Seismic reflector imaging using internal multiples with Marchenko-type equations

Abstract

We present an imaging method that creates a map of reflection coefficients in correct one-way time with no contamination from internal multiples using purely a filtering approach. The filter is computed from the measured reflection response and does not require a background model. We demonstrate that the filter is a focusing wavefield that focuses inside a layered medium and removes all internal multiples between the surface and the focus depth. The reflection response and the focusing wavefield can then be used for retrieving virtual vertical seismic profile data, thereby redatuming the source to the focus depth. Deconvolving the upgoing by the downgoing vertical seismic profile data redatums the receiver to the focus depth and gives the desired image. We then show that, for oblique angles of incidence in horizontally layered media, the image of the same quality as for 1D waves can be constructed. This step can be followed by a linear operation to determine velocity and density as a function of depth. Numerical simulations show the method can handle finite frequency bandwidth data and the effect of tunneling through thin layers.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

“…It has been shown that all events in the Green's functions can be retrieved with correct amplitudes for K → ∞, given that the initial focusing function obeys eq. (24) Slob et al 2014;Wapenaar et al 2014a). In practice, only a few iterations are generally sufficient to predict the dominant internal multiples in the wavefield with fairly accurate amplitudes, as we will demonstrate in the synthetic examples that follow.…”

“…also been mentioned by Sheiman (private communication, 2014). During higher-order iterations, the amplitudes of the events are updated, as illustrated by Wapenaar et al (2014a), Broggini et al (2014b) and Slob et al (2014).…”

“…In this paper, we provide an alternative view on Green's function retrieval by explicit iterative substitution of the coupled Marchenko equations, following Wapenaar et al (2014b) and Slob et al (2014). We build on knowledge and findings of seismic interferometry, where the retrieval of a seismic response through crosscorrelation is commonly interpreted by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals (Schuster 2009).…”

Single-sided Marchenko focusing of compressional and shear waves

“…Here the window function cuts off precisely one event at τ d (p), the arrival time of the direct wave of the scalar Green's function [24]. We generalize this for the elastodynamic situation.…”

On the role of multiples in Marchenko imaging

“…Marchenko imaging (Broggini and Snieder, 2012;Slob et al, 2014;Wapenaar et al, 2014) is a novel seismic imaging technique that has the potential to produce seismic reflection images, free of artifacts related to internal multiples van der Neut et al, 2015;Ravasi et al, 2016) and surface-related multiples (Singh et al, 2017). An intriguing question is whether the multiples are only eliminated or whether they also contribute to the imaged reflectors.…”