P-Waves, S-Waves, and How Earthquakes Revealed a Liquid Core

Two waves, one earthquake

When rock suddenly ruptures along a fault, the released energy radiates outward as elastic waves through the solid Earth, and it does so in two fundamentally different modes at once. P-waves (primary, or compressional waves) squeeze and stretch the rock along the direction of travel, exactly like sound moving through air -- particles oscillate back and forth parallel to the wave's motion. S-waves (secondary, or shear waves) instead shake the rock perpendicular to the direction of travel, like a shaken rope. That difference in restoring mechanism -- compression versus shear -- is also what makes one wave faster than the other.

Vp = sqrt((K + 4/3*mu) / rho)     P-wave speed
Vs = sqrt(mu / rho)                S-wave speed

K     bulk modulus (resistance to compression)
mu    shear modulus (resistance to shape distortion)
rho   density

Because the P-wave formula includes both the bulk modulus K and the shear modulus mu while the S-wave formula depends on shear alone, and K is always positive, P-waves are always faster -- typically around 1.7 times the S-wave speed in typical crustal rock. That is why a P-wave always arrives at a seismograph first (hence "primary") and the S-wave trails behind it ("secondary"); the time gap between the two arrivals grows with distance from the earthquake and is the standard method for estimating how far away a quake occurred.

The critical difference: S-waves cannot cross liquid

A shear wave requires a restoring force that resists a change of shape -- and a fluid, by definition, has no resistance to shear; it simply flows instead of springing back. Its shear modulus mu is zero, so the S-wave speed formula gives exactly zero: S-waves cannot propagate through a liquid at all. P-waves, which only need resistance to volume change (compression), pass through liquids and gases just fine -- it is exactly how sound travels through air and water.

The shadow zone: how seismology found the liquid core

This one fact -- S-waves die in liquid, P-waves don't -- is how seismologists discovered Earth's core is liquid, decades before anyone could sample it directly. Seismographs around the world after a large earthquake show a band roughly 103 to 142 degrees of arc away from the epicentre where no direct S-waves arrive at all, and where P-waves also arrive later and weaker than a uniform-Earth model predicts, because they refract sharply on entering the outer core. That gap is the shadow zone. Richard Oldham first proposed a core in 1906 from delayed P-arrivals, and Beno Gutenberg pinned down the core-mantle boundary depth in 1913; the complete absence of direct S-waves in the shadow zone became the clinching evidence that at least the outer core has to be liquid -- a solid or even highly viscous core could not block shear waves that thoroughly.

P-wave shadow zone:   103 deg to 142 deg from epicentre (weakened, refracted)
S-wave shadow zone:   > 103 deg from epicentre (essentially absent -- no path through liquid outer core)

Layered Earth, curved paths

Earth is not uniform, so wave speed changes with depth as pressure, temperature and composition change, and by Snell's law a wave bends whenever it crosses a boundary between materials of different speed -- exactly like light refracting at a lens. This makes seismic ray paths through the real Earth gently curved rather than straight lines, bending more sharply at sharp discontinuities such as the crust-mantle boundary (the Moho) and the mantle-core boundary. Reflections and refractions at these boundaries produce a whole family of secondary wave arrivals (with names like PcP, PKP, ScS) that seismologists use to map the depth and properties of every internal layer, essentially doing a full-planet CT scan using nothing but earthquakes as the light source and seismographs as the detectors.

What the simulation is modelling

The demo propagates two circular wavefronts outward from a source point at two different fixed speeds -- the P/S ratio of about 1.7 -- and records their arrival at one or more seismograph positions, reproducing the characteristic double-onset seismogram: a first, smaller P-wave jolt followed some seconds later by a larger, more damaging S-wave arrival. A full-Earth model would also render the liquid-core shadow zone by simply switching off S-wave propagation inside the outer-core region and bending both wave types at each layer boundary, which is exactly the calculation real seismologists run to infer Earth's internal structure from surface observations alone.

Frequently asked questions

Try it live

Everything above runs in your browser — open Seismic Waves and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.