For the purpose of one-way wave-equation imaging, a pseudoscreen propagator is developed for transversely isotropic media with vertical axes of symmetry. The phase shift for propagation through a depth slice is decomposed into three terms: a Gazdag phase shift for propagation in a laterally homogeneous reference medium, a correction for lateral variability of vertical propagation, and a remaining wide-angle term for oblique directions of propagation. Based on rational function approximation for this remaining wide-angle term, a Fourier finite-difference (FFD) approach with four-way splitting is applied. Fourth-order Padé approximation is unsatisfactory in anelliptic media for large propagation angles with respect to the vertical direction. Therefore, a method of coefficient optimization is developed in conjunction with a method of choosing an adequate homogeneous reference medium in a depth slice. By symmetrizing the finite-difference operators, and because of the choice of the optimized coefficients, the propagator is stable in the sense that the least-squares norm of the wavefield, measured for a frequency-depth slice, does not grow with increasing depth of propagation. A small amount of artificial damping is applied to suppress artifacts that appear at the critical angle defined by the velocities in the reference medium and the actual medium. Synthetic examples confirm that good kinematic accuracy is achieved for a wide range of propagation angles (typically up to 60°).
