On Green’s functions, propagator matrices, focusing functions and their mutual relations

Conference paper (2023)

Authors

C.P.A. Wapenaar Applied Geophysics and Petrophysics - CEG
Joeri Brackenhoff Quantairra Research and Development Services B.V.
Sjoerd de Ridder University of Leeds
E.C. Slob Applied Geophysics and Petrophysics - CEG
Roel Snieder Colorado School of Mines
Research Group
Applied Geophysics and Petrophysics (CEG) (TU Delft)
Copyright: © 2023 C.P.A. Wapenaar, J. Brackenhoff, S. De Ridder, E.C. Slob, R. Snieder
DOI: https://doi.org/10.3997/2214-4609.202310755
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Published Date

2023

Language

English

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Faculty

Civil Engineering & Geosciences

Department

Geoscience and Engineering

Research Group

Applied Geophysics and Petrophysics

Abstract

Green’s functions and propagator matrices are both solutions of the wave equation, but whereas Green’s functions obey a causality condition in time (G = 0 for t < 0), propagator matrices obey a boundary condition in space. Marchenko-type focusing functions focus a wave field in space at zero time. We discuss the mutual relations between Green’s functions, propagator matrices and focusing functions, avoiding up-down decomposition and accounting for propagating and evanescent waves. We conclude with discussing a Marchenko-type Green’s function representation, which forms a basis for extending the Marchenko method to improve the imaging of steeply dipping flanks and to account for refracted waves.

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