22. Calculating b-value, BVALUE

BVALUE is a program to make b-value plots using a NORDIC input file (also compact). The magnitude is selected among all magnitudes on all header lines, but when the first is found, no more are searched for. So only one value is used for each event. A magnitude agency can be specified for the magnitude selection.

Magnitudes can be in the range -2 to 8.

A postscript plot file is generated.

The questions are:

 Input file name, select.out or collect.out are defaults
    ! Give filename or return
 Which magnitude type, C,L,B,W or S, return for no type
    ! C: coda, L: Ml, B: mb and S: surface wave magnitude, W: Moment mag.
         blank: no magnitude type
 Magnitude agency, enter for any

 Number of events selected from file:    91 
Duration of catalog in years: 0.502

    ! Output number of events selected and duration of catalog
 New input:
 Magnitude step 1.0, 0.5, 0.25, 0.2 or 0.1
    ! Magnitude step for summing number of events, MUST be one of the above.
 Magnitude range m1,m2 for b value and fixed b-value
    ! Range for calculating b value, and the fixed b-value for which a-value 
is calculated. The a value is calculated as the average of N(i) + bfix * mag(i), 
where N(i) is the accumulated number of events at magnitude 
mag(i) and bfix is the fixed bvalue.
 Output is now:
      n    m1    m2 maxl a maxl b   sd  lsq a  lsq b   cor    rms   bfix   afix   sd
     52    2.0  4.0 3.25     0.68 0.46   3.77   0.93  0.93   0.14    1.0   4.02 0.16
 Normalized         3.55                 4.07                              4.32
 Normalized m1      2.19                 2.21                              2.32
 Norm. lin. m1     154.9                162.2                             208.9

! Normalized means normalized to one year (m=0), Normalized m1 (m=m1) 
and Norm. lin. m1 is just antilog the previous. So in the above example, 
it is expected that 162.2 earthquakes occur larger than or equal to 2 
in one year (least squares relation).

   mag  nmag  cmag
    0.4     1    91
    0.6     1    90
    0.8     3    89
    1.0     6    86
    1.2     6    80
    1.4     7    74
    1.6     4    67
    1.8    11    63
    2.0     8    52
    2.2    11    44
    2.4     6    33
    2.6     7    27
    2.8     5    20
    3.0     4    15
    3.2     7    11

 n: Number of values used
 m1 and m2: Magnitude range used for b value calculation
 maxl a and b: Maximum likelihood a and b
 sd: Standard deviation
 lsq a and b: Least squares a and b ( the one plotted) 
 cor and rms: Correlation coefficient and rms of above
 bfix: fixed b-value given at input
 afix: a-value for above
 sd: standard deviation for above
 mag: magnitude
 nmag: number of events within mag interval
 cmag: cumulated number of events

   ! This will make a plot and a postscript plot file.
     Note that only the last plot on screen is saved. The plot
     must be sent manually to the printer.

 Which b-value 1: Least squares (default)
               2: Fixed bvalue
               3: Maximum likelihood
   ! Choice of b-value to plot

 Run again with other parameters (y/n)
   ! Another step length or range can be selected 
The final output is:

Output file in bvalue.out
Last plot in file bvalue.eps

The output file bvalue.out contains the same information in the same format as shown in the example above. The file can be used with other plotting programs to make 'nicer looking' b-value plots. An example is shown in Figure 22.1.

Figure 22.1: An example of a b-value plot. The bars are number of events and crosses the accumulated number of events.