Secondary wave

In seismology, S-waves, secondary waves, or shear waves (sometimes called an elastic S-wave) are a type of elastic wave, and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves.

The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. The wave moves through elastic media, and the main restoring force comes from shear effects. These waves do not diverge, and they obey the continuity equation for incompressible media:

Its name, S for secondary, comes from the fact that it is the second direct arrival on an earthquake seismogram, after the compressional primary wave, or P-wave, because S-waves travel slower in rock. Unlike the P-wave, the S-wave cannot travel through the molten outer core of the Earth, and this causes a shadow zone for S-waves opposite to where they originate. They can still appear in the solid inner core: when a P-wave strikes the boundary of molten and solid cores, S-waves will then propagate in the solid medium. And when the S-waves hit the boundary again they will in turn create P-waves. This property allows seismologists to determine the nature of the inner core.

The prediction of S-waves came out of theory in the 1800s. Starting with the stress-strain relationship for an isotropic solid in Einstein notation:

where ${\displaystyle \tau }$ is the stress, ${\displaystyle \lambda }$ and ${\displaystyle \mu }$ are the Lamé parameters (with ${\displaystyle \mu }$ as the shear modulus), ${\displaystyle \delta _{ij}}$ is the Kronecker delta, and the strain tensor is defined

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