Posted by Roger Musson on November 22, 2000 at 03:13:32:
The b value is the slope parameter in the equation log N = a + b M where N is the number of events per year exceeding magnitude M. So to calculate it you need a set of data points for a range of magnitudes (the number of events in the time window exceeding each value) and then do a linear regression to calculate a and b. So it isn't a question of averaging anything. The fact is you can't estimate b with only four earthquakes. Normally one uses as long a catalogue as one can get. Trying to estimate temporal variations in b is tricky unless you have really intense activity so as to get plenty of events in each time window - I've discussed this with Max Wyss re his work in Alaska; he has a formula from Utsu that estimates whether differences between two b values are significant depending on sample size.
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