An Overview on Anisotropy and its Geological Constrains

The academy and seismic industry have shown the importance of considering anisotropy in velocity model building. There are several examples concerning imaging problems whenever anisotropic effects are neglected. By means of travel time matrices and seismic modeling, we analyze the effects of the two anisotropic classes (intrinsic and extrinsic), seeking to evaluate them separately and together. The results shows that for intercalations between shales and sandstones with low velocity contrast, the extrinsic anisotropic is very weak, with clear predominance of the shale intrinsic anisotropy. Introduction A long time ago, velocity models used for seismic imaging processes considered the physical medium as isotropic, assuming this assumption due to the greater operational ease in the implementation of the algorithms, as well as understanding that such methodology was enough for an adequate seismic imaging. Thomsen (1986) is a paramount paper that marks a starting point for considering anisotropy in seismic processing. In recent decades, papers such as Cetale Santos et al. (2004), Berryman (2008), Kumar (2013) and Nunes et al. (2019) have revived the discussion about the importance of considering anisotropy in velocity models. They have shown that reflector positioning and amplitude problems can be mitigated when the medium is treated according to its anisotropic characteristics. According to Romanelli (2013), it is possible to distinguish two types of anisotropy: intrinsic and extrinsic. The first is related to the characteristic properties of a specific lithology, as for instance in the case of shales, where the minerals alignment can generates a prominent anisotropic effect (Figure 1a). The extrinsic case, on the other hand, is the result of interleaving between different layers where each thickness has subseismic character (t) composing a larger layer (T), which can be identified in the seismic records (Figure 1b). As indicated by Valcke et al. (2006), major factors for intrinsic anisotropy are: crystals preferential orientation, variations in the spatial distribution of minerals, morphology of grains, alignment of fractures and pores, beyond the type of pore filling material. (a) (b) Figure 1: a) Laminated shale sample (Source: https://www.sandatlas.org/shale/ ), b) Interleaving model with shale and sandstone layers. One of the most important papers within this theme is from Thomsen (1986), due to its formulations opened the perspective of more practical and relatively simpler applications for the geophysics applied to the exploration and production of hydrocarbons. Thomsen op. cit. considers the premise that most cases of interest within the oil industry are composed by lithologies with relatively weak to moderate anisotropies, less than 20 %. He presents three parameters to describe the anisotropic characteristics of a rock, which are: Epsilon (ε), Gamma (γ) and Delta (δ ). Thomsen’s parameters can then be understood as derivations of the stiffness matrix (Equation 1), which represents the physical properties of each material. This matrix is responsible for weighing the resulting deformations from the application of a given stress, treating the contribution of each of its elements individually, according to the Hooke’s law: