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Clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data

Arthur B. Weglein, Haiyan Zhang, Adriana C. Ramirez, Fang Liu and Jose Eduardo M. Lira
Clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data (in Advances in seismic imaging and inversion, Stefan Buske (editor), Isabelle Lecomte (editor), Tamas Nemeth (editor), Stephane Operto (editor) and Valenti Sallares (editor))
Geophysics (November 2009) 74 (6, Suppl.): WCD1-WCD13


Linear inversion is defined as the linear approximation of a direct-inverse solution. This definition leads to data requirements and specific direct-inverse algorithms, which differ with all current linear and nonlinear approaches, and is immediately relevant for target identification and inversion in an elastic earth. Common practice typically starts with a direct forward or modeling expression and seeks to solve a forward equation in an inverse sense. Attempting to solve a direct forward problem in an inverse sense is not the same as solving an inverse problem directly. Distinctions include differences in algorithms, in the need for a priori information, and in data requirements. The simplest and most accessible examples are the direct-inversion tasks, derived from the inverse scattering series (ISS), for the removal of free-surface and internal multiples. The ISS multiple-removal algorithms require no subsurface information, and they are independent of earth model type. A direct forward method solved in an inverse sense, for modeling and subtracting multiples, would require accurate knowledge of every detail of the subsurface the multiple has experienced. In addition, it requires a different modeling and subtraction algorithm for each different earth-model type. The ISS methods for direct removal of multiples are not a forward problem solved in an inverse sense. Similarly, the direct elastic inversion provided by the ISS is not a modeling formula for PP data solved in an inverse sense. Direct elastic inversion calls for PP, PS, SS, ... data, for direct linear and nonlinear estimates of changes in mechanical properties. In practice, a judicious combination of direct and indirect methods are called upon for effective field data application.

ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 74
Serial Issue: 6, Suppl.
Title: Clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data
Title: Advances in seismic imaging and inversion
Author(s): Weglein, Arthur B.Zhang, HaiyanRamirez, Adriana C.Liu, FangLira, Jose Eduardo M.
Author(s): Buske, Stefaneditor
Author(s): Lecomte, Isabelleeditor
Author(s): Nemeth, Tamaseditor
Author(s): Operto, Stephaneeditor
Author(s): Sallares, Valentieditor
Affiliation: University of Houston, Houston, TX, United States
Affiliation: Freie Universitaet Berlin, Berlin, Federal Republic of Germany
Pages: WCD1-WCD13
Published: 200911
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 28
Accession Number: 2010-047903
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Secondary Affiliation: NORSAR, NOR, NorwayChevron, USA, United StatesUniversite Nice-Sophia Antipolis, FRA, FranceCSIC, Centre Mediterrani d'Investigacions Marines i Ambientals, ESP, SpainConocoPhillips, USA, United StatesWesternGeco, USA, United StatesPETROBRAS, BRA, Brazil
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2018, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 201026
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