Rayleigh Wave Creation and Propagation

Harvard EPS55

Understanding the formation and characteristics of Rayleigh surface waves - the rolling motion of the Earth

Particle Motion Pattern
Surface 0.2λ 0.4λ 0.6λ Surface Shallow Deep Wave Direction
Wave Creation Process
Source P-wave S-wave P+S Interaction Rayleigh Wave

What are Rayleigh Waves?

Rayleigh waves are surface seismic waves that produce an elliptical rolling motion similar to ocean waves. Key characteristics:

Property Value
Velocity ~0.9 × Vs (shear velocity)
Typical Speed 2-4 km/s
Frequency 0.02-0.5 Hz
Penetration Depth ~1 wavelength
Dispersion Yes (velocity varies with frequency)

Creation Mechanism

Rayleigh waves form through the interaction of P and SV waves at the free surface:

Step 1: Seismic source generates body waves
Step 2: P and SV waves reach the surface
Step 3: Constructive interference at critical angles
Step 4: Energy trapped near surface
Step 5: Elliptical particle motion established
Rayleigh equation: (2-c²/β²)² = 4√(1-c²/α²)√(1-c²/β²)

Where c = Rayleigh velocity, α = P-velocity, β = S-velocity

Particle Motion & Amplitude

The characteristic retrograde elliptical motion varies with depth:

  • At surface: Maximum amplitude, retrograde ellipse
  • At 0.2λ depth: Motion reverses to prograde
  • Below 1λ: Amplitude negligible
Amplitude ∝ exp(-2πz/λ)

Ground motion components:

  • Vertical: ~1.5× horizontal amplitude
  • Horizontal: In direction of propagation
  • Phase shift: 90° between components