Generalized imaging conditions for wave-equation migration

A typical imaging condition for seismic reflection data involves source and receiver wavefield matching, e.g. by cross-correlation, at every image location. This statement is true no matter how the two wavefields are reconstructed, for example by one-way wavefield extrapolation, or two-way reverse-time extrapolation, or Kirchhoff integral methods. This statement is also true when the source and receiver wavefields are reconstructed using different velocity models, as is the case for imaging of converted waves. Angle-dependent reflectivity information can be extracted from the source and receiver wavefield by retaining multiple lags of the imaging cross-correlation, i.e. by analyzing the match of wavefields shifted relative to one-another. Wavefields can be shifted in space (3D) or in time (1D), and each shift method has an associated angle-decomposition method. This paper explores the various types of imaging condition using space and time shifts and derives relations for angle decomposition for converted-wave imaging using time-shifts.