Practical Physics
Daily Seismoscope

We know a "great deal of a few things" about earthquakes.

For instance, we know, more or less, their location, we know they are produced probably by some fault slipping in Earth's crust, while building mechanical tension and accumulating energy. We know to classify them by their energy, and magnitude, which we know how to measure. We learnt something about Earth's inner structure by following the seismic waves propagating on a "seismic occasion". We also learnt much about earthquakes destructive local effects.

One major thing we do not know yet about such Geophysical Episodes: their timing, their timetable, their schedule, when do they arrive?

Is earthquakes occurrence predictable? Can we have a sort of earthquake forecasting?

On Earth's surface we lie far above the earthquake sources, which are located deeply in Earth's crust. Our sensors are probably not sensitive enough to detect possible precursory effects, or to single them out, and resolve them out, from the noise. By historical observations we know that some big earthquakes may recur quasi-periodically, with large, irregular deviations, while smaller aftershocks are expected very nearly after a main seismic shock. Are there foreshocks announcing a "big one"? We do not know.

Let an earthquake occur at this very moment. "What happens next?" is the most frequent question. There should be a probability P(t) for the occurrence of the next earthquake in time from now on. And there should be a probability P(M,t) for the occurrence of the next one with magnitude M in time t. Providing the former has the magnitude M₀, the probability for the next one is P(M,t|M₀). And so on.

http://www.infp.ro kindly provides us with the most recent Vrancea earthquake with magnitude M₀>3.

Figure 1:

Fig. 1 above shows the probability to have today, or tomorrow, or day after tomorrow, etc, a Vrancea earthquake of magnitude M>3, or one with magnitude 3<M<4, 4<M<5, etc. It is our Daily Seismoscope.

What we read in Fig. 1? We read days on the abscissa, elapsed from the reference earthquake, and probabilities in % on the coordinate axis. What means a probability, say, of 2%, as indicated in Fig. 1 above for an earthquake with approximately M>4 occurring in the same day as the reference earthquake? It means that if we live 50 times the same situation then we may have one. The same situation happens with a frequency of one in 5-6 days (there were about 2000 Vrancea earthquakes with M>3 in the last 30 years), which means that we may have one with M>4 in the same day approximately in about one year.

Figure 2:

Figure 3:

Similar Daily Seismoscopes are given in Figs. 2 and 3 for reference earthquakes with magnitude 3<M₀<4, 4<M₀<5, etc. Earthquakes with M>4.7, which might be felt in Bucharest, are forecast in Fig. 4.

Figure 4:

The most dramatic day in producing the next earthquake is the same day when the reference earthquake occurred, at least for small earthquakes (M<5). We note that probabilities are very small for higher magnitudes (M>4-5), and decrease considerably in time over 20-25 days.

In addition, there is always a confidence level, for each prediction. For instance, a confidence level of cca 77%, as for predicting small earthquakes (M<4), means that, approximately, the prediction fails 2 times in 10. A confidence level of 4%, as for predicting M>4.7 in Fig. 4, means that we fail roughly 19 times in 20 essays.

What we learn from all this above? We learn that we can predict earthquakes. But the prediction is very probable for those earthquakes that are most likely, and which are not interesting therefore (say, M<4-5), and it is very improbable precisely for those earthquakes which are very rare, but the most interesting (M>5). "But all things excellent are as difficult as they are rare" (Spinoza).

Where, however, lack of data prevents us from drawing more confident knowledge, we are rescued by Theory, by Pure Reason. This is Practical Physics. The next-earthquake distribution D() goes like an inverse power law for small , and like an exponential law for larger , scaled by the seismicity rate. Fig. 5 shows the probability rate per day of having two successive earthquakes in Vrancea both with magnitude M>5.

Figure 5

The results are based on statistical analysis of 1999 earthquakes recorded in Vrancea between 1974-2004 (30 years), within 45°N-46°N and 26°E-27°E, with magnitude M>3 (Romanian Earthquake Catalogue, 2005, updated, Institute for Earth's Physics, Magurele-Bucharest, Romania, http:www.infp.ro/eqsinfo.php, continuously updated Catalogue first published by M. C. Oncescu, V. I. Rizescu and M. Popa, 1999, in Vrancea Earthquakes and Tectonics, Hazard and Mitigation, eds. F. Wenzel and D. Lungu and co-ed. O. Novak, pp.43-47, Kluwer, Dordrecht, Netherlands).

apomaLab, J. Theor.Phys. 109-112 (2005)