It is natural to begin studies of waves with equations that describe plane waves in a medium of constant velocity.
Figure 7 depicts a ray moving down into the earth at an angle from the vertical.
Figure 7 Downgoing ray and wavefront.
Perpendicular to the ray is a wavefront. By elementary geometry the angle between the wavefront and the earth's surface is also .The ray increases its length at a speed v. The speed that is observable on the earth's surface is the intercept of the wavefront with the earth's surface. This speed, namely , is faster than v. Likewise, the speed of the intercept of the wavefront and the vertical axis is .A mathematical expression for a straight line like that shown to be the wavefront in Figure 7 is
In this expression z0 is the intercept between the wavefront and the vertical axis. To make the intercept move downward, replace it by the appropriate velocity times time: