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 to axial strain 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 A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at an ...

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. Mathematicall ...

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