Image-domain wavefield tomography for VTI media

Abstract

Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of [Formula: see text]-estimation. The impact of the trade-off between [Formula: see text] and [Formula: see text] is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of [Formula: see text]. Assuming that the depth profile of the Thomsen parameter [Formula: see text] is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and of the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.

Image‐domain wavefield tomography for tilted transversely isotropic media

“…The convergence of LSRTM can be expedited by applying non‐stationary matching filters to the LSRTM gradient (Guitton ; Li et al . ). The matching filters approximate the inverse Hessian of the data‐misfit objective function and produce so‐called ‘pseudoinverse’ images.…”

“…Similarly to Li et al . (), parameter updating is carried out by focusing energy in extended least‐squares reverse‐time migration (LSRTM) images. Application of LSRTM helps reduce kinematic artefacts in the extended domain and improve the robustness of model updating.…”

“…Therefore, we incorporate vertical δ‐profiles at available boreholes into the image‐domain objective function (Li et al . ) as follows: where δ ref is the reference δ‐field obtained from image‐guided interpolation between the boreholes, and α and β are model‐dependent weighting factors. To steer the algorithm towards geologically plausible solutions, image‐guided smoothing (Hale ; Wang and Tsvankin ) is applied to the inversion gradients.…”

“…Also, although elastic extended images can provide more accurate amplitudes compared to their acoustic counterparts, they are still contaminated by aperture‐truncation artefacts (Li et al . ) that need to be mitigated prior to back‐projecting the image residuals.…”

“…Here, we extend to tilted transverse isotropy the VTI IDT algorithm developed by Li et al . (), which requires addressing the following issues: wavefield extrapolation; computation of the gradient of the objective function; analysis of the sensitivity of the objective function to the TTI parameters. In principle, wavefield extrapolation for IDT purposes can be carried out with elastic wave‐equation operators. However, in addition to the high cost of elastic modelling, it requires either developing a suitable elastic imaging condition or employing expensive and often unreliable mode‐decomposition techniques.…”