Point-spread functions for interferometric imaging

Interferometric redatuming is a data-driven method to transform seismic responses with sources at one level and receivers at a deeper level into virtual reflection data with both sources and receivers at the deeper level. Although this method has traditionally been applied by cross-correlation, accurate redatuming through a heterogeneous overburden requires solving a multidimensional deconvolution problem. Input data can be obtained either by direct observation (for instance in a horizontal borehole), by modelling or by a novel iterative scheme that is currently being developed. The output of interferometric redatuming can be used for imaging below the redatuming level, resulting in a so-called interferometric image. Internal multiples from above the redatuming level are eliminated during this process. In the past, we introduced point-spread functions for interferometric redatuming by cross-correlation. These point-spread functions quantify distortions in the redatumed data, caused by internal multiple reflections in the overburden. In this paper, we define point-spread functions for interferometric imaging to quantify these distortions in the image domain. These point-spread functions are similar to conventional resolution functions for seismic migration but they contain additional information on the internal multiples in the overburden and they are partly data-driven. We show how these point-spread functions can be visualized to diagnose image defocusing and artefacts. Finally, we illustrate how point-spread functions can also be defined for interferometric imaging with passive noise sources in the subsurface or with simultaneous-source acquisition at the surface.