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

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.