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Abstract

The Collaboratory for the Study of Earthquake Predictability (CSEP) is an international effort to evaluate earthquake forecast models prospectively. In CSEP, one way to express earthquake forecasts is through a grid-based format: the expected number of earthquake occurrences within 0.1° × 0.1° spatial cells. The spatial distribution of seismicity is thereby evaluated using the Spatial test (S-test). The high-resolution grid combined with sparse and inhomogeneous earthquake distributions leads to a huge number of cells causing disparity in the number of cells, and the number of earthquakes to evaluate the forecasts, thereby affecting the statistical power of the S-test. In order to explore this issue, we conducted a global earthquake forecast experiment, in which we computed the power of the S-test to reject a spatially non-informative uniform forecast model. The S-test loses its power to reject the non-informative model when the spatial resolution is so high that every earthquake of the observed catalog tends to get a separate cell. Upon analysing the statistical power of the S-test, we found, as expected, that the statistical power of the S-test depends upon the number of earthquakes available for testing, e.g. with the conventional high-resolution grid for the global region, we would need more than 32 000 earthquakes in the observed catalog for powerful testing, which would require approximately 300 yr to record M ≥ 5.95. The other factor affecting the power is more interesting and new; it is related to the spatial grid representation of the forecast model. Aggregating forecasts on multi-resolution grids can significantly increase the statistical power of the S-test. Using the recently introduced Quadtree to generate data-based multi-resolution grids, we show that the S-test reaches its maximum power in this case already for as few as eight earthquakes in the test period. Thus, we recommend for future CSEP experiments the use of Quadtree-based multi-resolution grids, where available data determine the resolution.