Evolution-equation approach to seismic image, and data, continuation

In reflection seismology one places point sources and point receivers on the earth’s surface, forming an acquisition geometry. Each source generates acoustic waves in the subsurface, that are reflected where the medium properties vary discontinuously. The reflections that can be observed at the receivers are used to image these discontinuities or reflectors assuming a background medium. We analyze methods to circumvent the repeated imaging of reflectors under varying background media, or the repeated modelling of reflections under varying acquisition geometries. These methods involve the introduction of the notion of seismic continuation. Here, we develop the foundation of, and a comprehensive framework for seismic continuation while extending earlier approaches to allow for the formation of caustics. Traditionally, seismic continuation has been viewed from a geometrical (ray asymptotic) point of view; here, we introduce the notion of wave-equation continuation through the appearance of evolution equations.