Non-Rigid Rotation, Global Geodynamics and Free Nutation

Cheh Pan^{*}

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References

[1] C. Pan, “Observed Multiple Frequencies of the Chandler Wobble,” Journal of Geodynamics, Vol. 44, No. 1-2, 2007, pp. 47-65.

http://dx.doi.org/10.1016/j.jog.2006.12.004

[2] C. Pan, “Linearization of the Liouville Equation, Multiple Splits of the Chandler Frequency, Markowitz Wobbles, and Error Analysis,” International Journal of Geosciences, Vol. 3, No. 2, 2012, pp. 930-951.

http://dx.doi.org/10.4236/ijg.2012.325095

[3] T. Thomson, “Introduction to Space Dynamics,” Wiley, New York, 1986, 317 p.

[4] R. E. Roberson, “The Equivalence of Two Classical Problems of Free Spinning Gyrostats,” Journal of Applied Mechanics, Vol. 38, No. 3, 1971, pp. 707-708.

[5] G. M. T. D’Eleuterio and P. C. Hughes, “Dynamics of a Flexible Vehicle with a General Angular Momentum distribution,” Progress Report at the III PVI and SU/AIAA Symposium on the Dynamics and Control of Large Flexible Spacecraft, Blacksburg, Virginia, 1981.

[6] H. B. Hablani, “Modal Analysis of Gyroscopic Flexible Spacecraft: A Continuum Approach,” Guidance, Control and Dynamics, Vol. 5, No. 5, 1982, pp. 448-457.

[7] G. M. T. D’Eleuterio and P. C. Hughes, “Dynamics of Gyro-Elastic Continua,” AIAA/ASME/ASCE/AHS 24th Structures, Structural Dynamics & Materials Conference, 2-4 May 1983, 1983, 9 p.

[8] H. Rance, “Major Lineaments and Torsional Deformation of the Earth,” Journal of Geophysical Research, Vol. 72, No. 8, 1968, pp. 2213-2217.

http://dx.doi.org/10.1029/JZ072i008p02213

[9] H. Rance, “Lineaments and Torsional Deformation of the Earth: Indian Ocean,” Journal of Geophysical Research, Vol. 74, No. 12, 1969, pp. 3271-3272.

http://dx.doi.org/10.1029/JB074i012p03271

[10] B. F. Howell Jr., “Coriolis Force and the New Global Tectonics,” Journal of Geophysical Research, Vol. 75, No. 14, 1970, pp. 2769-2772.

http://dx.doi.org/10.1029/JB075i014p02769

[11] M. F. Kane, “Rotational Inertia of Continents: A Proposed Link between Polar Wandering and Plate Tectonics,” Science, Vol. 175, No. 4028, 1972, pp. 1355-1357.

http://dx.doi.org/10.1126/science.175.4028.1355

[12] K. W. Hudnut, “Geodetic Evidence for the Rotation of Crustal Blocks (Abstract), EOS,” Transactions— American Geophysical Union, Vol. 72, 1991, p. 124.

[13] D. E. Argus, and R. G. Gordon, “Rotation of the Sierra Nevada from VLBI data (Abstract), EOS,” Transactions—American Geophysical Union, Vol. 72, 1991, p. 124.

[14] C. Pan, “Polar Motion of a Triaxial Earth and Dynamical Plate Tectonics,” Tectonophysics, Vol. 25, No. 1-2, 1975, pp. 1-40.

http://dx.doi.org/10.1016/0040-1951(75)90009-8

[15] C. Pan, “Polar Instability, Plate Motion, and Geodynamics of the Mantle,” Journal of Physics of the Earth, Vol. 33, No. 5, 1985, pp. 411-434.

http://dx.doi.org/10.4294/jpe1952.33.411

[16] C. Pan, “The Multiple-Frequency Chandler Wobble,” Journal of Physics of the Earth, Vol. 30, No. 5, 1982, pp. 389-419. http://dx.doi.org/10.4294/jpe1952.30.389

[17] C. Pan, “Angular Momentum Perturbation, Polar Excitation, and Axial Near-Symmetry,” Geophysical Journal International, Vol. 137, No. 1, 1999, pp. 139-148.

http://dx.doi.org/10.1046/j.1365-246x.1999.00782.x

[18] W. H. Munk and G. J. F. MacDonald, “The Rotation of the Earth,” Cambridge University Press, London, 1960, 323 p.

[19] B. F. Chao, “On the Excitation of the Earth’s Free Wobble and Reference Frames,” Geophysical Journal International, Vol. 79, No. 2, 1984, pp. 555-563.

http://dx.doi.org/10.1111/j.1365-246X.1984.tb02240.x

[20] H. Moritz and I. I. Mueller, “Earth Rotation: Theory and Observation,” The Ungar Publishing Company, New York, 1988, 617 p.

[21] M. L. Smith, “Wobble and Nutation of the Earth,” Geophysical Journal International, Vol. 50, No. 1, 1977, pp. 103-140. http://dx.doi.org/10.1111/j.1365-246X.1977.tb01326.x

[22] K. Lambeck, “The Earth’s Variable Rotation: Geophysical Causes and Consequences,” Cambridge University Press, London, 1980, 449 p.

http://dx.doi.org/10.1017/CBO9780511569579

[23] R. A. Becker, “Introduction to Theoretical Mechanics,” McGraw-Hill, New York, 1954, 420 p.

[24] C. Pan, “The Earth’s Rotation Instability, Plate Motion, and Geodynamics of the Mantle (Abstract),” AGU Transactions, Vol. 59, 1978, pp. 1202-1203.

[25] F. M. Richter, “Dynamical Model for Sea-Floor Spreading,” Reviews of Geophysics, Vol. 11, No. 2, 1973, pp. 223-287. http://dx.doi.org/10.1029/RG011i002p00223

[26] W. Markowitz, “Sudden Changes in Rotational Acceleration of the Earth and Secular Motion of the Pole,” In: L. Mansinha, D. E. Smylie and A. E. Beck, Eds., Earthquake Displacement Fields and the Rotation of the Earth, Reidel, Dordrecht, 1970, pp. 69-81.

http://dx.doi.org/10.1007/978-94-010-3308-4_7

[27] W. Markowitz, “Rotational Accelerations,” In: P. Melchior and S. Yumi, Eds., Rotation of the Earth, IAU Symposium No. 48, Reidel, Dordrecht, 1972, pp. 162-164.

[28] K. Lambeck, “Effects of Tidal Dissipation in the Oceans on the Moon’s Orbit and the Earth’s Rotation,” Journal of Geophysical Research, Vol. 80, No. 20, 1975, pp. 2917-2925. http://dx.doi.org/10.1029/JB080i020p02917

[29] K. Lambeck, “Tidal Dissipation in the Oceans: Astronomical, Geophysical and Oceanographic Consequences, Philos,” Transactions of the Royal Society London A, Vol. 287, 1347, 1977, pp. 545-594.

http://dx.doi.org/10.1098/rsta.1977.0159

[30] K. Lambeck and A. Cazenave, “The Earth’s Rotation and Atmosphere Circulation—I. Seasonal Variations,” Geophysical Journal of the Royal Astronomical Society, Vol. 32, 1973, pp. 79-93.

[31] K. Lambeck and A. Cazenave, “The Earth’s Variable Rate of Rotation: A Discussion of Some Meteorological and Oceanic Causes and Consequences,” Philosophical Transactions of the Royal Society London A, Vol. 284, No. 1326, 1977, pp. 495-506.

http://dx.doi.org/10.1098/rsta.1977.0025

[32] L. V. Morrison, “Tidal Deceleration of the Earth’s Rotation Deduced from Astronomical Observations in the Period A. D. 1600 to the Present,” In: P. Brosche and J. Sunderman, Eds., Tidal Friction and the Earth’s Rotation, Springer-Verlag, Berlin, 1978, pp. 22-27.

[33] W. Alvarez and F. Asaro, “An Extraterrestrial Impact,” Scientific American, Vol. 263, No. 4, 1990, pp. 78-84.

http://dx.doi.org/10.1038/scientificamerican1090-78

[34] T. Sasao, S. Okubo and M. Saito, “A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth,” In: E. P. Fedorov, M. L. Smith and P. L. Bender, Eds., Nutation and the Earth’s Rotation, IAU Symposium No. 78, Reidel, Dordrecht, 1980, pp. 165-184.

[35] T. Sasao and J. M. Wahr, “An Excitation Mechanism for the Free ‘Core Nutation’,” Geophysical Journal of the Royal Astronomical Society, Vol. 64, No. 3, 1981, pp. 729-746. http://dx.doi.org/10.1111/j.1365-246X.1981.tb02692.x

[36] S. Flodmark, “The Earth’s Polar Motion,” In: S. Flodmark, Ed., New Approaches in Geomagnetism and the Earth’s Rotation, World Scientific, Singapore, 1991, pp. 3-52.

[37] S. Flodmark, “The Influence of Core Nutation on the Geogravitational Field and the Power Supply of Earth Dynamics,” Fysikum, Stockholm University, Stockholm, 1991.

[38] P. M. Mathews, T. A. Herring and B. A. Buffett, “Modeling of Nutation and Precession: New Nutation Series for Nonrigid Earth and Insights into the Earth’s Interior,” Journal of Geophysical Research, Vol. 107, No. B4, 2002, pp. ETG 3-1-ETG 3-26. B. F. Chao, “As the World Turns,” Eos, Transactions American Geophysical Union, Vol. 66, No. 46, 1985, pp. 766-770.

http://dx.doi.org/10.1029/EO066i046p00766

[39] B. F. Chao, “As the World Turns,” Eos, Transactions American Geophysical Union, Vol. 66, No. 46, 1985, pp. 766-770. http://dx.doi.org/10.1029/EO066i046p00766

[40] T. J. Ahrens, “The Origin of the Earth,” Physics Today, Vol. 47, No. 8, 1994, pp. 38-45.

http://dx.doi.org/10.1063/1.881436

[41] B. Wood, “The Formation and Differentiation of Earth,” Physics Today, Vol. 64, No. 12, 2011, pp. 40-45.

http://dx.doi.org/10.1063/PT.3.1362

[42] D. Pines and J. Shaham, “Quadrupolar Analysis of Storage and Release of Elastic Energy in the Mantle,” Nature (Physical Science), Vol. 243, No. 130, 1973, pp. 122-127.

[43] J. B. Minster, P. Molnar and E. Haines, “Numerical Modeling of Instantaneous Plate Tectonics,” Geophysical Journal International, Vol. 36, No. 3, 1974, pp. 541-576.

http://dx.doi.org/10.1111/j.1365-246X.1974.tb00613.x

[44] R. G. Gordon, “Present Plate Motions and Plate Boundaries,” Global Earth Physics, A handbook of Physical Constants, AGU References Shelf I, 1995, pp. 66-87.

[45] S. R. Dickman, “Investigation of Controversial Polar Motion Features Using Homogeneous International Latitude Service Data,” Journal of Geophysical Research, Vol. 86, No. B6, 1981, pp. 4904-4912.

http://dx.doi.org/10.1029/JB086iB06p04904

[46] R. S. Gross, “Earth Rotation: Long Period Variations,” In: T. A. Herring, Ed., Treatise of Geophysics, Vol. 3: Geodesy, Elsevier, Oxford, 2007, pp. 239-294.

[47] T. Gold, “Instability of the Earth’s Axis of Rotation,” Nature, Vol. 175, 1955, pp. 526-529.

http://dx.doi.org/10.1038/175526a0

[48] P. Goldreich and A. Toomre, “Some Remarks on Polar Wandering,” Journal of Geophysical Research, Vol. 74, No. 10, 1969, pp. 2555-2567.

http://dx.doi.org/10.1029/JB074i010p02555

[49] R. S. Gross, “The Excitation of the Chandler Wobble,” Geophysical Research Letters, Vol. 27, No. 15, 2000, pp. 2329-2332. http://dx.doi.org/10.1029/2000GL011450

[50] R. S. Gross, I. Fukumori and D. Menemenlis, “Atmospheric and Oceanic Excitation of the Earth’s Wobbles during 1980-2000,” Journal of Geophysical Research, Vol. 108, No. B8, 2003, pp. 2370-2386.

http://dx.doi.org/10.1029/2002JB002143

[51] L. Dones and S. Tremaine, “Why Does the Earth Spin Forward?” Science, Vol. 259, No. 5093, 1993, pp. 350-354. http://dx.doi.org/10.1126/science.259.5093.350

[52] C. Pan, “A Preliminary Study on Relations between Polar Wandering and Seismicity,” Thesis, Department of Geology and Geophysics, Massachusetts Institute of Technology, Cambridge, 1963.

[53] C. Pan, “On the Dynamical Theory of Polar Wandering,” Tectonophysics, Vol. 5, No. 2, 1968, pp. 125-149.

http://dx.doi.org/10.1016/0040-1951(68)90085-1

[54] C. Pan, “The Dynamical Evolution of a Layered Earth (Abstract),” Transactions, American Geophysical Union, Vol. 51, 1970, p. 430.

[55] C. Pan, “The Wandering of the Pole and the Earth’s Evolution Cycle (Abstract),” Transactions, American Geophysical Union, Vol. 52, 1971, p. 355.

[56] C. Pan, “Polar Wandering and the Earth’s Dynamical Evolution Cycle,” In: P. Melchior and S. Yumi, Eds., Rotation of the Earth, IAU Symposium No. 48, Reidel, Dordrecht, 1972, pp. 206-211.

[57] G. Spada, Y. Ricard and R. Sabadini, “Excitation of True Polar Wander by Subduction,” Nature, Vol. 360, No. 6403, 1992, pp. 452-454.

http://dx.doi.org/10.1038/360452a0

[58] B. Steinberger and R. J. O’Connell, “Changes of the Earth’s Rotation Axis Owning to Advection of Mantle Density Heterogeneities,” Nature, Vol. 387, No. 6629, 1997, pp. 169-173. http://dx.doi.org/10.1038/387169a0

[59] F. D. Stacey, “Physics of the Earth,” 3rd Edition, Brookfield Press, Brisbane, 1992, 513 pp.

[60] W. J. Morgan, “Convection Plumes in the Lower Mantle,” Nature, Vol. 230, No. 5288, 1971, pp. 42-43.

http://dx.doi.org/10.1038/230042a0

[61] P. Olson and H. Singer, “Creeping Plumes,” Journal of Fluid Mechanics, Vol. 158, 1985, pp. 511-531.

http://dx.doi.org/10.1017/S0022112085002749

[62] W. M. Elsasser, “Convection and Stress Propagation in the Upper Mantle,” In: S. K. Runcorn, Ed., The Application of Modern Physics to the Earth and Planetary Interiors, Wiley, New York, 1969, pp. 223-246.

[63] W. M. Elsasser, “Two-Layer Model of Upper Mantle Circulation,” Journal of Geophysical Research, Vol. 76, No. 20, 1971, pp. 4744-4753.

http://dx.doi.org/10.1029/JB076i020p04744

[64] F. M. Richter, “Mantle Convection Models,” Annual Review of Earth and Planetary Sciences, Vol. 6, 1978, pp. 9-19.

http://dx.doi.org/10.1146/annurev.ea.06.050178.000301

[65] M. Nakada, “Rheological Structure of the Earth’s Mantle Derived from Glacial Rebound in Laurentide,” Journal of Physics of the Earth, Vol. 31, No. 6, 1983, pp. 349-386.

http://dx.doi.org/10.4294/jpe1952.31.349

[66] L. Fleitout and D. A. Yuen, “Steady State, Secondary Convection beneath Lithospheric Plates with Temperature- and Pressure-Dependent Viscosity,” Journal of Geophysical Research, Vol. 89, No. B11, 1984, pp. 9227-9244.

http://dx.doi.org/10.1029/JB089iB11p09227

[67] B. D. Marsh and J. G. Marsh, “On Global Gravity Anomalies and Two-Layer Mantle Convection,” Journal of Geophysical Research, Vol. 81, No. 29, 1976, pp. 5267-5280. http://dx.doi.org/10.1029/JB081i029p05267

[68] C. G. Sammis, “Effects of Polymorphic Phase Boundaries on Vertical and Horizontal Motions in the Earth’s Mantle,” Tectonophysics, Vol. 35, No. 1-3, 1976, pp. 169-182.

http://dx.doi.org/10.1016/0040-1951(76)90036-6

[69] P. M. Kenyon and D. L. Turcotte, “Convection in a Two-Layer Mantle with a Strongly Temperature-Dependent Viscosity,” Journal of Geophysical Research, Vol. 88, No. B8, 1983, pp. 6403-6414.

http://dx.doi.org/10.1029/JB088iB08p06403

[70] M. A. Richards and B. H. Hager, “Geoid Anomalies in a Dynamic Earth,” Journal of Geophysical Research, Vol. 89, No. B7, 1984, pp. 5987-6002.

http://dx.doi.org/10.1029/JB089iB07p05987

[71] R. K. O’nions, “Relationships between Chemical and Convective Layering in the Earth,” Journal of the Geological Society, Vol. 144, No. 2, 1987, pp. 259-274.

http://dx.doi.org/10.1144/gsjgs.144.2.0259

[72] W. R. Peltier, “Layered Mantle Convection: New Perspectives on an Old Debate,” EOS, Vol. 80, 1999, p. S17.

[73] R. J. O’Connell, “On the Scale of Mantle Convection,” Tectonophysics, Vol. 38, No. 1-2, 1977, pp. 119-136.

http://dx.doi.org/10.1016/0040-1951(77)90203-7

[74] W. M. Elsasser, P. Olson and B. D. Marsh, “Depth of Mantle Convection,” Journal of Geophysical Research, Vol. 84, No. B1, 1979, pp. 147-155.

http://dx.doi.org/10.1029/JB084iB01p00147

[75] D. E. Loper, “A Simple Model of Whole-Mantle Convection,” Journal of Geophysical Research, Vol. 90, No. B2, 1985, pp. 1809-1836.

http://dx.doi.org/10.1029/JB090iB02p01809

[76] B. Travis and P. Olson, “Convection with Internal Heat Sources and Thermal Turbulence in the Earth’s Mantle,” Geophysical Journal International, Vol. 118, No. 1, 1994, pp. 1-19.

http://dx.doi.org/10.1111/j.1365-246X.1994.tb04671.x

[77] J. Weertman, “The Creep Strength of the Earth’s Mantle,” Reviews of Geophysics, Vol. 8, No. 1, 1970, pp. 145-168. http://dx.doi.org/10.1029/RG008i001p00145

[78] S. H. Kirby and C. B. Raleigh, “Mechanisms of High-Temperature, Solid-State Flow in Minerals and Ceramics, and Their Bearing on the Creep Behavior of the Mantle,” Tectonophyiscs, Vol. 19, No. 2, 1973, pp. 165-194.

http://dx.doi.org/10.1016/0040-1951(73)90038-3

[79] R. L. Post Jr. and D. T. Griggs, “The Earth’s Mantle: Evidence of Non-Newtonian Flow,” Science, Vol. 181, No. 4106, 1973, pp. 1242-1244.

http://dx.doi.org/10.1126/science.181.4106.1242

[80] M. L. Bell, S. T. Crouch and A. Nur, “Non-Newtonian Anti-Phase Flow and Its Application to Plate Deformation,” Tectonophysics, Vol. 39, No. 4, 1977, pp. 501-514.

http://dx.doi.org/10.1016/0040-1951(77)90150-0

[81] W. A. Heiskanen and F. A. Vening Meinesz, “The Earth and Its Gravity Field,” McGraw-Hill, New York, 1958, 470 p.