REFLECTION AMPLITUDES AND MIGRATION AMPLITUDES (ZERO-OFFSET SITUATION)

The effect of wave-equation migration on amplitudes is determined. This effect is derived for zero-offset traces and for second-order approximations of the traveltimes. Three steps are followed: firstly, the amplitudes of zero-offset traces are established; secondly minus half the traveltimes are used as input for downward continuation in migration (forward in space and time); thirdly, the amplitudes of the migrated events are determined by downward continuation (at zero-traveltimes). Layered models (piles of homogeneous layers) with smooth interfaces are used. The determinants of the 2 x 2 matrices B0 obtained for these models are responsible for the main effect on migration. The migration result primarily depends on the overburden as the inverse of det (B0). Drastic effects can occur over small distances. For weakly reflecting media, it is confirmed that wave-equation migration gives " correct " results (but the input data must be multiplied by V0 T0), i.e. amplitudes proportional to the reflection coefficient. For any velocity changes, the inverse of det (B0) will, in general, give inaccurate migration amplitudes and inaccurate lithological interpretations. In a simple step, true amplitude migration, or exact migration, is derived from our results. It is assumed that no focus phenomena are present. The effect of buried foci is discussed briefly.