Seismic Refraction Depth Calculator (Crossover Distance and Intercept Time)
Depth to a faster layer, such as bedrock or the water table, from the wave speeds of the two layers and the crossover distance or intercept time on a travel-time graph.
Results
The dashed line marks the value you entered.
What this tool does
In a refraction survey, a hammer blow sends waves along the ground; close to the source the first arrival is the direct wave in the top layer, but beyond the crossover distance a wave that dipped into the faster layer below, ran along its top and came back up arrives first. The speeds are the inverse slopes of the two straight segments on the time–distance graph, and the depth follows from where they cross, or from the intercept of the second segment on the time axis. The method needs each layer to be faster than the one above and the interface to be flat; a slower layer hidden below a faster one is invisible to it.
Formula
z = (x_c ÷ 2) √((v₂ − v₁) ÷ (v₂ + v₁)) · z = t_i v₁ v₂ ÷ (2 √(v₂² − v₁²)) · θ_c = asin(v₁ ÷ v₂)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v1 | Wave speed in the top layer | m/s |
v2 | Wave speed in the layer below | m/s |
xc | Crossover distance | m |
ti | Intercept time | ms |
ZX | Depth to the interface (from crossover distance) | m |
ZI | Depth to the interface (from intercept time) | m |
TC | Critical angle | ° |
XK | Critical distance (first refracted arrival) | m |
Worked example
- Wave speed in the top layer500 m/s
- Wave speed in the layer below2000 m/s
- Crossover distance40 m
- Intercept time60 ms
- Depth to the interface (from crossover distance)15.49 m
- Depth to the interface (from intercept time)15.49 m
- Critical angle14.48 °
- Critical distance (first refracted arrival)8.0 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.