To examine running horses it may be best to jump on a horse.
Likewise, to examine moving waves, it may be better to move along with them.
So to describe waves moving downward into the earth we might
abandon (*x*,*z*)-coordinates in
favor of moving (*x*,*z*' )-coordinates, where .

An alternative to the moving coordinate system is to define
*
retarded coordinates
*
where .The classical example of retarded coordinates is solar time.
Time seems to stand still
on an airplane that moves westward at the speed of the sun.

The migration process resembles the simulation of wave propagation
in either a moving coordinate frame or a retarded coordinate frame.
Retarded coordinates are much more popular than moving coordinates.
Here is the reason:
In solid-earth geophysics, velocity may depend
on both *x* and *z*, but the earth doesn't change
with time *t* during our seismic observations.
In a moving coordinate system the velocity could
depend on all three variables, thus unnecessarily increasing
the complexity of the calculations.
Fourier transformation is a popular
means of solving the wave equation, but it loses most of
its utility when the coefficients are nonconstant.

- Definition of independent variables
- Definition of dependent variables
- The chain rule and the high frequency limit
- Fourier transforms in retarded coordinates
- Interpretation of the modulated pressure variable Q
- Einstein's special relativity theory

10/31/1997