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Time-only Molchan test for the T-synchronizations 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 model of the T-synchronization field is built from the time-invariant reference model (average seismic potential, Ps(r)) in the following way:

T(r,t) = Ps(r) x PL(r,t); the complete model “TES synch M[2]”

Here, PL is the local interaction potential, which is defined based on the Time-synchronizations of the Omega-sequences. 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 in the area skill score of the T-synchronizations model is thus related to the temporal component and not to the spatial component.

In the test illustrated in the figure above, the global T-synchronization 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 (T-synchronization field as an alarm function) is non-random with a confidence level of 99 %. 

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



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  • CMT catalog. Accessed on 2022-05-24. Available at: