Conjugate guided gradient (CGG) method for robust inversion and its application to velocity-stack inversion |

**Jun Ji**

Department of Information System Engineering,

Hansung University, Samsun-dong 2-ga, Sungbuk-ku, Seoul, Korea

This paper proposes a modified conjugate gradient (CG) method,
called the conjugate guided gradient (CGG) method,
that is a robust iterative inversion method producing a parsimonious model estimation.
The CG method for solving least-squares (LS) (i.e. -norm minimization)
problems is modified to solve for different norms
or different minimization criteria by guiding the gradient vector appropriately during iteration steps.
The guiding is achieved by iteratively reweighting either the residual vector
or the gradient vector during iteration steps like IRLS (Iteratively Reweighted Least Squares) method does.
The robustness is achieved by weighting the residual vector
and the parsimonious model estimation is obtained by weighting the gradient vector.
Unlike the IRLS method, however, the CGG method doesn't change
the corresponding forward operator of the problem
and is implemented in a linear inversion template.
Therefore the CGG method requires less computation than the IRLS method does.
Since the solution in the CGG method is found in a least-squares sense
along the gradient direction guided by the weights,
the solution found by the CGG method can be interpreted
as the LS solution located in the guided gradient direction.
Guiding the gradient gives us more flexibility in choice of
weighting parameters than the one of the IRLS method.
I applied the CGG method to velocity-stack inversion,
and the results show that the CGG method gives
a far more robust and parsimonious model estimation
than the standard -norm solution,
with the results comparable to the -norm
IRLS solution.

- INTRODUCTION
- CG method for LS Inversion

- Conjugate-Guided-Gradient (CGG) method
- CGG with residual weight guide
- CGG with model weight guide
- CGG with residual and model weights guide

- Application of the CGG method in Velocity-stack inversion

- CONCLUSIONS
- ACKNOWLEDGEMENT
- Bibliography
- About this document ...

Conjugate guided gradient (CGG) method for robust inversion and its application to velocity-stack inversion |

2011-06-26