Features of the solution of linear equations systems in the problem of seismic signals correction.

№2 (2018)

Goreyavchev N.A., Mitrofanov G.M.

AbstractAbout the AuthorsReferences
Different aspects of seismic information processing procedures have a significant impact on the structure of geological models created in geoinformation systems. In the paper, systems of linear equations and their solutions under construction in problems of seismic signal correction, in particular, arrival times and amplitudes, are studied. In the construction of solutions, two approaches were considered: the iterative process of sequential refinement of factor estimates and the application of heuristic conditions that ensure the uniqueness and stability of the solution. It is shown that the iterative process, based on the separate estimation of factors, leads to the appearance of long period spatial components, determined by the ratio of the length of the seismic streamer to the total length of the observation profile. The components are a consequence of the applied process of factors estimation process, and the reason for their appearance is due to the weak coupling of the zero-manifold vectors of the corresponded linear operator on different parts of the profile. To eliminate such components, large volumes of a priori data are required. Otherwise, the subsequent construction of geomodels will absorb these distortions. An alternative way that eliminates the appearance of such components is to consider all observations and use special conditions that allow us to link different parts of the profile and significantly reduce the amount of necessary a priori information required to determine an unambiguous solution to the problem.

Goreyavchev Nikita Alekseevich, post-graduate student of the Trofimuk Institute of Petroleum Geology and Geophysics of Siberian Branch of Russian Academy of Sciences (IPGG SB RAS), junior scientist of the laboratory of dynamic seismic analysis of IPGG SB RAS. 630090, Novosibirsk, prosp. Akademika Koptyuga, 3. E-mail: n.goreyavchev1994@gmail.com.

Mitrofanov Georgy Mikhailovich, Doctor of Physics and Mathematics, Second Professor of the Chair of Geophysics of the Novosibirsk State University, Full-Professor of the Chair of Geophysical Systems, Novosibirsk State Technical University, Leading Researcher of the laboratory of dynamic seismic analysis of the Trofimuk Institute of Petroleum Geology and Geophysics of Siberian Branch of Russian Academy of Sciences (IPGG SB RAS). 630090, Novosibirsk, prosp. Akademika Koptyuga, 3. E-mail: georgymitrofanov@rambler.ru.

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Section: Modeling geo objects and geo-processes

Keywords: systems of linear equations, factor decomposition, multifold seismic data, iterative estimation, long period statics.