This posting is a long explanation of scales for earthquake magnitudes.
In short, the magnitude is the base 10 log of the ground movement
amplitude, with a bunch of fudging to make results come out the
same at different measuring sites and to make the results comparable
between different earthquakes.

In general, the magnitude is determined by a formula of the form
mag = log(a/T) + f(delta,h) + Cs + Cr
where mag is the magnitude, a is the ground amplitude in microns,
T is wave period in seconds, f is a function to correct for the
effects of distance and focal depth, delta is the epicentral distance
in degrees, h is the earthquake focal depth in km,
Cs is a correction for the local structures at the station and
Cr is a regional correction.

The original Richter scale was designed in 1935 for comparing local
earthquakes in Southern California and cannot be used directly for
comparing earthquakes in other areas.  It is defined as M sub L =
the logarithm of the maximum recorded trace amplitude in microns
of a Wood-Anderson torsion seismograph with specified constants
(free period=0.8s, magnification=2800, damping=0.8) at an epicentral
distance of 100 km.  (Note: all logarithms are base 10).

The magnitude M was designed in 1945 by Gutenberg based on surface
waves.  Considering Rayleigh surface waves in a period range of
20+-2 sec for earthquakes of normal depth, the equation becomes M
= log a + c1 log delta + c2, where a is the horizontal ground
amplitude in microns, delta is the epicentral distance in degrees,
and c1 and c2 are constants.  (As best as I can tell, this is the
magnitude normally reported.)

There is a third magnitude m, similar to M, based on body waves.

These magnitudes are related by:
m = 1.7 + 0.8 ML - 0.01 ML^2 (where ML is M sub L)
m = 0.56 M + 2.9

The International Geophysical Assembly in Zurich in 1967 adopted the
following recommendations for magnitude determinations of distant events:

1.  Magnitudes should be determined from (a/T)max for all waves for
    which calibrating functions f(delta,h) are avaliable: PZ, PH, PPZ, PPH,
    SH, LH, (LZ).  (Z=vertical component, H=horizontal component,
    L=surface wave).
2.  Amplitudes and periods used ought to be published.  Two magnitudes
    (m=body-wave magnitude, M=surface-wave magnitude) should be used.
    For statistical studies M is favoured.  The conversion formula m =
    0.56M+2.9 is recommended.
3.  For body waves the f(delta,h) values of Gutenberg and Richter are
    used.  For surface waves, the Moscow-Prague formula:
    M = log(a/T) + 1.66 log(delta) + 3.3 is used.
    (a is the horizontal componente of Rayleigh surface waves;  T should
    be in the period range of 10-30 sec.)
4.  If short period records are used exclusively, too low magnitudes
    result.  In order to eliminate this error, it is strongly recommended
    that for short-period readings either a/T or f(delta,h) be
    adjusted such that the agreement with long-period instruments is
    achieved.

The energy in ergs released by the earthquake is given by:
log E = 12.24 + 1.44 M, where M is the magnitude > 5.
This is an empirical equation, derived by integrating over the whole wave
train in time and space.  From this equation, each increase of 1 in
magnitude increases the energy released by a factor of 27.5.

The maximum acceleration a0 (in cm/sec^2) is related to magnitude by
M = 2 + 2 log(a0).

The information in this posting came from "Introduction to Seismology",
Markus Bath, 1973, John Wiley&Sons, New York.  This book explains
most of what I wanted to know, with lots of formulas.  Check it out.

Ken Shirriff	shirriff@cs.Berkeley.EDU