True polar wander as a mechanism for second-order sea-level variations

Science

Volumn 279, Issue 5350, 1998, Pages 534-537

  Mound, Jon E ^a   Mitrovica, Jerry X ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CRETACEOUS; ROTATION POLE; SEA LEVEL VARIATION; TERTIARY;

ARTICLE; ASTRONOMY; GEOMETRY; METHODOLOGY; PREDICTION; PRIORITY JOURNAL; ROTATION; TOMOGRAPHY; VISCOELASTICITY;

EID: 0032559276     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.279.5350.534     Document Type: Article

References (48)

1. Sea-level variations, as reflected in stratigraphic cycles, are classified in terms of their duration. For example, following A. D. Miall [Principles of Sedimentary Basin Analysis (Springer-Verlag, New York, 1990)], we define second-order cycles as lasting 10 million to 100 million years and third-order cycles as lasting 1 million to 10 million years.
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12. A. B. Watts and M. S. Steckler, in Deep Drilling Results in the Atlantic Ocean: Continental Margins and Paleoenvironment, M. Talwani et al., Eds. (AGU Maurice Ewing Series 3, American Geophysical Union, Washington, DC, 1979), pp. 218-234.
13. A. D. Miall (1), for example, has criticized the seismic stratigraphic method of sea-level analysis. An alternate method of estimating long-term eustatic sea-level trends involves a correlation of continental flooding events [for example, C. G. A. Harrison, in Sea Level Change, R. Revelle, Ed. (National Academy Press, Washington, DC, 1990), pp. 141-158]. This approach is susceptible to contamination from regional, tectonically driven, sea-level signals (8).
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18. R. Sabadini, C. Doglioni, and D. A. Yuen [Nature 345, 708 (1990)] considered the sea-level response of a radially stratified viscoelastic Earth subject to a constant polar wander of 1° per million years. Their calculations suggest that this level of TPW can produce ∼20 to 50 m of sea-level change over 1 My.
19. J. A. Andrews, J. Geophys. Res. 90, 7737 (1985).
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22. G. E. Williams, J. Phys. Earth 38, 475 (1990); Geophys. Res. Lett. 24, 421 (1997). Williams in the 1997 paper analyzed variations in the thickness of tidal rythmites and inferred that there were 401 ± 7 sidereal days per year at 620 Ma compared with the present value of 366.24 sidereal days per year. We assume that the change in the angular momentum over this time interval is linear in order to derive a variation in rotation rate over the last 130 My.
23. G. A. Milne and J. X. Mitrovica, Geophys. J. Int. 126, F13 (1996).
24. In the context of TPW induced by glacial isostatic adjustment, see D. Han and J. Wahr, in Slow Deformations and Transmission of Stress in the Earth, S. C. Cohen and P. Vanicek, Eds. (American Geophysical Union, Washington, DC, 1989), pp. 1-6; (18); B. G. Bills and T. S. James, Geophys. Res. Lett. 23, 3023 (1996).
25. In the context of TPW induced by glacial isostatic adjustment, see D. Han and J. Wahr, in Slow Deformations and Transmission of Stress in the Earth, S. C. Cohen and P. Vanicek, Eds. (American Geophysical Union, Washington, DC, 1989), pp. 1-6; (18); B. G. Bills and T. S. James, Geophys. Res. Lett. 23, 3023 (1996).
26. TPW acts to perturb the centrifugal potential associated with Earth rotation. The geographically varying component of this potential has an ellipsoidal (that is, degree two and order zero) form. The perturbing potential is thus the difference between two ellipsoidal forms whose axes are offset by a slight rotation. This difference, and the sea-level change that results, has a geometry (Fig. 3B) that may be described by the surface spherical harmonic of degree two and order one (14, 18, 19). As polar wander proceeds, the instantaneous orientation of the quadrants of this surface spherical harmonic (see Fig. 3B) changes.
27. We found no previous mention of the obvious correlation between the sea-level trend in Fig. 1 and the sense of the polar motion evident in Fig. 2.
28. The equation governing this calculation is derived by G. A. Milne and J. X. Mitrovica (18) (see their equations A7 through A10). The minor adjustments required to consider the case of internally forced TPW are discussed below their equation A10. The sea-level equation we solve incorporates not only the effect of TPW on both the geoid and solid surface but also the self-gravitation and loading effect of a time-dependent ocean distribution.
29. We adopt the preliminary reference Earth model specified in A. M. Dziewonski and D. L. Anderson, Phys. Earth. Planet. Inter. 25, 297 (1981).
30. The boundary between the upper-and lower-mantle region is taken to be at a depth of 660 km.
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32. Past changes in site location were derived from E. Irving, Geophys. Surv. 5, 299 (1983).
33. ∞]. We have found that the dominant, normal-mode contribution arises from the so-called M1 mode. The M1 mode arises from a deflection of the density discontinuity at a depth of 660 km between the upper and lower mantle. Thus, excitation of the mode requires that the discontinuity behaves nonadiabatically (that is, effectively as a chemical boundary) on the time scales we are considering. If this is not the case, then the mode would not be excited and the M1 contribution would vanish. As an example, the peak ∼54 m signal in Fig. 4 (curve A) has a contribution of ∼43 m from the elastic lithosphere and ∼11 m from the M1 mode.
34. We define rotational colatitude as the angular distance of a site from the instantaneous north pole of rotation.
35. In the seismic stratigraphic analysis of short-term (third-order cycles and higher) sea-level change (2, 4), North American and European sites dominate (Fig. 3C). The relative proximity of these sites suggests that they will experience similar TPW-induced sea-level trends. Thus, as has been suggested (14), it is unclear to what extent eustatic versus (TPW-induced) quadrant-localized signals contribute to the mean third-order sea-level trends.
36. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
37. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
38. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
39. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
40. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
41. See, for example, B. H. Hager, J. Geophys. Res. 89, 6003 (1984); M. A. Richard and B. H. Hager, ibid., p. 5987; M. Nakada and K. Lambeck, Geophys. J. Int. 96, 497 (1989); Y. Ricard and B. Wuming, ibid. 105, 561 (1991); J. X. Mitrovica, J. Geophys. Res. 101, 555 (1996); A. M. Forte and J. X. Mitrovica, Geophys. Res. Lett. 23, 1147 (1996).
42. The sensitivity to LT apparent in Fig. 5A follows from the arguments in (27). Furthermore, we have found that the contribution of the M1 mode to the sea-level signal (27) is sensitive to variations in upper mantle viscosity, and less sensitive to variations in lower mantle viscosity, for this range of Earth models; this explains the results in Fig. 5, B and C.
43. T. H. Jordan, Rev. Geophys. 13, 1 (1975); S. P. Grand, J. Geophys. Res. 92, 14065 (1987); A. M. Forte, A. M. Dziewonski, R. J. O'Connell, Science 268, 386 (1995).
44. T. H. Jordan, Rev. Geophys. 13, 1 (1975); S. P. Grand, J. Geophys. Res. 92, 14065 (1987); A. M. Forte, A. M. Dziewonski, R. J. O'Connell, Science 268, 386 (1995).
45. T. H. Jordan, Rev. Geophys. 13, 1 (1975); S. P. Grand, J. Geophys. Res. 92, 14065 (1987); A. M. Forte, A. M. Dziewonski, R. J. O'Connell, Science 268, 386 (1995).
46. B. M. Steinberger and R. J. O'Connell, Nature 387, 169 (1997).
47. Our sea-level predictions include the direct gravitational attraction and the loading effect of sea-level variations (22). The spatial geometry of these effects depends on the distribution of oceans, and therefore the sea-level trends we predict are more complicated than the simple illustrations in Fig. 3 imply.
48. We thank J. Wahr and two anonymous referees for their reviews of this report. We also thank D. Rowley for helpful comments. We are grateful for the ocean-continent geometry data provided by the PLATES Project of the Institute for Geophysics of the University of Texas at Austin. The work of J.X.M. was funded by Natural Sciences and Engineering Research Council of Canada and was supported by the Canadian Institute for Advanced Research (Earth Systems Evolution Program).