A Time-Domain Derivation of Optimal and Suboptimal Kirchhoff Quantitative Migrations Via a Least-Squares Approach
Abstract
We develop in this paper a general methodology for the derivation of optimal and suboptimal quantitative migration formula from the data misfit function associated to a given forward modeling operator. By construction, these migrations take into account any feature and approximation which has been incorporated into the data misfit function, such as finite aperture, band limited source, surface boundary conditions, multishot data, etc...\\ \indent This methodology is then applied to the case where the forward modelling is made via the Born plus rays approximation and the reflectivity of the earth is represented by an array of diffracting points. This leads to the construction of efficient suboptimal quantitative Kirchhoff migration formula which provide a good restitution of amplitudes under a wide variety of circumstances (finite aperture, band limited source, etc...) and for a wide range of propagators (slowness background).