*
This chapter is a condensation of
wave extrapolation and finite-difference basics from IEI
which is now out of print.
On the good side,
this new organization is more compact
and several errors have been corrected.
On the bad side,
to follow up on many
many interesting details
you will need to find a copy of IEI
(http://sepwww.stanford.edu/sep/prof/).
*

In chapter we learned how
to extrapolate wavefields down into the earth.
The process proceeded simply, since it is just a multiplication in the
frequency domain by .In this chapter
instead of multiplying a wavefield by a function of *k*_{x}
to downward continue waves,
we will convolve them along the *x*-axis
with a small filter that represents a differential equation.
On space axes, a concern is the seismic velocity *v*.
With

**lateral velocity variation**, say *v*(*x*),
then the operation of extrapolating wavefields upward and downward
can no longer be expressed as a product in the *k*_{x}-domain.
(Wave-extrapolation procedures in the
spatial frequency domain are no longer multiplication,
but convolution.)
The alternative we choose here is to go to finite differences
which are convolution in the physical *x* domain.
This is what the wave equation itself does.

- THE PARABOLIC EQUATION
- SPLITTING AND SEPARATION
- FINITE DIFFERENCING IN (omega,x)-SPACE
- WAVEMOVIE PROGRAM
- HIGHER ANGLE ACCURACY
- END OF CHAPTER FOR NOW
- SPLITTING AND SEPARATION APPLICATIONS
- THE ACOUSTIC WAVE EQUATION

12/26/2000