Earthquake Magnitude, Energy and
Intensity
Imtiyaz A. Parvez
C-MMACS, Bangalore
Imtiyaz A. Parvez, C-MMACS
1
Magnitude and Energy of Earthquakes
Once the earthquake is located, the next question
comes, what is the size of the earthquake, how much
energy released during the earthquake??
The concept of magnitude was introduced by Charles
Richter in 1935 at the California Institute of Technology
to provide an objective instrumental measure of the size
of earthquakes.
According to Richter, the local magnitude is the logarithm
of the maximum seismic wave amplitude, Ao (in µm),
measured on a seismogram made by a standard torsion
horizontal-component Wood-Anderson seismograph
located 100 km from the epicentre.
Imtiyaz A. Parvez, C-MMACS
2
ML =log [A(∆)/Ao(∆)]
or
ML =log A(∆) - log Ao(∆)
∆ is the epicentral distance and Ao and A are respectively the
maximum trace (recorded) amplitudes, written by a standard seismograph, of the standard event and of a given earthquake which
occurred at a known distance.
The standard earthquake i.e. ML = 0
at a distance of 100 km
maximum trace amplitude = 1 µm
Imtiyaz A. Parvez, C-MMACS
3
Richter’s empirical attenuation formula for southern California
Log A0 = 6.37 - 3 log (∆)
Bullen and Bolt (1985) refer to a slightly different amplitudedistance dependence
Log A0 = 5.12 - 2.56 log (∆)
Further, taking into account the magnification of 2800 for the
instrument, maximum trace amplitude A can be replaced by
actual ground amplitude a
Log A = log (2800 a)
Introducing the above equations, we obtain
ML =log a + 3 log (∆) -2.92
ML =log a + 2.56 log (∆) -1.67
Imtiyaz A. Parvez, C-MMACS
4
It was difficult to extend the amplitude-distance
dependence to distances much beyond 600 km for the
area of California. Hence ML magnitude was designed
to measure only the local or regional events and used
nonspecified wave types.
Then, Gutenberg (1945) extended the magnitude concept
to teleseismic distances and special wave types. He
developed the magnitude MS using 20-sec surface waves
from shallow earthquakes measured within the epicentral
distance from 15º to 130º.
The Ms scale was adjusted to give roughly a continuation
of ML for large-distance events.
MS =log A + 1.656 log (∆
∆) -1.818
Imtiyaz A. Parvez, C-MMACS
5
Gutenberg (1945) also introduced the concept of bodywave magnitude, mb, based on recorded P, PP and S
waves from shallow earthquakes. He observed that the
relative dependence of the ratio (A/T) for the three
phases remains roughly constant for a relatively broad
range of periods.
The formula introduced by Gutenberg has the form:
mb =log (A/T) + q(∆
∆) + 0.1(mb-7) +Cr
q(∆)
the amplitude-distance correction term constructed by theory
and observations and comprises correction for both geometrical
spreading and anelastic absorption.
Cr
an empirically determined station correction.
(mb-7) included in order to achieve agreement between mb and Ms
Imtiyaz A. Parvez, C-MMACS
6
In 1955, Gutenberg and Richter presented improved empirical
calibration functions and the body-wave magnitude mb is now
evaluated through a simplified formula
mb =log (A/T) + Q(∆
∆,h)
•Q(∆,h), the distance-depth correction factors are available in
tabular form for shallow shocks in the distance range 16º -170º
•For earthquakes with focal depths down to 700 km, Q(∆,h) are
available in diagrams covering the distance range 5º -110º
One important note is that the two magnitudes, mb and MS
are not compatible, which means that they cannot be made to
agree in their entire extent
Imtiyaz A. Parvez, C-MMACS
7
For shallow events, the following formulae have been found
empirically
mb = 0.63 MS + 2.5
MS = 1.59 mb - 3.97
Important to note that two values agree at mb = MS = 6.75
Above this Ms > mb
Below it
M s < mb
In 1950’s and 1960’s, magnitude formulae of Gutenberg and
Richter have been frequently used at individual seismograph
stations seismological laboratories, networks and agencies
around the world.
Imtiyaz A. Parvez, C-MMACS
8
The IASPEI Committee on Magnitude, met in Zurich, Switzerland
in 1967 and recommended the use standardized calibration
formula.
The Zurich recommendation for the surface-wave magnitude is
MS =log (A/T)max + 1.66 log(∆
∆) + 3.3
Where (A/T)max refers to the horizontal-component Rayleigh waves,
A
is the trace amplitude in µm
T
17-23 s (some authors use 18-22, 10-60 as well)
∆
20º - 160º
This formulae is commonly known as Moscow-Prague formula and
is applicable for the depth ≤ 50 km. It is possible to correct Ms for
focal depth using the depth correction suggested by Bath (1981)
Imtiyaz A. Parvez, C-MMACS
9
As far as body-wave magnitude is concerned, the Zurich
recommendation reads
mb =log (A/T)max + σ(∆
∆,h)
Where,
σ(∆,h) = 1.66log ∆ + 3.3
(A/T)max is determined for all wave types (PZ, PH, PPZ,
PPH, SH) for which the calibrating function σ(∆,h) are
available
Due to the finite bandwidth of instrumentation used at curren
seismographic stations, saturation effects influences both the MS
and Mb magnitudes at certain level.
For e.g. Ms saturates after 7 and mb after 6 to 6.5
Imtiyaz A. Parvez, C-MMACS
10
Saturation of magnitude scales
According to Brune (1970), the far field body-wave displacement
spectrum can be approximated by a constant long-period level
(Ωº) and a high frequency decay for frequencies above corner
frequency,fº.
Ωº and fº. are related, in a relatively simple manner, to the
seismic moment scalar Mo , fault length L and stress drop (∆σ).
Mo is proportional to Ωº while L is inversely proportional to fº.
As the first approximation, it can be assumed that log Mo be
linearly related to any magnitude
Imtiyaz A. Parvez, C-MMACS
11
Imtiyaz A. Parvez, C-MMACS
12
Moment magnitude (MW)
Recently developed alternative to the Richter scale used to measure
more accurately the amount of energy released by large earthquakes
and has no problem of saturation.
This scale involves measurement of an earthquake's seismic moment.
Hanks and Kanamori (1979) suggested the use of moment magnitude.
The basic idea was to determine the magnitude from an estimate of the
radiated energy obtained from a magnitude independent relation. They
show that the radiated energy;
ES = (∆σ
∆σ/2µ
∆σ µ)/ Mo
Where ∆σ
µ
stress drop
rigidity or shear modulus
Imtiyaz A. Parvez, C-MMACS
13
Taking e.g. the rigidity to be 5 x 107 dyne/cm2 and assumig the
constancy of the stress drop for crust-upper mantle, say 50 bars,
the previous equation reduces to
ES = (1/2 x 104)/ Mo
Now, there are ways to find out either Mo or Es either by displacement spectra or by waveform modelling
For example;
or
Ωo
3
Mo =
4πRρv
Rφ
Keilis-Borok, 1959
Log Es = 1.5 MS + 11.8 (erg)
Gutenberg-Richter relation
Imtiyaz A. Parvez, C-MMACS
14
Using the previous equations, moment magnitude is defined as
Log Mo = 1.5 MW + 16.1
Which is remarkably coincident with several relationships
defined empirically by other workers. In contrast to various
magnitude mentioned, Mw is frequently used by the seismolo
-gical community to evaluate especially large magnitude.
Ms, Mo and MW for four great events (Bullen & Bolt, 1985)
Date
Region
Ms
1952, Nov 4
1957, Mar 9
1960, May 22
1964, Mar 28
Kamchatka
Aleutian Is.
Chile
Alaska
8.25
8.25
8.3
8.4
Mo
x 1027 dyme cm
350
585
2000
820
Imtiyaz A. Parvez, C-MMACS
Mw
9.0
9.1
9.5
9.2
15
Earthquake Intensity
The intensity of an earthquake is a measure of the destructive
effects of the quake at the surface. It is measured on an arbitrary
scale of 12 degrees modified from an original scale devised by
the Italian seismologist Giuseppe Mercalli. The scale uses
information supplied by people living in the area of the quake.
Intensity
I
II
The Modified Mercalli Intensity Scale
Description
Characteristic effects
Instrumental
Feeble
Not felt by people, only detected by
seismographs
Felt only by a few people at
rest,especially on upper floors of
buildings. Delicately suspended objects
may swing.
Imtiyaz A. Parvez, C-MMACS
16
Intensity
Description
Characteristic effects
III
Slight
Felt noticeably indoors; like the
vibrations due to a passing truck.
Standing motor cars may rock slightly.
IV
Moderate
Felt indoors by many people, outdoors
by few. Dishes, windows, doors rattle.
May awaken some sleepers. Standing
cars rocked noticeably.
V
Rather strong
Felt by nearly everyone, many
awakened. Some dishes and windows
broken; occasional cracked plaster;
unstable objects overturned. Some
disturbance of trees, poles and other
tall objects.
Imtiyaz A. Parvez, C-MMACS
17
Intensity
Description
Characteristic effects
VI
Strong
Felt by all; many frightened and run
outdoors. Some heavy furniture
moved; some falling plaster or
damaged chimneys.Damage slight.
VII
Very strong
General alarm; people run outside.
Walls crack; chimneys fall.
Considerable damage in poorly
designed structures. Noticed by
persons in moving vehicles
VIII
Destructive
Considerable damage in ordinary
substantial buildings with partial
collapse. Fall of chimneys, factory
stacks, columns, monuments, walls.
Heavy furniture overturned. Changes
in well water. Car drivers seriously
disturbed.
Imtiyaz A. Parvez,
C-MMACS
18
Intensity
Description
Characteristic effects
IX
Ruinous
Considerable damage with partial
collapse of substantial buildings.
Buildings moved off foundations;
ground cracks conspicuous.
Underground pipes broken.
X
Disastrous
Ground cracks badly; landslides on
river banks and steep slopes; rails
bent; many buildings destroyed.
XI
Very disastrous
Broad fissures in ground; major
landslides and earth slumps; floods.
Few buildings remain standing;
bridges destroyed; nearly all services
(railways, underground pipes, cables)
out of action.
XII
Catastrophic
Total destruction. Ground rises and
falls in waves; lines of sight and level
distorted.
Imtiyaz A. Parvez,
C-MMACS Objects thrown into the
19 air.
The earthquake intensity felt at a location depends not only on the magnitude of
the quake but also on the distance from the epicentre, depth of the focus, and on
local surface and subsurface geological conditions. The intensity decreases
outwards from the source, areas of similar intensity forming a roughly circular
pattern around the epicentre.
Imtiyaz A. Parvez, C-MMACS
20