hmm. I wouldn't really call it a "standard deviation of standard deviations"....
So essentially you have a model for Earth quake data, where M denotes the model and M' denotes the estimate.
M_mean' = E[X] ------------------ M_mean prime
M_s.d' = sqrt( E{ (X-M_mean' )^2 } ) -------- M_s.d prime
So, by some modelling, you derive some concrete values for M_mean and M_s.d .
Now, you want to know whether M_mean' and M_s.d' are "similar" to M_mean and M_s.d or different. If it's "similar", then you say ok, this is not "too" different from my model for it not being an earthquake. If it is, then you say "yeah it is an earthquake"..
Now, how do we establish a notion of "similar"?...
WHy don't you take a look at Hypothesis Testing?.. I think, it would be appropriate for this problem.
http://en.wikipedia.org/wiki/Hypothesis_testing
The hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible samples assuming the hypothesis is correct. For example: The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both responses have the normal distribution with this unknown mean and the same known standard deviation ... (value).
The above quote is "testing" the mean. In your case, it'll be the s.d.