In the early days of earthquake studies, the effects it produced at different
places (varying from minor vibrations to large-scale destruction) formed the
basis of determining the severity of the earthquake. Depending on the observed
effects, earthquake intensities were assigned at places of observation.
Intensity varied from place to place, and normally decreased with increase in
distance from the epicenter. Intensities were based on observational data alone,
and were subjective (not based on measurement). In 1935 Charles F. Richter
introduced the magnitude scale for measuring earthquakes on the basis of the
size of the seismograms. Richter defined magnitude of an earthquake in terms of
the amplitude of the trace in a seismogram recorded by a standard Wood Anderson
seismograph (natural period 0.8 sec., damping 0.8 of critical and magnification
2800) as follows:

**M _{L} =
Log _{10} A – Log _{10 }A_{0 }**

Here
A is the maximum amplitude of the trace measured in microns and A_{0} is
the trace amplitude for the zero magnitude shock at that distance. M_{L}
was called **Local Magnitude**. According
to Richter the trace amplitude from a magnitude 3 earthquake in California at
100 km was about 1 mm. Richter
empirically determined the value of Log_{10}A_{0 }for the
Californian region. For distances between 100 and 500 km, Log_{10}A_{0
}varied between –3 and –4.8. These
values are listed in Table-2 below. During strong shallow focus earthquakes most
of the damage, which is inflicted by the earthquake, is due to surface waves.
Gutenberg and Richter defined Surface Wave Magnitude, M_{s}, of an
earthquake by a similar relationship except that, to account for of the
dispersive nature of the surface waves, the amplitude measurement was
standardized at 20 seconds period of the wave.
M_{s }is determined for teleseisms only. Again, it is not always
possible to measure amplitude at the specified period of 20 seconds because of
the dispersive nature of the surface waves. To overcome this difficulty
Gutenberg gave a general formula:

**M _{s} = Log _{10} (A) +1.656 Log _{10
}(**

Where
A is the maximum amplitude of the ground displacement for the horizontal
component of motion measured in microns for surface waves between 17 and 23
seconds period, D
is the epicentral distance in degrees and S is a correction for the
particular station and source combination. In 1982 Vanek and his associates at
the USGS gave a more general formula for Ms:

**M _{s}
= Log _{10 } (A/T) + 1.66
Log _{10 }( **

Where
T is the predominant period in the surface waves. This relation has been used in
the Earthquake Data Reports (EDRs) of the United States National Oceanic and
Atmospheric Administration (NOAA) for estimating Ms. Between 1968 and 75 the Ms
estimates were based on the vectorial combination of the horizontal and vertical
components of ground motion. Later on only the vertical component was used. In
1981 Japanese seismologist Abe demonstrated that the vertical amplitude is very
close to the vectorial combination of the two horizontal components. A third
magnitude scale has been defined for teleseisms. This is called the Body Wave
Magnitude, m_{b} , scale. This is defined by:

**m _{b} = Log _{10 }(A/T)
+Q ( **

Where A is the maximum amplitude of the ground motion measured in microns in the first few cycles of the recorded trace, T is the dominant period in the wave measured in seconds. Q (D, h) is a factor used to compensate for attenuation in the path traveled by the seismic waves. S and R are corrections to account for the anomalous structure in the receiver and source regions, respectively.

Earthquakes
having magnitudes less than 3 are called microearthquakes. These earthquakes are
recorded only in close proximity of the earthquake sources, and their signals
are rich in high frequencies, which get attenuated fast with increasing
epicentral distance. In the neighborhood of the microearthquake source the
signals are, often, saturated so that the trace amplitude cannot be measured
accurately. For such earthquakes duration of the seismic signal is used to
estimate the magnitude. The expression for the magnitude is of the form:

**M****t
= a _{0} +a_{1} Log _{10} (t)
+ a_{2} d + a_{3 }h … (10)**

Mt
is called the duration magnitude. t is the duration
of the seismic signal measured in seconds. d is the epicentral distance in km. h
is the depth of the earthquake source in km. a_{0}, a_{1}, a_{2}
and a_{3} are constants, which are to be determined empirically for a
region. In 1972 the following
formula was proposed for magnitudes of microearthquakes in California[1]:

**M****t
= -0.87 +2.0 Log _{10} (t)
+ 0.0035R**

Watanbe
gave the following formulae for Japanese earthquakes in 1971[2].

**M****t
= Log _{10} (A) + 2.3 Log _{10} (R) – 1.38**

for R < 40 km ….. **(12)**

**M****t
= 1.18 Log _{10} (A _{v}) + 2.04 Log _{10} (R)
+ 2.94 R**

for R < 200 km **…..(13)
**

Here
R is the hypocentral distance in km, A is the maximum ground displacement in
microns (mm)
and A_{v }is the maximum ground velocity. The magnitude estimates from
these expressions are said to be on the JMA (Japan Meteorological Agency) scale.

[1] Lee,W.H.K., Bennett, R.E. and Meagher,K.L.(1072). Amethod of estimating magnitudes of local earthquake from signal duration. Geol. Surv. Open File Report (USGS), 28.e

[2] Watanbe,H.(1971)

It
has been found that for earthquakes having magnitudes near 8 or greater the
surface wave and body wave magnitudes do not correlate well with the seismic
energy release. The magnitude scale, though apparently open ended, tends to
saturate because the trace amplitude in the seismogram does not increase with
increase in energy release beyond this limit. In 1979 a new formulation was
proposed for earthquake magnitude. This was called the Moment Magnitude Scale or
the M_{w} scale[1].

**M _{w
}= (2/3) Log _{10} M_{0 }–10.7…. (14)**

Where
M_{0 }is the seismic moment of the earthquake source defined by:

**M _{0
} = m
DS …..(15)
**

(m
= Rigidity in dynes/cm^{2}, D = Fault displacement in cm and S = area of
the fault moved fault in cm^{2}. At magnitude 8 the magnitudes on the Ms
and Mw scales are made to coincide. The
advantage of the moment magnitude is that, while it relates the estimated
magnitude to the energy release irrespective of the size of the earthquake, it
can be estimated from the measured physical parameters as well as from the
seismogram using analytical techniques.