It looks from Figure 3 that they fit a sinusoidal curve to the data, and then fit an exponential to the residuals of *that* fit. That exponential shows a sharp increase from hour -2, but the curve is not a good fit to the rest of the data, and it almost has to show an increase somewhere because of the functional form.
I would have assumed the way to evaluate this method would be to back-test it: figure out when in the past this would have predicted that there would be an earthquake, and measure the accuracy/precision/etc. of that prediction.
It often surprises me how often disciplines don't have take a predictive approach by convention: if you make predictions at least it's possible to be *wrong*.
