|MadSci Network: Earth Sciences|
Greetings. As you may know, earthquakes can be classified by three different categories: foreshocks, main shocks, and aftershocks. Unfortunately, the definitions of these categories are quite vague and often an earthquake can be simultaneously described as an aftershock of some past event and a foreshock of some future event. Since you specifically asked about aftershocks, let's talk about those.
First, how do we know if an earthquake is an aftershock caused by an earlier earthquake or a new event occurring by itself? It turns out that nature tends to follow a few simple laws describing the average behavior of earthquakes. The first of these is known as the Gutenberg-Richter law. This law says that on average, for every magnitude 5 earthquake there are ten magnitude 4 earthquakes, one hundred magnitude 3 earthquakes, one thousand magnitude 2 earthquakes, and ten thousand magnitude 1 earthquakes. A second law is known as the modified Omori's law. This law says that the rate, or number over time, of aftershocks following a main shock dies off quickly over time. For example, the likelihood of having an aftershock two days after an earthquake is about half the likelihood of having an aftershock one day after an earthquake, and the likelihood of having an aftershock one year after an earthquake is about 1/365 the likelihood of having an aftershock one day after an earthquake. There are a couple of other laws, but they're not as important.
It's important to note that these laws describe only the average behavior of aftershocks. The actual times, numbers, and locations of the aftershocks are mostly random, while tending to follow these patterns. Since these are empirical laws, values of the parameters are obtained by fitting to data after the mainshock occurred and they have no physical meaning for each aftershock individually.
Now to answer your question. Could a recent magnitude 1.8 earthquake be an aftershock of a magnitude 5.5 earthquake that occurred almost three hundred years ago? That depends on how you want to classify it (which brings us awfully close to begging the original question). If there is an abnormally large number of magnitude 1.8 earthquakes as determined by the Gutenberg-Richter law, then it's likely some of them are aftershocks. Which ones, however, can be classified by using the modified Omori's law. After close to three hundred years, the likelihood of having an aftershock is pretty low, but it never goes to zero. Like beauty, aftershocks are in the eye of the beholder.
I hope this has helped.
James R Holliday
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