Image-domain wavefield tomography in transversely isotropic media

Abstract

Image-domain tomography (IDT) operates with seismic reflection data and optimizes the background velocity model by improving the quality of image gathers obtained by prestack depth migration. In this thesis, I develop an acoustic wave-equation-based IDT algorithm for reconstructing transversely isotropic (TI) models from P-wave reflections. Parameter estimation is carried out by focusing energy in extended images, which are produced by reverse-time migration (RTM) and contain information about the angle-dependent illumination of the subsurface. First, I study the sensitivity of energy focusing in the extended domain to the parameters of VTI (TI with a vertical symmetry axis) media. Analysis of horizontal and dipping events shows that the most influential parameter is the zero-dip NMO velocity (Vnmo), whereas the contribution of the anellipticity parameter η increases with reflector dip. Energy focusing is sensitive only to the lateral variation of Thomsen’s parameter δ. These conclusions, consistent with the properties of time-domain reflection moveout, help develop an effective strategy for estimating the parameters Vnmo, δ, and η. Using both the differential and integral wave-equation operators for acoustic VTI media, I apply the adjoint-state method to derive the inversion gradients for image- and data-domain tomography. The data-domain gradients make it possible to incorporate vertical seismic profiling (VSP) data, which provide important constraints for anisotropic model updating, into the objective function. The gradients computed with the integral wave-equation operator are free of the unphysical shear-wave modes produced by differential wave-equation solutions. However, robust estimation of the VTI parameters (especially the coefficient η) requires mitigating illumination and aperture-truncation artifacts in RTM extended images. I demonstrate that these artifacts can be efficiently suppressed via least-squares RTM (LSRTM) preconditioned with nonstationary matching filters. The integral wave-equation operator and adjoint-state gradients allow me to develop a multistage IDT algorithm for VTI media. Image-guided smoothing of the inversion gradients of the parameters Vnmo and η helps ensure convergence towards geologically plausible solutions. The δ-field is tightly constrained by image-guided interpolation between available boreholes. A test on elastic data for the synthetic Marmousi-II model confirms that robust estimation of the VTI parameters is possible even for substantially distorted initial models. Application of the algorithm to a line from a 3D ocean-bottom node data set acquired in the Gulf of Mexico produces a refined η-field and improves the focusing of the LSRTM image. Finally, the IDT methodology is generalized for TI media with a tilted symmtry axis (TTI). I derive the P-wave separable dispersion relation for strongly anelliptic TTI models and implement the corresponding wave-equation operator, which is then employed to obtain the inversion gradient. A synthetic test for a dipping homogeneous TTI layer demonstrates that neglecting the symmetry- axis tilt can distort estimation of the other medium parameters. Analysis of the extended LSRTM images shows that, if the symmetry axis is orthogonal to the reflector, the coefficient δ contributes to focusing of dipping events, whereas the parameter η produces only weak linear defocusing regardless of reflector dip. To increase the robustness of IDT for TTI media, the image-focusing objective function is combined with a model-shaping term that contains borehole information about δ. A test on the BP benchmark TTI model shows that the algorithm can update the background Vnmo-, δ-, and η-fields even for a strongly distorted initial velocity field.