Love wave

In elastodynamics, Love waves, named after Augustus Edward Hough Love, are horizontally polarized surface waves.

The Love wave is a result of the interference of many shear waves (S-waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side.

The particle motion of a Love wave forms a horizontal line, perpendicular to the direction of propagation (i.e. are transverse waves).

Moving deeper into the material, motion can decrease to a "node" and then alternately increase and decrease as one examines deeper layers of particles.

The amplitude, or maximum particle motion, often decreases rapidly with depth.

Since Love waves travel on the Earth's surface, the strength (or amplitude) of the waves decrease exponentially with the depth of an earthquake.

represents the distance the wave has travelled from the earthquake.

Large earthquakes may generate Love waves that travel around the Earth several times before dissipating.

Since they decay so slowly, Love waves are the most destructive outside the immediate area of the focus or epicentre of an earthquake.

They are what most people feel directly during an earthquake.

In the past, it was often thought that animals like cats and dogs could predict an earthquake before it happened.

However, they are simply more sensitive to ground vibrations than humans and are able to detect the subtler body waves that precede Love waves, like the P-waves and the S-waves.

Love waves are a special solution (

coordinate, i.e., the Lamé parameters and the mass density can be expressed as

produced by Love waves as a function of time (

) have the form These are therefore antiplane shear waves perpendicular to the

The stresses caused by these displacements are If we substitute the assumed displacements into the equations for the conservation of momentum, we get a simplified equation The boundary conditions for a Love wave are that the surface tractions at the free surface

into two first order equations, we express this stress component in the form to get the first order conservation of momentum equations The above equations describe an eigenvalue problem whose solution eigenfunctions can be found by a number of numerical methods.