Figure 1: (GIF) (PS) A wave reflected from a mirror in an isotropic medium.
Figure 2: (GIF) (PS) A wave reflected from a mirror in an elliptically anisotropic medium. It is just Figure 1 stretched and rotated.
Another version of Figure 1 (GIF) (PS) , showing a seismic survey over an isotropic medium.
Another version of Figure 2 (GIF) (PS) , showing a seismic survey over an elliptically anisotropic medium. Again, it is just a stretched and rotated version of the previous figure, and thus a migration of this data would produce a sharp (but stretched) image. This shows that the elliptically anisotropic equivalent of ``time to depth'' mapping requires a layer-by-layer linear-transformation step that allows both a vertical stretch and a horizontal shear. As Francis Muir likes to say:
Migration = Focus + Map
(Also note that in this figure the source and geophones are stretched. The wavefield may be kinematically identical but since in practice we don't use stretched geophones the amplitudes will differ between the equivalent isotropic and elliptically anisotropic experiments.)
Figure 3: (GIF) (PS) Converting a two layer physical model to its isotropic equivalent. A wavefront radiating from a point source is shown in each layer. If the layer is isotropic, the wavefront is circular. On the left is the true depth picture. On the right is the picture that standard processing would infer from surface data alone using an isotropic assumption. Note the bottom interface appears horizontal, even though it actually dips to the left. The middle panel shows the conversion process after stretching the first layer.