Imaging condition for nonlinear scattering-based imaging: Estimate of power loss in scattering

Abstract

Imaging highly complex subsurface structures is a challenging problem because it ultimately necessitates dealing with nonlinear multiple-scattering effects (e.g., migration of multiples, amplitude corrections for transmission effects) to overcome the liminations of linear imaging. Most of the current migration techniques rely on the linear single-scattering assumption, and therefore, fail to handle these complex scattering effects. Recently, seismic imaging has been related to scattering-based image-domain interferometry in order to address the fully nonlinear imaging problem. Building on this connection between imaging and interferometry, we define the seimic image as a locally scattered wavefield and introduce a new imaging condition that is both suitable and practical for nonlinear imaging. A previous formulation of nonlinear scatteringbased imaging requires the evaluation of volume integrals that cannot easily be incorporated in current imaging algorithms. Our method consists of adapting the conventional crosscorrelation imaging condition to account for the interference mechanisms that ensure power conservation in the scattering of wavefields. To do so, we add the zero-lag autocorrelation of scattered wavefields to the zero-lag crosscorrelation of reference and scattered wavefields. In our development, we show that this autocorrelation of scattered fields fully replaces the volume scattering term required by the previous formulation. We also show that this replacement follows from the application of the generalized optical theorem. The resulting imaging condition accounts for nonlinear multiple-scattering effects, reduces imaging artifacts and improves both amplitude preservation and illumination in the images. We address the principles of our nonlinear imaging condition and demonstrate its importance in ideal nonlinear imaging experiments, i.e., we present synthetic data examples assuming ideal scattered wavefield extrapolation and study the influence of different scattering regimes and aperture limitation.

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

“…The Marchenko equations can also be useful to obtain a reflection response at the bottom of a seismic (sub)volume to turn recorded data with one-sided illumination into new data with two-sided illumination. Such an attempt could be highly relevant for nonlinear imaging, since a lack of illumination from below is known to limit its potential (Fleury & Vasconcelos 2012;Ravasi et al 2014). To obtain reflection responses from below, we could either invert eq.…”

“…By applying the methodology at each depth level in the subsurface and taking the response at zero time lag and zero space lag, an image with accurate amplitudes can be obtained without artefacts from internal multiple reflections Broggini et al 2014a;Behura et al 2014). By including non-zero lags, equivalent extended images can also be created (Vasconcelos & Rickett 2013), which can be useful input for migration velocity analysis (Sava & Vasconcelos 2011), reservoir characterization (De Bruin et al 1990;Thomson 2012) and novel schemes for nonlinear imaging (Fleury & Vasconcelos 2012;Ravasi & Curtis 2012) and waveform inversion (Vasconcelos et al 2014a). Alternatively, we can use the Marchenko equations to retrieve internal multiples at the acquisition level, which could then be adaptively subtracted from the recorded data .…”

Target-enclosed seismic imaging

“…By propagating wavefields backward in a detailed subsurface model, rather than in a smooth macro model, and crosscorrelating them with their associated source fields in the detailed model, we can image the primary reflections and internal multiples to improve seismic resolution (Youn and Zhou, 2001;Malcolm et al, 2009;Vasconcelos et al, 2010). Because internal multiples are used in this image, this strategy has also been referred to as nonlinear imaging (Fleury and Vasconcelos, 2012;Ravasi et al, 2014). Figure 7 is equivalent to Figure 6, apart from the fact that imaging has been conducted in the physical medium.…”

“…Hence, Marchenko imaging can also be interpreted as an internal multiple elimination process (Meles et al, 2015;van der Neut and Wapenaar, 2016;da Costa Filho et al, 2017). However, it has also been recently shown that novel imaging conditions can be derived for multiply reflected waves, given that a detailed model of the subsurface is available (Halliday and Curtis, 2010;Fleury and Vasconcelos, 2012;Ravasi et al, 2014Ravasi et al, , 2015b. To evaluate these imaging conditions, we require reflection and transmission responses from two boundaries that enclose the target volume.…”

On the role of multiples in Marchenko imaging

“…We analyze deconvolution and correlation imaging approaches that are currently being used in Marchenko imaging. Other imaging approaches, such as least-squares imaging (Nemeth et al, 1999) and nonlinear scattering-based imaging (Fleury and Vasconcelos, 2012), are beyond the scope of this analysis.…”