Traveltime moveout is a key ingredient of traditional and modern stacking schemes and, in addition to the constructive summation of redundant data components, has versatile application such as trace interpolation, regularization, or velocity model building. It has been shown that higher-order traveltime operators provide a better fit for curved target structures and complex overburdens. In addition, multidimensional stacking schemes have been shown to optimally utilize multi-channel data redundancy. Derivations of higher-order multidimensional moveout approximations require a simplified model to fit seismic data from a heterogenous overburden, i.e., an auxiliary medium and an analytical description of the reflector. The existing mechanisms to account for the overburden heterogeneity, either by a shift in velocity (effective medium), or by a shift of the reference time (optical medium), could not yet be extended to the 3D case. We suggest an auxiliary anisotropic medium, which in the 3D case allows to simulate wavefronts of complex shape. We show that this anisotropic auxiliary medium naturally incorporates properties of effective and optical auxiliary media. The auxiliary anisotropic medium and a locally analytical description of the reflector shape constitute the 3D simplified model, which enables the derivation of 3D extensions of the existing 2D multidimensional moveout approximations.


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