REFERENCES

Claerbout, J. F., and Muir, F., 1973, Robust modeling with erratic data: Geophysics, 38, no. 05, 826-844.

Foster, D. J., and Mosher, C. C., 1992, Suppression of multiple reflections using the Radon transform: Geophysics, 57, no. 03, 386-395.

Guitton, A., and Symes, W., 2003, Robust inversion of seismic data using the Huber norm: Geophysics, 68, no. 4, 1310-1319.

Herrmann, P., Mojesky, T., Magesan, M., and Hugonnet, P., 2000, De-aliased, high-resolution Radon transforms: Soc. of Expl. Geophys., 70th Ann. Internat. Mtg, 1953-1956.

Hindriks, C. O. H., and Duijndam, A. J. W., 1998, Radon domain reconstruction of 3-D irregularly sampled VSP data: Soc. of Expl. Geophys., 68th Ann. Internat. Mtg, 2003-2006.

Nichols, D., 1994, Velocity-stack inversion using ${\bf L_p}$ norms: SEP-82, 1-16.

Sacchi, M. D., and Ulrych, T. J., 1995, High-resolution velocity gathers and offset space reconstruction: Geophysics, 60, no. 04, 1169-1177.

Taner, M. T., and Koehler, F., 1969, Velocity spectra - Digital computer derivation and applications of velocity functions: Geophysics, 34, no. 06, 859-881.

Trad, D., Ulrych, T. J., and Sacchi, M. D., 2002, Accurate interpolation with high-resolution time-variant Radon transforms: Geophysics, 67, no. 2, 644-656.

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plusminus-nospike-HUBER
Figure 1 (a) Input data. Estimated model for (b) positive values and (c) negative values only. (d) Estimated sparse domain (b)+(c). (e) Estimated model without sparseness constraints.

 

cauchyres-gm2-HUBER
Figure 2 (a) Input CMP gather from a marine data experiment. Residual panels for the sparse model estimated with (b) the bounded models and (c) the Cauchy regularization. Sparse models estimated with (d) the bounded models and (e) the Cauchy regularization.