Comment on “Revisiting the 1894 Omori Aftershock Dataset with the Stretched Exponential Function” by A. Mignan

Abstract

ABSTRACT Mignan (2016) claimed that a stretched exponential function describes Omori’s original aftershock data of the 1891 Great Nobi earthquake better than the well‐known Omori law, which is a power law. Besides his preference for the stretched exponential function based on general physical reasoning, he proposed that the Omori law does not hold when the proper visualization method is used; that is, the complementary cumulative density function (CCDF) in a log–log plot. However, his proposed plot is misleading, because it compares data of a finite observation interval with functions integrated over infinite periods. Using the same data as Mignan (2016), we find that an appropriate comparison leads to visually indistinguishable fits for this dataset. The Omori law is preferred based on maximum‐likelihood values. Moreover, the extrapolation shows that it also fits the long‐term data until the centennial anniversary of the Nobi event significantly better than the stretched exponential.