Richter scale: Difference between revisions

The '''Richter scale'''<ref>{{Harvnb|Kanamori|1978|p=411}}. {{Harvtxt|Hough|2007|pp=122–126}} discusses the name at some length.</ref> ({{IPAc-en|ˈ|r|ɪ|k|t|ər}}), also called the '''Richter magnitude scale''', '''Richter's magnitude scale''', and the '''Gutenberg–Richter scale''',<ref>{{cite book |last1=McPhee |first1=John |title=Annals of the Former World |date=1998 |publisher=Farrar, Straus and Giroux |page=608}}</ref> is a measure of the strength of [[earthquake]]s, developed by [[Charles Francis Richter]] in collaboration with [[Beno Gutenberg]], and presented in hisRichter's landmark 1935 paper, where he called it the "magnitude scale".<ref>{{Harvnb|Kanamori|1978|p=411}}; {{Harvnb|Richter|1935}}.</ref> This was later revised and renamed the '''local magnitude scale''', denoted as ML or {{M|L}}.<ref>{{Harvnb|Gutenberg|Richter|1956b|p=30}}.</ref>

Because of various shortcomings of the original {{M|L}} scale, most seismological authorities now use other similar scales such as the [[moment magnitude scale]] ({{M|w}}) to report earthquake magnitudes, but much of the news media still erroneously refers to these as "Richter" magnitudes. All magnitude scales retain the [[logarithm]]ic character of the original and are scaled to have roughly comparable numeric values (typically in the middle of the scale). Due to the variance in earthquakes, it is essential to understand the Richter scale uses logarithms[[common logarithm]]s simply to make the measurements manageable (i.e., a magnitude 3 quake factors 10³ while a magnitude 5 quake isfactors 10010⁵ timesand strongerhas thanseismometer readings 100 times thatlarger).<ref>{{Cite web|title=Discovery Project 17: Orders of Magnitude|url=https://www.stewartmath.com/precalc_7e_dp/precalc_7e_dp17.html|access-date=2022-02-24|website=www.stewartmath.com}}</ref>

The Richter magnitude of an earthquake is determined from the [[logarithm]] of the [[amplitude]] of waves recorded by seismographs. (adjustmentsAdjustments are included to compensate for the variation in the distance between the various seismographs and the [[epicenter]] of the earthquake). The original formula is:<ref name="Ellsworth">{{cite book

| publisher=USGS

| last=Ellsworth

| first=William L.

| year=1991

| access-date=2008-09-14

The following describes the typical effects of earthquakes of various magnitudes near the epicenter.<ref name="GNSScience1">{{cite web | url=https://www.gns.cri.nz/Home/Learning/Science-Topics/Earthquakes/Monitoring-Earthquakes/Other-earthquake-questions/What-is-the-Richter-Magnitude-Scale | title=What is the Richter Magnitude Scale? | publisher=[[GNS Science]] | access-date=3 August 2021 | url-status=dead | archive-url=https://web.archive.org/web/20210803200647/https://www.gns.cri.nz/Home/Learning/Science-Topics/Earthquakes/Monitoring-Earthquakes/Other-earthquake-questions/What-is-the-Richter-Magnitude-Scale |archive-date=3 August 2021}}</ref> The values are typical only.and Theymay shouldnot be takenexact within extremea cautionfuture sinceevent because intensity and thus ground effects depend not only on the magnitude but also on (1) the distance to the epicenter, (2) the depth of the earthquake's focus beneath the epicenter, (3) the location of the epicenter, and (4) [[Seismic site effects|geological conditions]].

!Typical maximum [[Modified Mercalli intensity scale|Modifiedmodified Mercalli Intensityintensity]]<ref>{{cite web|title=Magnitude / Intensity Comparison|url=http://earthquake.usgs.gov/learn/topics/mag_vs_int.php|url-status=dead|archive-url=https://web.archive.org/web/20110623113247/http://earthquake.usgs.gov/learn/topics/mag_vs_int.php|archive-date=2011-06-23}}</ref>

|style="background:lightskyblue;"|1.0–1.9

|style="background:paleturquoise;"|2.0–2.9

|style="background:palegreen;"|3.0–3.9

|style="background:greenyellow;"|4.0–4.9

|style="background:yellow;"|5.0–5.9

|style="background:gold;"|6.0–6.9

|style="color:white; background:red;"|8.0–8.9

Prior to the development of the magnitude scale, the only measure of an earthquake's strength or "size" was a subjective assessment of the intensity of shaking observed near the [[epicenter]] of the earthquake, categorized by various [[seismic intensity scales]] such as the [[Rossi-ForelRossi–Forel scale]]. ("Size" is used in the sense of the quantity of energy released, not the size of the area affected by shaking, though higher-energy earthquakes do tend to affect a wider area, depending on the local geology.) In 1883, [[John Milne]] surmised that the shaking of large earthquakes might generate waves detectable around the globe, and in 1899 E. Von Rehbur Paschvitz observed in Germany seismic waves attributable to an earthquake in [[Tokyo]].<ref>{{Harvnb|Bolt|1993|p=47}}.</ref> In the 1920s, [[Harry O. Wood]] and [[John August Anderson|John A. Anderson]] developed the [[Wood–Anderson seismograph]], one of the first practical instruments for recording seismic waves.<ref>{{Harvnb|Hough|2007|p=}};</ref> Wood then built, under the auspices of the [[California Institute of Technology]] and the [[Carnegie Institution for Science|Carnegie Institute]], a network of seismographs stretching across [[Southern California]].<ref>{{Harvnb|Hough|2007|p=57}}.</ref> He also recruited the young and unknown Charles Richter to measure the seismograms and locate the earthquakes generating the seismic waves.<ref>{{Harvnb|Hough|2007|pp=57, 116}}.</ref>

Additional developments were required to produce a practical method of assigning an absolute measure of magnitude . First, to span the wide range of possible values, Richter adopted Gutenberg's suggestion of a [[logarithm]]ic scale, where each step represents a tenfold increase of magnitude, similar to the magnitude scale used by astronomers [[Apparent magnitude|for star brightness]].<ref>[pending]</ref> Second, he wanted a magnitude of zero to be around the limit of human perceptibility.<ref>{{Harvnb|Richter|1935|p=14}}: {{Harvnb|Gutenberg|Richter|1936|p=183}}.</ref> Third, he specified the Wood–Anderson seismograph as the standard instrument for producing seismograms. Magnitude was then defined as "the logarithm of the maximum trace amplitude, expressed in [[microns]]", measured at a distance of {{Convert|100|km|mi|abbr=on}}. The scale was calibrated by defining a magnitude 0 shock as one that produces (at a distance of {{Convert|100|km|mi|abbr=on}}) a maximum amplitude of 1&nbsp;micron (1&nbsp;µmμm, or 0.001&nbsp;millimeters) on a seismogram recorded by a Wood-Anderson torsion seismometer.<ref>{{Harvnb|Richter|1935|p=5}}. See also {{Harvnb|Hutton|Boore|1987|p=1}}; {{Harvnb|Chung|Bernreuter|1980|p=10}}.</ref> Finally, Richter calculated a table of distance corrections,<ref>{{Harvnb|Richter|1935|p=6}}, Table I.</ref> in that for distances less than 200 kilometers<ref>{{Harvnb|Richter|1935|p=32}}.</ref> the attenuation is strongly affected by the structure and properties of the regional geology.<ref>{{Harvnb|Chung|Bernreuter|1980|p=5}}.</ref>

When Richter presented the resulting scale in 1935, he called it (at the suggestion of Harry Wood) simply a "magnitude" scale.<ref>{{Harvnb|Richter|1935|p=1}}. His article is titled: "An Instrumental Earthquake Magnitude Scale".</ref> "Richter magnitude" appears to have originated when [[Perry Byerly]] told the press that the scale was Richter's and "should be referred to as such."<ref>{{Harvnb|Hough|2007|pp=123–124}}.</ref> In 1956, Gutenberg and Richter, while still referring to "magnitude scale", labelled it "local magnitude", with the symbol {{M|L}}, to distinguish it from two other scales they had developed, the [[surface wave magnitude]] (M_S) and [[body wave magnitude]] (M_B)<!-- These are non-standard: do not use the "M" template here. --> scales.<ref>{{Harvnb|Gutenberg|Richter|1956b|p=30}}.</ref>

The Richter and MMS scales measure the energy released by an earthquake; another scale, the [[Mercalli intensity scale]], classifies earthquakes by their ''effects'', from detectable by instruments but not noticeable, to catastrophic. The energy and effects are not necessarily strongly correlated; a shallow earthquake in a populated area with soil of certain types can be far more intense in effectsimpact than a much more energetic deep earthquake in an isolated area.

Several scales have historically been historically described as the "Richter scale",{{citation needed|date=January 2020}}, especially the ''local magnitude'' {{M|L}} and the surface wave {{M|s}} scale. In addition, the ''body wave magnitude'', {{M|b}}, and the ''moment magnitude'', {{M|w}}, abbreviated MMS, have been widely used for decades. A couple of new techniques to measure magnitude are in the development stage by seismologists.

The [[seismic moment]], '''''{{M|0}}''''', is proportional to the area of the rupture times the average slip that took place in the earthquake, thus it measures the physical size of the event. {{M|w}} is derived from it empirically as a quantity without units, just a number designed to conform to the {{M|s}} scale.<ref>{{cite journal | last1 = Hanks | first1 = T. C. | last2 = Kanamori | first2 = H. | year = 1979 | title = Moment magnitude scale | journal = Journal of Geophysical Research | volume = 84 | issue = B5| page = 2348 | doi=10.1029/jb084ib05p02348 | bibcode = 1979JGR....84.2348H}}</ref> A spectral analysis is required to obtain {{M|0}},. whereasIn contrast, the other magnitudes are derived from a simple measurement of the amplitude of a specificallyprecisely defined wave.

All scales, except {{M|w}}, saturate for large earthquakes, meaning they are based on the amplitudes of waves whichthat have a wavelength shorter than the rupture length of the earthquakes. These short waves (high -frequency waves) are too short a yardstick to measure the extent of the event. The resulting effective upper limit of measurement for {{M|L}} is about 7 and about 8.5<ref>{{cite web |url=http://www.weather.gov.hk/education/edu02rga/article/ele-EarthquakeMagnetude_e.htm |title=On Earthquake Magnitudes |first=Wang-chun |last=Woo |date=September 2012 |publisher=Hong Kong Observatory |access-date=18 December 2013 |archive-date=May 24, 2017 |archive-url=https://web.archive.org/web/20170524163729/http://www.weather.gov.hk/education/edu02rga/article/ele-EarthquakeMagnetude_e.htm |url-status=dead }}</ref> for {{M|s}}.<ref name="Local magnitude">{{cite web |url=https://earthquake.usgs.gov/hazards/qfaults/glossary.php |title=Richter scale |work=Glossary |publisher=[[United States Geological Survey|USGS]] |date=March 31, 2010 }}</ref>

New techniques to avoid the saturation problem and to measure magnitudes rapidly for very large earthquakes are being developed. One of these is based on the long-period P-wave;<ref>Di Giacomo, D., Parolai, S., Saul, J., Grosser, H., Bormann, P., Wang, R. & Zschau, J., 2008. "Rapid determination of the energy magnitude Me," in ''European Seismological Commission 31st General Assembly,'' Hersonissos.</ref> theThe other is based on a recently discovered channel wave.<ref>Rivera, L. & Kanamori, H., 2008. "Rapid source inversion of W phase for tsunami warning," in ''European Geophysical Union General Assembly,'' pp. A-06228, Vienna.</ref>

The [[energy]] release of an earthquake,<ref>{{cite journal | last1 = Vassiliou | first1 = Marius | last2 = Kanamori | first2 = Hiroo | year = 1982 | title = The Energy Release in Earthquakes | journal = Bull. Seismol. Soc. Am. | volume = 72 | pages = 371–387 }}</ref> which closely correlates to its destructive power, scales with the {{frac|3|2}} power of the shaking amplitude (see [[Moment magnitude scale]] for an explanation). Thus, a difference in magnitude of 1.0 is equivalent to a factor of 31.6 (<math>=({10^{1.0}})^{(3/2)}</math>) in the energy released; a difference in magnitude of 2.0 is equivalent to a factor of 1000 (<math>=({10^{2.0}})^{(3/2)}</math>) in the energy released.<ref>{{cite journal |first=William |last=Spence |first2=Stuart A. |last2=Sipkin |first3=George L. |last3=Choy |url=https://earthquake.usgs.gov/learn/topics/measure.php |title=Measuring the Size of an Earthquake |journal=Earthquakes and Volcanoes |volume=21 |number=1 |year=1989}}</ref> The elastic energy radiated is best derived from an integration of the radiated spectrum, but an estimate can be based on {{M|b}} because most energy is carried by the high -frequency waves.

These formulae for Richter magnitude <math>\ M_\mathsf{{M|L}}\ </math> are alternatives to using Richter correlation tables based on Richter standard seismic event (<math>\big(\ M_\mathrmmathsf{L} = 0\ ,</math>, <math>\ A = 0.001\mathrm \mathsf{mm}\ ,</math>, <math>\ D=100\mathrm \mathsf{km}\ \big) ~.</math>). BelowIn the formulas below, <math>\textstyle \Delta\ </math> is the epicentral distance (in kilometers[[kilometer]]s, unlessand otherwise<math>\ specified)\Delta^{\circ}\ </math> is the same distance represented as sea level [[great circle]] degrees.

* The '''Lillie empirical formula''' is:

:<math>\ M_\mathrmmathsf{L} = \log_{10} A - 2.48 + 2.76\ \log_{10} \Delta\ </math>

: where <math>\ A\ </math> is the amplitude (maximum ground displacement) of the [[P-wave]], in [[micrometre|micrometers (μm)]], measured at 0.8&nbsp;Hz.

*'''Lahr's Theempirical formula proposed by Lahr (1980)'''<ref name="Lahr">{{cite journalreport |last1last=Lahr |first1first=J. C. |year=1980 |title=HYPOELLIPSE: A Computercomputer Programprogram for Determiningdetermining Locallocal Earthquakeearthquake Hypocentralhypocentral Parametersparameters, Magnitudemagnitude, and Firstfirst-Motionmotion pattern Pattern|journal=US Geological Survey open-file report|date=1980 |volume=80-59|pages=59 pp.}}</ref> proposal is:

: <math>\ M_\mathrmmathsf{L} = \log_{10} A2.92 + 12.625\ \log_{10} D\left( \tau \right) - 0.15001\ \Delta^{\circ}\ ,</math>

where:: <math>A</math>\ is\Delta^{\circ}\ [[seismograph]] signal amplitude in mm and <math>D</math> is in kmdegrees.

* The Bisztricsany (1958)'''Tsumura empirical formula for epicentral distances between 4˚ and 160˚''' is:<ref name="Al-Arifi">{{cite journal|last1=Al-Arifi|first1=Nassir S.|last2=Al-Humidan|first2=Saad|title=Local and regional earthquake magnitude calibration of Tabuk analog sub-network, Northwest of Saudi Arabia|journal=Journal of King Saud University – Science|date=July 2012|volume=24|issue=3|pages=257–263|doi=10.1016/j.jksus.2011.04.001|doi-access=free}}</ref>

: <math>\ M_\mathrmmathsf{L} = -2.9253 + 2.2585 \log_{10} \left(F - P\tauright) -+ 0.0010014\ \Delta^{\circ}\ ,</math>

* The Tsumura'''Tsuboi''' (University of Tokyo) '''empirical formula''' is:<ref name="Al-Arifi"/>

:<math>\ M_\mathrmmathsf{L} = -2.53\log_{10} A + 21.8573\ \log_{10} (F-P)\Delta +- 0.0014 83\Delta^{\circ} ,</math>

: where <math>F-P\ A\ </math> is the total duration of oscillationamplitude in seconds. {{M[[micrometre|L}} is mainly between 3 and 5μm]].