Target-oriented least-squares migration/inversion with sparseness constraints

discussion

This paper presents a sparseness constrained LSI scheme that promotes sparsity of the reflectivity. This is a reasonable assumption if the reflectivity is indeed spiky; however, if the reflectivity changes smoothly, the sparseness constraint may lead to a biased solution. The parameters ${\sigma}$ and $\epsilon$ that control the strength of sparsity and the amount of regularization should also be chosen with extreme care. Because by promoting sparsity, we run the risk of penalizing true reflections that have very weak energy, over-regularization may lead to too-sparse solutions, forfeiting the ability to image weak reflections.

Recent study in curvelet (Kumar and Herrmann, 2008) and seislet (Fomel, 2006) transforms show that seismic images tend to have a sparse representation in these new domains, where a few number of coefficients are sufficient to describe images with complex structures. This feature makes these new domains good candidates for adding sparseness constraints. Therefore, promoting sparsity in either curvelet or seislet domain may potentially avoid the issues discussed before and lead to geologically more reasonable solutions. This remains a research area for further investigation.

Target-oriented least-squares migration/inversion with sparseness constraints