The imaging condition proposed by Claerbout (1971) should be modified if primaries and multiples are simultaneously imaged, whether the source position is known or unknown. The imaging condition I propose states that the radius of curvature of the wavefront equals zero. This is called the depth-focusing imaging condition. MacKay and Abma (1993) use depth focusing to carry out velocity analysis. If the migration velocity is larger than the medium velocity, then the focusing depth is less than the reflection depth, and the imaging depth is larger than the reflection depth; on the other hand, if the migration velocity is less than the medium velocity, then the focusing depth is greater than the reflection depth, and the imaging depth is less than the reflection depth. The real reflection depth lies at the mid-point between the focusing depth and the imaging depth. In that paper, the authors proposed a method for estimating the radius of the curvature of the wavefront. However the formula is suitable only for imaging the primaries. For a given scattering point, the primary and multiple scattering from it are simultaneously focused at the same depth in the model space and at different times in the data space with the downward wavefield continuation. The "focusing" means that the received scattered wavefield is collapsed into the scattering point, and the radius of curvature of the wavefront diminishes to zero. With the depth-focusing imaging condition, the focused imaging values of the primary and multiples can be simultaneously picked up from the depth-extrapolated wavefield, which is expressed in the time domain. The following are some advantages of depth-focusing imaging. The primaries and multiples (including the higher-order multiples) can be simultaneously imaged; the source position can be known (for the primaries) or unknown (for the multiples); all of the scattered wavefield can be added together, and computation efficiency can be improved. The disadvantage is that the depth-focusing imaging condition is difficult to use, especially for data with a lot of noise.

10/31/2005