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Time-only Molchan test for the shear traction model (time-dependent)

Molchan test is a standard test used by the Collaboratory for the Study of Earthquake Predictability (CSEP) for the evaluation of earthquake forecasts. Molchan test is alarm-based and evaluates whether a given alarm function has a skill, that is if it chooses better alarm sets than a random function.

The Molchan diagram shows the fraction of space-time occupied by alarms (x-axis) versus the miss-rate (y-axis). In the time-only Molchan test, the x-axis shows the fraction of time occupied by alarms. 

According to the Omega-Theory the time dependent shear traction model is built from the time- invariant reference model (average seismic potential, Ps(r)) in the following way: 

S(r,t) = (Ps(r) + δPs(r,t)) x W(r,t); the complete model “MES total N[1]”.

Here, δPs(r,t) = 0.5 dN(r,t) is the dynamic increase of the seismic potential due to an anomalously increased rate of events dN(r,t) in the hot spots (aftershocks, foreshocks, or swarms), and W(r,t) is the effect of the tectonic waves. The average seismic potential Ps(r) does not pass the time-only Molchan test and has no time-related forecasting skill. Its area skill score is close to 0.5 which is random guessing. Any increase (gain) in the area skill score of the shear traction is thus related to the temporal component and not to the spatial component. 

In the test illustrated in the figure above, the global shear traction field was used as an alarm function. The area skill score (af) is higher than the expected value af(α) for the critical significance level equal to 1 % (yellow line). This means that the forecasting gain due to the temporal component of the forecast (shear traction as an alarm function) is non-random with a confidence level of 99 %. 

The global shear traction field in the last two months passes the time-only Molchan test with a confidence level of 99 %. The performance of the shear traction as the alarm function is better than the performance of the reference model.

 

References:

  • Molchan, G.M., 1990. Strategies in strong earthquake prediction. Physics of the Earth and Planetary Interiors. 61, 84-98.
  • Molchan, G.M., 1991. Structure of optimal strategies in earthquake prediction. Tectonophysics. 193, 267-276.
  • Molchan, G.M., Kagan, Y.Y., 1992. Earthquake Prediction and Its Optimization. Journal of Geophysical Research. 97/B4, 4823-4838.
  • Molchan G.M., 2012. On the testing of seismicity models. Acta Geophysica. 60, 624-637.
  • Zechar, D.J., Jordan, T.H., 2007. Testing alarm-based earthquake predictions. Geophysical Journal International. 172(2), 715-724.