I don't believe that it is correct to describe the moment magnitude as a
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.