Meaning and mechanism
P waves and S waves differ in their transmission method and speed. If they originate from the same starting point, P waves generally arrive first, and the time difference increases as the distance increases.
A difference in the time of measurement for a single observation point does not determine the location. By overlapping the possible distance ranges from multiple observation points, the epicenter is narrowed.
Relationships and conditions
For uniform wave speeds, Δt=d(1/Vs−1/Vp). With the simulation’s Vp=6 and Vs=3.5 km/s, hypocentral distance is d=8.4Δt km.
If focal depth h is known, the surface radius is √(d²−h²). For Earth’s actual layered structure and refraction, travel-time data replace the simple straight-line propagation equation.
What to observe in the simulation
The epicenter is estimated using surface circles from three different observatories. When placing a straight line, the intersection point calculation is unstable.
Assume a homogeneous medium and straight propagation with Vp=6 km/s and Vs=3.5 km/s. It is a model that knows the depth in advance and obtains an accurate arrival time. The actual layer structure, refraction, and time errors are omitted, and the waveform amplitude is a virtual relative value.
Key relationships and symbols
d=8.4Δt (km), r=√(d²−h²)
| Symbol | Meaning | Unit |
|---|---|---|
| Δt | Difference between S-wave and P-wave arrival times | s |
| d, h | Hypocentral distance and focal depth | km |
Worked example
If Vp = 6 km/s, Vs = 3.5 km/s, and the S–P interval is 10 s, what is the hypocentral distance?
d=Δt×6×3.5/(6−3.5)=8.4Δt. This distance is the distance to the hypocenter and the surface radius is √(d²−h²).
Common misconceptions
- The distance to the hypocenter, calculated by the time difference between S-wave and P-wave, differs depending on the depth.