In seismology

Seismology

Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake effects, such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic,...

, a microseism is defined as a faint earth tremor caused by natural phenomena. The term is most commonly used to refer to the dominant background seismic noise signal on Earth, which are mostly composed of Rayleigh waves and caused by water waves in the oceans and lakes. Thus a microseism is a small and long-continuing oscillation

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

 of the ground.

Detection and characteristics

Microseisms are very well detected and measured by means of a broad-band seismograph, and can be recorded anywhere on Earth.

Dominant microseism signals from the oceans are linked to characteristic ocean swell periods, and thus occur between approximately 4 to 30 seconds. Microseismic noise usually displays two predominant peaks. The weaker is for the larger periods, typically close to 16 s, and can be explained by the effect of surface gravity waves in shallow water. These microseisms have the same period as the water waves that generate them, and are usually called 'primary microseisms'. The stronger peak, for shorter periods, is also due to surface gravity waves in water, but arises from the interaction of waves with nearly equal frequencies but nearly opposite directions. These tremors have a period which is half of the water wave period and are usually called 'secondary microseisms'. A slight, but detectable, incessant excitation of the Earth's free oscillations, or normal modes, with periods in the range 30 to 1000 s are also caused by water waves, and is often referred to as the "Earth hum". This hum is probably generated like the secondary microseisms but from the interaction of infragravity waves.

As a result, from the short period 'secondary microseisms' to the long period 'hum', this seismic noise contains information on the sea state

Sea state

In oceanography, a sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, period, and power spectrum. The sea state varies with...

s. It can be used to estimate ocean wave properties and their variation, on time scales of individual events (a few hours to a few days)
to their seasonal or multi-decadal evolution. Understanding these signals, however, requires a basic understanding of the microseisms generation processes

Generation of 'secondary' microseisms

The interaction of wave trains 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 in 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 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

Orbital velocity

Orbital velocity can refer to the following:* The orbital speed of a body in a gravitational field.* The velocity of particles due to wave motion, in particular in wind waves....

 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.

Form of Rayleigh waves modified by the ocean layer: free waves and forced waves

The waves that compose most of the secondary microseismic field are Rayleigh waves. Both water and solid Earth particles are displaced by the waves as they propagate, and the water layer
plays a very important role in defining the celerity, group speed and the transfer of energy
from the surface water waves to the Rayleigh waves.