Skip to Main Content
Book Chapter

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

By
Arthur B. Weglein
Arthur B. Weglein
1University of Houston, Houston, Texas, U.S.A. E-mail: aweglein@uh.edu; liufang23@hotmail.com.
Search for other works by this author on:
Haiyan Zhang
Haiyan Zhang
2Formerly University of Houston, Houston, Texas, U.S.A.; presently ConocoPhillips, Houston, Texas, U.S.A. E-mail: Haiyan.Zhang@conocophillips.com.
Search for other works by this author on:
Adriana C. Ramírez
Adriana C. Ramírez
3Formerly University of Houston, Houston, Texas, U.S.A.; presently WesternGeco, Houston, Texas, U.S.A. E-mail: acramirez@slb.com.
Search for other works by this author on:
Fang Liu
Fang Liu
1University of Houston, Houston, Texas, U.S.A. E-mail: aweglein@uh.edu; liufang23@hotmail.com.
Search for other works by this author on:
M. Lira Jose Eduardo
M. Lira Jose Eduardo
4PETROBRAS Research and Development Center, Rio de Janeiro, Brazil. E-mail: jelira@petrobras.com.br.
Search for other works by this author on:
Published:
January 01, 2010

Abstract

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.

You do not currently have access to this article.
Don't already have an account? Register

Figures & Tables

Contents

Geophysical References Series

Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary

Sergey Fomel
Sergey Fomel
Search for other works by this author on:
Society of Exploration Geophysicists
Volume
16
ISBN electronic:
9781560802273
Publication date:
January 01, 2010

GeoRef

References

Related

A comprehensive resource of eBooks for researchers in the Earth Sciences

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

View Article Abstract & Purchase Options

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Subscribe Now