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Earth tide

January 01, 1970

Earth tide (also known as solid-Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer. The largest body tide constituents are semi-diurnal, but there are also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational force causing earth tides and ocean tides is the same, the responses are quite different.

Tide raising force edit

 
 
Lunar tidal force: these images depict the Moon directly over 30° N (or 30° S) viewed from above the Northern Hemisphere, showing both sides of the planet. Red up, blue down.

The larger of the periodic gravitational forces is from the Moon but that of the Sun is also important. The images here show lunar tidal force when the Moon appears directly over 30° N (or 30° S). This pattern remains fixed with the red area directed toward (or directly away from) the Moon. Red indicates upward pull, blue downward. If, for example the Moon is directly over 90° W (or 90° E), the red areas are centred on the western northern hemisphere, on upper right. Red up, blue down. If for example the Moon is directly over 90° W (90° E), the centre of the red area is 30° N, 90° W and 30° S, 90° E, and the centre of the bluish band follows the great circle equidistant from those points. At 30° latitude a strong peak occurs once per lunar day, giving a significant diurnal force at that latitude. Along the equator two equally sized peaks (and depressions) impart semi-diurnal force.

Body tide components edit

 
Vertical displacements of sectorial movement.
Red up, blue down.
 
East-west displacements of sectorial movement.
Red east, blue west.
 
North-south displacements of sectorial movement.
Red north, blue south.
 
Vertical displacements of tesseral movement.
Red up, blue down.
 
East-West displacements of tesseral movement.
Red east, blue west.
 
North-South displacements of tesseral movement.
Red north, blue south.

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 tangent forces (see: equilibrium tide) and 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 kilometres. 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 perpendicular, 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 semi-diurnal tide (one maximum every 12 or so hours) is primarily lunar (only S2 is purely solar) and gives rise to sectorial (or sectoral) deformations which rise and fall at the same time along the same longitude.[1] 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. The tesseral variation has one cycle per latitude, one bulge and one depression; the bulges are opposed (antipodal), in other words the western part of the northern hemisphere and the eastern part of the southern hemisphere, for example. Similarly, the depressions are opposed, in this case the eastern part of the northern hemisphere and the western part of the southern hemisphere. 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, the east-west and north-south variations are often tabulated in milliarcseconds for astronomical use. The vertical displacement is frequently tabulated in μGal, since the gradient of gravity is location dependent, so that the distance conversion is only approximately 3 μGal per centimetre.

 
Vertical displacements of zonal movement. Red up, blue down.

Tidal constituents edit

Principal tidal constituents. The amplitudes may vary from those listed within several per cent.[2][3]

Semi-diurnal
Tidal
constituent 		Period Amplitude (mm)
vertical horiz.
M2 12.421 h 384.83 53.84
S2 (solar semi-diurnal) 12 h 179.05 25.05
N2 12.658 h 073.69 10.31
K2 11.967 h 048.72 06.82
Diurnal
Tidal
constituent 		Period Amplitude (mm)
vertical horiz.
K1 23.934 h 191.78 32.01
O1 25.819 h 158.11 22.05
P1 24.066 h 070.88 10.36
φ1 23.804 h 003.44 00.43
ψ1 23.869 h 002.72 00.21
S1 (solar diurnal) 24 h 001.65 00.25
Long Term
Tidal
constituent 		Period Amplitude (mm)
vertical horiz.
Mf 13.661 d 040.36 05.59
Mm (moon monthly) 27.555 d 021.33 02.96
Ssa (solar semi-annual) 0.5 yr 018.79 02.60
Lunar node 18.613 yr 016.92 02.34
Sa (solar annual) 1 yr 002.97 00.41

Ocean tidal loading edit

In coastal areas, because the ocean tide is quite out of step with the Earth tide, at high ocean tide there is an excess of water above what would be the gravitational equilibrium level, and therefore the adjacent ground falls in response to the resulting differences in weight. At low tide there is a deficit of water and the ground rises. Displacements caused by ocean tidal loading can exceed the displacements due to the Earth body tide. Sensitive instruments far inland often have to make similar corrections. Atmospheric loading and storm events may also be measurable, though the masses in movement are less weighty.

Effects edit

Seismologists have determined that microseismic events are correlated to tidal variations in Central Asia (north of the Himalayas);[citation needed] see: tidal triggering of earthquakes. Volcanologists use the regular, predictable Earth tide movements to calibrate and test sensitive volcano deformation monitoring instruments; tides may also trigger volcanic events.[4][5]

The semidiurnal amplitude of terrestrial tides can reach about 55 cm (22 in) at the equator which is important in geodesy using Global Positioning System, very-long-baseline interferometry, and satellite laser ranging measurements.[6][7] Also, to make precise astronomical angular measurements requires accurate knowledge of the Earth's rate of rotation (length of day, precession, in addition to nutation), which is influenced by Earth tides (see also: pole tide).

Terrestrial tides also need to be taken in account in the case of some particle physics experiments. [8] For instance, at the CERN or the SLAC National Accelerator Laboratory, the very large particle accelerators were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are circumference deformation for circular accelerators and also particle-beam energy. [9][unreliable source?] [10][unreliable source?]

In other astronomical objects edit

Body tides also exist in other astronomical objects, such as planets and moons. In Earth's moon, body tides "vary by about ±0.1 m each month."[11] It plays a key role in long-term dynamics of planetary systems. For example, it is due to body tides in the Moon that it is captured into the 1:1 spin-orbit resonance and is always showing us one side.[citation needed] Body tides in Mercury make it trapped in the 3:2 spin-orbit resonance with the Sun. [12] For the same reason, it is believed that many of the exoplanets are captured in higher spin-orbit resonances with their host stars. [13]

See also edit

References edit

  1. ^ Paul Melchior, "Earth Tides", Surveys in Geophysics, 1, pp. 275–303, March, 1974.
  2. ^ John Wahr, "Earth Tides", Global Earth Physics, A Handbook of Physical Constants, AGU Reference Shelf, 1, pp. 40–46, 1995.
  3. ^ Michael R. House, "Orbital forcing timescales: an introduction", Geological Society, London, Special Publications; 1995; v. 85; p. 1-18. http://sp.lyellcollection.org/cgi/content/abstract/85/1/1
  4. ^ Sottili G., Martino S., Palladino D.M., Paciello A., Bozzano F. (2007), Effects of tidal stresses on volcanic activity at Mount Etna, Italy, Geophys. Res. Lett., 34, L01311, doi:10.1029/2006GL028190, 2007.
  5. ^ Volcano watch, USGS.
  6. ^ IERS Conventions (2010). Gérard Petit and Brian Luzum (eds.). (IERS Technical Note ; 36) Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2010. 179 pp., ISBN 9783898889896, Sec. 7.1.1, "Effects of the solid Earth tides" [1]
  7. ^ User manual for the Bernese GNSS Software, Version 5.2 (November 2015), Astronomical Institute of the University of Bern. Section 10.1.2. "Solid Earth Tides, Solid and Ocean Pole Tides, and Permanent Tides" [2]
  8. ^ Accelerator on the move, but scientists compensate for tidal effects 2010-03-25 at the Wayback Machine, Stanford online.
  9. ^ (PDF). Archived from the original (PDF) on 2011-03-24. Retrieved 2007-03-25.
  10. ^ particle beam energy 2011-07-20 at the Wayback Machine affects
  11. ^ Williams, James G.; Boggs, Dale. H. (2015). "Tides on the Moon: Theory and determination of dissipation". Journal of Geophysical Research: Planets. 120 (4). American Geophysical Union (AGU): 689–724. Bibcode:2015JGRE..120..689W. doi:10.1002/2014je004755. ISSN 2169-9097. S2CID 120669399.
  12. ^ Noyelles, B.; Frouard, J.; Makarov, V. V. & Efroimsky, M. (2014). "Spin-orbit evolution of Mercury revisited". Icarus. 241: 26–44. arXiv:1307.0136. Bibcode:2014Icar..241...26N. doi:10.1016/j.icarus.2014.05.045. S2CID 53690707.
  13. ^ Makarov, V. V.; Berghea, C. & Efroimsky, M. (2012). "Dynamical Evolution and Spin–Orbit Resonances of Potentially Habitable Exoplanets: The Case of GJ 581d". The Astrophysical Journal. 761 (2): 83. arXiv:1208.0814. Bibcode:2012ApJ...761...83M. doi:10.1088/0004-637X/761/2/83. S2CID 926755. 83.

Bibliography edit

  • McCully, James Greig, Beyond the Moon, A Conversational, Common Sense Guide to Understanding the Tides, World Scientific Publishing Co, Singapore, 2006.
  • Paul Melchior, Earth Tides, Pergamon Press, Oxford, 1983.
  • Wylie, Francis E, Tides and the Pull of the Moon, The Stephen Greene Press, Brattleboro, Vermont, 1979.

January 01, 1970
earth, tide, also, known, solid, crustal, tide, body, tide, bodily, tide, land, tide, displacement, solid, earth, surface, caused, gravity, moon, main, component, meter, level, amplitude, periods, about, hours, longer, largest, body, tide, constituents, semi, . Earth tide also known as solid Earth tide crustal tide body tide bodily tide or land tide is the displacement of the solid earth s surface caused by the gravity of the Moon and Sun Its main component has meter level amplitude at periods of about 12 hours and longer The largest body tide constituents are semi diurnal but there are also significant diurnal semi annual and fortnightly contributions Though the gravitational force causing earth tides and ocean tides is the same the responses are quite different Contents 1 Tide raising force 2 Body tide components 2 1 Tidal constituents 3 Ocean tidal loading 4 Effects 5 In other astronomical objects 6 See also 7 References 8 BibliographyTide raising force edit nbsp nbsp Lunar tidal force these images depict the Moon directly over 30 N or 30 S viewed from above the Northern Hemisphere showing both sides of the planet Red up blue down The larger of the periodic gravitational forces is from the Moon but that of the Sun is also important The images here show lunar tidal force when the Moon appears directly over 30 N or 30 S This pattern remains fixed with the red area directed toward or directly away from the Moon Red indicates upward pull blue downward If for example the Moon is directly over 90 W or 90 E the red areas are centred on the western northern hemisphere on upper right Red up blue down If for example the Moon is directly over 90 W 90 E the centre of the red area is 30 N 90 W and 30 S 90 E and the centre of the bluish band follows the great circle equidistant from those points At 30 latitude a strong peak occurs once per lunar day giving a significant diurnal force at that latitude Along the equator two equally sized peaks and depressions impart semi diurnal force Body tide components edit nbsp Vertical displacements of sectorial movement Red up blue down nbsp East west displacements of sectorial movement Red east blue west nbsp North south displacements of sectorial movement Red north blue south nbsp Vertical displacements of tesseral movement Red up blue down nbsp East West displacements of tesseral movement Red east blue west nbsp North South displacements of tesseral movement Red north blue south 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 tangent forces see equilibrium tide and 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 kilometres 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 perpendicular 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 semi diurnal tide one maximum every 12 or so hours is primarily lunar only S2 is purely solar and gives rise to sectorial or sectoral deformations which rise and fall at the same time along the same longitude 1 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 The tesseral variation has one cycle per latitude one bulge and one depression the bulges are opposed antipodal in other words the western part of the northern hemisphere and the eastern part of the southern hemisphere for example Similarly the depressions are opposed in this case the eastern part of the northern hemisphere and the western part of the southern hemisphere 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 the east west and north south variations are often tabulated in milliarcseconds for astronomical use The vertical displacement is frequently tabulated in mGal since the gradient of gravity is location dependent so that the distance conversion is only approximately 3 mGal per centimetre nbsp Vertical displacements of zonal movement Red up blue down Tidal constituents edit Principal tidal constituents The amplitudes may vary from those listed within several per cent 2 3 Semi diurnal Tidalconstituent Period Amplitude mm vertical horiz M2 12 421 h 384 83 53 84 S2 solar semi diurnal 12 h 179 05 25 05 N2 12 658 h 0 73 69 10 31 K2 11 967 h 0 48 72 0 6 82 Diurnal Tidalconstituent Period Amplitude mm vertical horiz K1 23 934 h 191 78 32 01 O1 25 819 h 158 11 22 05 P1 24 066 h 0 70 88 10 36 f1 23 804 h 00 3 44 0 0 43 ps1 23 869 h 00 2 72 0 0 21 S1 solar diurnal 24 h 00 1 65 0 0 25 Long Term Tidalconstituent Period Amplitude mm vertical horiz Mf 13 661 d 0 40 36 0 5 59 Mm moon monthly 27 555 d 0 21 33 0 2 96 Ssa solar semi annual 0 5 yr 0 18 79 0 2 60 Lunar node 18 613 yr 0 16 92 0 2 34 Sa solar annual 1 yr 00 2 97 0 0 41Ocean tidal loading editIn coastal areas because the ocean tide is quite out of step with the Earth tide at high ocean tide there is an excess of water above what would be the gravitational equilibrium level and therefore the adjacent ground falls in response to the resulting differences in weight At low tide there is a deficit of water and the ground rises Displacements caused by ocean tidal loading can exceed the displacements due to the Earth body tide Sensitive instruments far inland often have to make similar corrections Atmospheric loading and storm events may also be measurable though the masses in movement are less weighty Effects editSeismologists have determined that microseismic events are correlated to tidal variations in Central Asia north of the Himalayas citation needed see tidal triggering of earthquakes Volcanologists use the regular predictable Earth tide movements to calibrate and test sensitive volcano deformation monitoring instruments tides may also trigger volcanic events 4 5 The semidiurnal amplitude of terrestrial tides can reach about 55 cm 22 in at the equator which is important in geodesy using Global Positioning System very long baseline interferometry and satellite laser ranging measurements 6 7 Also to make precise astronomical angular measurements requires accurate knowledge of the Earth s rate of rotation length of day precession in addition to nutation which is influenced by Earth tides see also pole tide Terrestrial tides also need to be taken in account in the case of some particle physics experiments 8 For instance at the CERN or the SLAC National Accelerator Laboratory the very large particle accelerators were designed while taking terrestrial tides into account for proper operation Among the effects that need to be taken into account are circumference deformation for circular accelerators and also particle beam energy 9 unreliable source 10 unreliable source In other astronomical objects editBody tides also exist in other astronomical objects such as planets and moons In Earth s moon body tides vary by about 0 1 m each month 11 It plays a key role in long term dynamics of planetary systems For example it is due to body tides in the Moon that it is captured into the 1 1 spin orbit resonance and is always showing us one side citation needed Body tides in Mercury make it trapped in the 3 2 spin orbit resonance with the Sun 12 For the same reason it is believed that many of the exoplanets are captured in higher spin orbit resonances with their host stars 13 See also editLove numbersReferences edit Paul Melchior Earth Tides Surveys in Geophysics 1 pp 275 303 March 1974 John Wahr Earth Tides Global Earth Physics A Handbook of Physical Constants AGU Reference Shelf 1 pp 40 46 1995 Michael R House Orbital forcing timescales an introduction Geological Society London Special Publications 1995 v 85 p 1 18 http sp lyellcollection org cgi content abstract 85 1 1 Sottili G Martino S Palladino D M Paciello A Bozzano F 2007 Effects of tidal stresses on volcanic activity at Mount Etna Italy Geophys Res Lett 34 L01311 doi 10 1029 2006GL028190 2007 Volcano watch USGS IERS Conventions 2010 Gerard Petit and Brian Luzum eds IERS Technical Note 36 Frankfurt am Main Verlag des Bundesamts fur Kartographie und Geodasie 2010 179 pp ISBN 9783898889896 Sec 7 1 1 Effects of the solid Earth tides 1 User manual for the Bernese GNSS Software Version 5 2 November 2015 Astronomical Institute of the University of Bern Section 10 1 2 Solid Earth Tides Solid and Ocean Pole Tides and Permanent Tides 2 Accelerator on the move but scientists compensate for tidal effects Archived 2010 03 25 at the Wayback Machine Stanford online circumference deformation PDF Archived from the original PDF on 2011 03 24 Retrieved 2007 03 25 particle beam energy Archived 2011 07 20 at the Wayback Machine affects Williams James G Boggs Dale H 2015 Tides on the Moon Theory and determination of dissipation Journal of Geophysical Research Planets 120 4 American Geophysical Union AGU 689 724 Bibcode 2015JGRE 120 689W doi 10 1002 2014je004755 ISSN 2169 9097 S2CID 120669399 Noyelles B Frouard J Makarov V V amp Efroimsky M 2014 Spin orbit evolution of Mercury revisited Icarus 241 26 44 arXiv 1307 0136 Bibcode 2014Icar 241 26N doi 10 1016 j icarus 2014 05 045 S2CID 53690707 Makarov V V Berghea C amp Efroimsky M 2012 Dynamical Evolution and Spin Orbit Resonances of Potentially Habitable Exoplanets The Case of GJ 581d The Astrophysical Journal 761 2 83 arXiv 1208 0814 Bibcode 2012ApJ 761 83M doi 10 1088 0004 637X 761 2 83 S2CID 926755 83 Bibliography editMcCully James Greig Beyond the Moon A Conversational Common Sense Guide to Understanding the Tides World Scientific Publishing Co Singapore 2006 Paul Melchior Earth Tides Pergamon Press Oxford 1983 Wylie Francis E Tides and the Pull of the Moon The Stephen Greene Press Brattleboro Vermont 1979 Retrieved from https en wikipedia org w index php title Earth tide amp oldid 1209181524, wikipedia, wiki, book, books, library,

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