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).
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 duration | Epicenter distance |
|---|---|
| 5 sec | approx. 37.5 km |
| 10 sec | approx. 75.0 km |
| 15 sec | approx. 112.5 km |
| 20 sec | approx. 150.0 km |
| 30 sec | approx. 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.
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