Examples

Figure a shows a synthetic CMP gather with five hyperbolas. First, the model is constrained to have positive values in Figure b. Note that this domain is artifacts free and extremely focused. Second, the model is constrained to have negative values in Figure c. Again, the model is very sparse. Finally, the sparse model obtained by adding Figures b and c is shown in Figure d. As expected, this model is very sparse compared to the radon panel obtained without sparseness constraints in Figure e. Now, this method is tested on one CMP gather from a marine dataset in the Gulf of Mexico. Here, the proposed method is also compared with the sparse result with the Cauchy regularization Sacchi and Ulrych (1995). Figure a shows the input data. The sparse models obtained by adding the bounded models and by using the Cauchy regularization are shown in Figures d and e, respectively. Both results are almost identical, with the new technique yielding a better panel. The residual, i.e., the difference between the input data and the remodeled data, is also very similar in both cases (Figures b and c).