Basic principles for evaluating an earthquake prediction method

A three year continuous sample of earthquake predictions based on the observation of Seismic Electric Signals in Greece was published by Varotsos and Lazaridou [1991]. Four independent studies analyzed this sample and concluded that the success rate of the predictions is far beyond chance. On the other hand, Mulargia and Gasperini [1992] (hereafter cited as MG) claim that these predictions can be ascribed to chance. In the present paper we examine the origin of this disagreement. Several serious problems in the study of MG are pointed out, such as: 1. The probability of a prediction's being successful by chance should be approximately considered as the product of three probabilities, P-T, P-E and P-M, i.e., the probabilities with respect to time, epicenter and magnitude. In spite of their major importance, P-E and P-M were ignored by MG. The incorporation of P-E decreases the probability for chancy success by more than a factor of 10 (when P-E is taken into account it can be shown that the VAN predictions cannot be ascribed to chance). 2. MG grossly overestimated the number of earthquakes that should have been predicted, by taking different thresholds for earthquakes and predictions. With such an overestimation, MG's procedure can ''reject'' even an ideally perfect earthquake prediction method. 3. MG's procedure did not take into account that the predictions were based on three different types of electrical precursors with different lead-times. 4. MG applied a Poisson distribution to the time series of earthquakes but included a large number of aftershocks. 5. The backward time correlation between predictions and earthquakes claimed by MG is due to misinterpretation of the text of some predictions and an incorrect use of aftershocks. Although even the discussion of the first problem alone is enough to invalidate the claims of MG, we also discuss the other four problems because MG violated some basic principles even in the time domain alone. The results derived in this paper are of general use when examining whether a correlation between earthquakes and various geophysical phenomena is beyond chance or not.