Group velocity (ray) equations describe the dynamic behavior of wave-equation extrapolators in the high-frequency limit. They are found in general from the dispersion relation of an arbitrary acoustic wave equation. Wave-equation operators require a background extrapolation velocity. As an application of the group velocity equations, a sensitivity analysis to the background-operator velocity illustrates the trade-off between uncertainty in velocity and precision in imaging. Exact wave extrapolators are most useful when the exact velocity function is known. Wave-equation imaging for velocity analysis in Snell midpoint coordinates requires velocity-insensitive extrapolation operators. In this frame of reference, approximations of the exact acoustic wave equation are referenced to an arbitrary angle of propagation. Group velocity equations show that in Snell midpoint coordinates, using wide-reference propagation angles, the fifteen-degree wave equation gives satisfactory velocity-independent images. The forty-five degree wave equation does not appreciably improve the image.

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