caa a22 4500 477047173 CHVBK 20180405111333.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00882064 doi (NATIONALLICENCE)springer-10.1007/BF00882064 Iversen Einar NORSAR, P.O. Box 51, N-2007, Kjeller, Norway aut Derivatives of reflection point coordinates with respect to model parameters [Elektronische Daten] [Einar Iversen] The motivation for this paper is to provide expressions for first-order partial derivatives of reflection point coordinates, taken with respect to model parameters. Such derivatives are expected to be useful for processes dealing with the problem of estimating velocities for depth migration of seismic data. The subject of the paper is a particular aspect of ray perturbation theory, where observed parameters—two-way reflection time and horizontal components of slowness, are constraining the ray path when parameters of the reference velocity model are perturbed. The methodology described here is applicable to general rays in a 3D isotropic, heterogeneous medium. Each ray is divided into a shot ray and a receiver ray, i.e., the ray portions between the shot/receiver and the reflection point, respectively. Furthermore, by freezing the initial horizontal slowness of these subrays as the model is perturbed,elementary perturbation quantities may be obtained, comprising derivatives of ray hit positions within theisochrone tangent plane, as well as corresponding time derivatives. The elementary quantities may be estimated numerically, by use of ray perturbation theory, or in some cases, analytically. In particular, when the layer above the reflection point is homogeneous, explicit formulas can be derived. When the elementary quantities are known,reflection point derivatives can be obtained efficiently from a set of linear expressions. The method is applicable for a common shot, receiver or offset data sorting. For these gather types, reflection point perturbationlaterally with respect to the isochrone is essentially different. However, in theperpendicular direction, a first-order perturbation is shown to beindependent of gather type. To evaluate the theory, reflection point derivatives were estimated analytically and numerically. I also compared first-order approximations to ‘true' reflection point curves, obtained by retracing rays for a number of model perturbations. The results are promising, especially with respect to applications in sensitivity analysis for prestack depth migration and in velocity model updating. Birkhäuser Verlag, 1996 Ray perturbation theory nationallicence velocity perturbations nationallicence reflection point perturbations nationallicence pure and applied geophysics Birkhäuser-Verlag 148/1-2(1996-03-01), 287-317 0033-4553 148:1-2<287 1996 148 24 https://doi.org/10.1007/BF00882064 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00882064 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Iversen Einar NORSAR, P.O. Box 51, N-2007, Kjeller, Norway aut NATIONALLICENCE 773 0- pure and applied geophysics Birkhäuser-Verlag 148/1-2(1996-03-01), 287-317 0033-4553 148:1-2<287 1996 148 24 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer