Seismic Refraction: Basement Velocity from the Head-Wave Slope
Unknown two-layer section. Time the first arrival at large offsets and recover v₂ from a fit of t versus x.
University / research· 24 min·Related simulator: Biophysics, Fluids & GeoscienceLayered Medium: P/S Fronts & Hodograph
Goal
Determine v₂ from the head-wave branch t = t₀ + x/v₂. The slope of t versus x is 1/v₂.
Equipment
- Shot point
- Geophone line
- Unknown two-layer section
- First-arrival timer
Experiment
Theory
When the lower layer is faster, a critically refracted head wave is first at large offset. Its travel time is linear: dt/dx = 1/v₂. The bench hides v₁, v₂, H and any “head possible” flag. A live geophone time is the instrument. Use offsets well beyond the crossover; the near-offset reflection branch is not a straight line of slope 1/v₂.
Procedure
- Layer velocities and thickness are hidden. You only change the geophone offset x.
- Watch the live first-arrival time. Record at large offsets (about 40 km and beyond) where the first arrival is the head wave.
- Each row stores x and t. Repeat for at least 6 offsets spanning a wide range.
- Fit t versus x; v₂ = 1 / slope. Compare with the reference.
Conclusion
The fitted v₂ agrees with the hidden basement. Main uncertainties: mixing in near-offset reflection times and timer noise.