Earth Tide - Body Tide

Body Tide

The Earth tide encompasses the entire body of the Earth and is unhindered by the thin crust and land masses of the surface, on scales that make the rigidity of rock irrelevant. Ocean tides are a consequence of the resonance of the same driving forces with water movement periods in ocean basins accumulated over many days, so that their amplitude and timing are quite different and vary over short distances of just a few hundred km. The oscillation periods of the earth as a whole are not near the astronomical periods, so its flexing is due to the forces of the moment.

The tide components with a period near twelve hours have a lunar amplitude (earth bulge/depression distances) that are a little more than twice the height of the solar amplitudes, as tabulated below. At new and full moon, the Sun and the Moon are aligned, and the lunar and the solar tidal maxima and minima (bulges and depressions) add together for the greatest tidal range at particular latitudes. At first- and third-quarter phases of the moon, lunar and solar tides are in opposition, and the tidal range is at a minimum. The semi-diurnal tides go through one full cycle (a high and low tide) about once every 12 hours and one full cycle of maximum height (a spring and neap tide) about once every 14 days.

The classical theory of Earth tides first became established in 1905, primarily to explain nutations, but are also used in Earth rotation predictions. The semi-diurnal tide (one maximum every 12 or so hours) is primarily lunar (only S₂ is purely solar) and gives rise to sectorial deformations which rise and fall at the same time along the same longitude. Sectorial variations of vertical and east-west displacements are maximum at the equator and vanish at the poles. There are two cycles along each latitude, the bulges opposite one another, and the depressions similarly opposed. The diurnal tide is lunisolar, and gives rise to tesseral deformations. The vertical and east-west movement is maximum at 45° latitude and is zero on the equator and at the poles. Tesseral variation have one cycle per latitude, one bulge and one depression; the bulges are opposed (antipodal), that is to say the western part of the northern hemisphere and the eastern part of the southern hemisphere, for example, and similarly the depressions are opposed, the eastern part of the northern hemisphere and the western part of the southern hemisphere, in this case. Finally, fortnightly and semi-annual tides have 'zonal' deformations (constant along a circle of latitude), as the Moon or Sun gravitation is directed alternately away from the northern and southern hemispheres due to tilt. There is zero vertical displacement at 35°16' latitude.

Since these displacements affect the vertical direction east-west and north-south variations are often tabulated in milliarcseconds for astronomical use. The vertical displacement is frequent tabulated in μgal, since the gradient of gravity is location dependent so that the distance conversion is only approximately 3 μgal per cm