There are two kinds of seismic body waves in solids, ''pressure waves'' (P-waves) and ''shear waves.'' In

linear elasticity Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mec ...

, the P-wave modulus

M

, also known as the longitudinal modulus, or the constrained modulus, is one of the elastic moduli available to describe isotropic homogeneous materials. It is defined as the ratio of axial

stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...

to axial

strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...

in a uniaxial strain state. This occurs when expansion in the transverse direction is prevented by the inertia of neighboring material, such as in an earthquake, or underwater seismic blast. :

\sigma_ = M \epsilon_

where all the other strains

\epsilon_

are zero. This is equivalent to stating that :

M_ = \rho_ V_\mathrm^2 ,

where ''V''_P is the velocity of a P-wave and ''ρ'' is the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of the material through which the wave is propagating.

References

* G. Mavko, T. Mukerji, J. Dvorkin. ''The Rock Physics Handbook''. Cambridge University Press 2003 (paperback). Materials science Elasticity (physics) {{materials-sci-stub