Single- and Double-Sided Marchenko Imaging Conditions in Acoustic Media

• Published in: IEEE transactions on computational imaging 2018-03, Vol.4 (1), p.160-171
• Main Authors: van der Neut, Joost, Brackenhoff, Joeri, Staring, Myrna, Zhang, Lele, de Ridder, Sjoerd, Slob, Evert, Wapenaar, Kees
• Format: Article
• Language: English
• Subjects: acoustic signal processing; Acoustics; Deconvolution; Focusing; Green's function methods; Image representation; Mathematical model; Receivers
• ISSN: 2573-0436; 2333-9403
• DOI: 10.1109/TCI.2017.2772440

In acoustic reflector imaging, we deploy sources and receivers outside a volume to collect a multisource, multioffset reflection response in order to retrieve the internal reflectivity of that volume. It has been shown that Green's functions inside the volume can be retrieved by single-sided wavefield focusing of the acquired reflection data, using so-called focusing functions, which can be computed by solving a multidimensional Marchenko equation. Besides the reflection data, this methodology requires a background model of the propagation velocity. We present several imaging conditions to retrieve the internal reflectivity of an acoustic medium with correct amplitudes and without artifacts, using the Green's functions and focusing functions that are derived from the Marchenko equation. We distinguish three types of imaging: 1) imaging by deconvolution, 2) imaging by double focusing, and 3) imaging by cross correlation. In all cases, reflectors can be approached either from above or from below. Imaging by deconvolution or double focusing requires single-sided illumination (meaning that sources and receivers are deployed at a single boundary above the volume only), whereas imaging by cross correlation requires double-sided illumination (meaning that sources and receivers are placed at two boundaries enclosing the volume). In order to achieve double-sided illumination, the required reflection response at the lower boundary can either be physically recorded or it can be retrieved from the reflection response at the upper boundary. When imaging by deconvolution or double focusing, the internal reflectivity is retrieved solely from primary reflections. When imaging by cross correlation, multiple reflections are focused at the image points, such that they contribute physically to the retrieved reflectivity values. This special feature can be beneficial for imaging weakly illuminated sections of strongly heterogeneous media.