Site Amplification: Two Physical Mechanisms

Harvard EPS55

Impedance Contrast + Ray Angle Effects on Seismic Wave Recording

Hard Bedrock (3000 m/s, High Z)
Soil Type 1 - Medium (800 m/s, Medium Z)
Soil Type 2 - Soft (400 m/s, Low Z)
Seismic Waves + 3-Component Sensors
Bedrock Velocity
3000 m/s
Soil Type 1 Velocity
800 m/s
Soil Type 2 Velocity
400 m/s
Total Amplification
7.5x

Mechanism 1: Impedance Contrast

When seismic waves cross from high impedance (Z = ρv) to low impedance materials, amplitude increases due to energy conservation at the interface.

Transmission Coefficient: T = 2Z₁/(Z₁+Z₂)

Key characteristics:

  • Primarily affects high-frequency energy
  • Depends on density (ρ) and velocity (v) contrast
  • Energy conservation requires amplitude increase when velocity decreases
  • More pronounced with larger impedance contrasts

Mechanism 2: Ray Angle Effect

Sensors record wave projections, not true amplitudes. As waves refract to more vertical paths in softer soils, the vertical component (Z) recording increases.

Recorded: Z = A·cos(θ), H = A·sin(θ)

Key characteristics:

  • Affects all frequencies based on geometry
  • Purely geometric projection effect
  • Smaller angles (more vertical) → larger Z recordings
  • Can create apparent amplification without energy increase

Combined Effects & Observations

Both mechanisms work together in real earthquakes:

  • High-frequency waves: Impedance contrast dominates
  • Low-frequency waves: Ray angle effect more important
  • Site amplification factors: Range from 2x to 10x+
  • Frequency dependent: Different amplification at different frequencies
Total Amplification = Impedance Effect × Geometric Effect

Toggle between modes to see each mechanism separately. Understanding both is crucial for accurate seismic hazard assessment.