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Another important consideration is the speed of convergence of the problem.
The size of most geophysical
problems make direct matrix inversion methods impractical.
An appealing alternative for linear problems is the family of
conjugate gradient methods. Unfortunately,
the operators used in seismic reflection problems
are often computationally expensive.
As a result it is important to minimize the number of steps it takes
to get to a reasonable solution.
One way that can reduce the number of iterations is by reformulating the
problem in terms of some new variable () with a preconditioning
operator (). Changing a tradition inversion problem where the
operator () maps the model () to the data (),
| |
(2) |

we can rewrite
| |
(3) |

where
| |
(4) |

** Next:** Helix transform
** Up:** THEORY/MOTIVATION
** Previous:** Regularization
Stanford Exploration Project

10/9/1997