Inversion of the traveltime delay between split shear-waves in anisotropic media
Ivan A. Simōes-Filho, Jessé C. Costa, Sharma Tadepalli, 1996. "Inversion of the traveltime delay between split shear-waves in anisotropic media", Seismic Anisotropy, Erling Fjær, Rune M. Holt, Jaswant S. Rathore
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We propose a kinematic inversion procedure based on the traveltime delay between qSl- and qS2-waves in anisotropic media. This procedure is valid for weakly anisotropic media, where traveltime perturbation equations from isotropic to anisotropic media can be used. These equations are presented and it is shown that the traveltime delay between split shear-waves depends on 9 combinations of the density-normalized elastic parameters, which we call the birefringence parameters. The values of the birefringence parameters are then used as indicators of the type and orientation of the main symmetry elements of the most common anisotropic symmetry systems. There is no need for prior assumptions on the medium symmetry. These results are then applied to factorized anisotropic inhomogeneous media, where the traveltime delav is shown to be independent of the heterogeneity of the medium. This independence
allows us to use straight ray traveltime delay tomography to invert for the medium symmetry system. We then show, through an analysis of the condition number of the matrix of partial derivatives of the traveltime delay with respect to the birefringence parameters, that the stability of the inversion procedure is strongly dependent on the acquisition geometry. The inversion procedure is then applied to synthetic data computed by ray tracing and laboratory data obtained with ultrasonic frequencies on a sample of foamglas, a synthetic material which exhibits transverse isotropy.