Velocity of Seismic Waves, Relationships with the Theory of Elasticity, Variation Factors

It is shown by the theory of elasticity that, in a non-porous medium, the velocities of compressional waves V_p and of shear waves V_s are given by the following formulae:$${V_P} = |\frac{E}{\rho }\frac{{(1 - v)}}{{(1 + v)(1 - 2v)}}{|^{1/2}} = |\frac{{K + 4/3\mu }}{\rho }{|^{1/2}}$$$${V_S} = |\frac{E}{\rho }\frac{1}{{2(1 + v)}}{|^{1/2}} = |\frac{\mu }{\rho }{|^{1/2}}$$where E = Young’s modulus μ = shear modulus ρ = density υ = Poisson’s ratio K = modulus of elasticity All these values refer to the behaviour of a material when it is subjected to a certain stress. For example, _U is a measure of the rigidity of the material.