Do aftershock probabilities decay with time?

Seismological Research Letters



So, do aftershock probabilities decay with time? Consider a thought experiment in which we are at the time of the mainshock and ask how many aftershocks will occur a day, week, month, year, or even a century from now. First we must decide how large a window to use around each point in time. Let's assume that, as we go further into the future, we are asking a less precise question. Perhaps a day from now means 1 day 10% of a day, a week from now means 1 week 10% of a week, and so on. If we ignore c because it is a small fraction of a day (e.g., Reasenberg and Jones, 1989, hereafter RJ89), and set p = 1 because it is usually close to 1 (its value in the original Omori law), then the rate of earthquakes (K=t) decays at 1=t. If the length of the windows being considered increases proportionally to t, then the number of earthquakes at any time from now is the same because the rate decrease is canceled by the increase in the window duration. Under these conditions we should never think "It's a bit late for this to be an aftershock."
Publication type Article
Publication Subtype Journal Article
Title Do aftershock probabilities decay with time?
Series title Seismological Research Letters
DOI 10.1785/0220120061
Volume 83
Issue 4
Year Published 2012
Language English
Publisher Seismological Society of America
Contributing office(s) Earthquake Science Center
Description 3 p.
First page 630
Last page 632
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