Seismic head wave

A critically refracted wave associated with a faster lower layer that travels along an interface and radiates back into the slower upper layer. Its travel-time branch has the lower-layer horizontal slowness and a positive intercept time.

For a P ray incident from a layer of speed ${\alpha }_1$ onto a faster layer ${\alpha }_2$, the transmitted ray is tangential when $\sin i_c={\alpha }_1/{\alpha }_2$. Angles are measured from the interface normal.

In a two-layer P wave model, the head-wave branch overtakes the direct upper-layer arrival at $X_c=2H\sqrt{({\alpha }_2+{\alpha }_1)/({\alpha }_2-{\alpha }_1)}$. It differs from the smaller minimum offset needed for the critical-ray construction.