## Moment magnitude scale |

Part of |

Characteristics |

The **moment magnitude scale** (**MMS**; denoted explicitly with **M _{w}** or

Moment magnitude (M_{w}) is considered the authoritative magnitude scale for ranking earthquakes by size^{[3]} because it is more directly related to the energy of an earthquake, and does not *saturate*. (That is, it does not underestimate magnitudes like other scales do in certain conditions.^{[4]}) It has become the standard scale used by seismological authorities (such as the ^{[5]}), replacing (when available, typically for M > 4) use of the _{L}_{s}_{ww} , etc.) reflect different ways of estimating the seismic moment.

- history
- current use
- definition
- relations between seismic moment, potential energy released and radiated energy
- comparative energy released by two earthquakes
- subtypes of m
_{w} - see also
- notes
- sources
- external links

At the beginning of the twentieth century, very little was known about how earthquakes happen, how seismic waves are generated and propagate through the earth's crust, and what they can tell us about the earthquake rupture process; the first magnitude scales were therefore ^{[6]} The initial step in determining earthquake magnitudes empirically came in 1931 when the Japanese seismologist ^{[7]} ^{[8]} He established a reference point and the now familiar ten-fold (exponential) scaling of each degree of magnitude, and in 1935 published his "magnitude" scale, now called the _{L} .^{[9]}

The Local magnitude scale was developed on the basis of shallow (~15 km (9 mi) deep), moderate-sized earthquakes at a distance of approximately 100 to 600 km (62 to 373 mi), conditions where the surface waves are predominant. At greater depths, distances, or magnitudes the surface waves are greatly reduced, and the Local magnitude scale underestimates the magnitude, a problem called *saturation*. Additional scales were developed^{[10]} – a surface-wave magnitude scale (_{s}^{[11]}, a body-wave magnitude scale (^{[12]} and a number of variants^{[13]} – to overcome the deficiencies of the M_{L} scale, but all are subject to saturation. A particular problem was that the M_{s} scale (which in the 1970s was the preferred magnitude scale) saturates around M_{s} 8.0, and therefore underestimates the energy release of "great" earthquakes^{[14]} such as the _{s} magnitudes of 8.5 and 8.4 respectively but were notably more powerful than other M 8 earthquakes; their moment magnitudes were closer to 9.6 and 9.3.^{[15]}

The study of earthquakes is challenging as the source events cannot be observed directly, and it took many years to develop the mathematics for understanding what the seismic waves from an earthquake can tell us about the source event. An early step was to determine how different systems of forces might generate seismic waves equivalent to those observed from earthquakes.^{[16]}

The simplest force system is a single force acting on an object. If it has sufficient strength to overcome any resistance it will cause the object to move ("translate"). A pair of forces, acting on the same "line of action" but in opposite directions, will cancel; if they cancel (balance) exactly there will be no net translation, though the object will experience stress, either tension or compression. If the pair of forces are offset, acting along parallel but separate lines of action, the object experiences a rotational force, or * couple*, also

The single couple and double couple models are important in seismology because each can be used to derive how the seismic waves generated by an earthquake event should appear in the "far field" (that is, at distance). Once that relation is understood it can be inverted to use the earthquake's observed seismic waves to determine its other characteristics, including fault geometry and seismic moment.^{[19]}

In 1923 Hiroshi Nakano showed that certain aspects of seismic waves could be explained in terms of a double couple model.^{[20]} This led to a three-decade long controversy over the best way to model the seismic source: as a single couple, or a double couple?^{[21]} While Japanese seismologists favored the double couple, most seismologists favored the single couple.^{[22]} Although the single couple model had some short-comings, it seemed more intuitive, and there was a belief – mistaken, as it turned out – that the ^{[23]} In principle these models could be distinguished by differences in the radiation patterns of their ^{[24]}

The debate ended when Maruyama (1963), Haskell (1964), and Burridge & Knopoff (1964) showed that if earthquake ruptures are modeled as dislocations the pattern of seismic radiation can always be matched with an equivalent pattern derived from a double couple, but not from a single couple.^{[25]} This was confirmed as better and more plentiful data coming from the ^{[26]}

A double couple model suffices to explain an earthquake's far-field pattern of seismic radiation, but tells us very little about the nature of an earthquake's source mechanism or its physical features.^{[27]} While slippage along a fault was theorized as the cause of earthquakes (other theories included movement of magma, or sudden changes of volume due to phase changes^{[28]}), observing this at depth was not possible, and understanding what could be learned about the source mechanism from the seismic waves requires an understanding of the source mechanism.^{[29]}

Modeling the physical process by which an earthquake generates seismic waves required much theoretical development of ^{[30]} More generally applied to problems of stress in materials,^{[31]} an extension by ^{[32]} In a series of papers starting in 1956 she and other colleagues used dislocation theory to determine part of an earthquake's focal mechanism, and to show that a dislocation – a rupture accompanied by slipping — was indeed equivalent to a double couple,^{[33]}

In a pair of papers in 1958, J. A. Steketee worked out how to relate dislocation theory to geophysical features.^{[34]} Numerous other researchers worked out other details,^{[35]} culminating in a general solution in 1964 by Burridge and Knopoff, which established the relationship between double couples and the theory of elastic rebound, and provided the basis for relating an earthquake's physical features to seismic moment.^{[36]}

* Seismic moment* – symbol M

The first calculation of an earthquake's seismic moment from its seismic waves was by ^{[40]} He did this two ways. First, he used data from distant stations of the ^{[41]} Second, he drew upon the work of Burridge and Knopoff on dislocation to determine the amount of slip, the energy released, and the stress drop (essentially how much of the potential energy was released).^{[42]} In particular, he derived a now famous equation that relates an earthquake's seismic moment to its physical parameters:

*M*_{0}=*μūS*

with μ being the rigidity (or resistance) of moving a fault with a surface areas of S over an average dislocation (distance) of ū. (Modern formulations replace ūS with the equivalent D̄A, known as the "geometric moment" or "potency".^{[43]}.) By this equation the *moment* determined from the double couple of the seismic waves can be related to the moment calculated from knowledge of the surface area of fault slippage and the amount of slip. In the case of the Niigata earthquake the dislocation estimated from the seismic moment reasonably approximated the observed dislocation.^{[44]}

Seismic moment is a measure of the ^{[45]} It is related to the total energy released by an earthquake. However, the power or potential destructiveness of an earthquake depends (among other factors) on how much of the total energy is converted into seismic waves.^{[46]} This is typically 10% or less of the total energy, the rest being expended in fracturing rock or overcoming friction (generating heat).^{[47]}

Nonetheless, seismic moment is regarded as the fundamental measure of earthquake size,^{[48]} representing more directly than other parameters the physical size of an earthquake.^{[49]} As early as 1975 it was considered "one of the most reliably determined instrumental earthquake source parameters".^{[50]}

Most earthquake magnitude scales suffered from the fact that they only provided a comparison of the amplitude of waves produced at a standard distance and frequency band; it was difficult to relate these magnitudes to a physical property of the earthquake. Gutenberg and Richter suggested that radiated energy E_{s} could be estimated as

(in Joules). Unfortunately, the duration of many very large earthquakes was longer than 20 seconds, the period of the surface waves used in the measurement of M_{s} . This meant that giant earthquakes such as the 1960 Chilean earthquake (M 9.5) were only assigned an M_{s} 8.2. ^{[51]} recognized this deficiency and he took the simple but important step of defining a magnitude based on estimates of radiated energy, M_{w} , where the "w" stood for work (energy):

Kanamori recognized that measurement of radiated energy is technically difficult since it involves integration of wave energy over the entire frequency band. To simplify this calculation, he noted that the lowest frequency parts of the spectrum can often be used to estimate the rest of the spectrum. The lowest frequency _{0} . Using an approximate relation between radiated energy and seismic moment (which assumes stress drop is complete and ignores fracture energy),

(where **E** is in Joules and M_{0} is in Nm), Kanamori approximated M_{w} by

The formula above made it much easier to estimate the energy-based magnitude M_{w} , but it changed the fundamental nature of the scale into a moment magnitude scale. _{w} scale was very similar to a relationship between M_{L} and M_{0} that was reported by Thatcher & Hanks (1973)

Hanks & Kanamori (1979) combined their work to define a new magnitude scale based on estimates of seismic moment

where is defined in newton meters (N·m).

Although the formal definition of moment magnitude is given by this paper and is designated by **M**, it has been common for many authors to refer to M_{w} as moment magnitude. In most of these cases, they are actually referring to moment magnitude **M** as defined above.

Other Languages

Afrikaans: Moment-magnitude-skaal

العربية: مقياس درجة العزم

বাংলা: মোমেন্ট পরিমাপক স্কেল

čeština: Momentová škála

Cymraeg: Graddfa maint moment

dansk: Momentmagnitude-skalaen

Deutsch: Momenten-Magnituden-Skala

Esperanto: Momant-magnituda skalo

euskara: Momentu magnitude eskala

فارسی: مقیاس بزرگای گشتاوری

français: Échelle de magnitude de moment

한국어: 모멘트 규모

հայերեն: Երկրաշարժի մագնիտուդ

हिन्दी: आघूर्ण परिमाण मापक्रम

Bahasa Indonesia: Skala magnitudo momen

italiano: Scala di magnitudo del momento sismico

עברית: סולם מגניטודה לפי מומנט

ქართული: მაგნიტუდა

Kreyòl ayisyen: Echèl valè MMS

македонски: Скала на моментна магнитуда

მარგალური: მაგნიტუდა

Bahasa Melayu: Skala magnitud momen

Nederlands: Momentmagnitudeschaal

日本語: モーメント・マグニチュード

norsk: Momentmagnitude

norsk nynorsk: Momentmagnitude

polski: Magnituda

português: Escala de magnitude de momento

русский: Магнитуда землетрясения

Scots: Moment magnitude scale

Simple English: Moment magnitude scale

slovenčina: Momentové magnitúdo

slovenščina: Momentna magnitudna lestvica

suomi: Momenttimagnitudi

svenska: Momentmagnitudskalan

தமிழ்: உந்தத்திறன் ஒப்பளவு

ไทย: มาตราขนาดโมเมนต์

Türkçe: Moment magnitüd ölçeği

українська: Магнітуда землетрусу

Tiếng Việt: Thang độ lớn mô men

中文: 矩震級