sqrt(3.6/2.8) (the near-surface shear velocity at a hard-rock site is assumed to be 2.8 km/s). Equality of high-frequency spectral levels then requires stress = 180 * [(3.6/3.8)*sqrt(2.8/3.6)](3/2) or stress = 180 * 0.76 = 137. We have conservatively chosen 150 bars rather than 137 bars as the stress parameter. Note that for long periods the spectra go as inverse shear velocity cubed, with no contribution from stress and little from amplification, so the spectral levels will be increased by (3.8/3.6)3=1.18. Note that this only considers the Fourier spectra; the ground motion amplitudes are also influenced by the duration. Note also that we have used a single-corner-frequency model rather than the two-corner-frequency model used by Atkinson and Boore (1995); this will have the effect of increasing the ground motions at intermediate periods.

Signal Duration: The signal duration was specified as in Boore and Atkinson (1987). The duration (in sec) is equal to 1/fc + 0.05R, where R is distance and fc is the corner frequency.

Path: The geometrical spreading and attenuation are those used by Atkinson and Boore (1995). We used a tripartite geometrical spreading function consisting of R-1 from 10 to 70 km, R0 from 70 to 130 km, and R-0.5 for greater than 130 km. Q was set equal to 680f0.36.

Site Amplification: The amplifications for Fourier spectral values are given in Table A5, and are intended to represent a hypothetical NEHRP B-C boundary site for the CEUS. They are obtained by converting an average velocity vs depth function to amplifications and frequencies using an approximate method discussed in Boore and Joyner (1991), as implemented by the program Site_Amp in Boore (1996). The underlying velocity vs. depth function was constructed by requiring the average velocity in the upper 30 m to be 760 m/s (= NEHRP B-C boundary of 2500 ft/sec). Table A6 contains the velocity and density profiles used. Figure A1 shows the shallow velocity profile. A steep linear gradient was imposed from the surface down to 200m depth. The velocity gradient was intended to be steeper than that for a typical WUS rock site. A less steep gradient was imposed below 200m, with the velocities approaching the hard-rock values at depth. The velocities and densities were chosen with consideration given to the gross differences in lithology and age of the rocks in ENA compared with those in coastal California (the source of much of the borehole data that can be used to constrain velocity--depth functions): we expect ENA rocks to be higher velocity and density than those in coastal California at any given depth below the surface. Figure A1 also shows the shallow velocities used in our simulations for hard-rock sites (see below).

Diminution of High Frequencies: The parameter kappa controls the loss of high frequencies at close to moderate distances, and exerts a strong control on peak acceleration. The proper choice of this parameter gave us some difficulty. For very hard rock sites in ENA kappa seems to be considerably less than 0.01; for firm-rock sites in WNA it seems to be between 0.03 and 0.04 (Silva and Darragh, 1995; Boore and Joyner, 1996). Studies of shear waves recorded at various levels in a borehole in Savannah River, GA, suggest values near 0.01 (Fletcher, 1995), and this is the conservative choice that we have taken. For the velocity model in Table 2, a kappa of 0.01 corresponds to a shear-wave Q of 43 and 72 if all the attenuation occurred within the upper 1 and 2 km, respectively. These numbers do not seem unreasonable to us, although we have little or no information regarding shear-wave Q in the upper few kilometers for firm-rock sites in eastern North America. To see the sensitivity of the ground motions to kappa, the ground motions have also been computed using kappa = 0.020. In general, the ground-motion parameter most sensitive to kappa is pga, with the motions using kappa = 0.020 being about 0.7 times those using kappa = 0.010. The 0.3 and 1.0 sec response spectra are reduced by factors of about 0.90 and 0.98, respectively.

Note the cap on MEDIAN ground motions described in the documentation above (see Attenuation Relations for CEUS).

 

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