Earthquakes, large and very small, are happening all over the world, all the time. For an illustration of this, click here to see earthquakes that have been located in California and Nevada in the past 7 days. We don't know exactly how small an earthquake has to be before it can't trigger any aftershocks, but it is well below the magnitude someone could feel (roughly magnitude 2).

Aftershocks and all other earthquakes follow an empirical rule called Gutenberg-Richter Law describing the number of earthquakes of different sizes. This law is a logarithmic relationship* that basically tells us that each time we go down a unit in magnitude, we should expect to see 10 times as many earthquakes. So for each earthquake we see of magnitude 5, we should expect to see, very roughly, 10 4's, 100 3's, 1000 2's, etc. The Gutenberg-Richter relationship may break down for the tiniest of earthquakes * (so small that they have negative magnitude), but even so, the number of teeny-tiny aftershocks generated by all of the tiny earthquakes that occur - most of which are so small and remote that nobody even feels them - has to be absolutely staggering.

So let's talk instead about how many aftershocks we could expect to see in a day following one really large earthquake. Another law, Omori's Law*, describes the number of aftershocks we expect to see over time following an earthquake of a given magnitude. Omori's Law tells us that there will be lots of aftershocks immediately following an earthquake, and that as time passes, the number of aftershocks will decay exponentially. So the first day after a major earthquake is when we would expect to see by far the largest number of aftershocks. Although the basic mathematical relationship in Omori's law doesn't change broadly, the numbers (the constants) used vary region to region, and even from sequence to sequence. But in 1989, two scientists* hammered out appropriate constants that seemed to work for California and put together Omori's Law and the Gutenberg-Richter relationship into a function for the expected number of aftershocks over a given time period after a California earthquake of some magnitude. As statistical measures, Omori's law, and the more detailed aftershock production rate rule constructed by Reasenberg and Jones, are not meant to predict exactly how many aftershocks of a given magnitude we will see over a given time interval, any more than knowing heart attack statistics could tell you exactly how many people will show up at a given hospital with one on a particular day.

The Reasenberg and Jones relationship is a mouthful: rate(t,M)=10^(-1.67+0.91(Mm-M))*(t+0.05)-1.08, where t is time in days, Mm is the magnitude of the mainshock, and M is the magnitude of aftershocks that we are looking at. So, for a magnitude 8 event, if we want to look only at magnitude 2 plus events, Mm-M would be 6. Plugging in the numbers, for a magnitude 8 earthquake, about the biggest that we could experience in California, we get an expected 5849 M2+ aftershocks, 720 M3+ aftershocks, 89 M4+ aftershocks, 11 M5+ aftershocks, and 1 M6+ aftershock. The vast majority of these thousands of aftershocks are between magnitude 2 and 3, just at the level that someone in the vicinity might start to feel them and certainly not big enough to cause any damage. However, though each of these aftershocks could potentially be felt by someone standing nearby, you certainly wouldn't feel all, or even most of them, which for a large earthquake is considerable. The 1857 M 7.9 Fort Tejon earthquake, in the running for California's largest earthquake in written history, ruptured over 350 km, which translates to an area for aftershocks spanning about 12000 square miles!

The largest earthquake ever recorded in the world was not of magnitude 8, however, but magnitude 9.5, in Chile in 1960. We can't use Reasenberg and Jones' California numbers for Chile, but this size of an event would probably generate more than 100,000 aftershocks of magnitude 2+ or above on the first day after the quake.

(1) log N = a-bM, where N is number, M is magnitude, and a and b are constants that vary by region.

(2) Breakdown (?) of the Gutenberg-Richter Frequency-Magnitude Relation for Earthquakes in the SAFOD Target Zone, Ellsworth, W. L.; Imanishi, K., American Geophysical Union, Fall Meeting 2010, abstract #T41A-2089

(3) n=C/(K+t)^P, where n is the rate of aftershocks at time t, and C, K, and P are constants that vary.

(4) Reasenberg, Paul A. and L.M. Jones (1989). Earthquake Hazard After a Mainshock in California, Science, 243, 1173 - 1176.