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Ground model and survey
Velocity must increase with depth for refraction to work; the page enforces that automatically.
Model checks
The science
What is modelled
A source at x = 0 sends energy into a layered ground. The direct wave travels in layer 1; a wave that hits the boundary at the critical angle runs along the faster layer below as a head wave and returns to the surface. Beyond the crossover distance the head wave arrives first, so the slopes of the first-arrival line segments give the layer velocities and the intercept times give thicknesses.
Equations
- Critical angle
sin θc = v1/v2, critical offset2 h1 tan θc. - Head-wave arrival
t = x/v2 + 2 h1 √(1/v1² - 1/v2²)(intercept time at x = 0). - Crossover
xc = 2 h1 √((v2 + v1)/(v2 - v1)). - Inversion: bounded multistart coordinate search minimising the rms of first-break misfit.
Checks run in the page
- The refracted arrival at 220 m against the intercept-time formula.
- The numerically scanned crossover distance against the closed form.
- The inversion of noisy picks reproduces the true first arrivals to within the pick noise.
Honest simplifications
Flat, homogeneous layers, no hidden layers or velocity inversions, ray theory only (no amplitudes from Zoeppritz equations; the wiggle record uses made-up amplitudes with Ricker pulses). The inversion is non-unique: different layer thicknesses can fit the same picks within noise, so only the fit is guaranteed, not the model.
What to try
- Drag the highlighted receiver offset past the crossover and watch the first break switch from the direct to the refracted ray.
- Raise the picking noise to 3 ms and compare the green inverted model with the white true one.
- Choose Shallow bedrock and note that the inversion trades off layer-1 thickness against layer-2 velocity.