2004 Wave Amplitudes & Magnitudes

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Charles Richter devised the ML magnitude scale for regional California EQs recorded by the Wood-Anderson seismographs

Basic idea:

• EQ size depends on wave amplitude, but given great variation in EQ 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 Calif. EQs 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 EQs, 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 Calif. EQs 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.

 

(Taken from Bolt, 1978)
The above classic depiction of the Richter scale shows a sterrottypical Califronia seismogram.

Gutenberg & Richter then went on to define the Ms magnitude scale that could be applied to all shallow EQs 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 EQs with hypocenter depth less than 100 km. See below a typical example of these waves recorded by OhioSeis from a far-away EQ in Algeria:

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