Migration and demigration

The work examines the physical foundations and mathematical description of migration and demigration in seismic exploration. Seismic imaging is treated as a focusing process in which the recorded wavefield is focused at image points associated with reflection, scattering, and diffraction. The relationship between migration and the common-depth-point (CDP) method is analyzed; imaging by the CDP method is interpreted as a special case of migration. Integral formulations of Kirchhoff migration before and after stacking in the time and depth domains are presented. The role of the stacking aperture and limitations associated with the Fresnel zone are considered. Wave-propagation times are determined either from the eikonal equation or from its linear approximation. Demigration is formulated as the inverse problem of recovering seismic observations from an image of the medium. A numerical demigration procedure is described, together with an iterative migration–demigration algorithm intended to improve image reconstruction. Model examples illustrate the relationship between the two transformations. The final part presents an example of migration tomography based on reflected waves. Seismic observations are first modeled from prescribed velocity and amplitude models by demigration and are then migrated to reconstruct the image. This procedure is regarded as tomography based on reflected waves, in contrast to classical tomography based on transmitted waves.