The application of a deconvolution imaging condition in wave-equation shot-profile migration is important to provide illumination compensation and amplitude recovery. Particularly if the aim is to successfully recover a measure of the medium reflectivity, an imaging condition that destroys amplitudes is unacceptable. We study a set of imaging conditions with illumination compensation. The imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced. In numerical experiments using a vertically inhomogeneous velocity model, the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield, also known as the illumination map. In an application to Marmousi data, unconditional division by autocorrelation turned out to be unstable. Effective stabilization was achieved by smoothing the illumination map.

Present-day techniques to estimate the traveltime parameters of the common-reflection-surface (CRS) stack are tedious, time-consuming, and expensive processes based on local coherence analyses along a large number of trial surfaces. With the 2D CRS method, faster and cheaper determination is possible. The complete set of CRS parameters can be extracted from seismic data by an application of modern local-slope-extraction techniques. The necessary information about the CRS parameters is contained in the slopes of the common-midpoint section at the central point and one or several common-offset sections in its vicinity. We studied two procedures for the CRS parameter extraction technique. Their difference lies in the way the common-offset parameters are determined. One technique requires slope-derivative information (a possible source of instability); the other uses slope information at two different locations and less data redundancy. Testing on a synthetic data example proved that the procedures are sufficiently robust to allow for high-quality extraction of all CRS parameters from the extracted slope fields. In this way, the CRS parameter extraction can be sped up by several orders of magnitude as compared to the conventional procedure based on coherence analysis along trial surfaces.

The quality of seismic images obtained by reverse time migration ͑RTM͒ strongly depends on the imaging condition. We propose a new imaging condition that is motivated by stationary phase analysis of the classical crosscorrelation imaging condition. Its implementation requires the Poynting vector of the source and receiver wavefields at the imaging point. An obliquity correction is added to compensate for the reflector dip effect on amplitudes of RTM. Numerical experiments show that using an imaging condition with obliquity compensation improves reverse time migration by reducing backscattering artifacts and improving illumination compensation.