Blocky velocity inversion by hybrid norm

Conclusions and Discussions

We successfully achieved blocky velocity models by using the hybrid norm. We also showed that the choice of the regularization operator has a great impact on how blocky the results are. Nonetheless, the hybrid norm always showed more detail and resolution than the $L2$ norm, even when blockiness was not achieved. An example of this can be seen by comparing Figures 4 and 9. Although the first Figure uses a Laplacian operator for regularization and the later Figure uses the first derivative in four directions (which we showed has the best results), the hybrid norm was still superior to the $L2$ norm in preserving more details and showing higher resolution.

Another point to keep in mind is that the hybrid norm has a flexibile threshold. In all previous cases, we set that threshold to 0.20, meaning that 80 percent of residuals (both data residuals and model residuals) are going to be in the $L1$ region and the rest in the $L2$ region. However, this is a parameter that can be adjusted based on the desired degree of blockiness.

Blocky velocity inversion by hybrid norm