Why do P waves always arrive before S waves?

P waves are compressional and travel faster than the shear S waves in the same material, so they reach a seismometer first; the growing gap between the P and S arrivals with distance is used to estimate how far away an earthquake occurred.

Why are surface waves usually the most damaging?

Surface waves are confined near the surface, so their energy spreads in two dimensions rather than three and attenuates more slowly with distance; combined with their long periods, this often makes them the largest-amplitude arrivals at the ground.

Seismic Wave Propagation

An elastic disturbance in the Earth spreads as P and S body waves through the interior and as Rayleigh and Love waves along the surface, refracting and reflecting at boundaries set by the velocity structure.

Definition

Seismic wave propagation is the transmission of elastic energy through the Earth governed by the wave equation, producing body waves that travel through the interior and surface waves that travel along the free surface, each refracted, reflected, and attenuated according to the medium's elastic moduli and density.

Scope

This topic covers the elastodynamic wave equation and the wave types it supports: compressional P waves, shear S waves, and the dispersive Rayleigh and Love surface waves. It treats reflection, refraction, and mode conversion at interfaces, Snell's law and ray theory, the formation of seismic phases and travel-time curves, attenuation and geometrical spreading, and surface-wave dispersion. The focus is on how elastic properties of the medium control the speed, path, and amplitude of seismic energy.

Core questions

What distinguishes P, S, Rayleigh, and Love waves in speed, motion, and path?
How do reflection, refraction, and mode conversion arise at velocity interfaces?
Why are surface waves dispersive, and what does dispersion reveal about structure?
How do attenuation and geometrical spreading reduce wave amplitude with distance?

Key concepts

Compressional (P) and shear (S) body waves
Rayleigh and Love surface waves and their dispersion
Snell's law, ray paths, and travel-time curves
Reflection, refraction, and mode conversion at interfaces
Seismic attenuation (Q) and geometrical spreading

Key theories

Elastic wave equation and ray theory: Linear elastodynamics yields a wave equation whose solutions separate into P and S body waves; in the high-frequency limit their energy follows rays obeying Snell's law, allowing travel times to be predicted from a velocity model.
Surface-wave dispersion: Because Rayleigh and Love waves sample depth as a function of frequency, longer-period components travel faster, producing characteristic dispersion whose inversion constrains the depth profile of seismic velocity.

Mechanisms

Stress applied to an elastic solid produces volumetric and shear strains that propagate as P and S waves, respectively; at a boundary where impedance changes, energy partitions into reflected and transmitted, possibly mode-converted, waves, while the free surface and layering trap energy into guided surface waves whose phase and group velocities depend on period.

Clinical relevance

Understanding wave propagation is essential for locating earthquakes, predicting how shaking will vary across a region, and designing the seismic surveys used to image the subsurface for water, energy, and engineering studies.

History

Rayleigh predicted surface waves on an elastic half-space in 1885 and Love explained horizontally polarized surface waves in 1911; twentieth-century instrumentation and the quantitative framework codified by Aki and Richards turned wave propagation into a precise tool for both source and structure studies.

Key figures

Lord Rayleigh
Augustus Edward Hough Love
Keiiti Aki

Seminal works

akirichards2002
shearer2009
steinwysession2003

Frequently asked questions

Why do P waves always arrive before S waves?: P waves are compressional and travel faster than the shear S waves in the same material, so they reach a seismometer first; the growing gap between the P and S arrivals with distance is used to estimate how far away an earthquake occurred.
Why are surface waves usually the most damaging?: Surface waves are confined near the surface, so their energy spreads in two dimensions rather than three and attenuates more slowly with distance; combined with their long periods, this often makes them the largest-amplitude arrivals at the ground.