ABSTRACT
Polycrystalline materials, metals and igneous rocks with randomly oriented crystals, and amorphous materials, such as glass, are elastically isotropic, with elasticity completely represented by two moduli. Although there are several ways of choosing moduli to describe various deformations and six that are commonly used, only two are independent, and all the others can be represented in terms of them. In geophysics it is convenient to select as the two independent moduli, bulk modulus (incompressibility, K or B) and rigidity (shear modulus, μ or G). There are two reasons for this. K represents pure compression, a volume change caused by hydrostatic pressure, with no change in shape. The values for constant temperature (isothermal) compression, KT , and adiabatic compression (constant entropy, with no heat exchange), KS , are related by a simple thermodynamic identity (Equation 21.24). The value of μ is the same for both isothermal and adiabatic deformation. The distinction between isothermal and adiabatic behaviour is much more complicated for the other moduli. The second reason is that μ and the combination χ = (KS + 4μ/3) are the moduli that control seismic wave speeds, observations of which provide values of KS , and hence the variation of density within homogeneous regions of the Earth. The other moduli are:
