Moment magnitude scale


The moment magnitude scale abbreviated as MMS; denoted as MW or M is used by seismologists to measure the size of earthquakes in terms of the energy released[1]

The scale was developed in the 1970s to succeed the 1930s-era Richter magnitude scale ML Even though the formulas are different, the new scale retains a similar continuum of magnitude values to that defined by the older one As with the Richter magnitude scale, an increase of one step on this logarithmic scale corresponds to a 1015 about 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 103 1,000 times increase in energy Thus, an earthquake of MW of 70 releases about 32 times as much energy as one of 60 and 1,000 times that of 50

The magnitude is based on the seismic moment of the earthquake, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the fault and the size of the area that slipped[2]

Since January 2002, the MMS has been the scale used by the United States Geological Survey to calculate and report magnitudes for all modern large earthquakes[3]

Popular press reports of earthquake magnitude usually fail to distinguish between magnitude scales, and are often reported as "Richter magnitudes" when the reported magnitude is a moment magnitude or a surface-wave or body-wave magnitude Because the scales are intended to report the same results within their applicable conditions, the confusion is minor

Contents

  • 1 Historical context
    • 11 The Richter scale: a former measure of earthquake magnitude
    • 12 The modified Richter scale
    • 13 Correcting weaknesses of the modified Richter scale
    • 14 Recent research
  • 2 Definition
  • 3 Comparative energy released by two earthquakes
  • 4 Radiated seismic energy
  • 5 Nuclear explosions
  • 6 Comparison with Richter scale
  • 7 See also
  • 8 Notes
  • 9 References
  • 10 External links

Historical context

The Richter scale: a former measure of earthquake magnitude

Main article: Richter magnitude scale

In 1935, Charles Richter and Beno Gutenberg developed the local magnitude M L scale popularly known as the Richter scale with the goal of quantifying medium-sized earthquakes between magnitude 30 and 70 in Southern California This scale was based on the ground motion measured by a particular type of seismometer a Wood-Anderson seismograph at a distance of 100 kilometres 62 mi from the earthquake's epicenter[3] Because of this, there is an upper limit on the highest measurable magnitude, and all large earthquakes will tend to have a local magnitude of around 7[4] Further, the magnitude becomes unreliable for measurements taken at a distance of more than about 600 kilometres 370 mi from the epicenter Since this ML scale was simple to use and corresponded well with the damage which was observed, it was extremely useful for engineering earthquake-resistant structures, and gained common acceptance[5]

The modified Richter scale

Although the Richter scale represented a major step forward, it was not as effective for characterizing some classes of quakes As a result, Beno Gutenberg expanded Richter's work to consider earthquakes detected at distant locations For such large distances the higher frequency vibrations are attenuated and seismic surface waves Rayleigh and Love waves are dominated by waves with a period of 20 seconds which corresponds to a wavelength of about 60 km Their magnitude was assigned a surface wave magnitude scale MS Gutenberg also combined compressional P-waves and the transverse S-waves which he termed "body waves" to create a body-wave magnitude scale Mb, measured for periods between 1 and 10 seconds Ultimately Gutenberg and Richter collaborated to produce a combined scale which was able to estimate the energy released by an earthquake in terms of Gutenberg's surface wave magnitude scale MS[5]

Correcting weaknesses of the modified Richter scale

The Richter Scale, as modified, was successfully applied to characterize localities This enabled local building codes to establish standards for buildings which were earthquake resistant However a series of quakes were poorly handled by the modified Richter scale This series of "great earthquakes", included faults that broke along a line of up to 1000 km Examples include the 1952 Aleutian Fox Islands quake and the 1960 Chilean quake, both of which broke faults approaching 1000 km The MS scale was unable to characterize these "great earthquakes" accurately[5]

The difficulties with use of MS in characterizing the quake resulted from the size of these earthquakes Great quakes produced 20 s waves such that MS was comparable to normal quakes, but also produced very long period waves more than 200 s which carried large amounts of energy As a result, use of the modified Richter scale methodology to estimate earthquake energy was deficient at high energies[5]

In 1972, Keiiti Aki, a professor of Geophysics at the Massachusetts Institute of Technology, introduced elastic dislocation theory to improve understanding of the earthquake mechanism This theory proposed that the energy release from a quake is proportional to the surface area that breaks free, the average distance that the fault is displaced, and the rigidity of the material adjacent to the fault This is found to correlate well with the seismologic readings from long-period seismographs Hence the moment magnitude scale MW represented a major step forward in characterizing earthquakes[6]

Recent research

Recent research related to the moment magnitude scale has included:

  • Timely earthquake magnitude estimates to improve early warnings of earthquakes and tsunami Earthquake early warning systems are operating in Japan, Mexico, Romania, Taiwan, and Turkey and are being tested in the United States, Europe, and Asia These systems rely on a variety of analytic methods to attain an early estimate of the moment magnitude of a quake[7]
  • Efforts to extend the moment magnitude scale accuracy for high frequencies, which are important in localizing small quakes Earthquakes below magnitude 3 scale poorly because the earth attenuates high frequency waves near the surface, making it difficult to resolve quakes smaller than 100 meters By use of seismographs in deep wells this attenuation can be overcome[8]

Definition

The symbol for the moment magnitude scale is M w , with the subscript w meaning mechanical work accomplished The moment magnitude [9] M w is a dimensionless number defined by Hiroo Kanamori as

M w = 2 3 log 10 ⁡ M 0 − 107 , =\log _M_-107,

where M 0 is the seismic moment in dyne⋅cm 10−7 N⋅m[1] The constant values in the equation are chosen to achieve consistency with the magnitude values produced by earlier scales, such as the Local Magnitude and the Surface Wave magnitude

Comparative energy released by two earthquakes

As with the Richter scale, an increase of one step on this logarithmic scale corresponds to a 1015 ≈ 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 103 = 1000 times increase in energy Thus, an earthquake of MW of 70 contains 1000 times as much energy as one of 50 and about 32 times that of 60

The following formula, obtained by solving the previous equation for M 0 , allows one to assess the proportional difference f Δ E in energy release between earthquakes of two different moment magnitudes, say m 1 and m 2 :

f Δ E = 10 3 2 m 1 − m 2 =10^m_-m_

For example, an earthquake with a moment magnitude of 70 is approximately 562 times greater than a quake with moment magnitude 65

Radiated seismic energy

Potential energy is stored in the crust in the form of built-up stress During an earthquake, this stored energy is transformed and results in

  • cracks and deformation in rocks
  • heat
  • radiated seismic energy E s

The seismic moment M 0 is a measure of the total amount of energy that is transformed during an earthquake Only a small fraction of the seismic moment M 0 is converted into radiated seismic energy E s , which is what seismographs register Using the estimate

E s = M 0 ⋅ 10 − 48 = M 0 ⋅ 16 × 10 − 5 , =M_\cdot 10^=M_\cdot 16\times 10^,

Choy and Boatwright defined in 1995 the energy magnitude [10]

M e = 2 3 log 10 ⁡ E s − 29 =\textstyle \log _E_ -29

where E s is in Nm

Nuclear explosions

The energy released by nuclear weapons is traditionally expressed in terms of the energy stored in a kiloton or megaton of the conventional explosive trinitrotoluene TNT

A rule of thumb equivalence from seismology used in the study of nuclear proliferation asserts that a one kiloton nuclear explosion creates a seismic signal with a magnitude of approximately 40[11] This in turn leads to the equation[12]

M n = 2 3 log 10 ⁡ m T N T Mt + 6 , =\textstyle \displaystyle \log _ +6,

where m T N T is the mass of the explosive TNT that is quoted for comparison relative to megatons Mt

Such comparison figures are not very meaningful As with earthquakes, during an underground explosion of a nuclear weapon, only a small fraction of the total amount of energy released ends up being radiated as seismic waves Therefore, a seismic efficiency needs to be chosen for the bomb that is being quoted in this comparison Using the conventional specific energy of TNT 4184 MJ/kg, the above formula implies that about 05% of the bomb's energy is converted into radiated seismic energy E s [13] For real underground nuclear tests, the actual seismic efficiency achieved varies significantly and depends on the site and design parameters of the test

Comparison with Richter scale

Main article: Richter magnitude scale

The moment magnitude M w scale was introduced in 1979 by Caltech seismologists Thomas C Hanks and Hiroo Kanamori to address the shortcomings of the Richter scale detailed above while maintaining consistency Thus, for medium-sized earthquakes, the moment magnitude values should be similar to Richter values That is, a magnitude 50 earthquake will be about a 50 on both scales This scale was based on the physical properties of the earthquake, specifically the seismic moment M 0 Unlike other scales, the moment magnitude scale does not saturate at the upper end; there is no upper limit to the possible measurable magnitudes However, this has the side-effect that the scales diverge for smaller earthquakes[1]

The concept of seismic moment was introduced in 1966,[14] but it took 13 years before the M w scale was designed The reason for the delay was that the necessary spectra of seismic signals had to be derived by hand at first, which required personal attention to every event Faster computers than those available in the 1960s were necessary and seismologists had to develop methods to process earthquake signals automatically In the mid-1970s Dziewonski[15] started the Harvard Global Centroid Moment Tensor Catalog[16] After this advance, it was possible to introduce M w and estimate it for large numbers of earthquakes

Moment magnitude is now the most common measure for medium to large earthquake magnitudes,[17] but breaks down for smaller quakes For example, the United States Geological Survey does not use this scale for earthquakes with a magnitude of less than 35, which is the great majority of quakes

Magnitude scales differ from earthquake intensity, which is the perceptible shaking, and local damage experienced during a quake The shaking intensity at a given spot depends on many factors, such as soil types, soil sublayers, depth, type of displacement, and range from the epicenter not counting the complications of building engineering and architectural factors Rather, magnitude scales are used to estimate with one number the size of the quake

The following table compares magnitudes towards the upper end of the Richter Scale for major Californian earthquakes[1][18]

Date Seismic moment M 0 × 10 25 \times 10^ dyne-cm Richter scale M L Moment magnitude M w
1933-03-11 2 63 62
1940-05-19 30 64 70
1941-07-01 09 59 60
1942-10-21 9 65 66
1946-03-15 1 63 60
1947-04-10 7 62 65
1948-12-04 1 65 60
1952-07-21 200 72 75
1954-03-19 4 62 64

See also

  • Earthquake engineering
  • Geophysics
  • List of earthquakes
  • Other seismic scales
  • Surface wave magnitude

Notes

  1. ^ a b c d Hanks, Thomas C; Kanamori, Hiroo May 1979 "Moment magnitude scale" PDF Journal of Geophysical Research 84 B5: 2348–50 Bibcode:1979JGR842348H doi:101029/JB084iB05p02348 Archived from the original on August 21, 2010  CS1 maint: Unfit url link
  2. ^ "Glossary of Terms on Earthquake Maps" USGS Retrieved 2009-03-21 
  3. ^ a b "USGS Earthquake Magnitude Policy implemented on January 18, 2002" 
  4. ^ "On Earthquake Magnetudes" 
  5. ^ a b c d Hiroo Kanamori, 1978, Quantification of Earthquakes, Nature 271, 411-414 doi:101038/271411a0
  6. ^ K Aki; Earthquake Mechanism; Tectonophysics; Elsevier BV; Vol 13, pages 423-446
  7. ^ Caprio, M, M Lancieri, G B Cua, A Zollo, and S Wiemer 2011, An evolutionary approach to real-time moment magnitude estimation via inversion of displacement spectra, Geophys Res Lett, 38, L02301, doi:101029/2010GL045403
  8. ^ Abercrombie, R E; Earthquake source scaling relationships from -1 to 5 using seismograms recorded at a 25 km depth; Journal of Geophysical Research, Vol 100, No B12, p 24, 015-24, 036, 1995
  9. ^ Hiroo Kanamori, 1977, The energy release in great earthquakes Journal of geophysical research, 8220, 2981-2987
  10. ^ Choy, George L; Boatwright, John L 1995, "Global patterns of radiated seismic energy and apparent stress", Journal of Geophysical Research, 100 B9: 18205–28, Bibcode:1995JGR10018205C, doi:101029/95JB01969 
  11. ^ "Nuclear Testing and Nonproliferation", "Chapter 5: Assessing Monitoring Requirements"
  12. ^ "Nevada Seismological Lab" 
  13. ^ Q: How much energy is released in an earthquake
  14. ^ Aki, Keiiti 1966 "4 Generation and propagation of G waves from the Niigata earthquake of June 14, 1964 Part 2 Estimation of earthquake moment, released energy and stress-strain drop from G wave spectrum" PDF Bulletin of the Earthquake Research Institute 44: 73–88 
  15. ^ Dziewonski, A M; Gilbert, F 1976 "The effect of small aspherical perturbations on travel times and a re-examination of the corrections for ellipticity" Geophys J R Astron Soc 44 1: 7–17 Bibcode:1976GeoJI447D doi:101111/j1365-246X1976tb00271x 
  16. ^ "Global Centroid Moment Tensor Catalog" Globalcmtorg Retrieved 2011-11-30 
  17. ^ Boyle, Alan May 12, 2008 "Quakes by the numbers" MSNBC Retrieved 2008-05-12 That original scale has been tweaked through the decades, and nowadays calling it the "Richter scale" is an anachronism The most common measure is known simply as the moment magnitude scale 
  18. ^ "Upper end magnitudes comparison" Fxsolver

References

  • Utsu, T 2002 Lee, WHK; Kanamori, H; Jennings, PC; Kisslinger, C, eds "Relationships between magnitude scales" International Handbook of Earthquake and Engineering Seismology International Geophysics Academic Press, a division of Elsevier A 81: 733–46 

External links

  • USGS: Measuring earthquakes
  • Earthquake Energy Calculator with seismic energy approximated in everyday equivalent measures


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