** Next:** Steering Filters
** Up:** THEORY/MOTIVATION
** Previous:** Preconditioning

The next question is how to choose ?
We have three general requirements:
- it produces relatively smooth (by some criteria) results;
- it spreads information quickly;
- and it is computationally inexpensive.

By defining our operators via the helix method
Claerbout (1997) we can meet all of these
requirements.
The helix concept is to transform *N*-Dimensional
operators into 1-D operators to take
advantage of the well developed 1-D theory.
In this case we utilize our ability to construct
stable inverses from simple, causal filters.
We can set , from equation (4) to
| |
(5) |

where is the roughening operator from fitting
goal (1), and is simulated using
polynomial division.
If is a small roughening
operator, is a large smoothing operator without the
heavy costs usually associated with larger operators.

** Next:** Steering Filters
** Up:** THEORY/MOTIVATION
** Previous:** Preconditioning
Stanford Exploration Project

10/9/1997