# Seismic Waves Simulator - P & S Waves, Epicentre, Magnitude, Earth Rays

> Animate P, S, Rayleigh and Love waves, locate an epicentre from S−P times, compute Richter and moment magnitude and energy, and trace rays through the Earth.

- URL: https://qilingtools.com/en/physics/seismology
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Pick a rock and get P, S, Rayleigh and Love wave speeds from its bulk modulus, shear modulus and density, then watch how particles move in each wave. Drag three stations and an epicentre, read S−P times from synthetic seismograms and find the epicentre as the least-squares intersection of three circles. Compute moment magnitude, energy and TNT equivalent from fault size, and trace rays through a layered PREM Earth with Snell's law to see the P and S shadow zones.

## How to use

1. On the Wave types tab, choose a rock or adjust the elastic moduli and watch the four waves and their speeds
2. On Locate epicentre, drag the stations and the epicentre, read the seismograms and circles, or type S−P times yourself
3. On Magnitude & energy, enter amplitude and distance for M_L, or fault length, width and slip for M_w, energy and TNT
4. On Earth's interior, set the number of rays, toggle P and S, drag the source and read the shadow zones and travel-time curves

## Features

- v_p and v_s from K, G and ρ; v_R from the Rayleigh equation; v_L from the Love-wave dispersion equation
- Particle-grid animations of P, S, Rayleigh (retrograde ellipse) and Love waves, alone or side by side
- Draggable stations and epicentre, synthetic seismograms, Levenberg–Marquardt least-squares location
- Local and moment magnitude, energy and TNT equivalent, a table of historic quakes and a log energy chart
- Spherical-shell ray tracing in the PREM model with computed P and S shadow zones and travel-time curves

## FAQ

### What is the difference between P and S waves?

P waves are compressional: particles move back and forth along the direction of travel, at v_p = √((K + 4G/3)/ρ), about 6 km/s in granite, and they cross solids, liquids and gases. S waves are shear waves: particles move across the direction of travel at v_s = √(G/ρ), about 3.5 km/s. A liquid has no shear stiffness (G = 0), so S waves cannot cross the liquid outer core. P waves always arrive first; P stands for primary.

### How does the S−P time tell you the distance?

Both waves leave the focus together but travel at different speeds, so the gap grows with distance: Δt = d/v_s − d/v_p, hence d = Δt · v_p v_s/(v_p − v_s). In the crust the factor is about 8 km per second of S−P. One station only gives a distance, so the source lies on a circle; three circles meet at the epicentre. Real errors keep them from meeting exactly, so the tool finds the least-squares best point.

### How much more energy does one magnitude step mean?

Amplitude goes up 10 times and energy about 31.6 times (10^1.5), because log₁₀E = 1.5M + 4.8. Two steps is about 1000 times. A magnitude 9 earthquake releases roughly as much energy as 1000 magnitude 7 quakes, or about 30,000 magnitude 6 quakes.

### Richter magnitude vs moment magnitude?

Richter (local) magnitude M_L comes from the largest amplitude on a seismogram and the distance. It works for nearby, small and moderate quakes but saturates for big ones (above about 7 it stops growing). Moment magnitude M_w comes from the seismic moment M₀ = μAD (rigidity × fault area × average slip), measures the size of the rupture directly, does not saturate, and is the standard for large earthquakes.

### Where do the seismic shadow zones come from?

Wave speed changes with depth, so rays bend following Snell's law for spherical shells, r sin i / v = constant. When P waves enter the liquid outer core their speed drops from about 13.7 to 8 km/s and they are bent sharply, leaving a band roughly 103°–142° from the epicentre with almost no direct P. S waves cannot enter the liquid core and vanish beyond about 103°. These shadows were key evidence for the core and for its liquid outer part.

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