## Ø     4.2 Local Richter magnitude, XMAG

(This is an excerpt from Chapter 4 of the HYPOELLIPSE earthquake location program manual.  http://jclahr.com/science/software/hypoellipse/hypoel/hypoman/pdf_word.htm )

### §        4.2.1 Equation used to compute Richter magnitude

The formula for computing Richter magnitude is:

 XMAG = Log base 10 of maximum zero-to-peak amplitude in mm as recorded on a standard Wood-Anderson seismograph. + Approximation to Richter's logA o from Eaton (1970), which accounts for amplitude attenuation with distance. See Figure 4-1. + Station Correction XMAG = log(A/2) + (-B1 + B2 log(X2)) + G

where:

A = Maximum peak-to-peak amplitude in mm

For 1 km < D < 200 km
B1 = 0.15
B2 = 0.80

For 200 km < D < 600 km
B1 = 3.38
B2 = 1.50

and D is the epicentral distance and Z the focal depth in km.

G = Station XMAG correction, as specified on the TIME DEPENDENT STATION parameter record (see 2.2.5.3).

XMAG is not computed if X is not in the range 1 to 1,000 km.

Figure 4-1. Comparison of the term logAo from Richter (1958) (dots) with the approximation (straight lines) used in HYPOELLIPSE.

…..

To calculate magnitudes equivalent to the local Richter magnitude it is necessary to calculate the amplitude B(f) that would have been read on the seismogram from a Wood-Anderson seismograph. The magnification of the Wood-Anderson is

with Fo = 1.25 and B = 0.8.  Note:  Urhammer and Collins (1990) found the static magnification to be 2080 rather than the value of 2800 given in Richter (1958).

The nomogram below from Richter (1958) can be used to find a very approximate ML magnitude.

The magnitude may be computed with the DOS/FORTRAN program mlmag.exe.  The source for this program is mlmag.for.

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.

References:

Richter, C. F., 1958, "Elementry Seismology."  Freeman, San Francisco, California.

Uhrhammer, R. A., and Collins, E. R., 1990, Synthesis of Wood-Anderson seismograms from broadband digital records, Bulletin of the Seismological Society of America, v. 80, p. 702-716.