Range and resolution analysis of wide-azimuth angle decomposition

Imaging in complex media benefits from uniform illumination of the target from all possible directions. Moreover, it is desirable to recover reflectivity from seismic data as a function of incidence and azimuthal angles at every location over the reflector. Applications of angle-dependent reflectivity include velocity and anisotropy estimation and amplitude versus angle (AVA) analysis. One way of constructing angle-dependent reflectivity is to apply an extended imaging condition to the extrapolated source and receiver wavefields. 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, 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 in this domain. This is the range of angles for which the energy is well focused, at the depth of the reflector, in the angle-domain common-image gathers. From the amplitude spectrum of the lag-domain common-image gathers, we can calculate the maximum angle that limits this range. For angles greater than this upper bound, the image energy starts to spread away from the depth of the reflector. 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.