S-P Interval (Distance to Epicenter) Calculator
Determines the distance to an earthquake epicenter using wave arrival times.
Formula first
Overview
This equation calculates the distance between a seismic station and an earthquake's origin point by analyzing the time delay between the arrival of primary (P) and secondary (S) waves. It relies on the distinct velocity differences of these waves as they travel through the Earth's crust to estimate the proximity of the seismic event.
Symbols
Variables
d = Distance, = P-Wave Speed, = S-Wave Speed, t = Time Interval
Apply it well
When To Use
When to use: Apply this formula when you have recorded arrival times for both P-waves and S-waves from a single seismic station. It assumes the waves travel through a medium with relatively constant or well-averaged velocities, making it ideal for regional crustal earthquake analysis.
Why it matters: Determining the distance to an epicenter is the critical first step in locating an earthquake. By finding the distance from at least three different stations, seismologists can triangulate the exact location of the epicenter to issue tsunami warnings and direct emergency response efforts.
Avoid these traps
Common Mistakes
- Using the wrong wave speeds for the local rock type.
- Convert units and scales before substituting, especially when the inputs mix km, km/s, 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 seismic station records a P-wave arrival at 08:00:10 and an S-wave arrival at 08:00:34. If the P-wave velocity is 8.0 km/s and the S-wave velocity is 4.5 km/s, calculate the distance from the station to the earthquake epicenter.
Solve for:
Hint: Subtract the P-wave arrival time from the S-wave arrival time to find the interval, then use the product-over-difference velocity formula.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: P-wave
- Wikipedia: S-wave
- Wikipedia: Epicenter
- Britannica: Seismology
- USGS Earthquake Glossary
- British Geological Survey (BGS) educational resources
- An Introduction to Seismology, Earthquakes, and Earth Structure by Stein and Wysession, 3rd Edition
- Fundamentals of Geophysics by Lowrie, 3rd Edition