Postby salsinawi » Wed Aug 16, 2006 10:21 pm


These days, an earthquake happens and right away you hear about it on the news, including its magnitude. Instant magnitudes seem like a routine achievement, like reporting the temperature. But that feat is the result of generations of scientific work.

Earthquakes, in fact, are very hard to measure. The problem is like coming up with one number to indicate the quality of a baseball pitcher. You can start with the pitcher's win-loss record, but the more you study the problem the more things you want to consider, like earned-run average, defensive range, strikeouts and walks, career longevity, and so on. Baseball statisticians love to tinker with indexes that weigh as many of these factors as possible. (And if you want to know more, visit the About Baseball Guide.)

Earthquakes are easily as complicated as pitchers. They are fast or slow. Some are gentle, others are violent. They are deep or shallow. They're even right-handed or left-handed. They are oriented different ways?horizontal, vertical, or in between. They occur in different geologic settings, deep within continents or out in the ocean. Yet somehow we want to get a single meaningful number we can use to rank the world's earthquakes. The goal has always been to figure out the amount of energy an earthquake releases, because that tells us profound things about the dynamics of the Earth's interior.

The pioneering seismologist Charles Richter started in the 1930s by simplifying everything he could think of. He chose one standard instrument, a Wood-Anderson seismograph, used only nearby earthquakes in Southern California, and took only one piece of data?the distance A in millimeters that the seismograph needle moved. He worked up a simple adjustment factor B to allow for near versus distant quakes, and that was the first Richter scale of local magnitude ML:

ML = log A + B

You'll notice that ML really measures the size of earthquake waves, not an earthquake's total energy, but it was a start. This scale worked fairly well as far as it went, which was for small and moderate sized earthquakes in Southern California. Over the next 20 years Richter and many other workers extended the scale to newer seismometers, different regions, and different kinds of seismic waves.

Soon enough Richter's original scale was abandoned, but the public and the press still use the phrase "Richter magnitude." Seismologists used to mind, but not any more.

Today small, local seismic events are usually measured by body-wave magnitude mb, which is dependable up to about magnitude 6.5, where it saturates?everything larger comes out 6.5 because of the way mb is measured.

Larger quakes are measured with surface-wave magnitude Ms, which matches mb well for events below magnitude 6 and extends above it to about 8.5. It saturates around magnitude 8. That's OK for most purposes because magnitude-8 events, officially called great earthquakes, happen only about once a year on average for the whole planet.

By now we've learned enough to tell that within their limits, these modern magnitude scales are a reliable gauge of the actual energy that earthquakes release.

The biggest earthquake whose magnitude we know was in 1960, in the Pacific right off central Chile on May 22. It would have destroyed most structures over hundreds of kilometers, except that they had already been knocked down by the great quake of the preceding day. Back then, it was said to be magnitude 8.5, but today we say it was 9.5. What happened in the meantime was that Hiroo Kanamori came up with a better magnitude scale in 1977.

His scale, called moment magnitude Mw, is not based on seismometer readings at all but on the total energy released in a quake, the seismic moment . This means that it does not saturate. At last there is a measurement to match anything the Earth can throw at us. Still, he had to insert an adjustment in his formula such that below magnitude 8 Mw matches Ms, which below magnitude 6 matches mb, which is close enough to Richter's old ML. So keep calling it the Richter scale if you like?that's the scale Richter would have made if he could.




Designator Name Formula

Mw Moment Magnitude Hanks and Kanamori formula (1979)
Mw = (2/3) log Mo - 10.7

where Mo is the scalar moment of the best double couple in dyne-cm.

Me Energy Magnitude These energy magnitudes are computed from the radiated energy using the Choy and Boatwright (1995) formula
Me = (2/3) log Es - 2.9

where Es is the radiated seismic energy in Newton-meters. Me, computed from high frequency seismic data, is a measure of the seismic potential for damage.

Ms Surface Wave Magnitude IASPEI formula
Ms = log (A/T) + 1.66 log D + 3.3


A is the maximum ground amplitude in micrometers (microns) of the vertical component of the surface wave within the period range 18 <= T <= 22.
T is the period in seconds.
D is the distance in geocentric degrees (station to epicenter) and 20° <= D <= 160°.

No depth corrections are applied, and Ms magnitudes are not generally computed for depths greater than 50 kilometers. The Ms value published is the average of the individual station magnitudes from reported T and A data.

If the uncertainty of the computed depth is considered great enough that the depth could be less than 50 kilometers, an Ms value may still be published, computed by the IASPEI formula and NOT corrected for depth.

In general, the Ms magnitude is more reliable than the MB magnitude as a means of yielding the relative "size" of a shallow-focus earthquake.

MB Compressional Body Wave (P-wave) Magnitude MB = log (A/T) +Q(D,h)
defined by Gutenberg and Richter (1956) except that T, the period in seconds, is restricted to 0.1 <= T <= 3.0 and A, the ground amplitude in micrometers, is not necessarily the maximum in the P group. Q is a function of distance (D) and depth (h) where D >= 5°.

mbLg Body Wave Magnitude using the Lg wave mbLg = 3.75 + 0.90 log D + log (A/T) for 0.5° <= D <= 4°

mbLg = 3.30 + 1.66 log D + log (A/T) for 4° <= D <= 30°

as proposed by Nuttli (1973) where A is the ground amplitude in micrometers and T is the period in seconds calculated from the vertical component 1-second Lg waves. D is the distance in geocentric degrees.

ML Local ("Richter") Magnitude ML = log A - log Ao
defined by Richter (1935) where A is the maximum trace amplitude in millimeters recorded on a standard short-period seismometer and log Ao is a standard value as a function of distance where distance <= 600 kilometers.




The Richter magnitude test scale (or more correctly local magnitude ML scale) assigns a single number to quantify the size of an earthquake. It is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude of the largest displacement from zero on a seismometer output. Measurements have no limits and can be either positive or negative.


Developed in 1935 by Charles Richter in collaboration with Beno Gutenberg, both of the California Institute of Technology, the scale was originally intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismometer. Richter originally reported values to the nearest quarter of a unit, but decimal numbers were used later. His motivation for creating the local magnitude scale was to separate the vastly larger number of smaller earthquakes from the few larger earthquakes observed in California at the time.

His inspiration for the technique was the stellar magnitude scale used in astronomy to describe the brightness of stars and other celestial objects. Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of 1 micrometre on a seismogram recorded using a Wood-Anderson torsion seismometer 100 km from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. However, the Richter scale has no upper or lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.
Because of the limitations of the Wood-Anderson torsion seismometer used to develop the scale, the original ML cannot be calculated for events larger than about 6.8. Many investigators have proposed extensions to the local magnitude scale, the most popular being the surface wave magnitude MS and the body wave magnitude mb. These traditional magnitude scales have largely been superseded by the implementation of methods for estimating the seismic moment and its associated magnitude scale.
Richter magnitudes

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquake). Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; in terms of energy, each whole number increase corresponds to an increase of about 31 times the amount of energy released.

Events with magnitudes of about 4.6 or greater are strong enough to be recorded by any seismographs all over the world.

The following describes the typical effects of earthquakes of various magnitudes near the epicenter. This table should be taken with extreme caution, since intensity and thus ground effects depend not only on the magnitude, but also on the distance to the epicenter, and geological conditions (certain terrains can amplify seismic signals).

Description Richter Magnitudes Earthquake Effects Frequency of
Micro Less than 2.0 Microearthquakes, not felt. About 8,000 per day

Very minor 2.0-2.9 Generally not felt, but recorded. About 1,000 per day

Minor 3.0-3.9 Often felt, but rarely causes damage. 49,000 per year (est.)

Light 4.0-4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely. 6,200 per year (est.)

Moderate 5.0-5.9 Can cause major damage to poorly constructed buildings over small regions. At most slight damage to well-designed buildings. 800 per year

Strong 6.0-6.9 Can be destructive in areas up to about 100 miles across in populated areas. 120 per year

Major 7.0-7.9 Can cause serious damage over larger areas. 18 per year

Great 8.0-8.9 Can cause serious damage in areas several hundred miles across. 1 per year

Rarely, great 9.0 or greater Devastating in areas several thousand miles across. 1 per 20 years

(Adapted from U.S. Geological Survey documents.)

Great earthquakes occur once a year, on average. The largest recorded earthquake was the Great Chilean Earthquake of May 22, 1960 which had a magnitude (MW) of 9.5 (Chile 1960).

The following table needs review. It currently lists the approximate energy equivalents in terms of TNT explosive force [1].
Richter Approximate Magnitude Approximate TNT forSeismic Energy

0.5 5.6 kg (12.4 lb)
Hand grenade

1.0 32 kg (70 lb) Construction site blast

1.5 178 kg (392 lb) WWII conventional bombs

2.0 1 metric ton late WWII conventional bombs

2.5 5.6 metric tons WWII blockbuster bomb

3.0 32 metric tons Massive Ordnance Air Blast bomb

3.5 178 metric tons Chernobyl nuclear disaster, 1986

4.0 1 kiloton Small atomic bomb

4.5 5.6 kilotons Average tornado (total energy)

5.0 32 kiloton Nagasaki atomic bomb

5.5 178 kilotons Little Skull Mtn., NV Quake, 1992

6.0 1 megaton Double Spring Flat, NV Quake, 1994

6.5 5.6 megatons Northridge quake, 1994

7.0 50 megatons Tsar Bomba, largest thermonuclear weapon ever tested (magnitude seen on seismographs reduced because detonated 4 km in the atmosphere.)

7.5 178 megatons Landers, CA Quake, 1992

8.0 1 gigaton
San Francisco, CA Quake, 1906

9.0 5.6 gigatons Anchorage, AK Quake, 1964

9.3 32 gigatons 2004 Indian Ocean earthquake

10.0 1 teraton

estimate for a 20 km rocky bolide impacting at 25 km/s

Problems with the Richter scale

The major problem with Richter magnitude is that it is not easily related to physical characteristics of the earthquake source. Furthermore, there is a saturation effect near 6.3-6.5, owing to the scaling law of earthquake spectra, that causes traditional magnitude methods (such as MS) to yield the same magnitude estimate for events that are clearly of different size. By the beginning of the 21st century, most seismologists considered the traditional magnitude scales to be largely obsolete, being replaced by a more physically meaningful measurement called the seismic moment which is more directly relatable to the physical parameters, such as the dimension of the earthquake rupture, and the energy released from the earthquake. In 1979, seismologists Tom Hanks and Hiroo Kanamori, also of the California Institute of Technology, proposed the moment magnitude scale (MW), which provides a way of expressing seismic moments in a form that can be approximately related to traditional seismic magnitude measurements.
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