Creating a virtual source inside a medium from reflection data with internal multiples: a stationary-phase analysis

Abstract

Seismic interferometry allows one to create a virtual source inside a medium, assuming a receiver is present at the position of the virtual source. We discuss a method that creates a virtual source inside a medium from reflection data measured at the surface, without needing a receiver inside the medium and, hence, going beyond seismic interferometry. In addition to the reflection data, an estimate of the direct arrivals is required. However, no information about the medium is needed. We analyze the proposed method for a simple configuration using physical arguments based on the stationary-phase method and show that the retrieved virtual-source response correctly contains the multiples due to the inhomogeneous medium. The proposed method can serve as a basis for data-driven suppression of internal multiples in seismic imaging.

Green's function retrieval with Marchenko equations: A sensitivity analysis

“…In the brief theoretical background given in this section, we follow Wapenaar et al (2012a) and only present the final outcome of the scheme for 2-dimensional media. The iterative scheme starts with an estimate of the direct arrival between the surface (x 0 ), and the virtual receiver position x F = (x F , z F ) in the subsurface.…”

“…where w(x 0 ,t) is a window function as explained in Wapenaar et al (2012a) and k the iteration number. After several iterations (in the examples shown in this paper, 10-15 iterations are sufficient), using construction equation (1) and (with subscript 0 replaced by k) update equation (2), the wavefield converges.…”

“…A new approach to retrieve the Green's function for a virtual source in the subsurface, from measured data at the surface, is introduced by Broggini et al (2012a,b); Wapenaar et al (2012a). The method is based on Marchenko-type equations and the virtual wavefield is constructed by an iterative scheme.…”