Seismic illumination can be predicted using one-way wavefield extrapolators and formulations for forward modeling and migration. Rather than compute a finely sampled set of frequencies over the bandwidth of interest, I compute only a decimated set of frequencies and rely on the fact that for a single reflecting horizon, or a set of nearby horizons, the effects of temporal wraparound can be neglected. The output of this process is a migrated image of the target structure showing illumination effects due to overburden velocity structure and acquisition sampling.
It is often useful to be able to study how accurately a seismic survey geometry images a hypothetical target reflector. Think of the process of modeling a seismic survey over a volume of the subsurface followed by processing that modeled data to make an image of the reflectors in that volume of subsurface as a "system". Heuristically, we can define seismic "illumination" to be the transfer function of that system.
Historically, ray tracing methods provided an inexpensive approach for studying the illumination of a target reflector surface in a seismic experiment. When the overburden and the target are relatively simple, ray-traced hit-count methods are often sufficient to predict seismic illumination. The ray-based method can be improved by using a boundary integral modeling formulation to deal with diffractions and more complex reflector surfaces. However, when the overburden velocity is complex, e.g. in the case of subsalt imaging, raytracing methods will likely fail to give accurate estimates of how well a seismic experiment images a reflector.
Full finite-difference modeling and subsequent processing/imaging is considered to be the "gold standard" for studying seismic illumination. Waves propagate in all directions, all orders of multiples are generated (if desired), and amplitudes are consistent with the acoustic wave equation, including transmission losses and reflection coefficients. Although relatively complete, the demands of a full finite-difference modeling project are such that even today, they are not carried out on a whim. Typically both velocity and density models must be constructed, the surfaces and bodies used to do this must be carefully QC''d; run times are long enough that such a project cannot be viewed as a "throwaway". Thus, there is a use for a waveequation based method for modeling the response of the seismic experiment on a target reflector surface that is more accurate than raytracing, and less expensive/demanding than full finite-difference modeling.
One-way wave equation modeling is usually a less expensive alternative to full 2-way time or frequency domain finite-difference modeling.
This sequence approximates the process of recording seismic data in the field and processing it to make an image.
Here, the Green''s functions for the migration step do not have to be the same as those in the modeling step. In the modeling step we may wish to incorporate effects such as transmission loss at discrete boundaries, where as in the migration step we may wish to include amplitude compensation terms commonly used when migrating real data.
