Previous research produces seemingly contradictory statements about the distribution of differences between mainshock and foreshock magnitudes. Specifically, some authors find that the magnitude difference between the mainshock and the foreshock is equally likely to be large as to be small. However, other authors find that the distribution of the magnitude differences between the foreshock–mainshock pairs is not uniform. We consider foreshock–mainshock pairs within the recent Japanese earthquake catalog and worldwide data to explore the discrepancies between these seemingly contradictory studies. The results of the previous studies differ because of the different foreshock–mainshock earthquake pairs that are considered by the two sets of authors. We show that using the definitions employed by either type of study permits the found distributions to be derived analytically and further explains how the results are dependent upon the assumed definition of foreshocks and the data selection.

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