Elements of basic theory of anisotropic wave propagation
Published:January 01, 2012
A medium (or a region of a continuum) is called anisotropic with respect to a certain parameter if this parameter changes with the direction of a measurement. If an elastic medium is anisotropic, seismic waves of a given type propagate in different directions with different velocities. This velocity anisotropy implies the existence of a certain structure (order) on the scale of seismic wavelength imposed by various physical phenomena. In typical subsurface formations, velocity changes with both spatial position and propagation direction, which makes the medium heterogeneous and anisotropic. The notions of heterogeneity and anisotropy are scale-dependent, and the same medium may behave as heterogeneous for small wavelengths and as anisotropic for large wavelengths (e.g., Helbig, 1994). For example, such small-scale heterogeneity as fine layering detectable by well logs may create an effectively anisotropic model in the long-wavelength limit.
Anisotropy in sedimentary sequences is caused by the following main factors (e.g., Thomsen, 1986):
intrinsic anisotropy due to preferred orientation of anisotropic mineral grains or the shapes of isotropic minerals
thin bedding of isotropic layers on a scale small compared to the wavelength (the layers may be horizontal or tilted)
vertical or dipping fractures or microcracks
Figures & Tables
Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Third Edition
This is a new edition of Ilya Tsvankin’s reference volume on seismic anisotropy and application of anisotropic models in reflection seismology. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Geophysical References Series No. 19, provides essential background information about anisotropic wave propagation, introduces efficient notation for transversely isotropic (TI) and orthorhombic media, and identifies the key anisotropy parameters for imaging and amplitude analysis. To gain insight into the influence of anisotropy on a wide range of seismic signatures, exact solutions are simplified in the weak-anisotropy approximation.