Seismic Wave Velocity Calculator

P-waves (primary or compressional waves) are longitudinal waves where particle motion is parallel to the direction of propagation — they compress and expand the material as they travel. S-waves (secondary or shear waves) are transverse waves where particles oscillate perpendicular to the propagation direction. P-waves always travel faster than S-waves in the same medium, which is why they arrive first at seismograph stations after an earthquake.

P-wave velocity is calculated as Vp = √((K + 4G/3) / ρ), where K is bulk modulus, G is shear modulus, and ρ is density. S-wave velocity is calculated as Vs = √(G / ρ). Both results are in m/s when K and G are in Pascals and ρ is in kg/m³.

Fluids (liquids and gases) have zero shear modulus because they cannot resist shear deformation — they simply flow. Since S-wave velocity depends entirely on the shear modulus (Vs = √(G/ρ)), a zero shear modulus yields zero S-wave velocity. This is why seismologists know that Earth's outer core is liquid: S-waves do not pass through it.

The Vp/Vs ratio (also written as the Poisson's ratio equivalent) provides critical information about a material's physical state. A ratio around 1.73 is typical for hard rock. Higher ratios (above 2.0) can indicate fluid-saturated or unconsolidated sediments, which is important in oil and gas exploration, earthquake hazard assessment, and geotechnical site characterisation.

Vp in granite is roughly 5,500–6,000 m/s; in limestone around 3,500–6,000 m/s; in sandstone 2,000–4,500 m/s; in unconsolidated soil 200–700 m/s; and in water approximately 1,450–1,500 m/s (P-wave only, no S-wave). Deeper mantle rock can exceed 8,000 m/s for P-waves.

Seismologists use the arrival time difference between P-waves and S-waves recorded at seismograph stations to determine the distance to an earthquake's epicentre — a technique called S-P time. The characteristic waveform shapes, particle motion directions, and frequency content also help distinguish wave types. Multiple station readings allow three-dimensional location of the seismic source.

As depth increases, pressure rises dramatically, causing minerals to become more tightly packed, which increases both bulk modulus and shear modulus faster than density increases. The net effect is higher wave velocities. Velocity also changes abruptly at compositional boundaries like the crust-mantle boundary (Moho), where it jumps from ~6 km/s to ~8 km/s for P-waves.

Shear wave velocity (Vs) is a direct measure of soil or rock stiffness and is used to classify site conditions for earthquake engineering (e.g., NEHRP site classes based on Vs30 — the average shear wave velocity in the top 30 m). Higher Vs30 values mean stiffer ground, less amplification of shaking, and lower seismic hazard. Vs measurements are obtained via surface wave methods (MASW), downhole tests, or seismic refraction surveys.