An explicit algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3-D. By using ideas from “compressed sensing”, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. According to compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is incoherent with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operatoion. A proof of principle for the “compressed sensing ” method is given for wavefield extrapolation in 2-D. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator.

Incomplete data, unknown source-receiver signatures and free-surface reflectivity represent challenges for a successful prediction and subsequent removal of multiples. In this paper, a new method will be represented that tackles these challenges by combining what we know about wavefield (de-)focussing, by weighted convolutions/correlations, and recently developed curvelet-based recovery by sparsity-promoting inversion (CRSI). With this combination, we are able to leverage recent insights from wave physics towards a nonlinear formulation for the multiple-prediction problem that works for incomplete data and without detailed knowledge on the surface effects. EAGE 69 th Conference & Exhibition — London, UK, 11- 14 June 2007Surface-related multiple prediction and seismic interferometry are examples where weighted multi-dimensional cross-convolutions and cross-correlations of seismic data volumes provide information on Green’s functions that describe the Earth response at the surface. For instance, surface-related multiples can approximately be predicted through a weighted multidimensional convolution of the data with itself, while ’daylight imaging ’ techniques extract the Green’s function by cross-correlation of wavefields (see e.g. Wapenaar et al., 2006, which contains a collection of the most recent papers on this

From seismic data to the composition of rocks: an interdisciplinary and multiscale approach to exploration seismology Felix J. Herrmann ∗ and the SLIM Team ∗ In this essay, a nonlinear and multidisciplinary approach is presented that takes seismic data to the composition of rocks. The presented work has deep roots in the ’gedachtengoed ’ (philosophy) of Delphi spearheaded by Guus Berkhout. Central themes are multiscale, object-orientation and a multidisciplinary approach.

noise: the good the bad and the ugly