# Moment Magnitude

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```					         What is Moment Magnitude?

L Braile, 1/26/2006
(revised, Sept., 2009)
http://web.ics.purdue.edu/~braile/new/MomentMagnitude.ppt
Moment Magnitude (Mw; also called
Magnitude or M, as in, “an M8.0 earthquake”)
Focus or hypocenter
(point of initiation       Epicenter (location on Earth’s surface
of the rupture)            above the hypocenter)
*

Moment = Mo = µ A D (dyne-cm)
µ = shear modulus ~ 32 GPa in crust (~3.2 x 1011 dynes/cm2),
~75 GPa in mantle
A = 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)
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
Magnitude versus Fault Length
generated using Seismic/Eruption program)
Magnitude versus fault length  Magnitude versus
10000
fault length
(determined from
aftershock zone
Sumatra, 2004                  length) for various
Fault Length (km)

1000
1964; Denali, 2002;
Denali, 2002
Landers, 1992; Loma
Landers, 1992               Prieta, 1989;
100
Northridge, 1994,
Loma Prieta, 1989
etc.). Results were
Northridge, 1994
quickly obtained using
Seismic/Eruption
10
views.
6   7        8          9         10
Magnitude
Magnitude Comparison: Three earthquakes of M7.0,
M8.1 and M9.0 recorded on an AS-1 Seismograph (WLIN)

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.

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

12/26/04 M9.0 Sumatra

Relative Time (minutes)
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.

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

Amplitude
For MS (20 s period waves)
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:
Comparison of AS-1 and USGS Magnitudes
9

Comparison                                AS-1 magnitudes are accurate!
of AS-1 and                          8
USGS
Magnitudes                           7

AS-1 Magnitude
mb magnitudes                 MS magnitudes

MS Magnitudes:                       6
N = 116; Standard
Deviation = 0.25
magnitude units.
5
mb Magnitudes:
N = 229; Standard
Deviation = 0.27
4             mbLg magnitudes
magnitude units.
mbLg Magnitudes:
N = 27; Standard
Deviation = 0.34                     3
3       4       5        6        7         8         9
magnitude units.                                   USGS (official) Magnitude
Comparison of AS-1 (mbLg, mb and MS) and USGS Mw Magnitudes
9
AS-1 mb, MS and
Comparison                          mbLg magnitudes
correlate well with M
of AS-1 and                    8
(Mw, moment
MS magnitudes
USGS Mw                             magnitude) except for
Magnitudes                          the largest
7
AS-1 Magnitude        earthquakes
mb magnitudes

6

5

4               mbLg magnitudes

3
3        4       5        6        7        8   9
USGS (official) Mw Magnitude

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