We consider implications of the Regional Earthquake Likelihood Models (RELM) test results with regard to earthquake forecasting. Prospective forecasts were solicited for earthquakes in California during the period 2006–2010. During this period 31 earthquakes occurred in the test region with . We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for tornadoes. We utilize a “skill score” based on the forecast scores of occurrence of the test earthquakes. A perfect forecast would have , and a random (no skill) forecast would have . The best forecasts (largest value of ) for the 31 earthquakes had values of to . The best mean forecast for all earthquakes was . The best forecasts are about an order of magnitude better than random forecasts. We discuss the earthquakes, the forecasts, and alternative methods of evaluation of the performance of RELM forecasts. We also discuss the relative merits of alarm-based versus probability-based forecasts. 1. Introduction Earthquakes do not occur randomly in space. Large earthquakes occur preferentially in regions where small earthquakes occur. Earthquakes are complex phenomena, but they do obey several scaling laws. One example is Gutenberg-Richter frequency-magnitude scaling. The cumulative number of earthquakes with magnitudes greater than in a region over a specified period of time is well approximated by the relation where is a near universal constant in the range and is a measure of the level of seismicity. Small earthquakes can be used to determine and (1) can be used to determine the probability of occurrence of large earthquakes. Kossobokov et al. [1] utilized the number of earthquakes in areas to map the global seismic hazard. A question that has been studied by many groups is whether there are temporal variations in seismicity that can be used to forecast the occurrence of future earthquakes. Earthquakes on major faults (say the San Andreas in California) occur quasiperiodically. A reasonable hypothesis would be that the rate of regional seismicity would accelerate during the period between the major earthquakes. There is no evidence that this occurs systematically. Background seismicity in California appears to be stationary. With the exception of years with large aftershock sequences, Rundle et al. [2] (Figure 1) showed that seismic activity in Southern California in the magnitude range for the period 1983 to 2000 was well represented on a yearly basis by (1) taking and . Figure 1:
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