Stress drop and aftershocks

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Abstract
Eighteen aftershock sequences, nine from California and nine from New Zealand, are studied. It is found that a general relationship exists between the local magnitude ML and the stress drop in the main shock. The stress drop in the main earthquake determines the principal characteristics of the aftershock sequences. A low stress drop leads to a low value of the coefficient b, high magnitude of the largest aftershock, and short duration, and conversely. A sequence is arbitrarily considered to be over when the rate of aftershock occurrence falls to a value of one shock per day. The duration depends on the area of fault surface and the stress drop in the main shock. For an average stress drop, the coefficient b has a value of 0.8 to 0.9, and the difference in magnitude between the main shock and the largest aftershock is 1.2, a relation often called Båth's law.