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Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

By
Ivan Vasconcelos
Ivan Vasconcelos
Formerly, Colorado School of Mines, Department of Geophysics, Center for Wave Phenomena, Golden, Colorado, U.S.A.; presently ION Geophysical, GXT Imaging Solutions, Egham, United Kingdom. E-mail: ivan.vasconcelos@iongeo.com.
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Roel Snieder
Roel Snieder
Colorado School of Mines, Department of Geophysics, Center for Wave Phenomena, Golden, Colorado, U.S.A. E-mail: rsnieder@mines.edu.
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Published:
January 01, 2008

Abstract

Interferometry allows for synthesis of data recorded at any two receivers into waves that propagate between these receivers as if one of them behaves as a source. This is accomplished typically by crosscorrelations. Based on perturbation theory and representation theorems, we show that interferometry also can be done by deconvolutions for arbitrary media and multidimensional experiments. This is important for interferometry applications in which (1) excitation is a complicated source-time function and/or (2) when wavefield separation methods are used along with interferometry to retrieve specific arrivals. Unlike using crosscorrelations, this method yields only causal scattered waves that propagate between the receivers. We offer a physical interpretation of deconvolution interferometry based on scattering theory. Here we show that deconvolution interferometry in acoustic media imposes an extra boundary condition, which we refer to as the free-point or clamped-point boundary condition, depending on the measured field quantity. This boundary condition generates so-called free-point scattering interactions, which are described in detail. The extra boundary condition and its associated artifacts can be circumvented by separating the reference waves from scattered wavefields prior to interferometry. Three wavefield-separation methods that can be used in interferometry are direct-wave interferometry, dual-field interferometry, and shot-domain separation. Each has different objectives and requirements.

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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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