From Transverse Isotropy to Arbitrary Anisotropy for qP-Waves in Weakly Anisotropic Media
Patrick N.J. Rasolofosaon, 2001. "From Transverse Isotropy to Arbitrary Anisotropy for qP-Waves in Weakly Anisotropic Media", Anisotropy 2000: Fractures, Converted Waves, and Case Studies, L. Ikelle, A. Gangi
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Solutions of many kinematic and dynamic problems regarding elastic wave propagation in transversely isotropic (TI) media have been published in the literature. In the case of more general types of anisotropy (e.g., triclinic, monoclinic or even orthorhombic), the solutions of such problems are, in general, much more complicated or simply not known. However, in some special cases the TI solutions can be generalized to the case of more complicated types of anisotropy simply by replacing the anisotropy parameters ε and δ in the TI equations by their azimuthally dependent counterparts, ε(λ) and δ(λ). This transformation is called the Azimuthaly Dependent Anisotropy Parameter Transformation, or, more simply, the ADAPT recipe. The aim of this paper is to discuss the applicability of this transformation to special cases of interest for seismic exploration.
The study is restricted to qP-waves, constituting the great majority of data acquisition in the field in media exhibiting weak anisotropy, which is a reasonable assumption in most of the sedimentary basins. In this context, the ADAPT recipe can be applied to any 2D kinematic problem in monoclinic media (with a horizontal symmetry plane), even in the presence of the most general type of velocity/density gradient, as long as the gradient vector is confined to the investigated plane. This is successfully checked in a numerical model. When dealing with triclinic media, the recipe is applicable in 1D geometry and if the “unperturbed isotropic” seismic ray from the source to the receiver is symmetric with respect to the vertical direction.
For dynamic problems the ADAPT recipe is not applicable in theory, except for the transmission of plane qP-waves at the plane interface between two weakly contrasted monoclinic media of moderate anisotropy strength. However, the recipe gives surprisingly good results (e.g., typical amplitude errors smaller than 6%) for the computation of the amplitudes of qP-waves radiated by a point source in a 1D multilayered model.
The generality of some of these results is striking and is particular convenient for the straightforward adaptation of existing modeling/processing TI codes to more complicated types of anisotropy.
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“This volume contains 25 papers that represent most of the best work in seismic anisotropy in 1998 and 1999. Fracture characterizations and processing of converted waves are the two main topics covered in this volume. They are addressed from both theoretical and practical viewpoints. Also included are papers describing the historical roots of seismic anisotropy.”