Resolution analysis of wide-azimuth angle decomposition for wave-equation migration

Angle-dependent reflectivity constructed from an extended imaging condition, applied to the extrapolated source and receiver wavefields, can be employed to velocity/anisotropy estimation and amplitude versus angle (AVA) analysis. This imaging condition allows one to construct images as a function not only of three-dimensional position but also space lags of the source/receiver wavefield cross-correlation. The information in the space-lag domain can be mapped into the angle domain which is defined by the reflection and azimuthal angles at every image point. The relationship between sampling parameters in the angle and space-lag domain, together with the equations used to perform the mapping, show that the sample interval in the space-lag domain controls the range of angles that can be accurately recovered from the image. From the amplitude spectrum of the lag-domain common-image gathers, we can calculate the maximum angle that limits this range. The range of space-lags also influences the sampling interval in the angle domain. This analysis is important for the case where the angle-domain common-image gathers are employed for amplitude versus angle analysis. In this case, the amplitudes corresponding to the angles outside of this range would not be reliable, regardless of how accurate wavefield reconstruction is.