Separation of the Forward and Backward Solutions of the One-Dimensional Wave Equation
, by R.S. Anderssen
A number of authors (see, for example, Corones [1] and Sluijter [2])
have discussed the significance of the decomposition of the solution
of the wave equation into forward and backward (up and down) wave
solutions. In particular, in the context of numberical holography,
Claerbout and co-workers have shown that the actual numerical
separation is an essential requirement, and have used wave equation
migration for this purpose (see, for example, Claerbout [3]). The
possibility of using variational methods as a basis for the
separation does not appear to have been investigated. In this
report, we can show that certain variation formulations for the
wave equation can be used to separate computationally these two
basic types of solutions. The actual separation depends heavily on
the choice of coordinate functions for the variational solution.
STANFORD