An important reason for elastic anisotropy of geological media is layering on a scale that is small to the wavelengths. If the parameters of the layering are known, the "effective parameters" of the compound medium can be derived from the parameters of the constituents. If the layering is periodic with the period small compared to the wavelengths, the compound medium can be replaced by a homogeneous medium. One way to achieve this description is to re-formulate Hooke's law. First, the six components of stress and strain that vary from constituent to constituent are expressed in terms of the six components that are, in view of the continuity condition, constant throughout the layer. Second, the effective stress- and strain components are determined as the thickness-weighted arithmetic averages of the corresponding constituents' components. Third, the standard form of Hooke's law (stress as a function of strain) is re-established. This algorithm can be applied to constituents of any type. For seismic applications, the most important layering is that of isotropic layers. There are two significant situations that afford a simplification: (i) if all constituents have the same shear stiffness, the replacement medium is homogeneous; (ii) if all constituents have the same Poisson's ratio, wave propagation in a relatively wide cone about the axis of symmetry cannot be distinguished from wave propagation in an isotropic medium.
Elastic anisotropy; Exploration seismics; Wave propagation
