Blocky velocity inversion by hybrid norm

Abstract:

Inverting a regularized Dix equation using the $L2$ norm produces smooth interval velocity models. To get a blocky interval velocity estimate that is more geologically reasonable, a regularized Dix inversion needs to be done using an $L1$ -like norm. In this paper, we compare different 2D regularizations using both the $L2$ norm and the hybrid $L1/L2$ norm to find the regularization that produces blocky velocity models while maintaining high accuracy and resolution. The results show that the hybrid $L1/L2$ norm successfully achieves blockiness when using the first derivative in multiple directions as a regularization.