## ABSTRACTAs we search for hydrocarbons in areas where the earth's subsurface is too complex to accurately image with migration algorithms, we find ourselves turning to imaging techniques such as least-squares. My version of least-squares inversion imaging uses a downward continuation operator to produce offset ray parameter gathers (equivalent to angle gathers) and a regularization operator that is a derivative along the angle axis. The regularization operator stabilizes the inversion and helps to fill in illumination gaps. Essentially, I assume that any large, sudden changes in amplitude along the reflection angle axis are caused by poor illumination. This methodology is effective for reducing artifacts and helping to compensate for poor illumination. However, there is still the question of how this regularization will affect any real amplitude variation with angle (AVA) that should be seen in the model. In this paper, I address the question of how the derivative type regularization operator affects expected AVA in a simple model with no illumination problems. I experiment with various numbers of iterations and various strengths of regularization. Overall, I find that this operator, as implemented in this paper, can have a minor effect on the true AVA due to edge effects. However, it does not affect all possible AVA information, so I remain hopeful that the derivative-type regularization operator can be modified to allow us to trust AVA information from models produced by my regularized least-squares inversion. |

- Introduction
- Review of regularized inversion
- The regularization operator
- Amplitude effects
- Conclusions
- REFERENCES
- About this document ...

5/23/2004