Riemannian wavefield extrapolation, a one-way wave-equation method for propagating seismic data on generalized coordinate systems, is extended to inline delayed-shot migra-tion using 3D tilted elliptical-cylindrical (TEC) coordinate meshes. Compared to Cartesian geometries, TEC coordi-nates are more conformal to the shape of inline delayed-source impulse response, which allows the bulk of wavefield energy to propagate at angles lower to the extrapolation axis, thus improving global propagation accuracy. When inline co-ordinate tilt angles are well matched to the inline source ray parameters, the TEC coordinate extension affords accurate propagation of both steep-dip and turning-wave components important for successfully imaging complex geologic struc-ture. Wavefield extrapolation in TEC coordinates is no more complicated than propagation in elliptically anisotropic me-dia and can be handled by existing implicit finite-difference methods. Impulse response tests illustrate the phase accuracy of the method and show that the approach is free of numerical anisotropy. Migration tests from a realistic 3D wide-azimuth synthetic derived from a field Gulf of Mexico data set demon-strate the imaging advantages afforded by the technique, in-cluding the improved imaging of steeply dipping salt flanks at a reduced computational cost.
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