The Memphis, Shelby County, Tennessee, Seismic Hazard Maps
|In Memphis, Shelby County, Tennessee damaging earthquakes are only moderately likely, but the consequences of earthquakes, from the New Madrid seismic zone, are likely to be very high.
This densely populated urban area is built on a 1-kilometer-thick (0.62 miles) sequence of soils, sands, clays and other sediments deposited in a trough known as the Mississippi embayment; geographically the embayment approximately underlies the Mississippi Valley. This thick pile of sediments significantly changes the way the ground shakes during earthquakes.
Cross-section of the sediments and rocks of the Mississippi embayment beneath Memphis. The shear wave velocity, Vs, is a property of these materials that greatly influences ground shaking. Diagram from P. Bodin.
Since 1998, the U.S. Geological Survey (USGS) and its partners have been working to produce earthquake (seismic) hazard maps that account for the effects of the sediments. These include maps of the expected ground shaking, the surficial geologic materials, and the susceptibility to the ground failure phenomena of liquefaction.
|Before describing the
main features of the Memphis seismic hazard maps, we explain how the
ground shaking is expressed on them. Because the
ground shaking level changes
with time as the waves pass, and only a single value can be shown on a
map, we choose three ways to capture and display this time varying
motion. These all use 'acceleration', which is a measure of how fast
something speeds up or slows down. Acceleration also is
proportional to the force applied to the ground or to an object
subjected to the accelerating ground (e.g. like a building!). One
measure used is the
maximum or peak acceleration (PGA), which depends most strongly on
wave motions that oscillate very rapidly, with periods of tenths of a
second (a period is the time required to for the ground to go through
one cycle of up and down motion). The other two measures are the
spectral acceleration (Sa) at 0.2 second and 1.0 second
periods. Spectral acceleration is meant to be a measure of
the motion that a building might experience at a specified single
period. The units of acceleration most often are 'g's, which is
the acceleration of a
falling object due to gravity.
The Memphis ground motion (shaking) hazard maps come in two types; one shows 'deterministic' ground motions and the other shows 'probabilistic' estimates of ground shaking. Deterministic maps show the ground shaking expected from a single, hypothetical earthquake (example below). These often are referred to as 'scenario' maps. Note that such maps only show our best esimtate of how the ground will shake for a particular earthquake, regardless of how likely or unlikely is the occurrence of such an earthquake. Therefore, they provide no information about the probability of experiencing the shaking shown on the map (e.g. some scenarios may be extremely improbable and others very probable).
Fault traces (northeast trending white lines) for the M7.7 (left) and M6.2 (right) scenario earthquake hazard maps (M7.7 hazard map shown above). Epicenters in the earthquake catalog since the mid-1970s are shown (black dots) and the darker orange area shows the region covered by Mississippi embayment sediments.
|Maps that also include information about the likelihood or probability of experiencing earthquake shaking of a particular severity are 'probabilistic' maps. We have also produced probabilistic maps of expected shaking for Memphis, using the same approach as used for the national seismic hazard maps. These maps include all the same information as the deterministic maps, but instead of just considering one earthquake, they consider all the plausible earthquakes that might affect the mapped area along with the likelihood of each occurring. Given the latter, what's shown on the maps is the shaking levels that we expect to be exceeded during some specified time period. Specifically, we show the shaking levels that have a specified chance of being exceeded. For example, a '2% probability of exceedance in 50 years' map shows the levels of ground shaking that have a 1-in-50 (i.e. a 2%) chance of being exceeded in a 50 year period. The choice of which map to use depends upon the needs of the user. Builders of a dam, for instance, might want to consider a lower likelihood that shaking will be exceeded (e.g. maybe 2% in 50 years) than a home builder (e.g. maybe 10% in 50 years). This is because damage to the dam would have a greater impact on society. The examples below compare maps for two different probabilities.|
Probabilistic seismic hazard maps showing ground motions with a 2% (left) and 10% (right) probability of being exceeded in 50 years. Motions are accelerations with oscillation periods of 1 second.
We illustrate the
effects of the sediments beneath Memphis on the hazard by comparing the
ground motions estimated with and without the sediments. The
latter is what is displayed in the USGS national seismic hazard maps,
which are calculated for what is called 'firm rock'. This has a
technical meaning for engineers, and corresponds to a specific soil
classification, the NEHRP classification, that distinguishes soils
partly based on their
average shear wave velocity for the top 30 meters. All of Memphis
within a NEHRP soil class 'D'. The figure below compares the
Memphis (with sediments) and
maps (without sediments).
Because the strongest ground motions are de-amplified by sediments for rapidly oscillating waves (shorter periods), the ground motions in the Memphis hazard maps are less than those in the national maps for PGA and 0.2 second period motions (above). The thicker sediments in the west result in greater de-amplification of ground motions westward. The ground motions estimated without the effects of the sediments (which can be thought of as the 'input' motions to the Memphis map calculations), shown in the national maps, also increase westward because the largest earthquake sources are northwest of Memphis. The net effect of the westward increasing de-amplification also increases westward resulting in ground motions that are more uniform in the Memphis maps than in the national maps.
The tremendous thickness of sediments beneath Memphis also causes amplification for slower oscillations (longer periods). The thicker sediments in the west tend to amplify the long period ground motions (as in the 1.0 second period above) more in the west so that relative to the national maps, the Memphis hazard maps retain a decreasing gradient of ground motion amplitudes to the southeast. This gradient in the national maps reflects the fact that the largest potential earthquake sources are to the northwest of Memphis.
Estimating ground shaking requires a wide variety of information, much of which is incomplete or inaccurate. In addition, there are multiple ideas about how to characterize the processes that control ground shaking and we know that nature is inherently complex and variable. To incorporate this range of ideas and variability, and to account for the inaccuracy in inputs, at each location many estimates of ground motion are calculated for different combinations of input parameters. The average of these estimates is found, with those estimates derived from more accurately known parameters given more weight in the averaging. This average ground motion estimate represents the 'best' estimate statistically and is what is plotted on the map. Importantly, the maps do NOT display the worst case ground motions. The same calculation strategy is used in both the deterministic and probabilistic maps, the only difference being that for the deterministic maps only a single set of parameters describing the earthquake source are used, corresponding to the chosen scenario (i.e. a specific magnitude, location, and frequency of occurrence).
|At each location on the map we perform a suite of calculations. In these calculations we include the effects of the sediments by using 'site amplification factors', which effectively multiply the ground motions expected without any sediments by an amount calculated for the particular sediment structure found at the site. The first step is to determine what is the range of reasonable site amplification factors. Examples of those derived for Memphis are shown below, followed by a summary of the steps followed to derive them.|
Site amplification ranges derived for a site in Memphis for ground motions with 0.2 second (left) and 1.0 second (right) periods. Solid and dotted red curves show mean values and the range encompassing 68% of all values, respectively. These show how motions with a given amplitude (measured in acceleration units, along the horizontal axis) may be amplified or de-amplified by the sediments at this site. For example, 1.0 second period motions between about 0.002 g and 0.1 g will be approximately 3 times larger than they would have been if there were no sediments. Note the logarithmic scales.
Map showing the locations where logs (circles) and shear wave velocity profiles (letter/number labels) were measured, and major waterways (blue lines) and interstate highways (thick black lines). Rectangles show the six 7.5' quadrangles for which we made hazard maps.
|While the observations are abundant for constraining the sedimentary structure in terms of the sediment types this description isn't exactly what's needed to calculate the expected amplification. Instead, one of the most important things we need to know is a material property called shear wave velocity. This is a measure of how fast certain kinds of seismic waves travel, and its variation mostly with depth determines how much waves will be amplified or de-amplified. Unfortunately such measurements are not simple to make and none existed prior to this project - thus, we measured many tens of new shear wave velocity profiles and have put them in an online database. Not surprisingly, there is a correlation between the sediment types and the shear wave velocities, which we quantify. This correlation allows us to use the 3-dimensional sedimentary structure model determined from the abundant log observations as a basis for interpolating between more sparse shear wave velocity measurements (see left). In this way we can estimate the range of reasonable shear wave velocities anywhere in the mapped region.|
|In addition to depending on certain material properties, the response of sediments to shaking depends on the shaking itself. If the waves that shake the ground oscillate rapidly up and down (i.e. have short periods) the energy may dissipate more quickly than for slower (longer period) wave motion, leading to greater de-amplification in the first case. The sediment response also depends on the strength of the shaking. If shaken sufficiently strongly, the sediments may begin to break apart so that waves can no longer efficiently be transmitted through them. This may have the beneficial effect of limiting the amplitude of the shaking, but eventually can lead to a catastrophic phenomenon called ground failure. This complex relationship between the input shaking and the sediment response is somewhat predictable and calculable, but still is a source of considerable uncertainty. To simulate the shaking input to the sediments we use real earthquake ground motions recorded at sites with no sediments at all. In this way we are guaranteed that all the various types of waves and complex processes that happen to generate and propagate seismic waves are included. For our input motions we sample from a suite of 16 recordings. Because the amplification factors are calculated for a specific period and amplitude of input ground motion, for each calculation we scale the recordings used so that they have the desired amplitude at the specified period.|