Green's Theorem in Time-Reversal Acoustics, Back Propagation and Source-Receiver Redatuming: a Tutorial

Abstract

Time-reversal acoustics, seismic interferometry, back propagation, source-receiver redatuming and imaging by double focusing are all based in some way or another on Green's theorem. An implicit assumption for all these methods is that data are available on a closed boundary, a condition that is never met in geophysical practice. As a consequence, although direct and primary scattered waves are handled very well, most methods do not properly account for multiply scattered waves. This can be significantly improved by replacing the back-propagating Green's functions in any of the aforementioned approaches by Marchenko-based focusing functions. We show how this improves time-reversal acoustics, back propagation and source-receiver redatuming and we indicate how it enables the monitoring and forecasting of responses to induced seismic sources.