    Waves in strata  Next: Root-mean-square velocity Up: Waves in strata Previous: Solution to kinematic equations

# CURVED WAVEFRONTS

The simplest waves are expanding circles. An equation for a circle expanding with velocity is (15)

Considering to be a constant, i.e. taking a snapshot, equation (3.15) is that of a circle. Considering to be a constant, it is an equation in the -plane for a hyperbola. Considered in the -volume, equation (3.15) is that of a cone. Slices at various values of show circles of various sizes. Slices of various values of show various hyperbolas.

Converting equation (3.15) to traveltime depth we get   (16)   (17)

The earth's velocity typically increases by more than a factor of two between the earth's surface, and reflectors of interest. Thus we might expect that equation (3.17) would have little practical use. Luckily, this simple equation will solve many problems for us if we know how to interpret the velocity as an average velocity.

Subsections    Waves in strata  Next: Root-mean-square velocity Up: Waves in strata Previous: Solution to kinematic equations

2009-03-16