# Seismic magnitude scales

Seismic magnitude scales are used to describe the overall strength or "size" of an earthquake. These are distinguished from seismic intensity scales that categorize the intensity or severity of ground shaking (quaking) caused by an earthquake at a given location. Magnitudes are usually determined from measurements of an earthquake's seismic waves as recorded on a seismogram. Magnitude scales vary based on what aspect of the seismic waves are measured and how they are measured. Different magnitude scales are necessary because of differences in earthquakes, the information available, and the purposes for which the magnitudes are used.

## Earthquake magnitude and ground-shaking intensity

The Earth's crust is stressed by tectonic forces. When this stress becomes great enough to rupture the crust, or to overcome the friction that prevents one block of crust from slipping past another, energy is released, some of it in the form of various kinds of seismic waves that cause ground-shaking, or quaking.
Magnitude is an estimate of the relative "size" or strength of an earthquake, and thus its potential for causing ground-shaking. It is "approximately related to the released seismic energy".
Intensity refers to the strength or force of shaking at a given location, and can be related to the peak ground velocity. With an isoseismal map of the observed intensities (see illustration) an earthquake's magnitude can be estimated from both the maximum intensity observed (usually but not always near the epicenter), and from the extent of the area where the earthquake was felt.
The intensity of local ground-shaking depends on several factors besides the magnitude of the earthquake, one of the most important being soil conditions. For instance, thick layers of soft soil (such as fill) can amplify seismic waves, often at a considerable distance from the source, while sedimentary basins will often resonate, increasing the duration of shaking. This is why, in the 1989 Loma Prieta earthquake, the Marina district of San Francisco was one of the most damaged areas, though it was nearly 100 km from the epicenter. Geological structures were also significant, such as where seismic waves passing under the south end of San Francisco Bay reflected off the base of the Earth's crust towards San Francisco and Oakland. A similar effect channeled seismic waves between the other major faults in the area.

## Magnitude scales

An earthquake radiates energy in the form of different kinds of seismic waves, whose characteristics reflect the nature of both the rupture and the earth's crust the waves travel through. Determination of an earthquake's magnitude generally involves identifying specific kinds of these waves on a seismogram, and then measuring one or more characteristics of a wave, such as its timing, orientation, amplitude, frequency, or duration. Additional adjustments are made for distance, kind of crust, and the characteristics of the seismograph that recorded the seismogram.
The various magnitude scales represent different ways of deriving magnitude from such information as is available. All magnitude scales retain the logarithmic scale as devised by Charles Richter, and are adjusted so the mid-range approximately correlates with the original "Richter" scale.
Most magnitude scales are based on measurements of only part of an earthquake's seismic wave-train, and therefore are incomplete. This results in systematic underestimation of magnitude in certain cases, a condition called saturation.
Since 2005 the International Association of Seismology and Physics of the Earth's Interior (IASPEI) has standardized the measurement procedures and equations for the principal magnitude scales, M$_L$ , M$_s$ , mb , mB  and mb$_{Lg}$ .

### "Richter" magnitude scale

The first scale for measuring earthquake magnitudes, developed in 1935 by Charles F. Richter and popularly known as the "Richter" scale, is actually the local magnitude scale, label ML or M$_L$. Richter established two features now common to all magnitude scales.
* First, the scale is logarithmic, so that each unit represents a ten-fold increase in the amplitude of the seismic waves. As the energy of a wave is proportional to A$^{1.5}$, where A denotes the amplitude, each unit of magnitude represents a 10$^{1.5}$ ≈ 32-fold increase in the seismic energy (strength) of an earthquake.
* Second, Richter arbitrarily defined the zero point of the scale to be where an earthquake at a distance of 100 km makes a maximum horizontal displacement of 0.001 mm (1 μm, or 0.00004 in.) on a seismogram recorded with a Wood-Anderson torsion seismograph. Subsequent magnitude scales are calibrated to be approximately in accord with the original "Richter" (local) scale around magnitude 6.
All "Local" (ML) magnitudes are based on the maximum amplitude of the ground shaking, without distinguishing the different seismic waves. They underestimate the strength:
* of distant earthquakes (over ~600 km) because of attenuation of the S waves,
* of deep earthquakes because the surface waves are smaller, and
* of strong earthquakes (over M ~7) because they do not take into account the duration of shaking.
The original "Richter" scale, developed in the geological context of Southern California and Nevada, was later found to be inaccurate for earthquakes in the central and eastern parts of the North American continent (everywhere east of the Rocky Mountains) because of differences in the continental crust. All these problems prompted the development of other scales.
Most seismological authorities, such as the United States Geological Survey, report earthquake magnitudes above 4.0 as moment magnitude (below), which the press describes as "Richter magnitude".

### Other "local" magnitude scales

Richter's original "local" scale has been adapted for other localities. These may be labelled "ML", or with a lowercase "l", either Ml, or M$_l$. (Not to be confused with the Russian surface-wave MLH scale.) Whether the values are comparable depends on whether the local conditions have been adequately determined and the formula suitably adjusted.

#### Japan Meteorological Agency magnitude scale

In Japan, for shallow (depth < 60 km) earthquakes within 600 km, the Japanese Meteorological Agency calculates a magnitude labeled MJMA, M$_{JMA}$, or M$_J$. (These should not be confused with moment magnitudes JMA calculates, which are labeled M$_w$(JMA) or M$^{(JMA)}$, nor with the Shindo intensity scale.) JMA magnitudes are based (as typical with local scales) on the maximum amplitude of the ground motion; they agree "rather well" with the seismic moment magnitude M$_w$  in the range of 4.5 to 7.5, but underestimate larger magnitudes.

### Body-wave magnitude scales

Body-waves consist of P waves that are the first to arrive (see seismogram), or S waves, or reflections of either. Body-waves travel through rock directly.

#### mB scale

The original "body-wave magnitude" – mB or m$_B$ (uppercase "B") – was developed by Gutenberg 1945c and Gutenberg & Richter 1956 to overcome the distance and magnitude limitations of the M$_L$  scale inherent in the use of surface waves. mB  is based on the P and S waves, measured over a longer period, and does not saturate until around M 8. However, it is not sensitive to events smaller than about M 5.5. Use of mB  as originally defined has been largely abandoned, now replaced by the standardized mB$_{BB}$  scale.

#### mb scale

The mb or m$_b$ scale (lowercase "m" and "b") is similar to mB , but uses only P waves measured in the first few seconds on a specific model of short-period seismograph. It was introduced in the 1960s with the establishment of the World-Wide Standardized Seismograph Network (WWSSN); the short period improves detection of smaller events, and better discriminates between tectonic earthquakes and underground nuclear explosions.
Measurement of mb  has changed several times. As originally defined by Gutenberg (1945c) m$_b$ was based on the maximum amplitude of waves in the first 10 seconds or more. However, the length of the period influences the magnitude obtained. Early USGS/NEIC practice was to measure mb  on the first second (just the first few P waves), but since 1978 they measure the first twenty seconds. The modern practice is to measure short-period mb  scale at less than three seconds, while the broadband mB$_{BB}$  scale is measured at periods of up to 30 seconds.

#### mb$_{Lg}$ scale

The regional mb$_{Lg}$ scale – also denoted mb_Lg, mbLg, MLg (USGS), Mn, and m$_N$ – was developed by Nuttli (1973) for a problem the original M$_L$ scale could not handle: all of North America east of the Rocky Mountains. The M$_L$ scale was developed in southern California, which lies on blocks of oceanic crust, typically basalt or sedimentary rock, which have been accreted to the continent. East of the Rockies the continent is a craton, a thick and largely stable mass of continental crust that is largely granite, a harder rock with different seismic characteristics. In this area the M$_L$ scale gives anomalous results for earthquakes that by other measures seemed equivalent to quakes in California.
Nuttli resolved this by measuring the amplitude of short-period (~ 1 second) Lg waves, a complex form of the Love wave that, although a surface wave, he found provided a result more closely related to the mb  scale than the M$_s$  scale. Lg waves attenuate quickly along any oceanic path, but propagate well through the granitic continental crust, and Mb$_{Lg}$ is often used in areas of stable continental crust; it is especially useful for detecting underground nuclear explosions.

### Surface-wave magnitude scales

Surface waves propagate along the Earth's surface, and are principally either Rayleigh waves or Love waves. For shallow earthquakes the surface waves carry most of the energy of the earthquake, and are the most destructive. Deeper earthquakes, having less interaction with the surface, produce weaker surface waves.
The surface-wave magnitude scale, variously denoted as Ms, M$_S$, and M$_s$, is based on a procedure developed by Beno Gutenberg in 1942 for measuring shallow earthquakes stronger or more distant than Richter's original scale could handle. Notably, it measured the amplitude of surface waves (which generally produce the largest amplitudes) for a period of "about 20 seconds". The M$_s$  scale approximately agrees with M$_L$  at ~6, then diverges by as much as half a magnitude. A revision by Nuttli (1983), sometimes labeled M$_{Sn}$, measures only waves of the first second.
A modification – the "Moscow-Prague formula" – was proposed in 1962, and recommended by the IASPEI in 1967; this is the basis of the standardized M$_{s20}$ scale (Ms_20, M$_s$(20)). A "broad-band" variant (Ms_BB, M$_s$(BB)) measures the largest velocity amplitude in the Rayleigh-wave train for periods up to 60 seconds. The M$_{S7}$ scale used in China is a variant of M$_s$ calibrated for use with the Chinese-made "type 763" long-period seismograph.
The MLH scale used in some parts of Russia is actually a surface-wave magnitude.

### Moment magnitude and energy magnitude scales

Other magnitude scales are based on aspects of seismic waves that only indirectly and incompletely reflect the force of an earthquake, involve other factors, and are generally limited in some respect of magnitude, focal depth, or distance. The moment magnitude scale – Mw or M$_w$ – developed by seismologists Thomas C. Hanks and Hiroo Kanamori, is based on an earthquake's seismic moment, M$_0$, a measure of how much work an earthquake does in sliding one patch of rock past another patch of rock. Seismic moment is measured in newton-meters (N m or N⋅m) in the SI, or dyne-centimeters (dyn⋅cm; 1 dyn⋅cm = 10$^{−7}$ N⋅m) in the older CGS system. In the simplest case the moment can be calculated knowing only the amount of slip, the area of the surface ruptured or slipped, and a factor for the resistance or friction encountered. These factors can be estimated for an existing fault to determine the magnitude of past earthquakes, or what might be anticipated for the future.
An earthquake's seismic moment can be estimated in various ways, which are the bases of the M$_{wb}$, M$_{wr}$, M$_{wc}$, M$_{ww}$, M$_{wp}$, M$_i$, and M$_{wpd}$ scales, all subtypes of the generic M$_w$ scale. See Moment magnitude scale § Subtypes for details.
Seismic moment is considered the most objective measure of an earthquake's "size" in regard of total energy. However, it is based on a simple model of rupture, and on certain simplifying assumptions; it does not account for the fact that the proportion of energy radiated as seismic waves varies among earthquakes.
Much of an earthquake's total energy as measured by M$_w$  is dissipated as friction (resulting in heating of the crust). An earthquake's potential to cause strong ground shaking depends on the comparatively small fraction of energy radiated as seismic waves, and is better measured on the energy magnitude scale, M$_e$. The proportion of total energy radiated as seismic waves varies greatly depending on focal mechanism and tectonic environment; M$_e$  and M$_w$  for very similar earthquakes can differ by as much as 1.4 units.
Despite the usefulness of the M$_e$  scale, it is not generally used due to difficulties in estimating the radiated seismic energy.
Two earthquakes differing greatly in the damage done
In 1997 there were two large earthquakes off the coast of Chile. The magnitude of the first, in July, was estimated at M$_w$ 6.9, but was barely felt, and only in three places. In October a M$_w$ 7.1 quake in nearly the same location, but twice as deep and on a different kind of fault, was felt over a broad area, injured over 300 people, and destroyed or seriously damaged over 10,000 houses. As can be seen in the table below, this disparity of damage done is not reflected in either the moment magnitude (M$_w$ ) nor the surface-wave magnitude (M$_s$ ). Only when the magnitude is measured on the basis of the body-wave (mb ) or the seismic energy (M$_e$ ) is there a difference comparable to the difference in damage.
| Date | ISC # | Lat. | Long. | Depth | Damage | M$_s$ | M$_w$ | mb | M$_e$ | Type of fault |
| 06 July 1997 | 1035633 | −30.06 | −71.87 | 23 km | Barely felt | 6.5 | 6.9 | 5.8 | 6.1 | interplate-thrust |
| 15 Oct. 1997 | 1047434 | −30.93 | −71.22 | 58 km | Extensive | 6.8 | 7.1 | 6.8 | 7.5 | intraslab-normal |
| Difference: | | | | | | 0.3 | 0.2 | 1.0 | 1.4 |
Rearranged and adapted from Table 1 in Choy, Boatwright & Kirby 2001, p. 13. Seen also in IS 3.6 2012, p. 7.

### Energy class (K-class) scale

K (from the Russian word класс, 'class', in the sense of a category) is a measure of earthquake magnitude in the energy class or K-class system, developed in 1955 by Soviet seismologists in the remote Garm (Tajikistan) region of Central Asia; in revised form it is still used for local and regional quakes in many states formerly aligned with the Soviet Union (including Cuba). Based on seismic energy (K = log E$_S$, in Joules), difficulty in implementing it using the technology of the time led to revisions in 1958 and 1960. Adaptation to local conditions has led to various regional K scales, such as K$_F$ and K$_S$.
K values are logarithmic, similar to Richter-style magnitudes, but have a different scaling and zero point. K values in the range of 12 to 15 correspond approximately to M 4.5 to 6. M(K), M$_{(K)}$, or possibly M$_K$ indicates a magnitude M calculated from an energy class K.

### Tsunami magnitude scales

Earthquakes that generate tsunamis generally rupture relatively slowly, delivering more energy at longer periods (lower frequencies) than generally used for measuring magnitudes. Any skew in the spectral distribution can result in larger, or smaller, tsunamis than expected for a nominal magnitude. The tsunami magnitude scale, M$_t$, is based on a correlation by Katsuyuki Abe of earthquake seismic moment (M$_0$ ) with the amplitude of tsunami waves as measured by tidal gauges. Originally intended for estimating the magnitude of historic earthquakes where seismic data is lacking but tidal data exist, the correlation can be reversed to predict tidal height from earthquake magnitude. (Not to be confused with the height of a tidal wave, or run-up, which is an intensity effect controlled by local topography.) Under low-noise conditions, tsunami waves as little as 5 cm can be predicted, corresponding to an earthquake of M ~6.5.
Another scale of particular importance for tsunami warnings is the mantle magnitude scale, M$_m$. This is based on Rayleigh waves that penetrate into the Earth's mantle, and can be determined quickly, and without complete knowledge of other parameters such as the earthquake's depth.

### Duration and coda magnitude scales

M$_d$ designates various scales that estimate magnitude from the duration or length of some part of the seismic wave-train. This is especially useful for measuring local or regional earthquakes, both powerful earthquakes that might drive the seismometer off-scale (a problem with the analog instruments formerly used) and preventing measurement of the maximum wave amplitude, and weak earthquakes, whose maximum amplitude is not accurately measured. Even for distant earthquakes, measuring the duration of the shaking (as well as the amplitude) provides a better measure of the earthquake's total energy. Measurement of duration is incorporated in some modern scales, such as M$_{wpd}$  and mB$_c$ .
M$_c$ scales usually measure the duration or amplitude of a part of the seismic wave, the coda. For short distances (less than ~100 km) these can provide a quick estimate of magnitude before the quake's exact location is known.

### Macroseismic magnitude scales

Magnitude scales generally are based on instrumental measurement of some aspect of the seismic wave as recorded on a seismogram. Where such records do not exist, magnitudes can be estimated from reports of the macroseismic events such as described by intensity scales.
One approach for doing this (developed by Beno Gutenberg and Charles Richter in 1942) relates the maximum intensity observed (presumably this is over the epicenter), denoted I$_0$ (capital I with a subscripted zero), to the magnitude. It has been recommended that magnitudes calculated on this basis be labeled M$_w$(I$_0$), but are sometimes labeled with a more generic M$_{ms}$.
Another approach is to make an isoseismal map showing the area over which a given level of intensity was felt. The size of the "felt area" can also be related to the magnitude (based on the work of Frankel 1994 and Johnston 1996). While the recommended label for magnitudes derived in this way is M$_0$(An), the more commonly seen label is M$_{fa}$. A variant, M$_{La}$, adapted to California and Hawaii, derives the local magnitude (M$_L$) from the size of the area affected by a given intensity. M$_I$ (upper-case letter "I", distinguished from the lower-case letter in M$_i$) has been used for moment magnitudes estimated from isoseismal intensities calculated per Johnston 1996.
Peak ground velocity (PGV) and peak ground acceleration (PGA) are measures of the force that causes destructive ground shaking. In Japan, a network of strong-motion accelerometers provides PGA data that permits site-specific correlation with different magnitude earthquakes. This correlation can be inverted to estimate the ground shaking at that site due to an earthquake of a given magnitude at a given distance. From this a map showing areas of likely damage can be prepared within minutes of an actual earthquake.

### Other magnitude scales

Many earthquake magnitude scales have been developed or proposed, with some never gaining broad acceptance and remaining only as obscure references in historical catalogs of earthquakes. Other scales have been used without a definite name, often referred to as "the method of Smith (1965)" (or similar language), with the authors often revising their method. On top of this, seismological networks vary on how they measure seismograms. Where the details of how a magnitude has been determined are unknown, catalogs will specify the scale as "unknown" (variously Unk, Ukn, or UK). In such cases, the magnitude is considered generic and approximate.
An M$_h$ ("magnitude determined by hand") label has been used where the magnitude is too small or the data too poor (typically from analog equipment) to determine a Local magnitude, or multiple shocks or cultural noise complicates the records. The Southern California Seismic Network uses this "magnitude" where the data fail the quality criteria.
A special case is the Seismicity of the Earth catalog of Gutenberg & Richter (1954). Hailed as a milestone as a comprehensive global catalog of earthquakes with uniformly calculated magnitudes, they never published the full details of how they determined those magnitudes. Consequently, while some catalogs identify these magnitudes as M$_{GR}$, others use UK (meaning "computational method unknown"). Subsequent study found many of the M$_s$  values to be "considerably overestimated". Further study has found that most of the M$_{GR}$  magnitudes "are basically M$_s$  for large shocks shallower than 40 km, but are basically mB  for large shocks at depths of 40–60 km". Gutenberg and Richter also used an italic, non-bold M without subscript – also used as a generic magnitude, and not to be confused with the bold, non-italic M used for moment magnitude – and a "unified magnitude" m (bolding added). While these terms (with various adjustments) were used in scientific articles into the 1970s, they are now only of historical interest. An ordinary (non-italic, non-bold) capital "M" without subscript is often used to refer to magnitude generically, where an exact value or the specific scale used is not important.