Are we being fooled by aftershocks?

If earthquakes were a purely Poisson process, then actual changes in the number of 4.5 < mb < 5.5 would virtually never be as large as those of the last few years. But aftershocks are a well-known departure of earthquakes from Poisson process behavior. Very large earthquakes are sufficiently rare that their number differs greatly from year to year, and they account for many of the mb > 4.5 aftershocks around the world. In a year with few really big earthquakes, the seismicity rate just might change because of a dearth of aftershocks.

I estimate number of aftershocks should occur in an interval by summing the estimated number of aftershocks for each event with a Harvard CMT. For the number of aftershocks for each Harvard event, I assume that

  • aftershocks have a size distribution with b = 1
  • the largest aftershock has magnitude MW - 1

With A and b of the size distribution set this way, for each event the number of aftershocks with magnitude < m is 10MW-1-m. The estimated number of 4.5 < m < 5.5 aftershocks for each of the last five years is well over half of all events in the ISC Bulletin with mb in that range. Perhaps the estimates are too large, or the Bulletin misses out some aftershocks in this range. Still, differences between estimates for each year are more or less consistent with the observed changes in total seismicity.

Aftershocks of Harvard CMT events from ratios method [Frohlich & Davis, 1986]. Each event with P(Tafter/Tbefore) < 0.99 is counted as 1-P aftershocks.

Small variance of the number of independent events suggests that aftershock removal is generally effective, despite occasional exceptions (e.g., 1994 May).

There are fewer aftershocks since 1995 partly because there are fewer very large earthquakes. But there is also a decrease in the rate of independent events.

It's not all down to aftershocks

There aren't enough aftershocks, and the apparent rate of mb < 4.5 independent events is decreasing.
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