ABSTRACT

Although full-waveform inversion (FWI) has shown significant promise in reconstructing heterogeneous velocity fields, most existing methodologies are limited to acoustic models. We extend FWI to multicomponent (PP and PS) data from anisotropic media, with the current implementation limited to a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. The algorithm is designed to estimate the interval vertical P- and S-wave velocities (VP0 and VS0) and Thomsen parameters ε and δ from long-spread PP and PSV reflections. The forward-modeling operator is based on the anisotropic reflectivity technique, and the inversion is performed in the time domain using the gradient (Gauss-Newton) method. We employ nonhyperbolic semblance analysis and Dix-type equations to build the initial model. To identify the medium parameters constrained by the data, we perform eigenvalue/eigenvector decomposition of the approximate Hessian matrix for a VTI layer embedded between isotropic media. Analysis of the eigenvectors shows that the parameters VP0, VS0, ε, and δ (density is assumed to be known) can be resolved not only by joint inversion of PP and PS data, but also with PP reflections alone. Although the inversion becomes more stable with increasing spreadlength-to-depth (X/Z) ratio, the parameters of the three-layer model are constrained even by PP data acquired on conventional spreads (X/Z=1). For multilayered VTI media, the sensitivity of the objective function to the interval parameters decreases with depth. Still, it is possible to resolve VP0, VS0, ε, and δ for the deeper layers using PP-waves, if the ratio X/Z for the bottom of the layer reaches two. Mode-converted waves provide useful additional constraints for FWI, which become essential for smaller spreads. The insights gained here by examining horizontally layered models should help guide the inversion for heterogeneous TI media.

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