Earthquake Hazard Information ?Hazard, Risk, Magnitude, Intensity, Earthquake Statistics ?Part 1 (Information for interpreting the results of building contest and shake table testing; L. Braile, 03/12/03)
Earthquake ground shaking and damage are related to the size (magnitude) of the earthquake, the distance from the epicenter, the local geological conditions and the characteristics of buildings. Assessment of earthquake effects involves evaluating the hazard and the risk. Definitions of these two concepts (from the USGS, http://earthquake.usgs.gov/image_glossary/) are:

Earthquake
hazard Earthquake hazard is anything associated with an earthquake that may affect the normal activities of people. This includes surface faulting, ground shaking, landslides, liquefaction, tectonic deformation, tsunamis, and seiches. Earthquake
risk 
Earthquake Magnitude: Several magnitude scales have been developed for measuring the size of an earthquake. Magnitude is a measure of the energy released by the earthquake. The earliest magnitude scale was Richter magnitude and news reports still often refer to magnitudes as Richter magnitude. However, today, the most reliable magnitude scale is the moment magnitude, now referred to simply as M. For wellrecorded, shallow, moderate to large earthquakes, estimates of the earthquake size using the various magnitude scales usually results in approximately the same numerical result. Current earthquake information, including magnitude, can be found at: http://earthquake.usgs.gov/ and http://www.iris.edu/seismon/. A more complete description of earthquake magnitude is given below (from http://neic.usgs.gov/neis/general/handouts/measure.html):
Measuring the Size of an Earthquake
Earthquakes range broadly in size. A rockburst in an Idaho silver mine may involve the fracture of 1 meter of rock; the 1965 Rat Island earthquake in the Aleutian arc involved a 650 kilometer length of the Earth's crust. Earthquakes can be even smaller and even larger. If an earthquake is felt or causes perceptible surface damage, then its intensity of shaking can be subjectively estimated. But many large earthquakes occur in oceanic areas or at great focal depths and are either simply not felt or their felt pattern does not really indicate their true size.
Today, state of the art seismic systems transmit data from the seismograph via telephone line and satellite directly to a central digital computer. A preliminary location, depthoffocus, and magnitude can now be obtained within minutes of the onset of an earthquake. The only limiting factor is how long the seismic waves take to travel from the epicenter to the stations  usually less than 10 minutes.
Magnitude
Modern seismographic systems precisely amplify and record ground motion (typically at periods of between 0.1 and 100 seconds) as a function of time. This amplification and recording as a function of time is the source of instrumental amplitude and arrivaltime data on near and distant earthquakes. Although similar seismographs have existed since the 1890's, it was only in the 1930's that Charles F. Richter, a California seismologist, introduced the concept of earthquake magnitude. His original definition held only for California earthquakes occurring within 600 km of a particular type of seismograph (the WoodsAnderson torsion instrument). His basic idea was quite simple: by knowing the distance from a seismograph to an earthquake and observing the maximum signal amplitude recorded on the seismograph, an empirical quantitative ranking of the earthquake's inherent size or strength could be made. Most California earthquakes occur within the top 16 km of the crust; to a first approximation, corrections for variations in earthquake focal depth were, therefore, unnecessary.
Richter's original magnitude scale (M_{L}) was then extended to observations of earthquakes of any distance and of focal depths ranging between 0 and 700 km. Because earthquakes excite both body waves, which travel into and through the Earth, and surface waves, which are constrained to follow the natural wave guide of the Earth's uppermost layers, two magnitude scales evolved  the m_{b} and M_{S} scales.
The standard bodywave magnitude formula is
m_{b} = log_{10}(A/T) + Q(D,h) ,
where A is the amplitude of ground motion (in microns); T is the corresponding period (in seconds); and Q(D,h) is a correction factor that is a function of distance, D (degrees), between epicenter and station and focal depth, h (in kilometers), of the earthquake. The standard surfacewave formula is
M_{S} = log_{10} (A/T) + 1.66 log_{10} (D) + 3.30 .
There are many variations of these formulas that take into account effects of specific geographic regions, so that the final computed magnitude is reasonably consistent with Richter's original definition of M_{L}. Negative magnitude values are permissible.
A rough idea of frequency of occurrence of large earthquakes is given by the following table:
M_{S} Earthquakes
per year
 
8.5  8.9 0.3
8.0  8.4 1.1
7.5  7.9 3.1
7.0  7.4 15
6.5  6.9 56
6.0  6.4 210
This table is based on data for a recent 47 year period. Perhaps the rates of earthquake occurrence are highly variable and some other 47 year period could give quite different results.
The original m_{b} scale utilized compressional body Pwave amplitudes with periods of 45 s, but recent observations are generally of 1 speriod P waves. The M_{S} scale has consistently used Rayleigh surface waves in the period range from 18 to 22 s.
When initially developed, these magnitude scales were considered to be equivalent; in other words, earthquakes of all sizes were thought to radiate fixed proportions of energy at different periods. But it turns out that larger earthquakes, which have larger rupture surfaces, systematically radiate more longperiod energy. Thus, for very large earthquakes, bodywave magnitudes badly underestimate true earthquake size; the maximum bodywave magnitudes are about 6.5  6.8. In fact, the surfacewave magnitudes underestimate the size of very large earthquakes; the maximum observed values are about 8.3  8.7. Some investigators have suggested that the 100 s mantle Love waves (a type of surface wave) should be used to estimate magnitude of great earthquakes. However, even this approach ignores the fact that damage to structure is often caused by energy at shorter periods. Thus, modern seismologists are increasingly turning to two separate parameters to describe the physical effects of an earthquake: seismic moment and radiated energy.
Fault Geometry and Seismic Moment, M_{O}
The orientation of the fault, direction of fault movement, and size of an earthquake can be described by the fault geometry and seismic moment. These parameters are determined from waveform analysis of the seismograms produced by an earthquake. The differing shapes and directions of motion of the waveforms recorded at different distances and azimuths from the earthquake are used to determine the fault geometry, and the wave amplitudes are used to compute moment. The seismic moment is related to fundamental parameters of the faulting process.
M_{O} = µS‹d?,
where ?is the shear strength of the faulted rock, S is the area of the fault, and <d> is the average displacement on the fault. Because fault geometry and observer azimuth are a part of the computation, moment is a more consistent measure of earthquake size than is magnitude, and more importantly, moment does not have an intrinsic upper bound. These factors have led to the definition of a new magnitude scale M_{W}, based on seismic moment, where
M_{W} = 2/3 log_{10}(M_{O})  10.7 .
The two largest reported moments are 2.5 X 10^{30} dyn·cm (dyne·centimeters) for the 1960 Chile earthquake (M_{S} 8.5; M_{W} 9.6) and 7.5 X 10^{29} dyn·cm for the 1964 Alaska earthquake (M_{S} 8.3; M_{W} 9.2). M_{S} approaches it maximum value at a moment between 10^{28} and 10^{29} dyn·cm.
Energy, E
The amount of energy radiated by an earthquake is a measure of the potential for damage to manmade structures. Theoretically, its computation requires summing the energy flux over a broad suite of frequencies generated by an earthquake as it ruptures a fault. Because of instrumental limitations, most estimates of energy have historically relied on the empirical relationship developed by Beno Gutenberg and Charles Richter:
log_{10}E = 11.8 + 1.5M_{S}
where energy, E, is expressed in ergs. The drawback of this method is that M_{S} is computed from an bandwidth between approximately 18 to 22 s. It is now known that the energy radiated by an earthquake is concentrated over a different bandwidth and at higher frequencies. With the worldwide deployment of modern digitally recording seismograph with broad bandwidth response, computerized methods are now able to make accurate and explicit estimates of energy on a routine basis for all major earthquakes. A magnitude based on energy radiated by an earthquake, M_{e}, can now be defined,
M_{e} = 2/3 log_{10}E  2.9.
For every increase in magnitude by 1 unit, the associated seismic energy increases by about 32 times.
Although M_{w} and M_{e} are both magnitudes, they describe different physical properites of the earthquake. M_{w}, computed from lowfrequency seismic data, is a measure of the area ruptured by an earthquake. M_{e}, computed from high frequency seismic data, is a measure of seismic potential for damage. Consequently, M_{w} and M_{e} often do not have the same numerical value.
Intensity
The increase in the degree of surface shaking (intensity) for each unit increase of magnitude of a shallow crustal earthquake is unknown. Intensity is based on an earthquake's local accelerations and how long these persist. Intensity and magnitude thus both depend on many variables that include exactly how rock breaks and how energy travels from an earthquake to a receiver. These factors make it difficult for engineers and others who use earthquake intensity and magnitude data to evaluate the error bounds that may exist for their particular applications.
An example of how local soil conditions can greatly influence local intensity is given by catastrophic damage in Mexico City from the 1985, M_{S} 8.1 Mexico earthquake centered some 300 km away. Resonances of the soilfilled basin under parts of Mexico City amplified ground motions for periods of 2 seconds by a factor of 75 times. This shaking led to selective damage to buildings 15  25 stories high (same resonant period), resulting in losses to buildings of about $4.0 billion and at least 8,000 fatalities.
The occurrence of an earthquake is a complex physical process. When an earthquake occurs, much of the available local stress is used to power the earthquake fracture growth to produce heat rather that to generate seismic waves. Of an earthquake system's total energy, perhaps 10 percent to less that 1 percent is ultimately radiated as seismic energy. So the degree to which an earthquake lowers the Earth's available potential energy is only fractionally observed as radiated seismic energy.
by William Spence, Stuart A.
Sipkin, and George L. Choy
Earthquakes and Volcanoes
Volume 21, Number 1, 1989
Earthquake intensity (usually described with the Modified Mercalli Intensity Scale) is a measure of earthquake effects and level of ground shaking at a particular location. A description of earthquake intensity is given below (from http://neic.usgs.gov/neis/general/handouts/mercalli.html):
The Modified Mercalli Intensity Scale
The effect of an earthquake on the Earth's surface is called the intensity. The intensity scale consists of a series of certain key responses such as people awakening, movement of furniture, damage to chimneys, and finally  total destruction. Although numerous intensity scales have been developed over the last several hundred years to evaluate the effects of earthquakes, the one currently used in the United States is the Modified Mercalli (MM) Intensity Scale. It was developed in 1931 by the American seismologists Harry Wood and Frank Neumann. This scale, composed of 12 increasing levels of intensity that range from imperceptible shaking to catastrophic destruction, is designated by Roman numerals. It does not have a mathematical basis; instead it is an arbitrary ranking based on observed effects.
The Modified Mercalli Intensity value assigned to a specific site after an earthquake has a more meaningful measure of severity to the nonscientist than the magnitude because intensity refers to the effects actually experienced at that place. After the occurrence of widelyfelt earthquakes, the Geological Survey mails questionnaires to postmasters in the disturbed area requesting the information so that intensity values can be assigned. The results of this postal canvass and information furnished by other sources are used to assign an intensity within the felt area. The maximum observed intensity generally occurs near the epicenter.
The lower numbers of the intensity scale generally deal with the manner in which the earthquake is felt by people. The higher numbers of the scale are based on observed structural damage. Structural engineers usually contribute information for assigning intensity values of VIII or above.
The following is an abbreviated description of the 12 levels of Modified Mercalli intensity.
I. Not felt except by a very few under especially favorable conditions.
II. Felt only by a few persons at rest, especially on upper floors of buildings.
III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck. Duration estimated.
IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably.
V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned. Pendulum clocks may stop.
VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight.
VII. Damage negligible in buildings of good design and construction; slight to moderate in wellbuilt ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys broken.
VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned.
IX. Damage considerable in specially designed structures; welldesigned frame structures thrown out of plumb. Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations.
X. Some wellbuilt wooden structures destroyed; most masonry and frame structures destroyed with foundations. Rails bent.
XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly.
XII. Damage total. Lines of sight and level are distorted. Objects thrown into the air.
Abridged from The Severity of an Earthquake, a U. S. Geological Survey General Interest Publication.
U.S. GOVERNMENT PRINTING OFFICE: 1989288913
This publication is one of a series of general interest publications prepared by the U.S. Geological Survey to provide information about the earth sciences, natural resources, and the environment. To obtain a catalog of additional titles in the series "General Interest Publications of the U.S. Geological Survey," write:
U.S. Geological SurveyEarthquake Facts and Statistics (from http://neic.usgs.gov/neis/eqlists/eqstats.html)
Frequency of Occurrence of
Earthquakes
Based on Observations since 1900
Descriptor 
Magnitude 
Average Annually 
Great 
8 and higher 
1 
Major 
7  7.9 
18 
Strong 
6  6.9 
120 
Moderate 
5  5.9 
800 
Light 
4  4.9 
6,200 (estimated) 
Minor 
3  3.9 
49,000 (estimated) 
Very Minor 
< 3.0 
Magnitude 2  3: about 1,000 per day 
The USGS estimates that several million earthquakes occur in the world each year. Many go undetected because they hit remote areas or have very small magnitudes. The NEIC now locates about 50 earthquakes each day, or about 20,000 a year.
Number of Earthquakes
Worldwide
for 1990  2002
Located by the US Geological Survey National Earthquake Information Center

Number of Earthquakes in the
United States
for 1990  2002
Located by the US Geological Survey National Earthquake Information Center

Red values indicate the earthquakes
occurred in Alaska.
Blue values indicate the
earthquakes occurred in
California.
* As of 08 January 2003
Earthquakes Located by the USGS NEIC 19801989.
Earthquakes Located by the USGS NEIC 19701979.
As more and more seismographs are installed in the world, more earthquakes can be and have been located. However, the number of large earthquakes (magnitude 6.0 or greater) have stayed relatively constant.
TABLE 4  Magnitude vs. Ground Motion and Energy

TABLE 4 shows, for example, that a magnitude 7.2 earthquake produces 10 times more ground motion that a magnitude 6.2 earthquake, but it releases about 32 times more energy. The energy release best indicates the destructive power of an earthquake.
Another example:
How much bigger is a
magnitude 9.7 earthquake than a 6.8 earthquake?
A magnitude 9.7 earthquake is 794 times BIGGER on a seismogram than a magnitude 6.8 earthquake. The magnitude scale is logarithmic, so
(10**9.7)/(10**6.8) = (5.01*10**9)/(6.31*10**6) = .794*10**3 = 794
OR
= 10**(9.76.8) = 10**2.9 = 794.328
Another way to get about the same answer without using a calculator is that since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 unit of magnitude is about 1.3 times the amplitude, we can get,
10 * 10 * 10 / 1.3 = 769 times [not exact, but a decent approximation]
The magnitude scale is really comparing amplitudes of waves on a seismogram, not the STRENGTH (energy) of the quakes. So, a magnitude 9.7 is 794 times bigger than a 6.8 quake as measured on seismograms, but the 9.7 quake is about 23,000 times STRONGER than the 6.8! Since it is really the energy or strength that knocks down buildings, this is really the more important comparison. This means that it would take about 23,000 quakes of magnitude 6.8 to equal the energy released by one magnitude 9.7 event. Here's how we get that number:
One whole unit of magnitude represents approximately 32 times (actually 10**1.5 times) the energy, based on a longstanding empirical formula that says log(E) is proportional to 1.5M, where E is energy and M is magnitude. This means that a change of 0.1 in magnitude is about 1.4 times the energy release. Therefore, using the shortcut shown eartlier for the amplitude calculation, the energy is,
32 * 32 * 32 / 1.4 = 23,405 or about 23,000
The actual formula would be:
((10**1.5)**9.7)/((10**1.5)**6.8)
= 10**(1.5*(9.76.8)) = 10**(1.5*2.9) = 22,387
This explains why big quakes are so much more devastating than small ones. The amplitude ("size") differences are big enough, but the energy ("strength") differences are huge. The amplitude numbers are neater and a little easier to explain, which is why those are used more often in publications. But it's the energy that does the damage.
Maps of intensity of ground shaking can be prepared for specific earthquakes. Today, color maps are prepared very quickly for significant events from predictions based on the earthquake location and magnitude or from reports of ground shaking (“felt reports? and the maps displayed on the USGS web page (http://earthquake.usgs.gov/shakemap/). Examples of these shake maps for the January 17, 1994 Northridge earthquake, the October 17, 1989 Loma Prieta earthquake, and the February 9, 1971 San Fernando earthquake are shown below. The table and color code beneath the maps illustrates the correlation between potential damage, peak ground acceleration and Modified Mercalli Intensity. The intensity of ground shaking (and therefore damage) is usually greatest near the earthquake epicenter and decreases rapidly with distance from the epicenter. Local geology (nearsurface ground conditions) and building characteristics also influence the intensity distribution.
A map of peak ground accelerations, an acceleration versus distance plot and an intensity map for the January 17, 1995 Kobe, Japan earthquake are shown below (from http://www.eqe.com/publications/kobe/kobe.htm):