On the focusing conditions in time-reversed acoustics, seismic interferometry and Marchenko imaging

Despite the close links between the fields of time-reversed acoustics, seismic interferometry and Marchenko imaging, a number of subtle differences exist. This paper reviews the various focusing conditions of these methods, the causality/acausality aspects of the corresponding focusing wavefields, and the requirements with respect to omnidirectional/singlesided acquisition. INTRODUCTION It has been noted by various authors that there exists a close link between time-reversed acoustics and seismic interferometry (Derode et al., 2003; Wapenaar et al., 2005; van Manen et al., 2005; Bakulin and Calvert, 2006). More recently, similar links have been discovered between seismic interferometry and autofocusing, also known as Marchenko imaging (Broggini and Snieder, 2012; Wapenaar et al., 2012). All these methods have in common that recorded wavefields are focused onto a point inside the medium, either by actually emitting these fields into the real medium or by processing them in the computer. The aim of this paper is to discuss a number of subtle differences between the focusing conditions in the various methods and to point out the causality/acausality aspects of the corresponding focusing wavefields. G(x,xA, t) G(x,xA,−t)