Extrapolation equations are not frequency-dispersive.

To prove that the familiar 15$^\circ$, 45$^\circ$, etc. wave extrapolators are not frequency-dispersive, recall from chapter that the dispersion relations all have the form $k_z / \omega = f( k_x / \omega )$, where f is a semicircle approximation, say, 15$^\circ$ or 45$^\circ$.No dispersion relation of this form can be frequency-dispersive. Performing the derivatives required by (29), you see that while the (x,t)-coordinates of a wavefront depend on the dip angle through the parameter $v k_x / \omega$, they do not depend explicitly on $\omega$.So any frequency dispersion observed in practice does not arise from a 15$^\circ$ or 45$^\circ$ approximation.