The role of layer-induced anisotropy in seismic exploration

184In this thesis we focus on anisotropy caused by fine layering. We analyse the conditions that must be satisfied so that fine layering is equivalent to anisotropy. In the long-wavelength (or quasi-static) approximation an interval of thickness H, consisting of a sequence of layers, is effectively homogeneous and anisotropic to seismic wave propagation. This approximation implies that H is much smaller than the seismic wavelength A. Closer inspection of this approximation shows that the degree of equivalence depends on several parameters. The equivalence is exact for infinitely long wavelengths. It is also exact (for all wavelengths) for those waves which are not back-scattered at the interfaces between the layers. This is the case when reflection coefficients are zero. We use a simple model where the interval of thickness H consists of a N times repeated set of two layers. These two layers form one period, the whole interval consists of N periods. The wave field that propagates through this sequence oflayers, consists of the sum of the primary wave and all the multiples. The effective medium for a given wave number depends on the interference of primary and multiples. For infinitely thin layers this results in an effectively homogeneous medium, with a pseudo-primary that is delayed compared to the primary wave