Probabilistic approach to earthquake prediction.

Abstract

The evaluation of any earthquake forecast hypothesis requires the application of rigorous statistical methods. It implies a univocal definition of the model characterising the concerned anomaly or precursor, so as it can be objectively recognised in any circumstance and by any observer.A valid forecast hypothesis is expected to maximise successes and minimise false alarms. The probability gain associated to a precursor is also a popular way to estimate the quality of the predictions based on such precursor. Some scientists make use of a statistical approach based on the computation of the likelihood of an observed realisation of seismic events, and on the comparison of the likelihood obtained under different hypotheses. This method can be extended to algorithms that allow the computation of the density distribution of the conditional probability of earthquake occurrence in space, time and magnitude. Whatever method is chosen for building up a new hypothesis, the final assessment of its validity should be carried out by a test on a new and independent set of observations. The implementation of this test could, however, be problematic for seismicity characterised by long-term recurrence intervals. Even using the historical record, that may span time windows extremely variable between a few centuries to a few millennia, we have a low probability to catch more than one or two events on the same fault. Extending the record of earthquakes of the past back in time up to several millennia, paleoseismology represents a great opportunity to study how earthquakes recur through time and thus provide innovative contributions to time-dependent seismic hazard assessment. Sets of paleoseimologically dated earthquakes have been established for some faults in the Mediterranean area: the Irpinia fault in Southern Italy, the Fucino fault in Central Italy, the El Asnam fault in Algeria and the Skinos fault in Central Greece. By using the age of the paleoearthquakes with their associated uncertainty we have computed, through a Montecarlo procedure, the probability that the observed inter-event times come from a uniform random distribution (null hypothesis). This probability is estimated approximately equal to 8.4% for the Irpinia fault, 0.5% for the Fucino fault, 49% for the El Asnam fault and 42% for the Skinos fault. So, the null Poisson hypothesis can be rejected with a confidence level of 99.5% for the Fucino fault, but it can be rejected only with a confidence level between 90% and 95% for the Irpinia fault, while it cannot be rejected for the other two cases. As discussed in the last section of this paper, whatever the scientific value of any prediction hypothesis, it should be considered effective only after evaluation of the balance between the costs and benefits introduced by its practical implementation.