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The science
In a uniform layer a wave front is a sphere (a circle in the cross-section) that grows at the wave speed. At a boundary the ray bends by Snell's law sinθ1/v1 = sinθ2/v2. When v2 > v1 there is a critical angle sinθc = v1/v2; a ray at θc runs along the boundary at v2 and keeps shedding energy upward as the head wave.
For a source at depth d and a layer of thickness h the travel times to a surface receiver at distance x are: direct √(x²+d²)/v1, Moho reflection √(x²+(2h−d)²)/v1, head wave x/v2 + (2h−d) cosθc / v1 (valid beyond the critical distance (2h−d) tanθc). Beyond the crossover distance the head wave arrives first, which is how the Moho depth is measured.
S waves travel at vP/(Vp/Vs); the S−P delay of the direct waves grows linearly with distance, so one station gives the source distance.
Simplifications: two homogeneous layers, flat surface, geometrical rays and fronts (no amplitude physics beyond a crude seismogram), no mode conversion at the Moho, no free-surface reflections. This is an educational model of an inanimate Earth.
What to try
- Move the receiver beyond the crossover distance: the first arrival switches from the direct wave to the refracted head wave.
- Thin the crust: the crossover distance shrinks.
- Raise Vp/Vs: the S wave lags further behind P.
- Use the S-P graph: read the distance from the delay and compare with the true distance.