I don't believe that it is correct to describe the moment magnitude as a
new scale.
By analogy, let's consider measuring the temperature. There are clearly two
common scales in use today, Fahrenheit and Celsius. They
are defined by their freezing points, 32 and 0, respectively, and their boiling
points, 212 and 100, respectively. This determines the size of their "units,"
because 212 minus 32, or 180 F units must equal 100 minus 0, or 100 C units.
This gives the well-known ratio of 100/180, or 5/9.
Now lets consider how temperature is measured. Let's say we us a glass
thermometer. At some high temperature the mercury will hit the end of the
capillary tube and if not, at some higher point the glass will melt. This is a
limitation of measuring temperature with a standard glass thermometer. Another
mechanism were devised to measure temperature, let say for example, by measuring
the emitted radiation with a device that generates a small current that is
proportional to the temperature. One could then make a table of measured
current versus degrees F and degrees C. This new replacement for the
thermometer could then be used for high temperatures where a glass thermometer
would fail or become non-linear. The output of the new device could be a
digital readout that shows current, or the readout could be calibrated to show
either degrees F or degrees C, or both, but lets say, for example, that the
output is calibrated to show degrees C.
Measurements made might be referred to as degrees C measured with a radiometer,
or perhaps radiation temperature, for short. One would not, however,
refer to measurements made on this instrument as temperature measured on the
new radiation temperature scale!
Now, getting back to earthquakes, the moment magnitude has been "defined" to
agree as well as possible with all of the other magnitude measurements
techniques that refer back to the original Richter magnitude scale. The
original Richter magnitude determination technique was limited to
moderate-sized, shallow earthquakes located in California and recorded within
600 km on a Wood-Anderson horizontal instrument. Many new measurement
techniques have been developed to allow the magnitude of larger, deeper, and
more distant earthquakes to determined, and these techniques have been
calibrated to agree with the original Richter magnitude; every effort has been
made to have the new magnitude techniques, such as mb, Ms, and Mw, agree with
the Richter magnitude within the range of validity of Richter's original
technique. Thus these are not new magnitude scales, but simply new
techniques for determining magnitude on the Richter scale.