EIKONAL EQUATION

The eikonal equation in two dimensions is as follows (Aki and Richards, 1980, ch.4):  

$$\Bigl( \t_x\Bigr) ^2 \ +\ \Bigl( \t_z\Bigr) ^2 \ =\ s^2(x,z),$$ (1)

where s(x,z) is the 2-dimensional slowness model and $\t = \t(x,z)$ is the traveltime field. Subscripts x and z denote partial derivatives with respect to x and z, respectively.