Moment Magnitude

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					         What is Moment Magnitude?

L Braile, 1/26/2006
(revised, Sept., 2009)
       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)
 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:; for
information on AS-1 magnitudes, see:
                    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
                                                                   fault length
                                                                   (determined from
                                               Alaska, 1964
                                                                   aftershock zone
                                    Sumatra, 2004                  length) for various
Fault Length (km)

                                                                   earthquakes (Alaska,
                                                                   1964; Denali, 2002;
                                             Denali, 2002
                                                                   Landers, 1992; Loma
                                       Landers, 1992               Prieta, 1989;
                                                                   Northridge, 1994,
                                 Loma Prieta, 1989
                                                                   etc.). Results were
                                Northridge, 1994
                                                                   quickly obtained using
                            6   7        8          9         10
 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
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              

                                            For MS (20 s period waves)

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

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

                    AS-1 Magnitude
                                              mb magnitudes                 MS magnitudes

MS Magnitudes:                       6
N = 116; Standard
Deviation = 0.25
magnitude units.
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
                                    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
              AS-1 Magnitude        earthquakes
                                          mb magnitudes



                               4               mbLg magnitudes

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

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