zmap a tool for analyses of seismicity patterns typical applications ...

this case, the routine found that a simple shift of +0.1 units applied to the background,
would best fit the foreground, while if a stretch is chosen, one needs to apply a shift of
+0.3 and a multiplicative factor of 0.82. Notice that in the selection panels, a simple
magnitude shift of +0.1 is input, which resulted in the plot shown in Figure 2.7A.
(B)
(A)
Figure 2.7. Comparison of rates as a function of magnitude for two time periods under the Compare-Fit
option. The three panels correspond to the Frequency-Magnitude curves, normalized, the non-cumulative
histogram as a function of magnitude, and the magnitude signatures for the original two periods (circles)
and for the synthetic foreground as compared to the original background (crosses). (A) Results of applying
a simple magnitude shift of +0.1 units, without any rate change. (B) Same as in (A) but including a rate
change of 0.78 (equivalent to the -%22 change in percent given in Figure 2.5).
The magnitude signature plot is useful for asserting the goodness of the fit from the latest
run (bottom panel of Figures 2.7A and B). It shows the original magnitude signature,
which results after comparing the two time periods, and a modeled signature obtained
from comparing the synthetic foreground (i.e. the corrected background) to the original
background. The best match between both signatures indicates that we have been able to
model the observed behavior by applying the given corrections to the background. In the
example, we can see that the shape of the signature is correctly modeled by applying a
simple magnitude shift (Figure 2.7A) while a rate decrease is still necessary to model the
position of the signature (Figure 2.7B).
The Compare-fit option is also useful in case one needs to determine the relation between
two different magnitude estimations for the same period and area. For this case, you
would need to first concatenate the two data sets (“Combine two catalogs” option in the
“Catalogs” pulldown menu from the Seismicity Map window) and treat them as separate
time periods.
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