# Microseism - Generation of 'secondary' Microseisms

Generation of 'secondary' Microseisms

The interaction of two trains of surface waves of different frequencies and directions generates wave groups. For wave propagating almost in the same direction, this gives the usual sets of waves that travel at the group speed, which is slower than phase speed of water waves (see animation). For typical ocean waves with a period around 10 seconds, this group speed is close to 10 m/s.

In the case of opposite propagation direction the groups travel at a much larger speed, which is now 2 π(f1+f2)/(k1-k2) with k1 and k2 the wave numbers of the interacting water waves.

For wave trains with a very small difference in frequency (and thus wavenumbers), this pattern of wave groups may have the same velocity as seismic waves, between 1500 and 3000 m/s, and will excite acoustic-seismic modes that radiate away.

As far as seismic and acoustic waves are concerned, the motion of ocean waves in deep water is, to the leading order, equivalent to a pressure applied at the sea surface. This pressure is nearly equal to the water density times the wave orbital velocity squared. Because of this square, it is not the amplitude of the individual wave trains that matter (red and black lines in the figures) but the amplitude of the sum, the wave groups (blue line in figures).

Real ocean waves are composed of an infinite number of wave trains and there is always some energy propagating in the opposite direction. Also, because the seismic waves are much faster than the water waves, the source of seismic noise is isotropic: the same amount of energy is radiated in all directions. In practice, the source of seismic energy is strongest when there are a significant amount of wave energy travelling in opposite directions. This occurs when swell from one storm meets waves with the same period from another storm, or close to the coast due coastal reflection.

Depending on the geological context, the noise recorded by a seismic station on land can be representative of the sea state close to the station (within a few hundred kilometers, for example in Central California), or a full ocean basin (for example in Hawaii). In order to understand the noise properties, it is thus necessary to understand the propagation of the seismic waves.