The relationship between the moment magnitude scale and other magnitude scales is a subject of continuing research ever since the moment magnitude (Mw) was first proposed. Empirical results show that in western North America, the moment magnitude is greater than, equal to, and less than the Richter (ML) and Nuttli magnitudes (mbLg), whereas over 97% of the earthquakes in eastern North America have an Mw value that is less than ML, mbLg, or Me. To explain the large differences that exist between the two regions, first it is shown theoretically that the magnitudes that are based on a peak amplitude measurement are approximately equal to the energy magnitude (Me) that is based on the square root of the observed seismic trace Lg coda energy. If we define p as the ratio Mw/Me and α as the seismic moment scaling constant, then it is shown theoretically that p=(4/9)α. Most of the major fault‐parameter relations such as stress drop, corner frequency, fault area, etc., can be obtained from the observed ratio of Mw/Me. The value of this ratio is not unique but depends on the nature of faulting and the tectonic environment. For self‐similar earthquakes α=3, Mw=(4/3)  Me. For most earthquakes in western North America, α varies from 2 to 3, leading to a range of values for the ratio Mw/Me, whereas for most earthquakes in eastern North America (α≈2 and Mw≈(8/9)  Me). This type of scaling for small‐to‐intermediate earthquakes may be due to earthquake fault zones being shaped by the geometry of sloping rock layers within the crust.

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