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Epicenter Distance Calculator

Estimate the distance to an earthquake's epicenter from the preliminary tremor duration (the P-wave to S-wave arrival gap) using Omori's formula.

Input

From the gap between the arrival of the P-wave (preliminary tremor) and the S-wave (principal motion)—the preliminary tremor duration—this tool estimates the distance to the epicenter using Omori's formula D = k × (S-wave − P-wave arrival time difference).

sec
km/s

Result

Distance to the epicenter (estimate)

75.0km

Epicenter distance

approx. 75.0 km

Preliminary tremor duration

10.0 sec

Coefficient k

7.50 km/s

This is an estimate from Omori's formula D = k × (preliminary tremor duration). The coefficient k varies by region and subsurface structure, typically around 6–8 km/s (default 7.5).


Epicenter distance by duration (calculated with coefficient k = 7.50 km/s)

Preliminary tremor durationEpicenter distance
5 secapprox. 37.5 km
10 secapprox. 75.0 km
15 secapprox. 112.5 km
20 secapprox. 150.0 km
30 secapprox. 225.0 km

Results from this tool are estimates only. For accurate earthquake information and disaster-prevention decisions, always consult official sources such as the meteorological agency.

How it works

  • This uses Omori's formula D = k × (S-wave arrival time − P-wave arrival time). The time difference in parentheses is the "preliminary tremor duration" (the interval from when the P-wave arrives until the S-wave arrives), and D is the distance to the epicenter.
  • The coefficient k reflects how readily seismic waves travel through the subsurface and varies by region and ground conditions. It is typically around 6–8 km/s; this tool uses a default value of 7.5 km/s.
  • If the P-wave speed Vp and S-wave speed Vs are known, the coefficient can be derived as k = (Vp × Vs) ÷ (Vp − Vs) and the distance calculated with the same formula.
  • For example, with a preliminary tremor duration of 10 seconds and k = 7.5 km/s, the epicenter distance is roughly 75 km. The longer the duration, the farther away the epicenter.
  • This gives an estimate of the straight-line distance from the observation point to the epicenter. It does not indicate the earthquake's magnitude or seismic intensity.
  • All results are rough estimates only. For accurate earthquake and disaster-prevention information and decisions, always refer to announcements from official agencies such as the meteorological agency.