Unification of single-configuration seismic imaging processes
H. Jaramillo and U. Albertin
Journal name: Geophysical Prospecting
Issue: Vol 56, No 2, March 2008 pp. 177 - 196
Info: Article, PDF ( 463.01Kb )
In this paper we derive an integral formula that encompasses all linear processes on seismic data. These include migration, demigration and residual migration, as well as data mapping procedures such as transformation to zero offset, inverse transformation to zero offset, residual transformation to zero offset and offset continuation. The derivation of the equation is different from all previous approaches to unification. Here we do not use a cascaded operation between two operators, but rather the superposition principle. In this regard, the derivation is not only more fundamental, but also simpler and more general. We study the kinematics and the dynamics of these processes and show that the signals can be reconstructed asymptotically either by finding the envelope of particular surfaces or by stacking energy along “adjoint” surfaces. For example, in the case of migration, the first set of surfaces are isochrons, while the “adjoint” surfaces are diffraction responses. In practice, the distinction between these two types of surfaces is equivalent to choosing the order of the computational loops with regard to the input and output seismic traces.