Richter scale

The expression Richter magnitude scale refers to a number of ways to assign a single number to quantify the energy contained in an earthquake.

In all cases, the magnitude is a base-10 logarithmic scale obtained by calculating the logarithm of the amplitude of waves measured by a seismograph. An earthquake that measures 5.0 on the Richter scale has a shaking amplitude 10 times larger and corresponds to an energy release of √1000 ≈ 31.6 times greater than one that measures 4.0.^[1]

Development

Developed in 1935 by Charles Richter in partnership with Beno Gutenberg, both of the California Institute of Technology, the scale was firstly intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismograph. Richter originally reported values to the nearest quarter of a unit, but values were later reported with one decimal place. His motivation for creating the local magnitude scale was to compare the size of different earthquakes.^[1]

His inspiration was the apparent magnitude scale used in astronomy to describe the brightness of stars and other celestial objects.^[2] Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of 1 µm (0.00004 in) on a seismogram recorded using a Wood-Anderson torsion seismograph 100 km (62 mi) from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. The smallest earthquakes that could be recorded and located at the time were of magnitude 3, approximately. However, the Richter scale has no lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.

M_L (local magnitude) was not designed to be applied to data with distances to the hypocenter of the earthquake greater than 600 km^[3] (373 mi). For national and local seismological observatories the standard magnitude scale is today still M_L. Unfortunately this scale saturates at M6.5, approximately, because the high frequency waves recorded locally have wavelengths shorter than the rupture lengths of large earthquakes.

To be able to measure the size of earthquakes around the globe, Gutenberg and Richter later developed a magnitude scale based on surface waves, surface wave magnitude M_S; and another based on body waves, body wave magnitude m_b.^[4] These are types of waves that are recorded at teleseismic distances. The two scales were adjusted such that they were consistent with the M_L scale. This succeeded better with the M_s scale than with the m_b scale. Both of these scales saturate when the earthquake is bigger than magnitude 8 and therefore the moment magnitude scale, M_w, was invented.^[5]

These older magnitude scales have been superseded by the implementation of methods for estimating the seismic moment, creating the moment magnitude scale, although the former are still widely used because they can be calculated quickly.

Details

The Richter scale proper was defined in 1935 for particular circumstances and instruments; the instrument used saturated for strong earthquakes. The scale was replaced by the moment magnitude scale (MMS); for earthquakes adequately measured by the Richter scale, numerical values are approximately the same. Although values measured for earthquakes now are actually M_w (MMS), they are frequently reported as Richter values, even for earthquakes of magnitude over 8, where the Richter scale becomes meaningless. Anything above 5 is classed as a risk.^{[by whom?]}

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 than a much more energetic deep earthquake in an isolated area.

There are several scales which have historically been described as the "Richter scale," 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, and a couple of new techniques to measure magnitude are in the development stage.

All magnitude scales have been designed to give numerically similar results. This goal has been achieved well for M_L, M_s, and M_w.^[6][7] The m_b scale gives somewhat different values than the other scales. The reason for so many different ways to measure the same thing is that at different distances, for different hypocentral depths, and for different earthquake sizes, the amplitudes of different types of elastic waves must be measured.

M_L is the scale used for the majority of earthquakes reported (tens of thousands) by local and regional seismological observatories. For large earthquakes worldwide, the moment magnitude scale is most common, although M_s is also reported frequently.

The seismic moment, M_o, 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.^[8] A spectral analysis is required to obtain M_o, whereas the other magnitudes are derived from a simple measurement of the amplitude of a specifically defined wave.

All scales, except M_w, saturate for large earthquakes, meaning they are based on the amplitudes of waves which 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 6.5 and about 8 for M_s.^[9]

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,^[10] the other is based on a recently discovered channel wave.^[11]

The energy release of an earthquake, which closely correlates to its destructive power, scales with the ³⁄₂ power of the shaking amplitude. Thus, a difference in magnitude of 1.0 is equivalent to a factor of 31.6 ( = (10^1.0)^{(3 / 2)}) in the energy released; a difference in magnitude of 2.0 is equivalent to a factor of 1000 ( = (10^2.0)^{(3 / 2)} ) in the energy released.^[12] The elastic energy radiated is best derived from an integration of the radiated spectrum, but one can base an estimate on m_b because most energy is carried by the high frequency waves.

Richter magnitudes

This Article_is_incorrectly_mixing_Richter_magnitude_values_with_moment_magnitude_values's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced. See the relevant discussion on the talk page. (March 2011)

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). The original formula is:^[13]

where A is the maximum excursion of the Wood-Anderson seismograph, the empirical function A₀ depends only on the epicentral distance of the station, δ. In practice, readings from all observing stations are averaged after adjustment with station-specific corrections to obtain the M_L value.

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 31.6 times the amount of energy released, and each increase of 0.2 corresponds to a doubling of the energy released.

Events with magnitudes greater than about 4.6 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake's shadow.

The following describes the typical effects of earthquakes of various magnitudes near the epicenter. The values are typical only and 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, the depth of the earthquake's focus beneath the epicenter, and geological conditions (certain terrains can amplify seismic signals).

(Based on U.S. Geological Survey documents.)^[15]

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 of 9.5 on the moment magnitude scale.^[16]

Examples

The following table lists the approximate energy equivalents in terms of TNT explosive force – though note that the earthquake energy is released underground rather than overground.^[17] Most energy from an earthquake is not transmitted to and through the surface; instead, it dissipates into the crust and other subsurface structures. In contrast, a small atomic bomb blast (see nuclear weapon yield) will not simply cause light shaking of indoor items, since its energy is released above ground.

Following, 31.623 to the power of 0 equals 1, 31.623 to the power of 1 equals 31.623 and 31.623 to the power of 2 equals 1000. Therefore, an 8.0 on the Richter scale releases 31.623 times more energy than a 7.0 and a 9.0 on the Richter scale releases 1000 times more energy than a 7.0.

• Quakes using the more modern magnitude scales will denote their abbreviations: M_W and M_S. Those that have no denoted prefix are M_L. Please be advised that the magnitude "number" (example 7.0) displayed for those quakes on this table may represent a significantly greater or lesser release in energy than by the correctly given magnitude (example M_W).

Magnitude empirical formulae

These formulae are an alternative method to calculate Richter magnitude instead of using Richter correlation tables based on Richter standard seismic event (M_L=0, A=0.001mm, D=100km).

The Lillie empirical formula:

M_L = log ₁₀A − 2.48 + 2.76log ₁₀Δ

Where:

• A is the amplitude (maximum ground displacement) of the P-wave, in micrometers, measured at 0.8 Hz.
• Δ is the epicentral distance, in km.

For distance less than 200km:

M_L = log ₁₀A + 1.6log ₁₀D − 0.15

For distance between 200km and 600km:

M_L = log ₁₀A + 3.0log ₁₀D − 3.38

where A is seismograph signal amplitude in mm, D distance in km.

The Bisztricsany (1958) empirical formula for epicentral distances between 4˚ to 160˚:

Where:

• M_L is magnitude (mainly in the range of 5 to 8)
• τ is the duration of the surface wave in seconds
• Δ is the epicentral distance in degrees.

The Tsumura empirical formula:

Where:

• M_L is the magnitude (mainly in the range of 3 to 5).
• F − P is the total duration of oscillation in seconds.
• Δ is the epicentral distance in kilometers.

The Tsuboi, University of Tokio, empirical formula:

M_L = log ₁₀A + 1.73log ₁₀Δ − 0.83

Where:

• M_L is the magnitude.
• A is the amplitude in um.
• Δ is the epicentral distance in kilometers.

See also

• Earthquake
• Largest earthquakes by magnitude
• Seismic scale
• Seismite
• Mercalli intensity scale
• Moment magnitude scale
• Japan Meteorological Agency seismic intensity scale
• Order of magnitude
• Rohn Emergency Scale for measuring the magnitude (intensity) of any emergency

References

External links

• IRIS Real-time Seismic Monitor of the Earth
• USGS: magnitude and intensity comparison
• USGS: Earthquake Magnitude Policy
• USGS: 2000–2006 Earthquakes worldwide
• USGS: 1990–1999 Earthquakes worldwide
• Alaska Railroad Earthquake with a table of yield-to-magnitude relations.