Geology & Earth ScienceSeismologyA-Level
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S-P Travel Time Calculator

Distance to an earthquake epicentre.

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Distance to Epicentre

Formula first

Overview

The S-P travel time equation relates the distance from a seismic source to the time interval between the arrival of P-waves and S-waves at a recording station. This calculation exploits the velocity difference between the faster primary (P) compressional waves and the slower secondary (S) shear waves to determine the earthquake's epicentral distance.

Symbols

Variables

D = Distance to Epicentre, Gap = S-P Time Diff, = P-Wave Velocity, = S-Wave Velocity

Distance to Epicentre
km
Gap
S-P Time Diff
P-Wave Velocity
km/s
S-Wave Velocity
km/s

Apply it well

When To Use

When to use: This equation is used when a seismogram clearly displays the distinct onset times of both P-waves and S-waves. It assumes a homogeneous crustal model where seismic velocities remain relatively constant along the travel path, making it most effective for local or regional seismic events.

Why it matters: Calculating the S-P gap is the foundational step in earthquake triangulation. By determining the distance from at least three different stations, seismologists can pinpoint the exact epicenter and depth of an earthquake, which is vital for emergency response and tsunami forecasting.

Avoid these traps

Common Mistakes

  • Using arrival times directly rather than the difference between them (S minus P).
  • Convert units and scales before substituting, especially when the inputs mix km, s, km/s.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

A seismograph at a remote station records a P-wave arrival at 08:12:10 and an S-wave arrival at 08:12:34. If the regional P-wave velocity is 6.0 km/s and the S-wave velocity is 3.5 km/s, calculate the distance from the station to the earthquake epicenter.

S-P Time Diff24 s
P-Wave Velocity6 km/s
S-Wave Velocity3.5 km/s

Solve for:

Hint: First calculate the S-P time gap by finding the difference in arrival times, then apply the formula.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Earthquake location
  2. Britannica: Seismology
  3. Seismology (Wikipedia article)
  4. Shearer, P. M. (2009). An Introduction to Seismology (2nd ed.). Cambridge University Press.
  5. Lowrie, W. (2007). Fundamentals of Geophysics (2nd ed.). Cambridge University Press.
  6. Fowler, C. M. R. (2005). The Solid Earth: An Introduction to Global Geophysics (2nd ed.). Cambridge University Press.
  7. A-Level Geology — Seismology