# Earthquake Hazards 101 - the Basics

## Science Center Objects

What is earthquake hazard?

Earthquake ground shaking varies from place to place and the hazard mapping in this project will show this variability. The mapped hazard refers to an estimate of the probability of exceeding a certain amount of ground shaking, or ground motion, in 50 years. The hazard depends on the magnitudes and locations of likely earthquakes, how often they occur, and the properties of the rocks and sediments that earthquake waves travel through.

### What are hazard maps?

The National Hazard Maps show the distribution of earthquake shaking levels that have a certain probability of occurring in the United States. These maps were created to provide the most accurate and detailed information possible to assist engineers in designing buildings, bridges, highways, and utilities that will withstand shaking from earthquakes in the United States. These maps are used to create and update the building codes that are now used by more than 20,000 cities, counties, and local governments to help establish construction requirements necessary to preserve public safety.

### Applications of the Hazard Maps:

1. Building Codes (NEHRP, IBC, ASCE 7) About building codes? (FEMA)
2. Highway bridge design nationwide (AASHTO)
3. Insurance rates
5. Estimations of stability and landslide potentials of hillsides
6. Construction standards for waste-disposal facilities (EPA)
7. Retrofit priorities
8. Allocation planning of assistance funds for education and preparedness (FEMA)
9. Concerned general public

### How to read a hazard map

Example hazard map for Nowhere City. (Public domain.)

Suppose the map on the right is the map given:

1. A 50-year time interval
2. A 5% chance of exceedence
3. A PGA map

We would read the shaking hazards for Nowhere City as:
The earthquake peak ground acceleration (PGA) that has a 5% chance of being exceeded in 50 years has a value between 4 and 8% g.

### What is probabilistic ground motion, and why use it for hazard determination?

Probabilistic ground motion maps depict earthquake hazard by showing, by contour values, the earthquake ground motions (of a particular frequency) that have a common given probability of being exceeded in 50 years (and other time periods).The ground motions being considered at a given location are those from all future possible earthquake magnitudes at all possible distances from that location. The ground motion coming from a particular magnitude and distance is assigned an annual probability equal to the annual probability of occurrence of the causative magnitude and distance.

So the goal of a hazard map is to depict the potential shaking hazard from future earthquakes. The following sequence explains why probabilistic ground motion is the best way to accomplish this goal:

Sequence showing why probablilistic ground motion is used for hazard determination. The sequence depics steps 1-4, respectively. (Public domain.)

Step 1

We can use a map showing the location and date of significant damaging earthquakes in the United States, but a map like that would not generalize from seismic history to indicate where other damaging earthquakes might be expected to occur in the future. To add this missing information…

Step 2

We can add to the map all the smaller earthquakes that have occurred in the past, and then we can use that seismic history information to assume that damaging earthquakes can also occur in the future in the same locations as the smaller earthquakes, but we can’t tell what the size of the expected ground motion hazard is. To add this missing information…

Step 3

We can make a map of the historical maximum seismic intensities (amount of shaking) to estimate the size of the hazard, but we are ignoring the fact that earthquakes occur at a much lower rate in some parts of the U.S. than in others. To add this missing information…

Step 4

We can incorporate seismicity rates in different parts of the country into the map using the methods of probabilistic ground motion hazard, but now the historical seismicity information is overemphasized compared to the evidence of seismic potential determined from geologic data. To add this missing information…

Example model of future seismicity in the U.S. (Public domain.)

Step 5
Finally, we add a model of future seismicity based on the prehistoric geologic information. In this way we arrive at the final hazard map.

The method assumes a reasonable future catalog of earthquakes, based upon historical earthquake locations and geological information on the recurrence rate of fault ruptures.When all the possible earthquakes and magnitudes have been considered, one can find a ground motion value such that the annual rate of its being exceeded has a certain value. Hence, on a given map, for a given probability of exceedance, PE, locations shaken more frequently, will have larger ground motions.

For a LARGE exceedance probability, the map will show the relatively likely ground motions, which are LOW ground motions, because small magnitude earthquakes are much more likely to occur than are large magnitude earthquakes.

For a SMALL exceedance probability, the map will emphasize the effect of less likely events: larger-magnitude and/or closer-distance events, producing overall LARGE ground motions on the map.The maps have this format, because they are designed to be useful in building codes, in which we assume that, for the most part, all buildings would be built to the same level of safety. For other applications, maps of another format might be more useful.For instance, many buildings across the US are built more or less the same, regardless of earthquake hazard. If we knew that a particular type of building was likely to fail at a particular ground motion level, we could make a map showing contours of the likelihood of that ground motion value being exceeded, due to earthquakes.

### Why are there different probability maps, and which one do I use?

The different probabilities are selected to provide an idea of the relative range of hazard across the US. The larger probabilities indicate the level of ground motion likely to cause problems in the western US. The smaller probabilities show how unlikely damaging ground motions are in many places of the eastern US. However, basically the values chosen reflect the more recent history in earthquake engineering.

Probability from the engineering point of view

Rather than start with the idea of probability, consider approaching the issue from this direction: A structure is designed to resist earthquake ground motion having a particular value. Given this design resistance, one might ask several questions:

• Under what ground motion will the building sway so much that it is uncomfortable to the persons working inside, and disrupts their work for the day? (This could occur with winds as well as with earthquakes.)
• Under what ground motion will the building bend so much that interior partitions crack and wall or ceiling fixtures drop?
• Under what ground motion will the building become permanently deformed and require expensive rehabilitation or abandonment. Under what ground motion will the building collapse during the shaking?

Using a hazard curve, one could determine the annual probability of occurrence of each of these ground motions. Then one could decide whether that corresponding probability is acceptable. If one of the probabilities is unacceptably high, the design would have to be revised.

The three different probability values reflect probabilities sometimes considered for design. The value 10 percent in 50 years seemed to provide values similar to those already used in design in the 1970s in California. On the other hand, this level of probability in the eastern US produced values too low for the seismic design then under consideration to provide residual toughness in the event of possible earthquakes (unlikely in any one location, but likely in some location). The probabilities more likely to produce useful design ground motions would be near 5 percent in 50 years.

The ground motions given by three probabilistic maps span a range of probabilities considered interesting to earthquake engineers and a range of ground motions which have some intuitive understanding for the consequences. There have been requests for maps of larger probabilities for purposes having to do with investment, insurance and banking. Eventually the web site will provide hazard curves and a means for obtaining either probabilities or ground motions from the hazard curves.

How do I know what map to choose then?

How does an individual person select a map? Technical users probably have to follow predefined rules. A non-technical person may be interested in avoiding living in a location where significant shaking will cause worry, deciding on whether to carry earthquake insurance, or deciding whether to do some rehabilitation for an existing dwelling. The probability level chosen should reflect how anxious one is to avoid earthquake shaking.

Here is some perspective on the 10 percent in 50 year map:
If one lives in a 100-year floodplain, there is about 1 chance in 100 of experiencing the flood in any given year. In 50 years one would expect 0.5 floods, and there is a 1 - exp(-0.5) = 39 percent chance of experiencing such a flood in 50 years. This is a higher likelihood than that of experiencing a damaging ground motion in an area where that ground motion has only a 10 percent chance of being exceeded in 50 years. In a 200-year floodplain the chance would be 22 percent, still larger than the chance for the damaging ground motion. People who are not comfortable with probabilities as large as 10 percent in 50 years for damaging earthquake ground motion should use maps with smaller probabilities. But they should also be aware that many other hazards are higher than earthquake hazards, even in California.

### How is a hazard map made? What is a hazard curve and how is it made?

How probabilistic ground motion is calculated:

Calculating the probability of a ground motion being exceeded

We demonstrate how to get the probability that a ground motion is exceeded for an individual earthquake - the “probability of exceedance”.

1. Show a curve of ground motion vs distance for a given magnitude, given a particular attenuation relation.
2. At a given distance show distribution of ground motion.
3. Intercept the distribution with a horizontal line at a given ground motion.
4. The area of the distribution above the horizontal line is divided by the total area of the distribution. The result is “Probability of Exceedance” of the given ground motion given that earthquake having that magnitude experienced at that distance, given that particular attenuation relation.

Annual rate of exceedance

How to get the expected number of exceedances in 1 year owing to that earthquake.

1. Multiply the annual occurrence rate of the earthquake times the probability of exceedance of the ground motion, given that earthquake.
2. Expected number of exceedances in 1 year = Annual rate of exceedance

Annual rate of exceedance, given several earthquakes

Expected number of exceedances for several earthquakes. “Adding exceedances”

1. The expected number of exceedances for several earthquakes is calculated by merely adding the annual rate of exceedance owing to each earthquake.

Calculating a hazard curve.

A hazard curve is calculated by plotting annual rate of exceedance vs ground motion

1. Perform the above calculation for 18 other ground motion levels.
2. Plot the results.
3. Make a smooth curve.

Now, for any ground motion we can find the annual rate of exceedance. Likewise, for any annual rate of exceedance we can find the corresponding ground motion.

Exceedance probability in Y years.

(This part is mathematical)

The expected number, n of exceedances in Y years is n = Y times r, the annual rate of exceedance. Assumption: The rate of earthquake occurrence in time is governed by the Poisson Law. Application: Under the Poisson Law, if you expect over some period of time n occurrences of “something”, the probability of 0 occurrences is e–n. If the “something” is exceedance of some ground motion, the probability of getting an exceedance is 1 – P(0). So, one can work backwards to find the annual rate of exceedance corresponding to “the probability of exceedance is 5% in 50 years.”

$1- P(0) = \frac{5}{100}$  (5%)
$P(0) = 1 -0.05 = 0.95 = e^{-n}$

Take the log to the base e of both sides of the last equality.

$n = - ln(0.95) = 0.05129 = Yr = 50 r$
$r=\frac{0.05129}{50}=0.0010258=\frac{1}{974.8}$

The last result tells us that at low exceedance probabilities (less than 10%) r is approximately PE / (100 Y). Now one can use the hazard curve to find the corresponding ground motion. The hazard maps are just the contoured version of the corresponding ground motion plotted on a geographic grid.

Hazard map showing chance of exceedence in a 50-year time interval for Nowhere City. (Public domain.)

There are 3 types of maps:

• Peak Ground Acceleration (PGA)
• 0.2 second Spectral Acceleration (SA)
• 1.0 second Spectral Acceleration (SA)

Units for all 3 maps are %g (percent of gravity). This can also be expressed in decimal form, example 10%g = 0.1g. The ground motion values apply to ground motion expected for future individual earthquakes. The probabilistic ground motion calculation takes into account all possible future ground motions from all modeled earthquake magnitudes at all possible distances from the map site. The spatial distribution of probabilistic ground motion values is shown with contours on the map, like a topo map shows different elevations, with each color representing a different range of levels of shaking.

TIME INTERVAL (X). A time interval during which all possible earthquakes may occur is set in order to determine the shaking hazard. The time interval is typically set to 50 years. The 50-year period can be ANY 50 years, not just the NEXT 50 years; the red bar above can span any 50-year period. (Public domain.)

% CHANCE of EXCEEDENCE (Y) The percent (%) chance that a certain amount of mapped shaking distribution will occur over the time period being considered. Typically the values of 2%, 5% and 10% are used. Keep in mind that a 5% chance of exceedence means there is a 95% chance that the shaking will NOT exceed the value. (Public domain.)

### What data are used to make hazard maps?

Three basic pieces of information are needed to produce probabilistic ground motion maps:

1. Model of Future Earthquakes

Using information about past historical earthquakes, Quaternary faults (prehistoric earthquakes), and present crustal deformation (geodetic data), USGS analysts make a model of the potential for future earthquakes. This model includes areal sources and fault sources. For each source the relative rate for earthquakes  of different magnitudes is given, and the absolute rate for magnitudes larger than some minimum magnitude.

2. Attenuation Relations

An attenuation relation is an equation or a table that describes how earthquake ground motion decreases as the distance to the earthquake increases. Because earthquake ground motion increases with magnitude, the attenuation relation also depends on magnitude. Strong motion data (recordings close to the earthquake) and geophysical attenuation models are used to establish the attenuation relations.

3. Geologic Site Condition

Earthquake ground motion waves travel rapidly in the earth’s crust and mantle. That part of the earth’s solid crust closest to the surface is called bed rock. The size of the ground motion experienced at the earth’s surface is affected by the geology of the material between bed rock and the surface. Because the earthquake waves move more slowly in this material than in rock, the size of the ground motion increases.

This material, often called alluvium or “the soil column,” increases the ground motion in such a way that “softer” soils, soils with less density, have lower seismic velocity, and hence experience larger increases in ground motion. It is necessary to know the geologic site condition in order to estimate the surface ground motion.

Maps are usually made for a common widespread site condition, and then rules are given for the user to adjust to other site conditions.

### Who uses hazard maps?

Hazard maps can be used by public and private groups for land-use planning, mitigation, and emergency response. The scale of the maps does not allow them to be used in a site-specific manner (such as a house-by-house assessment), but it does show a neighborhood overview to guide where more detailed studies are needed.

### Why do the hazard maps keep changing and getting updated?

The maps are updated as additional data becomes available from scientific analysis of earthquake-related data, such as:

1. new fault data
2. new attenuation relations
3. new geodetic data
4. more seismic data

### I just want to know what faults are near me; how will these maps help?

Knowing where the faults are is not the most relevant information when trying to learn what your risks are of being affected by an earthquake. Since a large earthquake can affect distant locations, you can be affected by a fault tens of miles away from where you are, because of the prolonged shaking that can occur.

Nearby faults can represent a hazard from ground rupture accompanying an earthquake. Faults, both near and far, provide a source for hazard from shaking. Furthermore, in the Eastern US there are earthquakes for which the actual location or extent of faulting is poorly known. In this case, historical seismicity is the source for understanding the shaking hazard.

These maps integrate all the faulting and seismicity information into an indication of shaking hazard. The actual values of the shaking hazards depend upon the ground motion parameter of interest and degree of safety which one wants. This is why the maps are different for different ground motions and different probabilities. The ground motion hazard values can be compared with the capacity of a structure to withstand shaking, and thus give an indication of safety.