Omori's Law Calculator

Formula first

Overview

Omori's Law is an empirical formula that describes the temporal decay of aftershock frequency following a major earthquake. It establishes that the rate of aftershocks decreases roughly with the reciprocal of time elapsed since the mainshock.

Symbols

Variables

n(t) = Aftershock frequency, K = Productivity constant, c = Time offset constant, t = Time since mainshock

Apply it well

When To Use

When to use: Apply this equation when modeling the expected frequency of aftershocks in a seismic sequence over time. It is most effective in the days and weeks following a mainshock, assuming the geological setting remains relatively consistent without new major ruptures.

Why it matters: Predicting aftershock decay is vital for public safety, as it allows engineers and emergency responders to estimate the window of high risk for structural collapse. It also provides a baseline for seismologists to detect anomalies, such as a potential second large earthquake disguised as an aftershock.

Avoid these traps

Common Mistakes

• Confusing the rate of aftershocks (n) with the magnitude of the aftershocks.
• Ignoring the 'c' constant when calculating values close to t = 0.

One free problem

Practice Problem

After a magnitude 7.2 earthquake, a seismologist determines the productivity constant K is 150 and the time offset c is 0.5 days. Calculate the expected frequency of aftershocks exactly 2.5 days after the mainshock.

Solve for: $n$

Hint: Add the time offset to the elapsed time before dividing the productivity constant by the result.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Wikipedia: Omori's Law
2. Britannica: Omori's Law
3. Omori, F. (1894). On the after-shocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7, 111-200.
4. An Introduction to Seismology, Earthquakes, and Earth Structure (Stein & Wysession)
5. Stein, S., & Wysession, M. (2003). An Introduction to Seismology, Earthquakes, and Earth Structure (2nd ed.). Blackwell Publishing.
6. University Seismology — Aftershock Statistics