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Using the preceding results, I can invert for the Hessian in
equation (9), either with or without regularization.
The fitting goal is
| |
(28) |
with and .The matrix equation we want to solve is
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(29) |
where and are the unknowns.
For , I use the bottom row of equation (25).
For , I use the top row of equation (26).
We have, then,
| |
(30) |
| |
| (31) |
| |
which can be simplified as follows:
| |
(32) |
| (33) |
is the coherent noise resolution matrix,
whereas is the signal resolution
matrix. Denoting and yields the following simplified expression for and
:
| |
(34) |
- With model space regularization
The fitting goal becomes
| |
(35) |
| (36) |
with , and
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(37) |
The matrix equation we want to solve is
| |
(38) |
Using equations (25) and (26) we obtain
| |
(39) |
where and .
Next: About this document ...
Up: Appendix
Previous: Inversion of a 22
Stanford Exploration Project
4/29/2001