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Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

By
A. B. Weglein
A. B. Weglein
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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B. G. Nita
B. G. Nita
Montclair State University, Department of Mathematical Sciences, 1 Normal Avenue, Montclair, New Jersey 07043. E-mail: nitab@mail.montclair.edu.
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K. A. Innanen
K. A. Innanen
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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E. Otnes
E. Otnes
Statoil Research Center, N-7005 Trondheim, Norway.
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S. A. Shaw
S. A. Shaw
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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F. Liu
F. Liu
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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H. Zhang
H. Zhang
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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A. C. Ramirez
A. C. Ramirez
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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J. Zhang
J. Zhang
University of Houston, 617 Science and Research Building 1, Houston, Texas 77204. E-mail: aweglein@uh.edu; kinnanen@uh.edu; shawsa@earthlink.net.
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G. L. Pavlis
G. L. Pavlis
Indiana University, Bloomington, 1001 East 10th Street, Bloomington, Indiana 47405. E-mail: pavlis@geology.indiana.edu; cfan@indiana.edu.
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C. Fan
C. Fan
Indiana University, Bloomington, 1001 East 10th Street, Bloomington, Indiana 47405. E-mail: pavlis@geology.indiana.edu; cfan@indiana.edu.
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Published:
January 01, 2008

Abstract

The starting point for the derivation of a new set of approaches for predicting both the wavefield at depth in an unknown medium and transmission data from measured reflection data is the inverse scattering series. We present a selection of these maps that differ in order (i.e., linear or nonlinear), capability, and data requirements. They have their roots in the consideration of a data format known as the T-matrix and have direct applicability to the data construction techniques motivating this special issue. Of particular note, one of these, a construction of the wavefield at any depth (including the transmitted wavefield), order-by-order in the measured reflected wavefield, has an unusual set of capabilities (e.g., it does not involve an assumption regarding the minimum-phase nature of the data and is accomplished with processing in the simple reference medium only) and requirements (e.g., a suite of frequencies from surface data are required to compute a single frequency of the wavefield at depth when the subsurface is unknown). An alternative reflection-to-transmission data mapping (which does not require a knowledge of the wavelet, and in which the component of the unknown medium that is linear in the reflection data is used as a proxy for the component of the unknown medium that is linear in the transmission data) is also derivable from the inverse scattering series framework.

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Seismic Interferometry: History and Present Status

Kees Wapenaar
Kees Wapenaar
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Deyan Draganov
Deyan Draganov
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Johan O.A. Robertsson
Johan O.A. Robertsson
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Society of Exploration Geophysicists
Volume
26
ISBN electronic:
9781560801924
Publication date:
January 01, 2008

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