Seismic body wave

P and S-waves are the two forms of seismic body waves. P or primary-waves, are longitudinal or compressional waves which means that the material is displaced in the direction of propagation. S or secondary-waves are transverse or shear waves meaning the medium in which they travel is displace perpendicular to the direction of propagation. Figure 1 illustrates the difference between P and S-waves.

The velocity of seismic body waves depends essentially on three parameters that are the bulk modulus ($\kappa$), the shear modulus ($\mu$) and the density ($\rho$). The P-wave velocity, $V_p$ is expressed by equation 1 whereas S-wave, $V_s$, is expressed by equation 2.

$$V_p=\sqrt{\frac{\kappa+\frac{4}{3}\mu}{\rho}}$$ (1)

$$V_s=\sqrt{\frac{\mu}{\rho}}$$ (2)

図 1: Illustration showing oscillation mode for a P- and S-waves