# Richter magnitude scale

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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 seismogram. So, for example, an earthquake of magnitude 5 is ten times greater than one of magnitude 4 and an earthquake of magnitude 8 is 10(8 − 4) or 10000 times greater than one of magnitude 4.

However, the energy of an earthquake is proportional to the square root of the cube of the amplitude. So each step of the Richter scales has an energy 103/2 (~ 31.6) times that of the previous step. So a magnitude 9 has 10,000 times the amplitude of a magnitude 5, but a million times more energy.

The diminution of amplitude due to distance between the earthquake epicenter and the seismometer is corrected for by subtracting the common logarithm of the expected amplitude of a magnitude 0 event at that distance. This correction for distance is intended to make the local magnitude an absolute measure of earthquake size.

The magnitude of the earthquake, M, is given by:

M = log10A + 3log10(8Δt − 2.92)

where A is amplitude in millimeters and t is time in seconds.

## History

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.

## 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 8.3-8.5, 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.

Magnitude must not be confused with intensity. Intensity scales, such as the Modified Mercalli Intensity Scale and Japanese seismic intensity scale, are used to describe relative earthquake effects. Intensity is sensitive to a host of local site conditions and is not an absolute measurement of earthquake size.

## Richter magnitudes

Events with magnitudes of about 4.5 or greater are strong enough to be recorded by 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).

Descriptor Richter magnitudes Earthquake Effects Frequency of Occurrence
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
Rare 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 Great Chilean Earthquake of May 22, 1960 which had a magnitude (MW) of 9.5 (Chile 1960).

The following table lists the approximate energy equivalents in terms of TNT explosive force.

 Richter Magnitude Approximate TNT for Seismic Energy Yield Example TNT equivalent of example 0.5 5.6 lb (2.5 kg) Hand grenade 6 lb 1.0 32 lb (14 kg) Construction site blast 30 lb 1.5 178 lb (81 kg) WWII conventional bombs 320 lb 2.0 1 metric ton late WWII conventional bombs 1 metric ton 2.5 5.6 metric tons WWII blockbuster bomb 4.6 metric tons 3.0 32 metric tons Massive Ordnance Air Blast bomb 29 metric tons 3.5 178 metric tons Chelyabinsk nuclear accident, 1957 73 metric tons 4.0 1 kiloton Small atomic bomb 1 kiloton 4.5 5.6 kilotons Average tornado (total energy) 5.1 kiloton 5.0 32 kiloton Nagasaki atomic bomb 32 kiloton 5.5 178 kilotons Little Skull Mtn., NV Quake, 1992 80 kiloton 6.0 1 megaton Double Spring Flat, NV Quake, 1994 1 megaton 6.5 5.6 megatons Northridge quake, 1994 approx. 5 megatons 7.0 32 megatons Largest thermonuclear weapon 32 megatons 7.5 178 megatons Landers, CA Quake, 1992 approx. 160 megatons 8.0 1 gigaton San Francisco, CA Quake, 1906 approx. 1 gigaton 8.5 5.6 gigatons Anchorage, AK Quake, 1964 approx. 5 gigaton 9.0 32 gigatons Indian Ocean quake/tsunami, 2004 approx. 30 gigaton 10.0 1 teraton estimate for a 10 km rocky bolide impacting at 25 km/s 1 teraton