The Memphis, Shelby County, 

Tennessee, Seismic Hazard Maps 

By Chris H. Cramer, Joan S. Gomberg, Eugene S. Schweig, Brian A. 

Waldron, and Kathleen Tucker 

This report is preliminary and has not been reviewed for conformity with the U.S. 

Geological Survey editorial standards or with the North American Stratigraphic Code. 

Any use of trade, firm, or product names is for descriptive purposes only and does not 

imply endorsement by the U.S. Government. 

U.S. Geological Survey Open-File Report 04-1294

U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEOLOGICAL SURVEY 

1 
The Memphis, Shelby County, Tennessee, Seismic Hazard Maps 

By Chris H. Cramer, Joan S. Gomberg, Eugene S. Schweig, Brian A. Waldron, and 

Kathleen Tucker 

Contents 

Introduction 1 

Methodology 1 

Characterizing the Shallow Geology 3 

Site-Specific Amplification and Attenuation 4 

Hazard Maps 7 

Uncertainties 8 

Summary 10 

Acknowledgements 11 

References 12 

Tables 15 

Figure Captions 17 

Figures 20 

Introduction 

Memphis, Shelby County, Tennessee, is located where damaging earthquakes are 

only moderately likely, but the consequences of earthquakes, mainly from the New 

Madrid seismic zone, can be very high. This densely populated urban area is built on a 1-

kilometer-thick sequence of sediments deposited in a trough known as the Mississippi 

embayment. This thick pile of sediments significantly affects earthquake ground motions. 

We, the authors, have generated a suite of seismic hazard maps for a six-quadrangle area 

(fig. 1) in Memphis, Shelby County, Tennessee, that accounts for these effects. These 

maps and their derivative products represent the collaborative efforts of the U.S. 

Geological Survey (USGS) and its partners. Herein, we document how these seismic 

hazard maps (probabilistic and scenario) were generated. The Memphis maps 

complement the USGS national seismic hazard maps (Frankel and others, 2002), which 

do not include the effects of local geologic structure. Otherwise, both sets of maps use 

the same information and methodology. We emphasize that the Memphis maps are 

regional in nature and should not be used for site-specific analyses or as a basis for 

structural design. 

Methodology 

The methodology developed to generate the Memphis seismic hazard maps builds 

on that used for the USGS national seismic hazard maps (Frankel and others, 2002). 

Unlike the national maps, our approach also includes the effects of local sediment 

structure in such a way that fully preserves the probabilistic nature of the maps (Cramer, 

2003). Probabilistic maps express the hazard in terms of the levels of horizontal ground 

shaking that have a specified chance of being exceeded in a given time period. The 

general state of practice in calculating a site-specific probabilistic ground motion has 

1
been to calculate a probabilistic bedrock ground motion and then to multiply it by a 

deterministic site-amplification factor. If the site-amplification factor has no uncertainty 

(unlikely!), the resulting site-specific ground motion would still be a probabilistic result. 

The site-amplification factor, however, typically represents the median value from some 

distribution so that the resulting ground motion is a hybrid answer that is no longer 

completely probabilistic. In other words, the ground motions estimated using this stateof-practice approach will not have the probability specified for the bedrock ground 

motions, and at large ground motions (greater 0.3 g – g is the acceleration of gravity at 

the earth’s surface) will underestimate the true probability of exceedance. For example, 

ground-motion estimates for a 2%-in-50-year (1 in 2,475 annual) probability of 

exceedance made using a completely probabilistic approach will be about 10 percent 

greater than those estimated by simply multiplying a bedrock probabilistic ground motion 

by a median site-amplification factor. This difference will be even larger at smaller 

probabilities of exceedance. In addition, the completely probabilistic hazard explicitly 

incorporates the uncertainty in our knowledge of site amplification of ground motions in 

the estimates. 

Generally, site-specific amplification is developed from geological, geophysical, 

and geotechnical subsurface information (Kramer, 1996). A soil profile above bedrock is 

developed to represent soil type, boundaries, shear-wave velocity (Vs), bulk density, 

intrinsic shear-wave damping or attenuation (Qs), and dynamic soil properties (usually 

representative modulus and damping versus strain curves). Commonly, this soil profile 

information is input into a soil-response program (often SHAKE – see Idriss and Sun, 

1992), and a single site-amplification factor calculated. To account for variability and 

uncertainty in this information, the state-of-practice approach, such as used in Toro and 

Silva (2001), may randomly sample profiles from the ranges of soil boundaries, Vs, and 

dynamic soil properties, calculate the corresponding soil response, and from these, 

estimate a median site-amplification. This then is applied to the probabilistic ground 

motion estimated for hard-rock conditions. The state-of-the-art fully probabilistic 

approach (Silva, 2000, personal communication; McGuire et al., 2001; Cramer, 2003), 

employed in generating the Memphis seismic hazard maps, accounts for the effects of 

local geology by making the ground-motion attenuation relations site specific. These 

also are derived from distributions of possible amplifications at a particular site, but prior 

to doing the probabilistic calculations. We combine the site-amplification distributions 

with bedrock ground-motion attenuation relations to obtain site-specific attenuation 

relations, which then are used in the probabilistic calculations for that site (see below). 

In addition to probabilistic maps that include the effect of site geology, we also 

have generated scenario maps for the six-quadrangle study area. These maps were 

generated using the deterministic program hazDXv3.f (provided by Art Frankel), 

modified to apply the median site amplification to median hard-rock ground-motion 

attenuation relations. Thus, the scenario maps represent the median ground motion 

expected for the given scenario earthquake, which are the ground motions one expects 

will be exceeded 50 percent of the time when that scenario earthquake occurs. 

The Memphis probabilistic seismic hazard maps display the hazard for 2, 5, and 

10 percent probabilities of exceedance in 50 years and characterize the ground shaking in 

terms of the maximum or peak acceleration (PGA) and the spectral acceleration (Sa) at 

0.2 second and 1.0 second periods. For each scenario earthquake, scenario ground2
motion maps are also generated at these same periods. Although displayed as smooth 

color contours, the hazard is calculated on a grid with spacing sufficiently fine for major 

geologic detail to be apparent (every 0.01 degree or about every kilometer). For each 

grid point, the basic idea is to derive site-specific probabilistic or scenario hazard 

estimates. For the probabilistic maps, we used the same range of earthquake source 

models and magnitude- and distance-dependent ground-motion attenuation functions 

used to calculate the national seismic hazard maps. The scenario maps also use these 

same ground-motion attenuation functions. In order to add the effects of local geology, 

the attenuation functions, in essence, have to become site specific at each grid point. This 

is accomplished by developing a distribution of amplification factors at each grid point 

that represents the range of possibilities at that particular site. The purpose of this 

document is to describe how these distributions are derived, what their major sources of 

uncertainty are, and how they are used to estimate the probabilistic and scenario seismic 

hazard maps (ground motions). We first summarize the information used to characterize 

the geology local to each site. We then describe our procedure for deriving the associated 

distribution of amplification functions and how they are used to estimate the probabilistic 

seismic hazard. Next, we summarize the most significant features of the Memphis, 

Shelby County maps (both probabilistic and scenario) and how they differ from the 

national seismic hazard maps. Finally, we discuss the sources of uncertainty in the site 

amplifications and hazard maps. 

Characterizing the Shallow Geology 

The physical property that controls site amplification most significantly is the 

shear-wave velocity (Vs) of the sediments and rocks, at least until the motions become so 

large that they begin to respond non-linearly (that is, an increase in shaking-levels input 

to the base of the sediments does not produce a proportional increase in surface motions). 

Unfortunately, Vs measurements did not exist for Memphis, Shelby County, prior to this 

project and, although we made many tens of new Vs measurements (Gomberg and others, 

2003), they are still too sparsely spaced to provide the needed resolution. Thus, we 

derived and employed a model of the sediment layering throughout the area based on 

hundreds of well and engineering logs in order to estimate Vs, its uncertainties, and 

variations throughout Memphis, Shelby County (see below and Gomberg and others, 

2003). In short, we used the more densely sampled geologic structure as a guide to 

extrapolate from sparsely measured Vs profiles. In addition to Vs information, 

calculation of site-amplification functions requires knowledge of density, water content, 

attenuation, and dynamic soil properties. 

We built a three-dimensional model of the sediment layering beneath Memphis 

from interpretations of hundreds of well logs and engineering boring logs as well as 

surface geologic maps. Surficial materials (fig. 2) were classed as either wind-blown 

glacial deposits (loess) or river deposits (alluvium), based on new geologic maps of 

Memphis (Broughton and Van Arsdale, 2004; Cox, 2004; Moore and Diehl, 2004a, 

2004b; and Van Arsdale, 2004a, 2004b). The locations, surface elevations (fig. 3a), 

depths to the top of each lithologic layer estimated from each log by a geologist (fig. 3b), 

and other information obtained for nearly 1200 shallow (to ~500 meter depth) logs have 

been compiled in a database maintained by the Ground Water Institute at The University 

of Memphis (http://gwidc.memphis.edu/website/introduction). Deeper layer boundary 

3
depths (the top of the Cretaceous sediments and Paleozoic limestones, fig. 4) are based on 

data described in Van Arsdale and TenBrink (2000). Although the constraints on the two 

deeper boundaries are sparse, they are sufficient to provide a regional trend within Shelby 

County. 

To extrapolate the layer boundary depths estimated from the well and deeper data 

to a uniform grid, we fit surfaces to each boundary by using a moving least-squares 

algorithm (Gomberg and others, 2003). At each grid point, this algorithm locally fits a 

polynomial surface to the observations within a radius of about 100 meters (m) from the 

point. Uncertainties associated with natural variability and measurement error are 

estimated as a weighted root-mean-square difference between modeled and observed 

boundary depths, and uncertainties that describe the stability of the fit surface are derived 

using a bootstrap resampling method (Gomberg and others, 2003). Both uncertainties are 

used to derive the site-amplification distributions and the correlations between lithology 

and Vs. 

For the uppermost 100 m, we then derived a correspondence between geologic 

layer material and Vs by using 76 measured Vs profiles and the modeled sedimentary 

structures beneath each corresponding measurement site. These correlations can be found 

in Gomberg and others (2003). Shear-wave velocity estimates for greater depths were 

made by using logs from a 420-m Memphis Light, Gas, and Water (MLGW) water well 

(fig. 5) and the 900-m Wilson 2 oil and gas exploration well (fig. 6). Both S-wave and Pwave velocities were logged in the MLGW well but only P-wave velocities (Vp) in the 

Wilson 2 well. To estimate Vs below 420 m, we used the trend of Vp/Vs versus Vp from 

the MLGW log (which approached 2.3 with increasing Vp) with the Vp measurements in 

the Wilson 2 log. For the velocities of the Paleozoic limestones beneath the sediments, 

we used the measured Vp at the bottom of the Wilson 2 well and assumed a Vp/Vs ratio 

of 1.7. 

Table 1 summarizes the remaining soil properties used in the determination of 

site-amplification distributions. Densities for various lithologic units were determined 

from six logged wells in Shelby County ranging from 130 to 800 m in depth. A density 

log from the 900-m exploration well in the Mississippi embayment also was used. Site 

amplification is not very sensitive to shallow Vs attenuation (Qs) of 10 or greater 

(damping of 0.05 or less); Qs in the region has been determined by Pujol et al. (2002) to 

be no less than 20 to 40. There are no existing measurements of dynamic properties 

(modulus and damping) for Mississippi embayment sediments. Hence, we assumed a 

distribution described by the generic EPRI (1993) curves and their natural lognormal 

standard deviation of 0.35. 

Site-Specific Amplification and Attenuation 

Amplification depends not only on the shear velocities and other material 

properties of the sediments but also on the amplitudes and frequency content of the 

ground-motion input to the base of the sediment layers. For each type (frequency content) 

of ground motions mapped (PGA, 0.2 s Sa, or 1.0 s Sa), our amplification factor 

distributions are represented by mean values and their standard deviations of 

multiplicative factors for a range of input amplitudes (fig. 7). To capture the true natural 

complexity of earthquake seismograms, we employ real recordings of earthquake ground 

4
motions as inputs to our amplification calculations. We use ground motions recorded on 

rock outcrops because our resulting amplification-factor distributions have to be 

combined with ground-motion attenuation relations (see below) that predict ground 

motions on rock. Specifically, we use 14 horizontal recordings from seven M~7 

earthquakes (see table 2) obtained from the PEER strong motion database 

(http://peer.berkeley.edu/smcat/). Most of these earthquakes and many of the records 

used in this study also are part of the NRC CEUS database of time histories (McGuire 

and others, 2001). In addition, we used two synthetic M7.5 and M 8.0 records for hard 

rock from Atkinson and Beresnev (2002), as these are more representative of CEUS 

source characteristics, CEUS wave-propagation properties, and upper-bound New Madrid 

earthquake magnitudes than the real M7 records from outside the CEUS. As discussed in 

the uncertainty section below, figure 17 compares site-amplification results from the real 

earthquake records with those from the CEUS synthetic records. 

Because soil amplification is nonlinear, it depends on both the amplitude and 

frequency of input ground motion. To build a distribution of site amplifications at a 

particular amplitude and frequency, a ground-motion record is randomly selected and 

scaled to the input ground-motion level. We scale (adjust the amplitude of) the real 

ground motions to obtain input rock ground motions at ten different shaking levels (0.01, 

0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, and 1.0 g). The scaling is done at the particular 

frequency of interest (PGA, 0.2 s Sa, or 1.0 s Sa). The scaled record then is input to a 

computer program that simulates the response (amount of amplification or 

deamplification) of the overlying sediments (see below). The properties of the sediments 

also are selected randomly from the suite of Vs profiles and dynamic soil properties 

described above. For each frequency and amplitude, this process of randomly choosing a 

ground-motion record and scaling it, randomly choosing a set of sediment properties, and 

calculating the response of these sediments to the scaled input motions is repeated 100 

times. A mean and standard deviation is then derived from these 100 estimates of the 

amplified (or deamplified) ground motion. 

An important aspect of determining site amplifications is the proper handling of 

the free-surface effect (which effectively increases the motions by a factor of two) 

because ground-motion attenuation relations predict surface ground motions. We use 

motions measured at the surface as proxies for motions at the bedrock-soil interface in the 

sediment-response calculations, so the scaled surface ground motions must be reduced by 

a factor of two, independent of frequency. Once the soil response has been calculated, 

the free surface effect must be put back in by multiplying the output motions by a factor 

of two, again independent of frequency. How a particular soil-response program does or 

does not handle the free surface must be determined and understood so that proper siteamplification distributions can be determined. 

To simulate the sediment response, we use the computer program SHAKE91 

(Idriss and Sun, 1992). However, to more accurately approximate nonlinear soil behavior 

at high-frequency ground shaking, we allow nonlinear response in the sediments only 

above 300 m depth (see comparisons below). Predictions of theoretical models and 

computer programs that more completely account for the underlying physics show that 

SHAKE91 overpredicts the attenuation of ground motions at high frequencies (fig. 8). 

We performed our own comparisons using the more complete programs DEEPSOIL 

(Hashash and Park, 2001, 2002) and TREMORKA (Bonilla, 2003, written commun.; 

5
Kausel and Assimaki, 2002). For the MLGW well 236 site of figure 5, figure 8 shows a 

comparison of the soil responses for input motions of 0.1 g and 0.5 g (surface) and 

common dynamic soil properties between SHAKE91, DEEPSOIL, TREMORKA, and 

SHAKE91 limited to linear response below 80 m, 300 m, and 400 m. For the 0.1 g input 

surface time series, the differences among the various programs and constraints are less 

than 50 percent. Differences are much greater for the 0.5 g input surface time series 

(please see the Uncertainty Section). These show that SHAKE91 overly damps the highfrequency motions if applied to the entire 1-km soil column. DEEPSOIL has a lower 

high-frequency response than TREMORKA. SHAKE91 limited to linear soil response 

below 300 m seems the best compromise to matching the newer soil-response codes, 

although it seems to consistently underestimate the amplitude response between 0.2 and 

0.5 s (5 to 2 Hertz) in figure 8. Unfortunately, these more complete programs are too 

computationally demanding to use for the map calculations. 

Figure 7 shows representative site-amplification distributions for PGA, 0.2 s Sa, 

and 1.0 s Sa for the Memphis study area. The site-amplification distributions are 

represented in figure 7 by the median and the 16th and 84th percentiles (68 percent 

confidence interval). Also shown are the NEHRP 1997 factors (taken from Joyner and 

Boore, 2000) for converting hard rock (NERHP soil class A) seismic amplitudes to those 

for NEHRP soil class D site conditions based on Vs30, the average shear-wave velocity 

for the top 30 meters of soil. Typically for Memphis at very strong ground motions (~ 

1.0 g), PGA shows little amplification (near 1.0), 0.2 s Sa motions tend to be deamplified 

(amplification below 1.0), and 1.0 s Sa motions are amplified by 150 to 200 percent. 

Because Memphis has very thick soils (about 1 km), we would expect the median soil 

amplification to deviate from the NEHRP factors, which are based on Vs30. As shown 

on figure 7, this is the case. PGA and 0.2 s Sa have higher weak-motion (<0.1 g) median 

amplification but lower strong-motion median amplification relative to the NEHRP 

factors. For 1.0 s Sa, weak motion has similar (about 200 percent) median amplification 

as the NEHRP factors, but does not decrease as much as the NEHRP factors for stronger 

motions due to resonance in the thicker soils beneath Memphis. Bodin and Horton 

(1999) measured site periods of 4 to 5 s in Memphis. 

The final step in estimating the ground motions combines the site-specific 

amplification-factor distributions with the regional attenuation relations. To calculate a 

site-specific seismic hazard, the ground-motion attenuation relations for rock need to be 

adjusted so they represent ground motions at the site being considered (Cramer, 2003). 

For a given frequency of ground motion, a ground-motion attenuation relation gives the 

distribution of possible ground motions for a specified magnitude and distance from an 

earthquake. Like the national maps, we employ five CEUS ground-motion attenuation 

relations: Atkinson and Boore (1995), Frankel and others (1996), Toro and others (1997), 

Campbell (2003), and Somerville and others (2001). Figure 9 shows the median groundmotion attenuation with distance for M 5, 6, and 7 earthquakes for PGA and 1.0s Sa. We 

have followed the USGS national hazard model and used all five relations for the largest 

New Madrid earthquakes (weighted 0.25, 0.25, 0.25, 0.125, and 0.125, respectively), and 

only the first four relations for the smaller magnitude earthquakes (weighted 0.286, 

0.286, 0.286, and 0.143, respectively). The Campbell and Somerville and others relations 

were down weighted because they were new relations and not well accepted yet (in 

6
2002). The Somerville and others relation is a finite-fault relation, unlike the others, and 

is not applicable to earthquakes below M6. 

For each magnitude (M) and distance (R) used in a hazard calculation, the rock 

ground motions (Ar) are adjusted by the site-amplification cumulative distribution [P(As 

< Ao | Ar)] to determine the corresponding distribution of site-specific ground motions 

(As) using the probability (P) integral formula: 

P(As > Ao | M,R) = 1 - ∫ArP(As < Ao | Ar) P(Ao = Ar | M,R) dAr, 

where Ao is a level of ground motion that the soil ground motion is to have some 

probability of exceeding and | is a conditional probability symbol that means given the 

values that follow it. P(Ao = Ar | M,R) is the probability of Ao being Ar given M and R, 

which is derived from the original hard-rock attenuation relation. An example of 

applying this formula is shown in figure 10. Additional details may be found in Cramer 

(2003). Once the ground-motion attenuation relations are adjusted, the hazard calculation 

proceeds using the earthquake sources modeled in the national seismic hazard maps. 

Hazard Maps 

Memphis probabilistic ground motion seismic hazard maps have been generated 

for PGA, 0.2 s Sa, and 1.0 s Sa for 2%-, 5%-, and 10%-in-50-year probabilities of 

exceedance (figures 11 through 13). These maps have been smoothed by averaging over 

four grid-points (~4 km) and reassigning that average to the coordinate center of the four 

grid-points to remove spatial variability on the order of 0.05 g or less. In other words, the 

smoothed grid values are offset by one-half grid unit in latitude and longitude from the 

original grid used to estimate seismic hazard. When compared to the 2002 USGS 

national seismic hazard maps, the Memphis hazard maps have similar ground-motion 

levels for PGA, 0-30 percent lower levels for 0.2 s Sa, and about 100 percent higher 

levels for 1.0 s Sa. Note that the national map calculations assume a uniform geologic 

structure. Soil classification is dominated by the National Earthquake Hazard Reduction 

Program’s (NEHRP) classification scheme, which is based on the average shear-wave 

velocity over the uppermost 30 m. The national seismic hazard maps correspond to the 

B/C boundary soil class (average S-velocity of 760 m/s over the top 30 m of soil), and 

this site class has higher earthquake ground motions than ground motions on rock 

outcrops (NEHRP soil class A). All of Memphis falls entirely within NEHRP soil 

category D, and the sediments thicken westward. This causes westward decreasing 

amplification and even deamplification of the strongest ground motions at high 

frequencies. Thus the 2%- and 5%-in-50-year PGA and 0.2 s Sa maps (figures 11 and 

12) show a decrease or flattening of the ground-motion gradient across the study area 

relative to the motions in the national seismic hazard maps. The largest earthquake 

sources are located to the northwest of Memphis. Memphis ground motions are 

amplified at lower frequencies, as shown by 1.0 s Sa maps, due to the presence of the 

thick sediments and limited nonlinear response at this period. We summarize the average 

ground-motion levels for each map in table 3. 

Two scenarios with the effects of site geology also have been generated for PGA, 

0.2 s Sa, and 1.0 s Sa (figures 14 and 15). These scenario maps are for median ground 

motions using the same five ground-motion attenuation relations and weights as the 

national maps (see last paragraph of the preceding section), and also have been smoothed 

in the same manner as the probabilistic maps. The first scenario (figure 14) is for a M7.7 

7
earthquake on the southwesterly trending line of seismicity of the New Madrid seismic 

zone. For comparison, these scenarios are also shown with the equivalent scenario maps 

for the B/C boundary soil conditions of the national maps, just as the probabilistic maps 

in figures 11 through 13. The general trend of the M7.7 scenario ground motions relative 

to the B/C boundary maps is similar to that of the probabilistic maps discussed above. 

Relative to the national maps, the M7.7 scenario PGA ground motions show some 

amplification except in a portion of the northwest corner, and for the 1.0 s Sa ground 

motions are amplified by about 200 percent. For 0.2 s Sa, the M7.7 scenario map shows 

some deamplification. 

The second scenario (fig. 15) is for a M6.2 earthquake at Marked Tree, Arkansas, 

at the southern end of the southwest-trending arm of seismicity of the New Madrid 

seismic zone. This scenario represents the 1843 Marked Tree earthquake and uses the 

Bakun and Hopper (2004) estimate for the magnitude of 6.2. Like the M7.7 scenario 

maps, the M6.2 scenario maps are for median ground motions and are compared with the 

equivalent B/C boundary maps. Clearly, the median ground motions are small enough 

for the M6.2 scenario that nonlinear soil behavior is not significant. The effect of the 

sediments is to increase the ground motions by as much as a factor of two over those of 

the B/C boundary soil conditions for all three periods (PGA, 0.2 s Sa, and 1.0 s Sa). 

Table 4 summarizes the ground-motion levels for each scenario map in a manner 

similar to table 3 for the probabilistic maps. Notice that the M7.7 scenario ground 

motions (average and range) in table 4 are almost identical to those for the 5%-in-50-year 

exceedance maps in table 3. This also is seen in comparing figure 14 with the 5%-in-50-

year maps of figures 11 through 13. This is a consequence of the probabilistic seismic 

hazard estimation process and the characteristic M 7.7 New Madrid earthquakes having a 

500-year mean recurrence interval (Wang and others, 2003) and represents a link 

between probabilistic and scenario ground-motion estimates (Frankel, 2004). This may 

provide some insight for building codes and structural design in Memphis. If this 

scenario earthquake were to occur, these results imply that a 10%-in-50-year exceedance 

ground motion probabilistic hazard value may be exceeded in an 1811-1812-magnitude 

earthquake on the southwest arm of the New Madrid seismic zone. This could lead to 

disastrous consequences similar to those that occurred in the 1988 Armenia earthquake 

(Wyllie and Filson, 1989). 

Uncertainty 

Probabilistic and scenario maps have uncertainties associated with them. Cramer 

(2001a, 2001b) and Cramer and others (2002) indicate that probabilistic estimates can 

have uncertainties on the order of 50 percent, mainly due to the knowledge uncertainty as 

to where future large ruptures will occur, in the choice of ground-motion attenuation 

relation, and in the magnitude and recurrence interval of the New Madrid characteristic 

earthquakes. Similar uncertainties apply to scenario estimates, with the exception of 

recurrence interval because the earthquake is assumed to occur. 

We have conducted an uncertainty and sensitivity analysis for the siteamplification distributions generated for Memphis. Overall uncertainty has been 

estimated using the observed variability in input ground motions (time series), soil 

profiles (velocity, layer boundaries, and top layer lithology), and dynamic soil properties. 

The Monte Carlo randomization procedure used in generating the site-amplification 

8
distributions provides an estimate of uncertainty. We examine the sensitivity to a specific 

parameter by fixing the Monte Carlo choices for all other parameters. Sensitivity then is 

determined from analyzing the statistics of 100 Monte Carlo simulations for the 

parameter of interest. 

Figure 16 shows some representative PGA, 0.2 s Sa, and 1.0 s Sa overall 

uncertainty and sensitivity analysis results for the MLGW well site, which differs from 

the site used in figure 7 located at the northeast corner of the study area. There are small 

offsets among the various individual-parameter median site-amplifications from the 

overall median site-amplification due to the choice for the parameters that are held fixed 

in the sensitivity analysis. Figure 16 shows that the greatest sensitivity to parameter 

uncertainty is at large ground motions (greater than 0.2 g), with the exception of the 

choice of input time series, which has a large sensitivity at all levels of ground motion. 

The major contributors to uncertainty are the choice of input time series, the variability 

observed in the soil profile, and the assumed lognormal uncertainty of 0.35 in the 

dynamic soil properties. The amplification appears insensitive to the choice of lithology 

(loess or alluvium) for the shallowest layer, which is not surprising because Gomberg and 

others (2003) indicate only small differences in the Vs distributions for these two soil 

types. Table 5 summarizes the sensitivity results. 

The state-of-practice for assessing the uncertainty in site-amplification estimates 

is to use several (seven or more) different earthquakes. Actual records from earthquakes 

have more realistic phase relations (although not necessarily for the site being considered 

in the analysis) than synthetic time series. Synthetic time series may better match some 

characteristics of local earthquake records than actual records imported from other 

regions. In this study, we have used a mixture of 14 actual and 2 synthetic time series 

recorded at or generated for rock site-conditions (table 2). Figure 17 presents the 

variability among amplifications estimated for these input time series for a fixed profile 

(MGLW well site) and dynamic soil conditions. For ground motions less than 0.2 g, 

PGA soil response shows greater sensitivity to the choice of input time series than 0.2 s 

and 1.0 s Sa soil response. Site amplification roughly correlates inversely with the 

magnitude of the earthquake associated with the input record. This is seen most strongly 

at 0.2 s Sa and at strong input ground motions. This may be due to the effect of 

increasing duration of strong ground motion with increasing magnitude. Longer duration 

strong ground motion tends to allow nonlinear effects to occur more readily, which 

lowers site amplification at higher frequencies and generates the observed inverse 

correlation between magnitude and site amplification. 

We also examined the sensitivity of site amplification to individual layer 

velocities and boundaries using parameters corresponding to the MLGW well site. 

Figure 18 shows the median and variability due to each layer’s uncertainty in Vs (when 

the other layer Vs values are held fixed at their mean values). Clearly, the site 

amplification is sensitive to uncertainties in Vs for the first five layers (to 300 m) and 

most sensitive to layers 1 through 3 (to 82 m). Figure 19 presents the sensitivity results 

for the uncertainties in the depths to top of each layer. Interestingly, for weak ground 

motions (less than 0.1 g), amplifications are most sensitive to uncertainties in the depth to 

the top of basement (hard rock), and to a somewhat lesser extent to layer 2 depths for 0.2 

s Sa. At stronger ground motions, this sensitivity shifts to layers 2 and 3 for PGA and 0.2 

s Sa and layer 2 for 1.0 s Sa. However, these sensitivities are much smaller then those 

9
arising from the uncertainties in Vs, and the latter drive the amplification variability in 

figure 16. 

Uncertainty in site amplification also arises from uncertainties in site-specific 

dynamic soil properties, the choice of computer program used to calculate site response, 

and our inability to model dynamic pore-pressure effects (fig. 20). In this study, a 

lognormal (base e) standard deviation of 0.35 (EPRI, 1993) is used to represent our 

ignorance of local dynamic soil properties (see fig. 16). Expert opinion (EPRI, 1993) 

suggests that this is a reasonable assumption. This uncertainty leads to estimated 

amplifications that vary from 10 to 100 percent for weak to strong ground motion, 

respectively. Although uncertainties have not been quantified, preliminary work shows 

that the median site response predicted by different programs may differ by about +50% 

for the same set of input parameters. Modeling of dynamic pore-pressure effects on site 

amplification was not feasible for this study and is a focus of research so that it may be 

included in the future. As figure 20 shows, this important effect also can contribute 

significantly to site amplification and ground-motion estimates. 

Summary 

State-of-the-art seismic hazard maps that include the effects of local geology have 

been produced for six 1;24,000 quadrangles in the Memphis area. The hazard maps are 

based on the national seismic hazard model and methodology, a three-dimensional 

lithology model derived from hundreds of well logs, geotechnical borings, and surface 

geophysical measurements, and empirical correlations between lithology and shear-wave 

velocity, Vs. Site amplification distributions, in the form of medians and natural 

logarithmic 16th and 84th percentile estimates (68 percent confidence limits), were 

derived from the lithology model and its correlation with Vs at each point of a 1-km grid. 

The site-amplification distributions were used to modify CEUS hard-rock ground-motion 

attenuation relations to obtain site-specific relations prior to calculating the hazard at each 

grid point. 

Our products include probabilistic seismic hazard maps with the effects of local 

geology for 2%-, 5%-, and 10%-in-50-year probability of exceedance for peak ground 

acceleration (PGA) and 0.2 s and 1.0 s spectral acceleration (Sa). Compared with the 

national seismic hazard maps, which are calculated for a constant NEHRP B/C boundary 

soil conditions (760 m/s Vs30), the Memphis seismic hazard maps show similar levels of 

expected ground motion for PGA, up to 30 percent reductions in expected ground 

motions for 0.2 s Sa, and twice the level of expected ground motions for 1.0 s Sa. At 

short periods (PGA and 0.2 s Sa), the strong gradient in probabilistic ground motions of 

the national maps is flattened to nearly uniform ground motions across Memphis due to 

the effects of the local geology. 

We also provide two scenario maps with the effects of local geology for PGA, 0.2 

s Sa, and 1.0 s Sa. They present median expected ground motions across Memphis from 

a M7.7 earthquake on a fault coinciding with the southwestern line of seismicity in the 

New Madrid seismic zone and a M6.2 earthquake at the southern end this linear zone of 

seismicity, near Marked Tree, Arkansas. The M7.7 scenario indicates average expected 

ground motions in Memphis of 0.35, 0.5, and 0.4 g for PGA, 0.2 s Sa, and 1.0 s Sa, 

respectively. For the M6.2 scenario, these average values are 0.1, 0.2, and 0.1 g. Due to 

the nature of probabilistic and scenario hazard calculations, the M7.7 scenario maps are 

10
very similar to the 5%-in-50-year probability of exceedance hazard maps, which is what 

is expected from the 500-year mean recurrence interval of the 1811-1812 magnitude 

earthquakes on the New Madrid seismic zone. This suggests that 10%-in-50-year ground 

motions currently used for building design in Memphis may underestimate ground 

motions from a repeat of the 1811-1812 earthquakes. 

We have performed uncertainty analyses for the ground-motion maps and the siteamplification distributions. Without the inclusion of the effects of local geology, the 

probabilistic seismic hazard estimates have been shown to have an uncertainty of plus or 

minus 50 percent for Memphis due to knowledge uncertainty in rupture location, 

magnitude, recurrence interval, and ground-motion attenuation. The major sources of 

uncertainty in the site-amplification estimates arise from the uncertainties in input 

motions, soil profile, and dynamic soil properties, which provide an overall coefficient of 

variation (standard deviation divided by the mean) of 10 to 60 percent. Additionally, the 

choice of soil-response computer program used to calculate the site-amplification 

distributions leads to uncertainties in the range of plus or minus 50 percent. 

In light of the large uncertainties, which apply to both the probabilistic and 

scenario estimates, why should we have any confidence in the results of this or any other 

such study? It would be easy, but simplistic, to discount any and all results of such 

studies as this one. The power of a statistical approach comes to the fore in addressing 

this concern. Probabilistic approaches can incorporate knowledge variability and 

uncertainty into the results. Both in probabilistic and scenario estimates, the focus is on 

deriving a ‘best’ estimate of expected ground motion, which statistically corresponds to 

the expected (mean) value. Most importantly, use of the concept of expected value 

avoids extreme and worst-case estimates, which are very unlikely to occur. Thus, we do 

not have to fear uncertainty. With probabilistic estimates, an acceptable level of risk can 

be chosen both in economic and societal terms (Leyendecker and others, 2000). This 

choice of risk level, combined with a best estimate of the ground-motion hazard, provides 

a rational basis for setting public policies. 

The maps presented herein represent our best estimate of the groundmotion hazard for Memphis. (We leave the choice of risk level and policy setting to 

others.) The Memphis hazard maps incorporate state-of-the-art science, our current 

understanding, and our knowledge of both what we know and what we do not know. 

Future improvements in our knowledge and understanding certainly will improve our 

estimates and reduce the overall uncertainty. We conclude on a cautionary note, 

emphasizing that the Memphis maps are regional in nature and not site specific. They 

should not be directly used in a site-specific analysis and structural design, but rather 

only as guidance as to what generally can be expected. 

Acknowledgments 

We thank Ken Campbell and Steve Hartzell for their helpful comments and 

reviews, which helped us improve this manuscript. We also thank Alene Brogan and Bob 

Olmstead for their editing suggestions. 

11
References 

Atkinson , G.M., and Beresnev, I.A., 2002, Ground motions at Memphis and St. Louis 

from M 7.5-8.0 earthquakes in the New Madrid seismic zone, Bulletin Seismological 

Society of America, vol. 92, p. 1015-1024. 

Atkinson, G.M. and Boore, D.M., 1995, Ground motion relations for eastern North 

America, Bulletin Seismological Society of America, vol. 85, p. 17-30. 

Bakun, W.H., and Hopper, M.G, 2004, Magnitudes and locations of the 1811-1812 New 

Madrid, Missouri, and the 1886 Charleston, South Carolina, earthquakes, Bulletin 

Seismological Society of America, vol. 94, p. 64-75. 

Bodin, P., and Horton, S., 1999, Broadband microtremor observation of basin resonance 

in the Mississippi embayment, central US, Geophysical Research Letters, vol. 26, p. 903-

906. 

Broughton, J., and Van Arsdale, R., 2004, Geologic map of the Northwest Memphis 7.5-

minute quadrangle, USGS MF map, in preparation. 

Campbell, K.W., 2003, Prediction of strong ground motion using the hybrid empirical 

method and its use in the development of ground-motion (attenuation) relations in eastern 

North America, Bulletin Seismological Society of America, vol. 93, p. 1012-1033. 

Cox, R., 2004, Geologic map of the Ellendale 7.5-minute quadrangle, USGS MF map, in 

preparation. 

Cramer, C.H., 2001a, The New Madrid seismic zone: capturing variability in seismic 

hazard analyses, Seismological Research Letters, vol. 72, p. 664-672. 

Cramer, C.H., 2001b, A seismic hazard uncertainty analysis for the New Madrid seismic 

zone, Engineering Geology, vol. 62, p. 251-266. 

Cramer, C.H., 2003, Site-specific seismic hazard analysis that is completely probabilistic, 

Bulletin Seismological Society of America, vol. 93, p. 1841-1846. 

Cramer, C.H., Wheeler, R.L., and Mueller, C.S., 2002, Uncertainty analysis for seismic 

hazard in the southern Illinois basin, Seismological Research Letters, vol. 73, p. 792-805. 

EPRI, 1993, Guidelines for determining design basis ground motions, Earthquake 

Engineering Research Institute, TR-102293. 

Frankel, A., 2004, How can seismic hazard around the New Madrid seismic zone be 

similar to that in California?, Seismological Research Letters, vol. 75, in press. 

12
Frankel, A., Mueller, C., Barnhard, T., Perkins, D., Leyendecker, E.V., Dickman, N., 

Hanson, S., and Hopper, M., 1996, National Seismic-Hazard Maps: Documentation June 

1996, U.S. Geological Survey, Open-File Report 96-532. 

Frankel, A.D., Petersen, M.D., Mueller, C.S., Haller, K.M., Wheeler, R.L., Leyendecker, 

E.V., Wesson, R.L., Harmsen, S.C., Cramer, C.H., Perkins, D.M., and Rukstales, K.S., 

2002, Documentation for the 2002 update of the national seismic hazard maps, U.S. 

Geological Survey, Open-File Report 02-420. 

Gomberg, J., Waldron, B., Schweig, E., Hwang, H., Webbers, A., Van Arsdale, R., 

Tucker, K., Williams, R., Street, R., Mayne, P., Stephenson, W., Odum, J., Cramer, C., 

Updike, R., Hutson, S., and Bradley, M., 2003, Lithology and shear velocity in Memphis, 

Tennessee, Bulletin Seismological Society of America, vol. 93, p. 986-997. 

Hashash, Y.M.A, and Park, D., 2001, Non-linear one-dimensional seismic ground motion 

propagation in the Mississippi embayment, Engineering Geology, vol. 62, p. 185-206. 

Hashash, Y.M.A, and Park, D., 2002, Viscous damping formulation and high frequency 

motion propagation in non-linear site response analysis, Soil Dynamics and Earthquake 

Engineering, vol. 22, p. 611-624. 

Idriss, I.M., and Sun, J.I., 1992, User’s manual for SHAKE91, Center for Geotechnical 

Modeling, Department of Civil and Environmental Engineering, University of California, 

Davis, California. 

Joyner, W.B., and Boore, D.M., 2000, Recent developments in earthquake ground motion 

estimation, Proceedings of the Sixth International Conference on Seismic Zonation, 

November 12-15, 2000, Palm Springs, CA, Earthquake Engineering Research Institute, 

Oakland, CA, 7 pp. 

Kausel, E., and Assimaki, D., 2002, Seismic simulation of inelastic soils via frequencydependent moduli and damping, Journal of Engineering Mechanics, vol. 128, p. 34-47. 

Kramer, S.L., 1996, Geotechnical Earthquake Engineering, Prentice Hall, Upper Saddle 

River, New Jersey, 653 pp. 

Leyendecker, E.V., Hunt, R.J., Frankel, A.D., and Rukstales, K.S., 2000, Development of 

maximum considered earthquake ground motion maps, Earthquake Spectra, vol. 16, p. 21 

– 40.

McGuire, R.K., Silva, W.J., and Constantino, C., 2001, Technical basis for revision of 

regulatory guidance on design ground motions: hazard- and risk-consistent ground 

motion spectra guidelines, NUREG/CR-6728, prepared for the U.S. Nuclear Regulatory 

Commission, Office of Nuclear Regulatory Research, Division of Engineering 

Technology. 

13
Moore, D., and Diehl, S., 2004a, Geologic map of the Southeast Memphis 7.5-minute 

quadrangle, USGS MF map, in preparation. 

Moore, D., and Diehl, S., 2004b, Geologic map of the Southwest Memphis 7.5-minute 

quadrangle, USGS MF map, in preparation. 

Pujol, J., Pezeshk, S., Zhang, Y., and Zhao, C., 2002, Unexpected values of Qs in the 

unconsolidated sediments of the Mississippi embayment, Bulletin Seismological Society 

of America, vol. 92, p. 1117-1128. 

Somerville, P., Collins, N., Abrahamson, N., Graves, R., and Saikia, C., 2001, Ground 

motion attenuation relations for the central and eastern United States, Final Report to the 

USGS, June 30, 2001, URS Group, Inc., Pasadena, CA, 36 pp. 

Toro, G., Abrahamson, N., and Schneider, J., 1997, Model of strong ground motions 

from earthquakes in central and eastern North America: best estimates and uncertainties, 

Seismological Research Letters, vol. 68, p. 41-57. 

Toro, G.R., and Silva, W.J., 2001, Scenario earthquakes for Saint Louis, MO, and 

Memphis, TN, and seismic hazard maps for the central United States region including the 

effect of site conditions, Final technical report to the USGS, 10 January 2001, Rick 

Engineering, Inc., Boulder, Colorado. 

Van Arsdale, R.B., and TenBrink, R.K., 2000, Late Cretaceous and Cenozoic geology of 

the New Madrid seismic zone, Bulletin Seismological Society of America, vol. 90, p. 

345-356. 

Van Arsdale, R., 2004a, Geologic map of the Germantown 7.5-minute quadrangle, 

USGS MF map, in preparation. 

Van Arsdale, R., 2004b, Geologic map of the Northeast Memphis 7.5-minute quadrangle, 

USGS MF map, in preparation. 

Wang, Z., Woolery, E.W., Shi, B., and Kiefer, J., 2003, Communicating with uncertainty: 

a critical issue with probabilistic seismic hazard analysis, EOS, Transactions of the 

American Geophysical Union, vol. 84, p. 501, 506, and 508. 

Wessel, P., and Smith, W.H.F. , 1991, Fee software helps map and display data, EOS, 

Transactions of the American Geophysical Union, vol. 72, p. 445-446. 

Wyllie, L.A., and Filson, J.R., 1989, Armenia Earthquake Reconnaissance Report, 

Earthquake Spectra, Special Issue, 175 pp. 

14
Table 1: Soil Properties used in Analysis 

Formation S-Velocity Density Qs

 (m/s) (g/cc) 

Alluvium 169+/- 24 0.20 10 

Loess 191+/-35 0.20 10 

Lafayette (sand, gravel) 268+/-72 0.20 25 

Upper Clairborne (clay) 360+/-50 0.20 25 

Memphis Sand 550+/-200 0.20 25 

Flour Island (clay) 675+/-100 0.20 25 

Fort Pillow Sand 775+/-50 0.20 50 

Old Breastworks (clay) 850+/-50 0.20 50 

Cretaceous (clay) 1175+/-125 0.25 50 

Paleozoic Limestone 3400+/-150 0.28 500 

Table 2: M~7 Strong-Motion Time Series on Rock used in Analysis 

Earthquake Station Components 

1989 M6.9 Loma Prieta, CA G01 E, N 

1992 M7.1 Cape Mendocino, CA CPM E, N 

1992 M7.3 Landers, CA JOS E, N 

1995 M6.9 Kobe, Japan KJM E, N 

1999 M7.4 Kocaeli, Turkey GBZ W 

IZT S 

1999 M7.6 Chi Chi, Taiwan TCU046 N, W 

1999 M7.1 Duzce, Turkey 1060 E, N 

Atkinson and Beresnev, 2002 M7.5 & M8.0 at Memphis, TN 

Table 3: Average Ground-Motion Values with Range (not standard deviation). PGA – 

peak ground acceleration; Sa – spectral acceleration. 

Probability\Motion PGA (g) 0.2 sec Sa (g) 1.0 sec Sa (g) 

2% in 50 years 0.58 + 0.09 0.71 + 0.15 0.71 + 0.23 

5% in 50 years 0.38 + 0.07 0.48 + 0.10 0.36 + 0.12 

10% in 50 years 0.24 + 0.04 0.33 + 0.07 0.18 + 0.05 

Table 4: Scenario Average Ground-motion Values with Range (not standard deviation). 

PGA – peak ground acceleration; Sa – spectral acceleration. 

Scenario\Motion PGA (g) 0.2 sec Sa (g) 1.0 sec Sa (g) 

M7.7 earthquake 0.36 + 0.07 0.48 + 0.10 0.39 + 0.18 

M6.2 earthquake 0.13 + 0.07 0.20 + 0.04 0.08 + 0.05 

15
Table 5: Site-amplification Sensitivity (multiplicative/divisor factors for 84th and 16th 

percentile). PGA – peak ground acceleration; Sa – spectral acceleration. 

Type\Sensitivity PGA 

Overall 1.2-1.7 

0.2 sec Sa 

1.1-1.4 

1.0 sec Sa 

1.1-1.4 

Input Time Series 1.2-1.4 

Soil Profile 1.07-1.2 

1.08-1.4 

1.1-1.2 

1.09-1.4 

1.1-1.2 

Dynamic Properties 1.03-1.4 

Top Layer Lithology 1.003-1.018 

1.03-1.2 

1.007-1.08 

1.03-1.3 

1.004-1.03 

16
Figure Captions 

Figure 1: Map showing the location of the six 7.5-minute quadrangle Memphis, 

Tennessee, study area (box). Also shown is the outline of the Mississippi embayment 

(heavier lines), and the location of the MLGW water well (circle) and Wilson 2 

exploration well (triangle). 

Figure 2: Map of the distribution of alluvium (blue) and loess (white) in the six 7.5-

minute quadrangles (outlined by the blue square) of the current mapping effort. The 

distribution in the Collierville quadrangle east of these is shown as it will be used when 

the hazard map area is expanded to include Collierville (an area of rapid development in 

Shelby County). More complete geologic maps (ref) are available that show the 

distribution of all sedimentary units. 

Figure 3: (a) Surface elevation data from the water wells used to define a well-top 

elevation map for extrapolating geology model data to a uniform grid. (b) Subsurface 

elevations of tops of lithologic units as interpreted from water wells. In both (a) and (b) 

the elevation and boundary surfaces have been contoured in GMT (Wessel and Smith, 

1991). The black dots indicate the locations of the wells. 

Figure 4: Estimated depths to the top of the Paleozoic limestones (top figures) and 

Cretaceous sediments (bottom figures). Black dots indicate locations where well log 

observations (from Van Arsdale and TenBrink, 2000) constrain these boundaries. 

Surfaces on the left are contoured in GMT (Wessel and Smith, 1991) and those on the 

right are estimated using the approach in Gomberg et al. (2003); the latter are used in the 

site-amplification calculations. 

Figure 5: P-wave (red) and shear wave (blue) logs for the Memphis Light, Gas, and 

Water (MLGW) well (circle in fig. 1). Black horizontal lines indicate lithologic 

boundaries (units labeled) from a gamma-ray log for the hole. 

Figure 6: P-velocity (Vp) suspension log for the Wilson 2 exploration well (triangle in 

fig. 1). Black horizontal lines indicate lithologic boundaries from a gamma-ray log for 

the hole. The high velocity excursion in the second layer is due to the steel casing 

installed in that shallow portion of the well. 

Figure 7: Example of median site-amplification estimates (solid curves) and 16th and 84th 

percentile uncertainties (dotted curves) for a site in Memphis, assuming hard-rock 

beneath the sediments. Circles represent NEHRP site factors for soil class D 

amplification over soil class A ground motions (see text for details). 

Figure 8: Response spectra comparisons for 0.1 g input (top) and 0.5 g input (bottom) at 

the MLGW well site (circle in fig. 1). The black spectrum is the surface response 

spectrum of the input ground motion. The colored spectra are surface soil-response 

spectra for various soil response programs and constraints: SHAKE91 unconstrained 

(red), DEEPSOIL (magenta), TREMORKA (green), SHAKE91 linear below 300 m 

17
(blue), SHAKE91 linear below 400 m (light blue), and SHAKE91 linear below 80 m 

(yellow). 

Figure 9: Eastern North America ground-motion attenuation relations (for uniform 

NEHRP B/C boundary soil conditions) used in the USGS national and Memphis seismic 

hazard maps. PGA (top) and 1.0 s Sa (bottom) median attenuation curves for M5.0 

(dashed), M6.0 (dotted), and M7.0 (solid) earthquakes predicted by the relations of 

Frankel et al. (1996) in red, Atkinson and Boore (1995) in blue, Toro et al. (1997) in 

green, Somerville et al. (2001) in light blue, and Campbell (2003) in magenta. Distance 

is epicentral distance and has been calculated using the assumption of a vertical strikeslip fault with a hypocentral depth of 10 km. 

Figure 10: Comparison of hard-rock PGA (squares) and soil PGA (diamonds) probability 

of exceedance (hazard) curves for a specific magnitude (M) and distance (R). This 

illustrates what happens to a hazard curve when it is transformed from a hard rock curve 

to a site-specific curve (from Cramer, 2003). This example is for a median ground 

motion of 0.85 g with a natural logarithmic standard deviation of 0.75. 

Figure 11: Probabilistic seismic hazard maps showing ground motions with a 2%-in-50-

year probability of exceedance. Smaller maps (inset squares) for Memphis, Shelby 

County that include the effects of site geology (site amplification) are superimposed on 

the 2002 national seismic hazard maps, which are for a constant soil condition (NEHRP 

B/C boundary or 760 m/s Vs30). As labeled, the maps are for 0.2 s Sa, 1.0 s Sa, and 

PGA. 

Figure 12: Probabilistic seismic hazard maps showing ground motions with a 5%-in-50-

year probability of exceedance. Presentation is the same as in figure 11. 

Figure 13: Probabilistic seismic hazard maps showing ground motions with a 10%-in-50-

year probability of exceedance. Presentation is the same as in figure 11. 

Figure 14: Scenario maps for a M 7.7 earthquake on a fault coincident with the southwest 

trending line of seismicity in the New Madrid seismic zone. The presentation is similar 

to that in figure 11. 

Figure 15: Scenario maps for a M6.2 earthquake at the southern end of the southwest 

trending line of seismicity in the New Madrid seismic zone. The presentation is the same 

as in figure 14. 

Figure 16: Overall uncertainty and major sensitivities for the MLGW well site (circle in 

fig. 1) for PGA, 0.2 s Sa, and 1.0 s Sa. Median amplification curves (solid lines) are 

shown with their corresponding 16th and 84th percentile uncertainties (dotted lines). 

Uncertainties are derived by allowing all parameters to vary (red), only the input time 

series (blue), only the soil profile (light blue), only the dynamic soil properties (green), 

and only the top-layer geology (alluvium versus loess) (magenta). 

18
Figure 17: Site amplification variations due to the choice of input time series presented in 

a manner similar to figure 16. Each curve is the site-amplification response for the 

indicated earthquake record as input (lower legend applies to all three panels) for a 

common soil profile and dynamic soil properties. These variations in site amplification 

lead to the input time series sensitivity shown in figure 16. 

Figure 18: Individual-layer Vs sensitivity for the MLGW-well soil profile for PGA, 0.2 s 

Sa, and 1.0 s Sa. For each period the layer sensitivities are split between two plots (1-5 

on left and 6-10 on right; center legend applies to all three panels). Layers 1 and 2 are for 

alternative surface geology (alluvium and loess, respectively). The presentation is similar 

to that in figure 16. 

Figure 19: Individual-layer depth-to-top sensitivity for the MLGW-well soil profile 

presented in a manner similar to figure 18. Soil geology is not distinguished for the top 

layer in this figure and the layer numbers correspond to the actual layers in the MLGW 

soil model ending with bedrock as layer 9. 

Figure 20: Seismograms at soft-soil sites demonstrating nonlinear soil responses that are 

enriched (top) and depleted (bottom) in high-frequencies. The former is of the Nisqually, 

WA earthquake recorded at SNS (north component) and the latter is of the Loma Prieta, 

CA earthquake recorded at TRI (north component). 

19
92 ̊W 90 ̊W 88 ̊W

34 ̊N 

36 ̊N 

38 ̊N 

92 ̊W 90 ̊W 88 ̊W

34 ̊N

36 ̊N

38 ̊N

Mississippi 

Tennessee 

Arkansas 

Missouri 

Kentucky 

Illinois 

MEMPHIS 

Figure 1. 
Mississippi 

River 

35 00'N 

35 12'N 

AR TN 

MEMPHIS 

COLLIERVILLE 

90 12'W 90 00'W 89 48'W 89 36'W

Figure 2
( )

35 ̊ 12'N 

35 ̊ 00'N 

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

Figure 3(a) 

0 

Mississippi 

River 

20 

40 

60 

80 

100 

120 

Surface Elevations meters 

MEMPHIS 

AR TN 

a
90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

Lafayette

0

20

40

60

80

100

120

meters

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

Upper Clairborne

0

20

40

60

80

100

120

meters

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

Memphis Sand

35 ̊ 00'N

35 ̊ 12'N -20

0

20

40

60

80

100

meters

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

Flour Island

-500

-450

-400

-350

-300

-250

-200

-150

-100

meters

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

35 ̊ 12'N

Fort Pillow

-500

-450

-400

-350

-300

-250

-200

-150

-100

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

Old Breastworks

35 ̊ 12'N -500

-450

-400

-350

-300

-250

-200

-150

-100

meters meters

35 ̊ 00'N

35 ̊ 12'N

35 ̊ 00'N

35 ̊ 12'N

35 ̊ 00'N

35 ̊ 12'N

Figure 3(b)

(b)
90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

35 ̊ 12'N

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

35 ̊ 12'N -1000

-950

-900

-850

W 90 ̊W 88 ̊W

92 ̊ 90 ̊W 88 ̊W

-1000

-800

-600

-400

-200

0

Figure 4

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

35 ̊ 12'N

Cretaceous

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W

35 ̊ 00'N

35 ̊ 12'N -700

-650

-600

-550

-500

-450

-400

meters

92 ̊W 90 ̊W 88 ̊W92 ̊W 90 ̊W 88 ̊W

-1000

-800

-600

-400

-200

0

200

meters

Memphis, Shelby Co. Map Area

Memphis, Shelby Co. Map Area
-50 

-100 

-150 

Depth, (meters) ) 

MLGW Well 236 Velocity Profiles 

0 

/

-300 

-250 

-200 

Alluvium Lafayette 

Upper Clairborne 

Flour Island 

Memphis Sand 

Memphis Sand 

Clay 

Old Breastworks 

Fort Pillow 

-350 

-400 

-450 

-500 

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 

Velocity, (meters/second) 

Figure 5 
Wilson-2 Well Vp Profile 

0 

-100 

-200 

-300 

-400 

-500 

-600 

-700 

-800 

-900 

-1000 

1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 

( ) Depth, meters

Clay 

Sand 

Flour Island 

Memphis Sand 

Old Breastworks 

Fort Pillow 

Cretaceous Sediments 

Paleozoic Limestones 

Velocity, (meters/second) 

Figure 6 
( ) 

PGA 

Amplification 

Site Amplifications Soil over Hard Rock

PGA (g) 

0.2 s Sa 

Amplification

0.2 s Sa (g) 

(g) 

1.0 s Sa 

1.0 s Sa 

Amplification 

Figure 7
Sa (g) Sa (g) 

Response Spectra: 0.1 g Input 

input 

period (seconds) 

( ) 

Response Spectra: 0.5 g Input 

period seconds

input 

Figure 8
M7.0

M6.0

M5.0

Distance (kilometers)

PGA (g)

Attenuation Relations

Figure 9

1.0 s Sa (g)

Distance (kilometers)

M7.0

M6.0

M5.0
As 

A

r

Probability of Exceedance 

Acceleration (g) 

Figure 10
Mississippi 

River 

0 

g 

35 ̊00'N 

35 ̊12'N 

TN 0.2 s Sa AR 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.8 

1.0 

1.2 

1.6 

2.0 

2.4 

2.8 

Ground Motions with 2%-in-50-Year Exceedance Probability 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

N 

Mississippi 

River 

0 

g 1.0 s Sa 

35 ̊00'N 

35 ̊12'

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

3

Mississippi 

River 

0 

g

PGA 

5 ̊00'N 

35 ̊12'N 

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

Figure 11 
Ground Motions with 5%-in-50-Year Exceedance Probability

Mississippi 

River 

0 

g 

35 ̊00'N 

35 12'N 

TN 0.2 s Sa AR 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.8 

1.0 

1.2 

1.6 

2.0 

2.4 

2.8 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

Mississippi 

River 

0 

g 1.0 s Sa 

35 ̊00'N 

35 ̊12'N 

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

3

Mississippi 

River 

0 

g

PGA 

5 ̊00'N 

35 ̊12'N 

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

Figure 12 
Ground Motions with 10%-in-50-Year Exceedance Probability

Mississippi 

River 

0 

g 

35 ̊00'N 

35 ̊12'N 

TN 0.2 s Sa AR 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.8 

1.0 

1.2 

1.6 

2.0 

2.4 

2.8 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

N 

Mississippi 

River 

0 

g

1.0 s Sa 

35 ̊00'

35 ̊12'N 

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

3

Mississippi 

River 

0 

g

PGA 

35 ̊00'N 

5 ̊12'N 

AR TN 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

90 ̊24'W 90 ̊12'W 90 ̊00'W 89 ̊48'W 89 ̊36'W 

Figure 13 
M7.7 Scenario Ground Motions

35 ̊ 12'N 

35 ̊ 00'N 

90 ̊ 24'W 

Mississippi 

River 

0.2 s Sa AR TN 2.8 

2.4 

2.0 

1.6 

1.2 

1.0 

0.8 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

g 

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

0 

Mississippi 

River 

g 

35 ̊ 00'N 

35 ̊ 12'N 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

1.0 s Sa AR TN 

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

3

3

0 

Mississippi 

River 

g 

5 ̊ 00'N 

5 ̊ 12'N 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 PGA AR TN 

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

Figure 14 
M6.2 Scenario Ground Motions

35 ̊ 12'N 

35 ̊ 00'N 

Mississippi 

River 

0.2 s Sa AR TN 

g 

2.8 

2.4 

2.0 

1.6 

1.2 

1.0 

0.8 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

35 ̊ 12'N 

35 ̊ 00'N 

90 ̊ 24'W 

Mississippi 

River 

1.0 s Sa AR TN 

g 

1.3 

1.2 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

Mississippi 

River 

PGA AR TN 

g 1.3 

1.2 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

35 ̊ 12'N 

35 ̊ 00'N 

90 ̊ 24'W 90 ̊ 12'W 90 ̊ 00'W 89 ̊ 48'W 89 ̊ 36'W 

Figure 15 
PGA

1.0 s Sa

0.2 s Sa

Hard Rock PGA (g)

0.2 s Sa (g)

1.0 s Sa (g)

Amplification Amplification Amplification

Figure 16

Site-Amplification Sensitivities
red solid - Cape Mendocino

green solid - Kobe

blue solid - Landers

light blue solid - ChiChi

orange solid - Duzce

red dashed - Kocaeli GBZ

green dashed - Kocaeli IZT

blue dashed - Loma Prieta

light blue dashed - M7.5 synthetic

orange dashed - M8.0 synthetic

Hard Rock 1.0 s Sa (g)

PGA

1.0 s Sa

0.2 s Sa

Hard Rock 0.2 s Sa (g)

Amplification Amplification Amplification

Figure 17

Site-Amplification Sensitivities

Hard Rock PGA (g)
Layer - Color

 1 - red 

 2 - green

 3 - blue

 4 - light blue

 5 - orange

Layer - Color

 6 - red 

 7 - green

 8 - blue

 9 - light blue

 10 - magenta

Hard Rock 1.0 s Sa (g)

Hard Rock 0.2 s Sa (g)

Amplification Amplification Amplification

Figure 18

Hard Rock PGA (g)

PGA

1.0 s Sa

0.2 s Sa

Site-Amplification Sensitivities

Hard Rock PGA (g)

Hard Rock 0.2 s Sa (g)

Hard Rock 1.0 s Sa (g)
Layer - Color

 1 - red 

 2 - green

 3 - blue

 4 - light blue

 5 - orange

Layer - Color

 6 - red 

 7 - green

 8 - blue

 9 - light blue

 

Hard Rock 1.0 s Sa (g)

Hard Rock 0.2 s Sa (g)

Amplification Amplification Amplification

Figure 19

Hard Rock PGA (g)

PGA

1.0 s Sa

0.2 s Sa

Site-Amplification Sensitivities

Hard Rock PGA (g)

Hard Rock 0.2 s Sa (g)

Hard Rock 1.0 s Sa (g)
(g) Acceleration 

Time (seconds) 

Figure 20