ABSTRACT
The sampling theorem requires minimum two points per wavelength to ensure the proper reconstruction of a wavefield. Violation of this limit will result in data aliasing. With the increased demand for high-frequency seismic processing, data recorded in a field may not have sufficient spatial sampling. Reverse time migration (RTM) using a conventional scheme will not be able to produce a high-quality image from such an aliased input data set. However, when the wavefield and its gradients are available, the generalized sampling theorem relaxes the requirement to only one point per wavelength. Stereo-modeling methods use a system of wave equations to compute a vector containing the particle displacement and its spatial gradients in wavefield propagation. Therefore, in cases in which a wavefield and its spatial gradients are available, such as a multicomponent data set, RTM using the stereo-modeling methods can be potentially much more accurate and efficient than those commonly used ones, such as Lax-Wendroff correction. We investigated the merits of one such method, called the nearly analytic central difference, in RTM to produce high-quality images. Numerical experiments on different data sets produce consistent results with the generalized sampling theorem, which indicates that the stereo-modeling method can yield high-quality images from insufficiently sampled data compared with conventional finite-difference methods.
