Earthquake aftershocks are earthquakes in the same region of the main shock with smaller magnitude. In general terms, aftershock sequences can be described by three empirical scaling relations:
- The Gutenberg-Richter frequency-magnitude scaling
- Bath's law for the difference in the magnitude of a main shock and its largest aftershock
- The modified Omori's law for the temporal decay of aftershock rates
The generalized or modified Omori's law for aftershock decay depends on several parameters specific for each given seismic region and can be represented by the following equation:
- n(t) - is the number of earthquakes n measured in a certain time t
- K - is the amplitude
- C - is the "time offset" parameter
- p - modifies decay rate and typically falls in the range 0.7 - 1.5.
The rate of aftershocks is proportional to the inverse of time since the main shock.
The length of the fault scales with the magnitude of the main shock as well as the aftershocks. For example, the aftershock zone of a magnitude 5 main shock will be under 5 miles across, that of a magnitude 6.5 will be about 20 miles across, while that of magnitude 8 main shock might be over 200 miles long. Larger earthquakes have more and larger aftershocks. As the magnitude of the main shock increases, the magnitude of the largest aftershock, on average, increases as well. The question is often asked, how many aftershocks will there be? On average, for each magnitude 5 aftershocks in a sequence, there will be 10 magnitude 4 aftershocks, 100 magnitude 3 aftershocks, 1000 magnitude 2 aftershocks, etc. In general, an earthquake large enough to cause damage will produce several felt aftershocks within the first hour. The rate of aftershocks dies off quickly with time. The second day has many fewer aftershocks than the first.
Large aftershocks may pose a substantial hazard to populated areas. They can cause even more damage than the main shock as, for example, during the M=6.1 aftershock of the 2002 M=7.4 earthquake in Hindu Kush, Afghanistan. Another example of a significant aftershock is the M5.8 aftershock of the 1999 M7.4 Izmit, Turkey earthquake, which caused the death of 7 people and left 420 injured. Therefore, the prediction and study of aftershock impact is of great interest. The main purpose of the aftershock survey is to obtain accurate hypocentral locations so that the size and orientation of the fault plane that ruptured in the earthquake can be determined.
It is very important to an aftershock study to deploy as many simultaneously recording stations as possible within a 24- to 48-hour time period. Recording stations may operate from a few weeks to several months depending on the aftershock sequence activity. In order to obtain quality seismic data from the main event(s) and aftershocks, a substantial field effort is necessary to efficiently deploy temporary seismic stations in remote areas. The installation area can cover from a few kilometers to 100 km of the fault to constrain aftershock locations.
It is practical to co-site the seismic recorders with strong-motion accelerographs that recorded the main shock. Aftershock records from these sites, especially near the fault zone, can be used as empirical Green's functions to model the main-shock strong motions. While the strong-motion accelerographs typically trigger on only the largest aftershocks, the more sensitive portable seismographs assure a much richer empirical-Green's-function dataset.