Resolution in seismic imaging: Is it all a matter of perspective?

Classical wave-equation migration of seismic data combines both acoustic wave propagation and an imaging condition to produce a subsurface section. Integral methods implicitly combine high-frequency ray asymptotics of the wave equation with a ray-dependent imaging condition. The inherent limits on subsurface resolution imposed by acoustic-wave generation (e.g., source bandwidth), subsurface propagation (e.g., attenuation), and recording (e.g., receiver arrays and aperture) have been studied extensively. This article studies how (or whether) the choice of imaging condition affects resolution. We will see in particular that the phenomenon of migration wavelet stretch, wherein the vertical resolution of steeply dipping reflectors is preferentially lowered by migration, is neither an artifact of an imaging condition nor a reduction of resolution on steeply dipping reflectors. In fact, we will discover that in seismic imaging of prestack data, steeply dipping reflectors are ultimately better resolved than horizontal beds. Finally, the concept of "superresolution" from seismic inversion, a generalization of thin-bed tuning analysis, is explored and explicated with a simple example of multiple reflections.