The Choice of Variables for Elastic Wave Extrapolation
, by Robert W. Clayton and David Brown
The choice of variables for elastic extrapolation problems deter-
mines the form of the one-way wave equations. Three sets of
variables are considered: displacements, potentials, and a mixed
set of variables which eliminate troublesome -- terms from the
full wave equation. The displacements satisfy boundary conditions
at internal interfaces but presently lack a recurrence relation to
generate higher order approximation. The potential variables
(P and S waves) appear to have problems similar to those of the
displacements for variable velocity media, because the equation
contains a complicated term which is difficult to factor into up
and downgoing waves. The mixed set of variables have the desired
recurrence relation but fail to satisfy the boundary conditions.
They also appear to be unstable for variable velocity.
STANFORD