caa a22 4500 477046983 CHVBK 20180405111333.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF00874584 doi (NATIONALLICENCE)springer-10.1007/BF00874584 Weak-contrast approximation of the elastic scattering matrix in anisotropic media [Elektronische Daten] [Bjørn Ursin, Geir Haugen] The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux. Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified. When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation. For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves. Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media. Birkhäuser Verlag, 1985 Anisotropy nationallicence amplitude versus offset and azimuth (AVO-A) nationallicence approximative scattering matrix nationallicence weak-contrast approximation nationallicence Ursin Bjørn Faculty of Earth Science and Metallurgy, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, 7034, Trondheim, Norway aut Haugen Geir Faculty of Earth Science and Metallurgy, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, 7034, Trondheim, Norway aut pure and applied geophysics Birkhäuser-Verlag 148/3-4(1996-09-01), 685-714 0033-4553 148:3-4<685 1996 148 24 https://doi.org/10.1007/BF00874584 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00874584 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ursin Bjørn Faculty of Earth Science and Metallurgy, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, 7034, Trondheim, Norway aut NATIONALLICENCE 700 1- Haugen Geir Faculty of Earth Science and Metallurgy, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, 7034, Trondheim, Norway aut NATIONALLICENCE 773 0- pure and applied geophysics Birkhäuser-Verlag 148/3-4(1996-09-01), 685-714 0033-4553 148:3-4<685 1996 148 24 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer