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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).

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** Up:** Guitton: High resolution Radon
** Previous:** Estimating sparse radon domains
Stanford Exploration Project

5/3/2005