On Green’s functions, propagator matrices, focusing functions and their mutual relations
K. Wapenaar (TU Delft - Applied Geophysics and Petrophysics)
Joeri Brackenhoff (Quantairra Research and Development Services B.V.)
Sjoerd de Ridder (University of Leeds)
E. Slob (TU Delft - Applied Geophysics and Petrophysics)
Roel Snieder (Colorado School of Mines)
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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.