    Waves in strata  Next: Snell waves Up: DIPPING WAVES Previous: DIPPING WAVES

## Rays and fronts

It is natural to begin studies of waves with equations that describe plane waves in a medium of constant velocity.

Figure 3.7 depicts a ray moving down into the earth at an angle from the vertical.

front
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 . 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 . 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 3.7 is (4)

In this expression is the intercept between the wavefront and the vertical axis. To make the intercept move downward, replace it by the appropriate velocity times time: (5)

Solving for time gives (6)

Equation (3.6) tells the time that the wavefront will pass any particular location . The expression for a shifted waveform of arbitrary shape is . Using (3.6) to define the time shift gives an expression for a wavefield that is some waveform moving on a ray. (7)    Waves in strata  Next: Snell waves Up: DIPPING WAVES Previous: DIPPING WAVES

2009-03-16