GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 63 J.T. Ma, F.C. Yao, X.H. Chen, and Y. Liu: VSP Multiple Attenuation Theory Using SRME Technique, 73rd EAGE Conference & Exhibition incorporating SPE EUROPEC 2011 Vienna, Austria, 23-26 May 2011 Pica, A., G. Poulain, B. David, M. Magesan, S. Baldock, T. Weisser, P. Hugonnet, and P. Herrmann, 2005, 3D surface- related multiple modeling, principles and results: 75th Annual International Meeting, SEG, Expanded Abstracts, 2080-2083. J. O’Brien, B. Farmani, B. Atkinson, 2013, VSP Free-Surface Multiple Imaging - ADetailed Case Study: 75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013 D.J. Verschurr , and A.J. Berkhout, 1992, Adaptive surface-related multiple elimination: GEOPHYSICS, VOL. 57, NO. 9 (September 1992), 10.1190/1.1443330 P. Wang, H. Jin, S. Xu, and Y. Zhang, 2011, Model-based Water-layer Demultiple: 2011 SEG San Antonio Annual Meeting Wiggins, J. W., 1988, Attenuation of complex water-bottom multiples by wave-equation-based prediction and subtraction: Geophysics, 53, 1527–1539 D. Zhang and G. T. Schuster, 2014, Least-squares reverse time migration of multiples: GEOPHYSICS,VOL. 79, NO. 1 (January-February 2014), 10.1190/geo2013-0156.1 SEISMIC INTERPOLATION VIA CONJUGATE GRADIENT PURSUIT L. Fioretti 1 , P. Mazzucchelli 1 , N. Bienati 2 1 Aresys, Milano, Italy 2 eni E&P, San Donato Milanese, Italy Introduction. Seismic processing methods often assume data to be regularly and densely sampled in space, but acquisition techniques, in particular in marine environments, rarely achieve this requirement in practice. Thus, during the years, a large number of interpolation algorithms have been developed based on different strategies. One class of methods is related to the integral of continuation operators (Canning and Gardner, 1996; Bleistein and Jaramillo, 2000; Stolt, 2002; Fomel, 2003), but, despite the connection with the physics of wave propagation, in case of complex geological structure the accuracy is strongly affected. Moreover, this kind of algorithms suffers from coarse sampling, introducing strong artifacts that need to be removed via post-processing. One of the most popular approaches of the last years is based on the convolution filters (Spitz, 1991; Abma and Claerbout, 1995; Mazzucchelli et al. , 1998). This kind of algorithms works very well when input data are regularly sampled, but the regularity assumption is a heavy limitation to their usage. Fourier theory provides another way for handling this problem (Sacchi and Ulrych, 1995; Duijndam et al. , 1999). Algorithms from this class first estimate Fourier coefficients from input data, then recover data on any desired grid. Again, these methods are effective in interpolating from regularly sampled data, but when irregularities show up, the orthogonality of Fourier basis falls bringing to the so-called ‘spectral leakage’ effect: the energy of one spectral component ‘leaks’ onto others, introducing erroneous contributes to the spectral representation. A new Fourier-based approach was proposed in the last years for facing the spectral leakage problem (Xu and Pham, 2004; Zwartjes and Sacchi, 2004; Xu et al. , 2005a, 2005b; Özbek et al. , 2009), the earliest one was the Antileakage Fourier Transform (ALFT): given the input data, estimate its Fourier representation, then pick the most energetic Fourier coefficient and subtract its contribution from residual data, and so on iteration by iteration, until some stopping criterion is met. This method exploits the assumption that seismic data can be sparsely represented in the Fourier domain. Based on the same assumption, a similar strategy has been proposed for improving efficiency (Nguyen and Winnett, 2011): it precomputes the matrix of Fourier components once for all and then, at each iteration, the data is simply projected onto the