Bath’s law Derived from the Gutenberg-Richter law and from Aftershock Properties
نویسندگان
چکیده
The empirical Bath’s law states that the average magnitude difference 〈∆m〉 between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. We first point out that the standard interpretation of Bath’s law in terms of the two largest events of a self-similar set of independent events is incorrect, because it neglects the selection procedure entering the definition of aftershocks. We reconcile Bath’s law with (i) the existence of a universal Gutenberg-Richter (GR) law for all earthquakes and (ii) with the empirical observation (productivity law) that each earthquake of magnitude m triggers other earthquakes at a rate ∼ 10 with α ≈ 0.8.
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