# Computing  Body-Wave (mb) Magnitude

The formula for teleseismic body-wave magnitude is:

mb = log10(A/T) + Q

A is the zero-to-peak amplitude in microns of the P phase
(not necessarily limited to the first few cycles)
T is period in seconds **
Q is a function of distance (degrees) and depth (kilometers)

For shallow events, Gutenberg and Richter (1956) provide a table of Q values as a function of distance.  See:  http://www.seismo.com/msop/msop79/par/tab_3.2.1.gif

For arbitrary depth, Gutenberg and Richter (1956) provide a contour graph of Q values as a function of both distance and depth.  See:
http://www.seismo.com/msop/msop79/par/fig_3.2.1.2a.gif
The NEIC uses a table to approximate the Q values shown in this graph.  This table is given here:  qtab.txt .

Larry Braile gives this formula for mb:
mb = log10(A/T) + 0.01*D + 5.9
See:  http://www.eas.purdue.edu/~braile/edumod/as1mag/as1mag3.pdf

The comparison table, below, shows how the Q values differ for these various formulations.  The largest differences in computed magnitudes will be for delta in the range of 100 to 109 degrees.  For these distances the Braile formula may underestimate the magnitude by as much as one unit.

 Braile formula:  0.01*delta + 5.9 PZ** = Q for  shallow  earthquakes NEIC qtab NEIC  qtab Delta Z=0 Z=500 16 6.1 5.9 5.9 6.4 20 6.1 6.0 6.1 6.4 30 6.2 6.6 6.6 6.3 40 6.3 6.4 6.4 6.3 50 6.4 6.7 6.7 6.2 60 6.5 6.8 6.9 6.2 70 6.6 6.9 6.9 6.3 80 6.7 6.7 6.7 6.2 90 6.8 7.0 7.0 6.7 100 6.9 7.4 7.3 7.2 109 7.0 8.0 7.9 7.8
 **From Gutenberg and Richter (1956) table for shallow events. ("Magnitude and energy of earthquakes," Annali di Geofisica, v. 9, no. 1, p. 1-15.)

 This is the version of the Q graph from Richter (1958) Elementary Seismology, W. H. Freeman and Company.

FORTRAN code for computing mb magnitude based on Ray Buland's NEIC nreloc program is listed in mbmag.formbmag.exe is a compiled version of this code which will run on a PC in a DOS window.  This program reads the qtab.txt file.  But even better, Bob McClure has converted the DOS program to a Visual Basic Windows program.  Just download and unzip MagCalc.zip and run the program MagCalc.exe.