| Abstract: | 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 × 2 matrices B 0 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 ( B 0). 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 V0T0), i.e. amplitudes proportional to the reflection coefficient. For any velocity changes, the inverse of det ( B 0) 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. |
