Snell's Law (Seismic Refraction) Calculator

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Overview

Snell's Law in seismology describes how seismic waves change direction and speed as they transition between geological layers with differing elastic properties. This relationship is fundamental for determining the ray paths of P-waves and S-waves as they refract across boundaries like the crust-mantle interface.

Symbols

Variables

${\theta }_2$ = Refraction Angle, ${\theta }_1$ = Incidence Angle, $v_1$ = Velocity 1, $v_2$ = Velocity 2

Apply it well

When To Use

When to use: Use this equation when calculating the trajectory of a seismic wave encountering a distinct boundary between two rock types or layers. It assumes the layers are isotropic and that the seismic velocity is constant within each layer.

Why it matters: This principle is the foundation of seismic refraction surveys, which allow geologists to map subsurface structures for oil exploration and engineering projects. It is also used to locate the depth of the Mohorovičić discontinuity and other internal Earth layers.

Avoid these traps

Common Mistakes

• Using degrees in calculator when sin() expects radians.
• Convert units and scales before substituting, especially when the inputs mix °, 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 seismic P-wave travels through a layer of weathered rock (v1 = 2500 m/s) and strikes a limestone basement (v2 = 4500 m/s) at an incident angle of 20°. Calculate the angle of refraction as the wave enters the limestone.

Solve for: $t2$

Hint: Rearrange the formula to solve for sin(t2) by multiplying v2 by the ratio of sin(t1) to v1.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. An Introduction to Seismology, Earth Structure, and Earthquakes by Seth Stein and Michael Wysession
2. Fundamentals of Geophysics by William Lowrie
3. Wikipedia: Snell's Law
4. Britannica: Snell's law
5. Snell's law (Wikipedia article title)
6. Fundamentals of Physics by Halliday, Resnick, and Walker
7. Stein, S., & Wysession, M. (2003). An Introduction to Seismology, Earthquakes, and Earth Structure. Blackwell Publishing.
8. Lowrie, W. (2007). Fundamentals of Geophysics. Cambridge University Press.