P-wave modulus

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.

${\displaystyle {\sigma }_{zz}=M{ϵ}_{zz}}$

where all the other strains ${\displaystyle {ϵ}_{\ast \ast }}$ are zero.

This is equivalent to stating that

${\displaystyle M_x={\rho }_x{V}_{\mathrm{P}}^2,}$

where V_P is the velocity of a P-wave and ρ is the density of the material through which the wave is propagating.