Translations:The eikonal equation - book/11/en

The left-hand side of equation 16 involves the wavefront; the right-hand side involves the ray. As we have seen, velocity is called swiftness. The reciprocal of velocity is slowness. The connecting link is the slowness. In the above equation, the function ${\displaystyle t\left(x,y\right)}$ is the traveltime from the source to the point with the coordinates (x,y), and ${\displaystyle n\left(x,y\right){\rm {=}}{\rm {1}}/v\left(x,y\right)}$ is the slowness (or reciprocal velocity) at that point. The apparent swiftnesses along the coordinate directions are, respectively, ${\displaystyle \partial x{\rm {/}}\partial t,\partial y/\partial t}$. Thus, the apparent slownesses along the coordinate directions are ${\displaystyle \partial t{\rm {/}}\partial x,\partial t/\partial y}$. The actual swiftness along the raypath direction is ${\displaystyle v{\rm {=}}ds/dt}$. Thus the actual slowness along the raypath direction is ${\displaystyle n{\rm {=}}dt/ds}$.