L Braile, 1/26/2006(revised, Sept., 2009)

What is Moment Magnitude?

http://web.ics.purdue.edu/~braile/new/MomentMagnitude.ppt

Moment = Mo = µ A D (dyne-cm)µ = shear modulus ~ 32 GPa in crust (~3.2 x 1011 dynes/cm2), ~75 GPa in mantleA = LW = area (cm2)D = average displacement during rupture (cm)(http://neic.usgs.gov/neis/general/measure.html http://earthquake.usgs.gov/image_glossary/seismic_moment.html)

Moment Magnitude (Mw; also called Magnitude or M, as in, “an M8.0 earthquake”)

Epicenter (location on Earth’s surface above the hypocenter)

Focus or hypocenter(point of initiation of the rupture)

*

Then, the Moment Magnitude is calculated by: Mw (or just M) = 2/3 log10(Mo) - 10.7

Mo, and therefore Mw, can be determined by (µ is generally assumed to be ~3 x 1011 dynes/cm2): 1. Geological measurements of fault offset and fault mapping. 2. Estimates of fault area from the aftershock distribution and slip (from surface rupture). 3. Modeling of the waveforms of very long period seismograms to estimate fault slip, fault area and earthquake source mechanism (strike-slip, reverse fault, etc., and orientation of the fault plane).Except for very large earthquakes, other magnitude calculations (mb, MS, mbLg, ML [Richter magnitude]) generally provide a good estimate of Mw. (see:http://web.ics.purdue.edu/~braile/edumod/MagCalc/AS1Results.htm; for information on AS-1 magnitudes, see: http://web.ics.purdue.edu/~braile/edumod/as1mag/as1mag3.htm)

Magnitude of earthquake is controlled by fault length (or area) that ruptures (data for diagram generated using Seismic/Eruption program)

Magnitude versus fault length (determined from aftershock zonelength) for various earthquakes (Alaska, 1964; Denali, 2002; Landers, 1992; Loma Prieta, 1989; Northridge, 1994, etc.). Results were quickly obtained using Seismic/Eruption views.

Alaska, 1964

Denali, 2002

Landers, 1992

Sumatra, 2004

Magnitude versus fault length

Northridge, 1994Loma Prieta, 1989

Magnitude Comparison: Three earthquakes of M7.0, M8.1 and M9.0 recorded on an AS-1 Seismograph (WLIN) from about the same distance.

Format of Excel file used for cataloging AS-1 earthquake data (http://web.ics.purdue.edu/~braile/new/EarthquakeList.xls)

2/2401

Magnitude Comparison: Three earthquakes of M7.0, M8.1 and M9.0 recorded on an AS-1 Seismograph (WLIN) from about the same distance, plotted at the same scale.

2/24/01 M7.0 N. Molucca Sea

12/23/04 M8.1 Macquarie Is. Reg.

Relative Time (minutes)

12/26/04 M9.0 Sumatra

Note ~9 minutes of strong P wave energy caused by ~ 9 minutes of rupture propagation over the ~1200 km long fault plane.

AmplitudeFor mb

AmplitudeFor MS (20 s period waves)

Magnitude (M) – a consistent measure of size (energy release) of an earthquake. Should be able to be measured from many types of seismographs and for a large distance range from the earthquake. Calculated from amplitude on a seismogram with a correction for distance and the amplification of the seismograph. MS, mb, mbLg and ML generally approximate M.

To calculate distance, use:http://neic.usgs.gov/neis/travel_times/

http://web.ics.purdue.edu/~braile/edumod/MagCalc/MagCalc.htm

Online magnitude calculator for mb, MS and mbLg magnitudes for the AS-1 Seismograph:

Magnitude calculator in AmaSeis for mb, MS and mbLg magnitudes for the AS-1 Seismograph:

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mbLg magnitudes

mb magnitudes MS magnitudes

USGS (official) Magnitude

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MS Magnitudes: N = 116; Standard Deviation = 0.25 magnitude units.mb Magnitudes: N = 229; Standard Deviation = 0.27 magnitude units.mbLg Magnitudes: N = 27; Standard Deviation = 0.34 magnitude units.

Comparison of AS-1 and USGS Magnitudes

AS-1 magnitudes are accurate!

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9Comparison of AS-1 (mbLg, mb and MS) and USGS Mw Magnitudes

mbLg magnitudes

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USGS (official) Mw Magnitude

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Comparison of AS-1 and USGS Mw Magnitudes

AS-1 mb, MS and mbLg magnitudes correlate well with M (Mw, moment magnitude) except for the largest earthquakes