MAGNITUDE OF EARTHQUAKE:
The magnitude of earthquake is a measure of the amount of
energy released.
It is actually a measure of earthquake size and is determined
from the logarithm of the maximum displacement or amplitude of the earthquake
signal as seen on the seismogram, with a correction for the distance between
the focus and seismometer.
Earthquake magnitudes are based on direct measurement of size
amplitude of seismic waves, made with recording instruments.
The total energy released by an earthquake can be calculated
from the amplitude of waves and distance from epi-center.
The amount of ground shaking is related to the magnitude of
earthquake
Earthquake magnitude and most often reported using the
RICHTER magnitude scale.|
Amplitude: Amplitude of a wave is its maximum disturbance
from its undisturbed position
 |
The Richter magnitude is based on the energy release of
earthquake which is closely related to the length of the fault on which
slippage occurs.
A magnitude number is assigned to an earthquake on the basis
of the amount of ground displacement or vibration procedures as measured by
seismograph.
The Richter scale is a logarithmic scale, meaning that an
earthquake of magnitude 4 causes 10 times as much as one of the magnitude 2 and
so on.
To say simply, the magnitude ‘x’ is 33 times more than
previous one.
Fig: Richter scale graphic
representation
Technically there is no upper limit for Richter scale.
It must be noted that the Richter scale number is not a good
measure of damage potential of an earthquake the longer duration of shaking may
produce greater damage.
MEASUREMENT OF MAGNITUDE:
The magnitude (M) of the earthquake is given by |
M =
log10(A)
|
Where,
A= Maximum amplitude (µm) at
a point 100km from epicenter
However a standard seismometer is not always set at a point
100km from the epi-center in which case one may use the logarithmic form of
Richter magnitude scale, ‘M’ is given as|
M =
log10(A) - log10
(A0)
|
Where,
A0 à
Amplitude for a particular earthquake selected as standard
A
à
Maximum recorded trace amplitude for a given earthquake at a distance.
We have another equation to calculate the
magnitude using special factors, which is better than previous one. Because the
magnitude is a measure of seismic energy related, which is proportional to A/T.|
M =
log10(A/T)max
+ σ(δ, h) + Cr +
Cs
|
Where,
A
= Ground displacement amplitude
T=
Time period of considered wave
σ(δ, h) =
Distance correction factor at epi central distance (δ) and focal depth (h)
δ
= Epicentral distance
h
= Focal depth
Cr=
Regional source correction factor
Cr
= Station correction factor.
The Magnitude can also be expressed in terms of
length of fault line ‘L’ as|
M =
0.98 log10 (L) + 5.65
|
Where, L = Length of fault line.
The Magnitude in terms of slip ‘U’ in the fault
line can be given as|
M = 1.32 log10
(U) + 4.27
|
Where, U = Slip in the fault line
The value of surface wave magnitude is given by |
M = log10
(As/T)max
+ 1.66 log10
δ +
3.3
|
Where,
As
à
Amplitude of horizontal ground motion in μm.
T
à
Time period (20±2 s)
δ
à
Epicentral distance indegrees
Body wave Magnitude is given by equation |
Mb =
log (As/T)max
+ σ(δ, h)
|
Where,
σ(δ,
h) à
correction factor
δ
à
Epi central distance
h
à
Focal depth
Gutenberg and Richter have given following
relationship between energy of seismic waves and magnitude of surface waves, Ms.|
Log10(E) =
4.4 + 1.5 Ms
|
Where,
E
à
Energy of seismic wave
Ms
à
Magnitude of surface wave
-
All the magnitudes numerically give similar
results.
- Additional magnitude scales such as moment magnitude (Mw) have been introduced to improve the standards.
-
The moment magnitude may be calculated using the
relationship given by Kanamore.
|
M =
2/3 [log10(M0 – 16)
|
Where,
Mw
à
Moment magnitude
M0
à
Seismic moment in (dyne-cm)
M0
= μAd
A
à
Area of rupture
d
à
Displacement
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