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Earthquake Magnitude

    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:

ML = Log 10 A Log 10 A0

Here A is the maximum amplitude of the trace measured in microns and A0 is the trace amplitude for the zero magnitude shock at that distance. ML 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 Log10A0 for the Californian region. For distances between 100 and 500 km, Log10A0 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, Ms, 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.   Ms 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:

 Ms = Log 10 (A) +1.656 Log 10   (D) +1.818 + S

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:

Ms = Log 10  (A/T) + 1.66 Log 10  ( D)  + 3.3

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, mb , scale. This is defined by:

mb = Log 10 (A/T) +Q ( D,  h) + S + R 

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.

 Magnitude Of Microearthquakes

 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:

Mt = a0 +a1 Log 10 (t) + a2 d + a3 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. a0, a1, a2 and a3 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]:

Mt =  -0.87 +2.0 Log 10 (t) + 0.0035R

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

Mt  = Log 10 (A) + 2.3 Log 10 (R) 1.38

                                                                            for R < 40 km .. (12)

Mt = 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 Av 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)

Moment Magnitude

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 Mw scale[1].

Mw  = (2/3) Log 10 M0 10.7. (14)

Where M0 is the seismic moment of the earthquake source defined by:

M0  = m DS   ..(15)

(m = Rigidity in dynes/cm2, D = Fault displacement in cm and S = area of the fault moved fault in cm2. 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.  




This page was updated on 11-01-11  

[1] Hanks, T. C. and Kanamori,H.(1979). A  Moment Magnitude Scale. J. Geophys. Res. 84,2348-2350.