Dr. Aybige Akinci, Postdoc. Resear., Saint Louis University, email:akinci@eas.slu.edu
Dr. Robert B. Herrmann, Saint Louis University, email: rbh@eas.slu.edu

Abstract
The objective of this effort is to update the 1996 NEHRP probabilistic seismic hazard maps for the United States by focusing on modifications for the Central United States. The primary change will be to incorporate the effects of deep alluvial sediment deposits, sometimes in exceedence of 1000+ m as in Mississippi Embayment. Deep sediments affect the ground motions because of the site amplification and anelastic linear attenuation. The 1996 NEHRP hazard maps give expected ground motions for a single, generic, nationwide site 'the B-C boundary'.
To estimate more realistic site effects within the Mississippi Embayment, we estimate shear-wave velocity and Q as a function of depth. In the absence of deep boreholes logged to obtain these parameters, we synthesize several types of information:

• shallow borehole logs (NUREG/CR-0985,1980)
• behavior of low strain shear modulus and damping with confining pressure (EPRI/TR-102293,1993)
• estimates of soil column attenuation at New Madrid
• deep borehole sonic logging (USGS Linda Well)

Introduction
A probabilistic seismic hazard map indicates the geographic distribution of ground motion amplitudes associated with a certain annual probability of being exceeded. Seismic hazard calculations utilize attenuation function and soil amplification factors, which includes the effects of ruptures and crustal structure and the effects of surface geology, soil column thickness, and soil nonlinearity, respectively. Calculation of ground motion for a given magnitude and distance is performed in two steps, calculation of bedrock ground motion and multiplication by a site amplification factor, (Toro et. al., 1992).
Local site effects have enormous influence on the intensity and character of earthquake motion. Damage to property and loss of life in earthquakes is frequently a direct result of the local site geological conditions affecting the incident ground motion. Consequently, any attempt of seismic zonation must take into account the local site conditions. It has been long known that each soil type responds differently when it is subjected to ground motion from earthquakes. Due to the concern about structures built over a great variety of geological sites, it is important to measure the site amplification of ground motion throughout metropolitan regions.
The amplitude and frequency content of the ground motions from on earthquake can be greatly affected by properties (e.g. impedance contrasts) and configuration of the near surface materials via mechanisms such as selective filtering (including resonance) damping and focusing. Other complications sometimes included in the study of site effects are soil anisotropy (Malin et al. 1988, Lynn 1991) the incidence angle of the seismic waves at the base of the soil column (Papagergiou and Kim 1991, Bard et al., 1991) and the generation of the surface waves in alluvial basin (Finn 1991, Frankel 1994).
The problem of the site effects is a particular importance to much of the central United States, The New Madrid seismic zone is centered in the upper Mississippi Embayment and many of the larger population centers are located on thick deposits (Figure-1)of semiconsolidated to unconsolidated sediments. Complicating the assessment of the site affects in the Upper Mississippi Embayment is the lack of detailed shear wave velocity profiles of the sediments down to the bedrock espeacially with Q models. R. Street et al., 1997 observed that the impedance contrast at the soil/ bedrock interface has a strong effect on the resulting ground motions at the surface. This finding is in agreement with Bard and Chavez Garcia (1993) who concluded that deeper layers significantly affect ground motions at the surface and that models that consider only the uppermost soft layers will be wrong in their prediction of the surface motion.
Toro et al, 1992 calculated the hazard in the Mississippi Embayment including the effect of the site condition for spectral acceleration at 1 and 10 Hz and for peak acceleration. Their maps show that soil depth has a dramatic effect on surface motion. The seismic hazard maps indicate a strong dependence on site conditions, suggesting that soil depth should be an included in seismic hazard map at regional and local events.
To successfully model ground motions at a site for a hypothetical earthquake, the shear velocities and densities of the bedrock and overlying soils must be known, as well as the shear wave velocities of the deeper soils as a site.
In this study, in order to interpret the site amplifications based on shear wave velocity, density and attenuation as a function of depth, amplifications are computed using the quarter-wavelength approximation introduced by Joyner et al., (1980). The upper 30m is accessible in engineering site investigation. Boore et al., (1993, 1994); Boore & Joyner, (1997); Boore & Brown, (1998), have shown the sensitivity of site amplification to this shallow structure. Amplifications have been calculated for different sites with V₃₀= 413 m/sec and V₃₀= 325m/sec using different velocity and Q models which are reasonable for New Madrid zone.

The Quarter-Wavelength Approximation and synthetic site amplification from velocity and Q models
For particular frequency, the amplification is given by the square root of the ratio between the seismic impedance averaged over depth corresponding to a quarterwavelength and the seismic impedance at the depth of the source. The approximation is relatively insensitive to discontinuities in the seismic velocity; the method does not produce the peaks and valleys that are due to the interference of multiply reflected, converted waves. Its lack of resonant effects to be an advantage if a smoothed amplification function is desired.
Using this algorithm, we repeat here the essentials of the quarter-wavelength algorithm given in Boore and Brown (1998). First convert velocity to travel time (tt) as a function of depth (z)

Where h_i is the layer thickness and V_i the interval velocity. From the travel time, average V_avr from the surface to a given depth is calculated using the equation

We then use the quarter-wavelength approximation of Joyner et al, 1981 to form a ratio of amplifications produced by the different velocity models. The amplification is given by
 
 

Where A(f) is the motion at the surface divided by the motion at the surface of a halfspace with material properties equal to those at the reference depth. V_r and i_r are shear-wave velocity and angle of incidence at the reference depth and the corresponding quantities averaged from the surface to a depth z are given by V and cos(i). The frequency corresponding to this amplification is given by

from equation (2), it is easy to show that the depth z is equal to a quarter wavelength  (z = 0.25V_avr/f).
The site response of interest includes attenuation, therefore, we have considered the amplification and attenuation separately and parametrize the attenuation by exp(-p k _of), where k _ois obtained by integrating  dz/(V_sQ) over the thickness of the soil column.
Seismic shear wave velocity models as a function of depth for generic sites have been estimated from borehole (shallowpart inform.) and seismological data (deeper part inform.) using the S_p - P converted wave time differences as ~1 sec (Andrew et al.,1985; Chen 1994a) and k_o=0.045 sec (Zuyuan Lui, 1994)_.
Velocity model V was obtained as a function of depth using the following function
V_s ~ (Z) ^1/4 Q_s ~ (Z) ^1/4 V₃₀=325m/sec
Q_s ranges between 11 to 32 between 10 to 600m depth respectively.
Velocity model U was obtained as a function of depth using the following function
V_s ~ (Z) ^1/4 Q_s ~ (Z) ^1/2 V₃₀=325m/sec
Qs ranges between 6 to 48 from 10 to 600m depth respectively.
Velocity model T was obtained as a function of depth using the following function
V_s ~ (Z) ^1/6 Q_s ~ (Z) ^1/2 V₃₀=413m/sec
Q_s ranges between 11 to 32 between 10 to 600m depth respectively.
Figure 2 shows the velocity and Q models used in this study.
Amplifications are represented as a function of alluvium thickness with frequency in Figure3, 4, 6, 8, 10. Amplifications have been calculated also for different sites with V₃₀= 413m/sec (NEHRP class C corresponding a mix of rock and soil sites), and V₃₀= 325m/sec (average soil and NEHRP class D). We also show the combined effects of amplification and attenuation inFigure 5, 7, 9,11 (geometrical + attenuation = total effect). All calculated amplifications in this study are compared with B-C boundary amplification values as column given at the left and right side of the figures.

Conclusions and Discussion

• As it is seen clearly in Figures 3 through 11 that amplifications increase with sedimentary thickness and frequency. Calculated amplifications at 1 Hz is 1.3 with 10m soil while it is 3.5 for the 1000m thick alluvium site for V₃₀=325 m/sec.
• B-C boundary amplification results differ significantly from the amplifications that are obtained in this study. The B-C values are much lower near 1 Hz and much higher at high frequencies for New Madrid seismic zone. Amplification is 3.5 at 1 Hz and B-C boundary site is 1.5 at that frequency.
• The shallow average velocity (30m) is important especially at high frequencies (10-20Hz). Amplification at 10 Hz is 4.2 for depths in the range of 10-1000m using V₃₀=325 m/sec velocity while it is 3.6 with 10-1000m using V₃₀=416 m/sec average velocity
• The large amplifications at high frequencies are greatly damped by attenuation. For reasonable values of the attenuation parameter k_o, the combined affect of attenuation and amplifications for New Madrid zone peaks between about 0.5 - 5 Hz with a max. Level of less than 3.0. The combine effect is about a factor of 2.5 at 1 Hz and less than unity for frequencies in the range of 10-20 Hz. It is important to note that the overall affect of the amplification and attenuation is still larger than unity over a wide range of frequencies of engineering interest. It is quite different from B-C boundary total site effect especially at high frequencies, because of the different velocity model and kappa value.

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