Interferometric redatuming by sparse inversion

Abstract

Assuming that transmission responses are known between the surface and a particular depth level in the subsurface, seismic sources can be effectively mapped to this level by a process called interferometric redatuming. After redatuming, the obtained wavefields can be used for imaging below this particular depth level. Interferometric redatuming consists of two steps, namely (i) the decomposition of the observed wavefields into downgoing and upgoing constituents and (ii) a multidimensional deconvolution of the upgoing constituents with the downgoing constituents. While this method works in theory, sensitivity to noise and artefacts due to incomplete acquisition require a different formulation. In this letter, we demonstrate the benefits of formulating the two steps that undergird interferometric redatuming in terms of a transform-domain sparsity-promoting program. By exploiting compressibility of seismic wavefields in the curvelet domain, the method not only becomes robust with respect to noise but we are also able to remove certain artefacts while preserving the frequency content. Although we observe improvements when we promote sparsity in the redatumed data space, we expect better results when interferometric redatuming would be combined or integrated with least-squares migration with sparsity promotion in the image space.

Target‐level waveform inversion: a prospective application of the convolution‐type representation for the acoustic wavefield

“…Further, the inputs used in the MDD process to get the local-impulse responses, are the same inputs used in the TLWI to estimate directly the medium properties from the target zone: the down-and upgoing wavefields at the target level. However, this interferometry method is formulated as an inversion problem to retrieve Green's function from the convolution-type representation for the wavefield, which can be an ill-posed problem and which in turn depends on the number of available sources distributed along the surface, the source aperture and the source bandwidth (Minato et al 2011;Wapenaar et al 2011;van der Neut and Herrmann 2013). This may result in inaccuracies in the redatumed data set with genuine information from the target zone being mixed with some artefacts from the limited space aperture, which may still work well for migration, but may not give optimum FWI results.…”

“…Further, it is well known that in exploration seismology interpretation and characterization of the reservoir is a challenge when it is localized beneath a complex overburden Calvert 2004, 2006;Valenciano et al 2006;van der Neut and Herrmann 2013;Vasconcelos, Ravasi and van der Neut 2017), that is, the upper section of the subsurface with strong heterogeneities, such as salt bodies or weathering zones. This difficulty stems from the fact that in such media wave propagation can result in very complex phenomena, such as geometric dispersion and multipathing, leading to a very distorted wavefield.…”

Target‐oriented imaging using extended image volumes: a low‐rank factorization approach

“…The second method is called interferometric redatuming, which has been studied extensively in the literature (Snieder ; Schuster and Zhou ; Snieder, Sheiman and Calvert ; Wapenaar and Fokkema ; Mehta et al . ; Schuster ; Curtis and Halliday ; Broggini, Snieder and Wapenaar ; Wapenaar, Broggini and Snieder ; van der Neut and Herrmann ). In interferometric redatuming, seismic data are acquired by placing both sources and receivers at the surface during the acquisition.…”

“…One drawback of this method is that one has to invert this composition matrix, which can be challenging because it exhibits singularities at critical angles. We can overcome this by regularizing the least‐square solutions to generate the down‐ and upgoing wavefields as shown in van der Neut and Herrmann (), where the authors proposed to solve a sparsity‐promotion‐based least‐squares formulation. Alternatively, Wapenaar and van der Neut () and Vasconcelos and Rickett () proposed multi‐dimensional deconvolution‐based imaging conditions using extended image volumes, where two‐way wave equation–based extrapolation is used to generate the full non‐linear reflection response at a given target‐datum in the subsurface, as a function of time or frequency.…”

AVP-preserving Estimation of Reservoir Impulse Responses

“…JMI is similar to data-driven Marchenko redatuming (van der Neut and Herrmann, 2013;Wapenaar et al, 2014) in the sense that it also constructs up-and downgoing waves in the medium. But unlike Marchenko redatuming, JMI does not rely on dense source sampling and can update errors in the background velocity field.…”