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Derivatives of the displacement tensor with respect to the independent modelparameters of the subsurface, also called Fr\'echet derivatives (or sensitivitykernels), are a key ingredient for seismic full-waveform inversion with alocal-search optimization algorithm. They provide a quantitative measure of theexpected changes in the seismograms due to perturbations of the subsurfacemodel parameters for a given survey geometry. Since 2.5-D wavefield modelinginvolves a real point source in a 2-D geological model with 3D (spherical) waveproperties, it yields synthetic data much closer to the actual practical fielddata than the commonly used 2-D wave simulation does, which uses an unrealisticline source in which the waves spread cylindrically. Based on our recentlydeveloped general 2.5-D wavefield modeling scheme, we apply the perturbationmethod to obtain explicit analytic expressions for the derivatives of thedisplacement tensor for 2.5-D/2-D frequency-domain seismic full-waveforminversion in general viscoelastic anisotropic media. We then demonstrate thenumerical calculations of all these derivatives in two common cases: (i)viscoelastic isotropic and (ii) viscoelastic tilted transversely isotropic(TTI) solids. Examples of the differing sensitivity patterns for the variousderivatives are investigated and compared for four different homogeneous modelsinvolving 2-D and 2.5-D modeling.

Numerical Fr\'echet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media