Reflection coefficients are often defined for either displacement-amplitude ratios or potential ratios. For a pure compressional wave the displacement field can be expressed as the gradient of a potential field. Taking the divergence of the displacement and using the wave-equation for the potential leads to

(1) |

It is clear that the above formulation is restricted to isotropic cases
where P waves are described by a single velocity *v*_{p}, however the
background media, used for the time extrapolation is considered
to be anisotropic. This means that anisotropic behavior is correctly
handled in the propagation through the overburden, but not at the target zone.
The displacement reflection coefficient relates to the potential reflection
coefficient through

(2) |

It is important to emphasize that the wavefield decomposition to separate the purely compressional field is performed only at the imaging step but the propagation (depth extrapolation) uses the full wavefield. Therefore, all elastic effects of mode conversion in all interfaces are taken into account.

11/18/1997