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The seismic gap hypothesis has been widely cited in Mexico to predict the location of future earthquakes. However, no analysis of the outcome of any predictions of the hypothesis in Mexico has been done to date. This work analyzes the outcome of the prediction by Nishenko and Singh (1987a), which is based on probability distribution functions over time in defined segments that allow for a formal evaluation. Specific probabilities were given for 5, 10, and 20 yr after 1986, using the cumulative distribution function. The prediction relies on the precise repeat times of characteristic earthquakes to define the segments, but we show that the catalog the authors use relies on an imprecise definition of characteristic earthquakes. We discuss some of their decisions in building their catalog to explain how we analyze the outcome of the prediction. An unexpected result is that the very catalog the authors use to create the gap hypothesis prediction does not seem to support a narrow recurrence interval and instead seems to suggest large variability in earthquake recurrence intervals along the Mexican subduction zone. We generate null model earthquake catalogs using the average number of earthquakes that occur in the subduction zone and randomly distribute these along the segments according to their relative lengths. We find that the null model performs better than the seismic gap hypothesis prediction. No earthquakes occur in segments with a 70% or higher probability according to NS1987 (there were four such segments in the 20-year time frame), but an MW 8.0 earthquake occurs in a segment with a less than 16% probability of an earthquake. We conclude that the gap hypothesis performed poorly at predicting earthquakes in Mexico and, in fact, its predictions were worse than predicting earthquakes by chance. [ABSTRACT FROM AUTHOR]

The Collaboratory for the Study of Earthquake Predictability (CSEP) is an international effort to evaluate probabilistic earthquake forecasting models. CSEP provides the cyberinfrastructure and testing methods needed to evaluate earthquake forecasts. The most common way to represent a probabilistic earthquake forecast involves specifying the average rate of earthquakes within discrete spatial cells, subdivided into magnitude bins. Typically, the spatial component uses a single-resolution Cartesian grid with spatial cell dimensions of 0.1° × 0.1° in latitude and longitude, leading to 6.48 million spatial cells for the global testing region. However, the quantity of data (e.g., number of earthquakes) available to generate and test a forecast model is usually several orders of magnitude less than the millions of spatial cells, leading to a huge disparity in the number of earthquakes and the number of cells in the grid. In this study, we propose the Quadtree to create multi-resolution grid, locally adjusted mirroring the available data for forecast generation and testing, thus providing a data-driven resolution of forecasts. The Quadtree is a hierarchical tree-based data structure used in combination with the Mercator projection to generate spatial grids. It is easy to implement and has numerous scientific and technological applications. To facilitate its application to end users, we integrated codes handling Quadtrees into pyCSEP, an open-source Python package containing tools for evaluating earthquake forecasts. Using a sample model, we demonstrate how forecast model generation can be improved significantly in terms of information gain if constrained on a multi-resolution grid instead of a high-resolution uniform grid. In addition, we demonstrate that multi-resolution Quadtree grids lead to reduced computational costs. Thus, we anitcipate that Quadtree grids will be useful for developing and evaluating earthquake forecasts. [ABSTRACT FROM AUTHOR]