Least-squares migration/inversion of blended data

discussion

Imaging through LSI in blended acquisition geometries is an underdetermined problem; hence there are an infinite number of solutions that fit the observed data equally well. Therefore, regularization is very important for constraining the corresponding solution. In the Marmousi example, a simple regularization operator that imposes horizontal smoothness seems to be working well. However, this choice may not be optimal, because it may wash out dipping reflectors. Regularization operators that better predict the inverse model covariance, for example, by imposing continuities along reflection angles and geological dips (Clapp, 2005), or promoting sparseness in the image domain (Tang, 2009), should be able to reduce the null space and further improve the inversion result. How to incorporate accurate prior information to constrain the inversion remains a research area for further investigation.