3D primary estimation by sparse inversion using the focal domain parameterization

Abstract

SUMMARYRecently, a new approach to multiple removal has been introduced: estimation of primaries by sparse inversion (EPSI). Although based on the same relationship between primaries and multiples as surface-related multiple elimination (SRME), it involves quite a different process: instead of prediction and subtraction of multiples, in EPSI the unknown primaries are the parameters of a large-scale inversion process. Based on a sparseness constraint, primaries are estimated in such a way that -together with their corresponding surface multiplesthey explain the input data. In this paper a new algorithm is proposed to extend the EPSI process to the full 3D case, in which data reconstruction and primary estimation are combined, based on parameterization of the primaries in the socalled focal domain. This algorithm will allow reconstruction of large data gaps and yields reliable primaries. Results of this algorithm for a simple 3D example are shown.

The utilization of the double focal transformation for sparse data representation and data reconstruction

“…Note that the robustness of this method against inaccuracies in the focal operators is not only utilized for seismic data reconstruction (Kutscha, Verschuur, and Berkhout ) but also for primary estimation (Lopez and Verschuur ) and deblending (Doulgeris, Verschuur, and Blacquiere ; Kontakis and Verschuur ).…”

Closed-loop surface-related multiple elimination and its application to simultaneous data reconstruction

“…To use CL-SRME to remove multiples from data sets with severe undersampling (which is typical for 3D geometries), we will follow the parameterization similar to the one described by Lopez and Verschuur (2013) such that data reconstruction and multiple removal are achieved. Our goal is to use CL-SRME to remove the multiples and to reconstruct big portions of missing data.…”

“…To fulfill the first condition, we propose the use of the focal transform (Berkhout and Verschuur, 2006;Kutscha et al, 2010;Kutscha and Verschuur, 2012;Lopez and Verschuur, 2013) applied to the primary data. In this description, we will make use of some rough normal moveout (NMO)-velocity information to create propagation operators W that will allow us to back-propagate the wavefields.…”

The Double Focal Transformation and its Application to Seismic Data Reconstruction

“…Even though the focusing in the focal domain is not perfect, still a decent aliasing noise suppression is achieved, which leads to the desired data reconstruction and a small data residual (Figure 3.13e,f). Please note that the robustness of the double focal transformation against inaccuracies in the focal operators is not only utilised for seismic data reconstruction (Kutscha et al, 2010), but also for primary estimation (Lopez and Verschuur, 2013a) and deblending (Doulgeris et al, 2012). The observation that a good aliasing noise suppression is achievable even with an imprecise focal operators is actually not surprising if one considers that also reflector two and three are properly reconstructed.…”