Magnitud
Stein & Wysession: pp. 263-266
Richter Measurements
*Wood Anderson Standard Torsion Seismometer
*Earthquakes recorded in S. California at distances < 600 km
*Amplitude measured in millimeters
Richter Magnitude, ML
Set reference event :
amplitude of 1 micron (10-3 mm) at a distance of
100 km from the recording station
Magnitude Scale :
ML = log(At) – log A0
where:
At = Peak amplitude from seismogram (in mm)
A0 = Amp for reference event at same distance
Local Magnitude, ML
Southern California
Other Magnitudes

The two most common magnitude
scales:
MS, Surface-wave magnitude (Rayleigh Wave)
 mb, Body-wave magnitude (P-wave)

Body-Wave Magnitude
Measured Phase: P
0.1 - 3.0 sec period
Applicable Range
Δ = 5 - 95 deg
EQ Depth: 0 to 700 km
Surface-Wave Magnitude
Applicable Range
Δ = 20 - 160 deg
EQ Depth < 50 km
Magnitude: Average Value
In practice, the magnitude
assigned to an earthquake
corresponds to the average of the
values calculated at different sites
However, amplitudes recorded at
different azimuths vary due to
seismic-wave radiation pattern
Ideally, magnitudes should be
calculated at all azimuths to
minimize errors in assigned value
(error ~ 0.3 mag units)
Magnitude Properties
• Independent of station location
• Based on amplitude of recorded phase
• Logarithmic: 10-fold increase in ground
motion amplitude corresponds to unitary
increase in magnitude
• Open-ended: No minimum or maximum
General Classification
•
•
•
•
•
Small
Moderate
Strong
Major
Great
mag < 5
5 < mag < 5.9
6 < mag < 6.9
7 < mag < 7.9
mag >= 8
Disagreement in Magnitude Scales
Differences between magnitudes obtained
using different scales are due to:
– Variations in magnitude assignment due to
incomplete azimuthal coverage (+/- 0.3 units)
– Magnitude saturation:
There is an upper limit to magnitude due to
“saturation”. For instance, Ms is limited to
values of ~8.3-8.5 and mb is seldom above 7.0
Example: mb “Saturation”

mb is measured in
the first 5 seconds

P amplitudes in
this time interval
do not increase
proportionately to
earthquake size

P-wave does not
identify real
earthquake size
above mb ~6.2
Saturation
mb saturates at ~ 6.5
MS saturates at ~ 8.0
Amplitude Variations
Amplitudes depend on:
- size of the earthquake
- station location relative to radiation pattern
- distance from the source
- source depth
Amplitudes also vary with the frequency of the
generated wave. These frequencies are
different for different rupture dimensions and
durations.
What Causes Saturation?

The rupture process.
– Small earthquakes rupture small areas and the seismic
waves are relatively enriched in short period signals.
– Large earthquakes rupture large areas and the seismic
waves are relatively depleted in high frequencies.
Seismic Moment
gives more
accurate
representation of
earthquake size,
since it takes into
account the actual
displacement over
the rupture area
(Units: dyne-cm,
newton-meters)
Mo = (shear rigidity) x (rupture area) x (average slip)
Moment Magnitude, MW
Magnitude scale based on the seismic
moment M0.
MW = log(M0) / 1.5 - 10.73
Magnitude value related to rupture
process
 Does not saturate
 Requires detailed analysis of
seismograms to compute M0

Moment Magnitude
Sumatra, 26 dec 2004
Sumatra, 28 mar 2005
Peru, 15 aug 2007
7.0 mb
7.2 mb
---
8.8 Ms
8.5 Ms
7.7 Ms
9.3 Mw
8.7 Mw
8.0 Mw
Summary
•
Magnitude is a measure of ground shaking amplitude.
Summary
•
Magnitude is a measure of ground shaking amplitude.
•
More than one magnitude scale is used to study
earthquakes.
•
All magnitude scales have the same logarithmic form.
•
Since different scales use different waves and different
period vibrations, they do not always give the same value.
Magnitude
Symbol
Local (Richter) ML
Body-Wave
mb
Surface-Wave
Ms
Moment
Mw
Basis
S or Surface-wave amp
P-wave amp
Rayleigh-wave amp
Rupture Area, Slip
Period
0.8 s
1s
20 s
> TR