Extended imaging conditions for wave-equation migration

Wavefield-based migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in common-image-gathers (CIG) which represent reflectivity as a function depth and extensions, e.g. reflection angles. We introduce extended common-image-point (CIP) gathers constructed only as a function of the spaceand time-lag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIPs constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIPs also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIPs remove the depth bias of CIGs constructed as a function of the depth axis. An interpretation of the CIPs using scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIPs are characterized by focused energy at the origin of the spaceand time-lag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefield-based tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinateindependent CIPs can be decomposed function of the angles of incidence.