Pre-Stack Kirchhoff Inversion of Common Offset Data

摘要

A pre-stack inversion algorithm is developed for acoustic Kirchhoff, high frequency, common offset data. Given the velocity above a reflector, the interface is located and an angularly-dependent reflection coefficient is computed at each reflection point. A quick post-processing step then calculates the velocity of the lower medium. Lateral velocity variations in the second layer are naturally recovered since each reflection point provides an independent measure of the reflection coefficient. The inversion is performed as a mapping where the response to subsurface test points is examined by an integration over the data. If a test point is on the reflector, the reflection coefficient is returned. Inversion and migration operators both utilize an integral over the data, with each trace in the summation weighted by an amplitude and a phase term. The Kirchhoff offset inversion is first formulated for data acquired over a plane, producing a 3-D reflectivity map. Since data are commonly collected along a single line, a 2.5-D specialization is also developed. A method for determining the velocity of the lower medium from an angularly-dependent reflection coefficient is then detailed for the 2.5-D case.