Often, interpreters only have access to seismic sections and, at times, well data, when making an interpretation of structures and depositional features in the subsurface. The validity of the final interpretation is based on how well the seismic data are able to reproduce the actual geology, and seismic modeling can help constrain that. Ideally, modeling should create complete seismograms, which is often best achieved by finite-difference modeling with postprocessing to produce synthetic seismic sections for comparison purposes. Such extensive modeling is, however, not routinely affordable. A far more efficient option, using the simpler 1D convolution model with reflectivity logs extracted along verticals in velocity models, generates poor modeling results when lateral velocity variations are expected. A third and intermediate option is to use the various ray-based approaches available, which are efficient and flexible. However, standard ray methods, such as the normal-incidence point for unmigrated poststack sections or image rays for simulating time-migrated poststack results, cannot deal with complex and detailed targets, and will not reproduce the realistic (3D) resolution effects of seismic imaging. Nevertheless, ray methods can also be used to estimate 3D spatial prestack convolution operators, so-called point-spread functions. These are functions of the survey, velocity model, and wavelet, among others, and therefore they include 3D angle-dependent illumination and resolution effects. Prestack depth migration images are thus rapidly simulated by spatial convolution with detailed 3D reflectivity models, which goes far beyond the limits of 1D convolution modeling. This 3D convolution modeling should allow geologists to better assess their interpretations and draw more definitive conclusions.

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