Efficient estimates of subsurface illumination for Kirchhoff prestack depth migration

Abstract

Summary Because of its computational efficiency, prestack Kirchhoff depth migration is currently the most popular algorithm used in 2-D and 3-D subsurface imaging. Nevertheless, Kirchhoff algorithms in their typical embodiment produce less than ideal results in complex terranes where we may encounter multipathing from the surface to a given image point, and beneath fast carbonates, salt or volcanics where ray theoretical energy cannot penetrate through to illuminate slower velocity sediments. When faced with particularly difficult to understand illumination problems, we might exploit full acoustic or elastic wave equation forward modeling to evaluate the effectiveness of a proposed seismic acquisition program. Unfortunately, seismic events that are predicted to reach the earth’s surface with sufficient amplitude may not be among those that can be imaged by our production Kirchhoff imaging scheme. Worse yet, full wave equation prestack modeling may well cost more than the field acquisition itself, and several orders of magnitude more than the Kirchhoff migration step that produces a useful image. We show here how Kirchhoff modeling, the mathematical adjoint of Kirchhoff migration, can be most useful in determining which components of signal and noise, including diffractions, can be imaged by Kirchhoff migration before acquisition begins. Kirchhoff modeling is a necessary element of least square Kirchhoff migration that produces an improved estimate of reflectivity that compensates for irregularities in surface sampling, including missing data, as well as for irregularities in ray coverage due to strong lateral variations in velocity. As a by-product we also obtain an image of subsurface illumination that is a measure of our confidence in our least square reflectivity estimate.