Omori’s Law is an empirical relationship that describes the pattern of aftershock decay following a major earthquake. This law is named after Fusakichi Omori, a Japanese seismologist who formulated it in the late 19th century based on observations of earthquake sequences. Omori’s Law is an important tool in understanding the behavior of aftershocks and their frequency distribution over time.

**Key Points of Omori’s Law:**

**Aftershock Frequency:**Omori’s Law states that the rate of aftershock occurrences follows a specific decay pattern over time after a mainshock (the largest earthquake in a sequence).**Inverse Power Law:**The relationship is described mathematically as an inverse power law, where the number of aftershocks decreases with time according to a power-law decay.**Time Dependence:**The rate of aftershock occurrence is initially high immediately after the mainshock and gradually decreases over time.**Parameter “p”:**The exponent “p” in Omori’s Law determines the rate of decay of aftershocks. The value of “p” is typically between 0.7 and 1.5.**Time Delay:**There is often a time delay between the occurrence of the mainshock and the onset of aftershocks, known as the “aftershock delay.” Aftershocks can begin within minutes to days after the mainshock.

**Mathematical Representation:**

Omori’s Law can be represented mathematically as follows:

N(t) = k / [(c + t)^p]

- N(t) is the number of aftershocks that occur in a specified time period “t” after the mainshock.
- “k” is a scaling constant that depends on the mainshock magnitude and other factors.
- “c” is another constant related to the aftershock delay.
- “p” is the exponent that determines the rate of decay of aftershocks.

**Significance:**

Omori’s Law is significant because it provides a framework for understanding the temporal distribution of aftershocks after a major earthquake. While the law does not predict specific aftershocks, it helps seismologists and emergency responders estimate the frequency of aftershock occurrences within a given time frame. This information is essential for assessing the ongoing seismic hazard in an area following a significant seismic event.

In summary, Omori’s Law is an empirical relationship that describes the decay pattern of aftershock occurrences following a major earthquake. This law is valuable for understanding the behavior of aftershocks and contributes to seismic hazard assessment and disaster preparedness.