Identifying regional seismic relationships by cross-correlation

The identification of relationships between seismicity in different regions is commonly based on establishing the statistical significance of the largest absolute value in the cross-correlogram between time series of seismicity. The assessment of significance typically ignores the selection of the largest absolute value in the cross-correlogram and consequently exaggerates significance. In this note, a simple method for correcting the significance level for selection is presented. The method is valid as long as the two series are each serially independent. An example concerning seismicity in Mexico and Kamchatka is presented. In this case, correcting for selection has a dramatic effect.