Hit the ground, time the first arrival at each geophone, and plot time against distance. Near the shot the direct wave wins; further out the wave that dived into faster rock arrives first. The two slopes are the two velocities, and the depth follows — by the crossover distance, and again by the intercept time. If the two disagree, the model is wrong.
| material | P velocity m/s |
|---|
Water is 1450 to 1500 m/s whatever it is in, so saturated sand and weathered rock can look identical. A refraction line across a water table finds the water table, not the rockhead — which is the commonest misreading of the method.
Push current into the ground through two electrodes, measure the voltage across two others, and the ratio is a resistance. The geometry turns it into a resistivity — and for a Wenner array the geometry is as simple as it gets: ρ = 2πa·R.
| material | resistivity Ω·m |
|---|
In a clean rock the electricity goes through the water, not the grains. Archie's law puts that into numbers — resistivity depends on porosity, on saturation, and on how salty the water is, and on nothing else. Which is why the same rock reads differently above and below the water table, and why clay breaks the law entirely.
Every geophysical method is blind to something, and the blindness does not announce itself — the data look perfectly good and the interpretation is simply wrong.
| the trap | what happens |
|---|
A layer thin enough never to overtake the layers around it never appears as a first arrival — and the depth to everything below it comes out too shallow. This is how thick a layer must be before refraction can see it at all.
A velocity is also a statement about whether ground can be dug — Foundations and tunnels reads the same number that way. And where these methods are being used to look for a cavity, Karst and sinkholes is the instrument that says what to do about one.