Simple computations of scalar seismic moment and moment magnitude

In my classes and for research, sometimes it is useful to calculate the scalar seismic moment (M₀; basically a geometric measure of the total static energy release at a 0th order). It is a function of the area of a fault that slipped times the average slip times the shear modulus of the volume. The latter is usually assumed to be 30GPa. The main challenge (after determining the parameters) is to get the units all to be the same (dimensions of Newtons and meters):

M₀= mu*Length*Width*U_bar.

And, once we have that scalar moment in Nm, then we usually want to convert it to moment magnitude (M_w):

M_w = 2/3 log10(M₀) – 6.

Here is a simple spreadsheet to do this calculation: LINK
Here is a simple and older lecture I have used in introductory level geoscience courses: LINK