🎓 Lesson 16
D5
Seismic Refraction for Bedrock Depth — Field Setup and Velocity Inversion
Seismic refraction is a method that uses the travel time of sound waves through the ground to figure out how deep the bedrock is and how fast the waves move in different layers.
🎯 Learning Objectives
- ✓ Calculate P-wave velocities in soil and bedrock layers from field refraction travel-time data
- ✓ Design an optimal geophone spread geometry (offset, spacing, length) for a target bedrock depth of 30 m
- ✓ Analyze and interpret a first-arrival time-distance plot to identify layer breaks and compute layer depths using the intercept time method
- ✓ Explain the physical assumptions and limitations of the seismic refraction method in heterogeneous or low-velocity layer settings
- ✓ Apply the generalized reciprocal method (GRM) to improve depth estimates in cases of dipping interfaces
📖 Why This Matters
Knowing bedrock depth is critical before designing foundations, tunnels, or slope stabilization systems — especially where overburden thickness varies significantly. Unlike drilling every meter, seismic refraction provides rapid, cost-effective, non-invasive profiling across dozens of meters in under an hour. In mining, it guides blast design by revealing competent rock geometry beneath weathered zones — preventing misfires, excessive vibration, or unexpected cratering.
📘 Core Principles
Seismic refraction exploits the fact that when a P-wave encounters a boundary between two materials with increasing seismic velocity, part of the energy is refracted along the interface at the critical angle. This critically refracted ray travels faster than the direct wave in the upper layer and arrives first at distant receivers — producing a distinct linear segment on the time-distance (t-x) plot. The slope of this segment gives the bedrock velocity (V2), while its intercept with the time axis (t-intercept) yields the overburden thickness (h1) via h1 = (t_i × V1 × V2) / (2 × √(V2² − V1²)). Assumptions include planar, parallel layers; velocity increase with depth; and lateral homogeneity. Violations (e.g., a low-velocity layer, or steep dip) cause misinterpretation — hence the need for complementary methods like MASW or reflection.
📐 Intercept Time Method for Two-Layer Model
The intercept time method computes overburden thickness (h₁) from the t-x plot’s intercept (tᵢ) and the measured velocities of the upper (V₁) and lower (V₂) layers. It assumes a horizontal, two-layer system and is the foundational inversion for field practitioners.
Overburden Thickness (Two-Layer Intercept Method)
h₁ = (tᵢ × V₁ × V₂) / (2 × √(V₂² − V₁²))Computes depth to the top of the first refracting layer (e.g., bedrock) assuming two horizontal, isotropic layers.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| h₁ | Overburden thickness | m | Vertical depth from surface to top of refracting layer (e.g., bedrock) |
| tᵢ | Intercept time | s | Extrapolated time where the refracted line intersects the time axis (x = 0) |
| V₁ | P-wave velocity of Layer 1 (overburden) | m/s | Velocity of the upper, slower layer (e.g., soil, weathered rock) |
| V₂ | P-wave velocity of Layer 2 (bedrock) | m/s | Velocity of the lower, faster refracting layer |
Typical Ranges:
Sandy soil to granite: V₁ = 300–800 m/s; V₂ = 2500–6000 m/s
Clay to basalt: V₁ = 500–1200 m/s; V₂ = 4000–7000 m/s
💡 Worked Example
Problem: A seismic refraction survey records first arrivals: direct wave slope = 0.5 ms/m (V₁ = 2000 m/s); refracted wave slope = 0.25 ms/m (V₂ = 4000 m/s); intercept time tᵢ = 12 ms. Calculate overburden thickness h₁.
1.
Step 1: Convert velocities to consistent units — V₁ = 2000 m/s, V₂ = 4000 m/s.
2.
Step 2: Compute denominator: √(V₂² − V₁²) = √(16×10⁶ − 4×10⁶) = √(12×10⁶) ≈ 3464 m/s.
3.
Step 3: Apply formula: h₁ = (tᵢ × V₁ × V₂) / (2 × √(V₂² − V₁²)) = (0.012 s × 2000 × 4000) / (2 × 3464) ≈ 96 / 6928 ≈ 13.85 m.
4.
Step 4: Verify against typical engineering range: For V₂/V₁ = 2.0, h₁ ≈ 12–16 m is reasonable for glacial till over granite.
Answer:
The overburden thickness is 13.9 m, which falls within the typical range of 10–20 m for moderate-depth bedrock investigations.
🏗️ Real-World Application
At the Cadia East gold mine (NSW, Australia), seismic refraction was deployed prior to open-pit expansion to map the depth to competent porphyry bedrock beneath variable colluvium and saprolite. A 120-m spread with 24 geophones (2-m spacing) and a 5-kg sledgehammer source revealed V₁ = 750 m/s (weathered zone), V₂ = 3200 m/s (fresh andesite), and tᵢ = 24 ms → h₁ ≈ 28.5 m. This guided placement of 30-m drill holes — all confirming bedrock within ±1.2 m of prediction — reducing exploration drilling by 37% and accelerating geotechnical model calibration.
📋 Case Connection
📋 Urban Transit Tunnel Alignment Through Mixed-Soil Stratigraphy
Variable soil profile (soft clay → weathered volcanic tuff → dense sand) causing differential settlement and excavation...