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Next: NUMERICAL TEST
Up: Fomel: Linearized Eikonal
Previous: THE LINEARIZED EIKONAL EQUATION
Linearization of the eikonal equation suggests the following algorithm
of traveltime computation:
- Start with an initial traveltime field
. The initial
traveltime may be the result of a previous computation or (for simple
models) the result of an approximate analytic evaluation.
- Compute the finite-difference gradient
and the
corresponding slowness model
with equation
(2).
- Compute the slowness perturbation
as the difference
between the true slowness model
and
. Exit the computation if
the perturbation is smaller than the desired accuracy.
- Solve numerically equation (5) for the traveltime
perturbation
.
- Update the traveltime field
by adding
to it.
- Repeat the loop.
Equation (5) can be solved numerically with a simple explicit
upwind finite-difference method.
2013-03-03