The isotropic layer

Although the formalism extends to velocity anisotropy, it is informative to look at the isotropic case. Most of the results will not be new, but it is a check on the general theory and a link to the familiar. Starting with the basic time/offset equation t_x² = t₀² + x²/v², the equations for time, offset, and velocity as functions of p are

$$t(p) = \frac{t_{0}}{\sqrt{1-v^{2}p^{2}}}$$

and

$$x(p) = \frac{v^{2}pt_{0}}{\sqrt{1-v^{2}p^{2}}}$$

and

v(p) = v