Basic definition of magnitude
Charles Richter (1935) devised the ML magnitude scale for regional California earthquakes recorded by the Wood-Anderson seismographs
Basic idea:
- Earthquake size depends on wave amplitude, but given great variation in earthquake size, Richter decided that M will vary as log(Wave Amplitude).
- The absolute numbers of magnitude have no physical meaning, Richter chose the scale shift constant so that the California earthquakes he recorded would have "convenient" values for M, i.e. between 0 and 10.
- The hard work: Since wave amplitudes decrease with epicentral distance, Richter had to empirically determine the functional behavior. The main result is that: Amplitude(X) = a*X**b, where the exponent b is around 1.
- Thus, Richter produced the formula: M = C1 + log(A) + b*log(X), where the units of A and X are fixed by the choice of C1.
- Complications: Variable wave period. If the measured wave amplitude has a different dominant period between different stations or between different earthquakes, then more stable magnitude estimates are produced by a modified formula: M = C2 + log(A/T) + b*log(X), where T is the period of measured wave amplitude, A. Of course, the quantity (A/T) is also proportional to ground velocity.
- Complications: Exactly which wave or peak do you measure? Richter's original intent was quite simple: measure the largest peak on the seismogram. It turns out that regional seismograms of California earthquakes are simple in that the S wave is clearly the largest arrival (see below picture). But, seismograms from other parts of the world (including central and eastern North America) have a different character. THIS IS THE MAIN PROBLEM WE FACE IN THE GREAT LAKES REGION.
The above classic depiction of the Richter scale shows a stereotypical California seismogram (Taken from Bolt, 1978).
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Gutenberg and Richter (1942) then went on to define the Ms magnitude scale that could be applied to all shallow earthquakes of the world. It followed in the same spirit as Richter's local magnitude where you measure the largest amplitude in a long-period or broad-band seismogram — it is invariably the "20 second" Rayleigh waves for earthquakes with hypocenter depth less than 100 km. See below a typical example of these waves recorded by OhioSeis from a far-away earthquake in Algeria:
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