### Abstract

Mitrovica et al. (2005), following calculations by Nakada (2002), demonstrated that the traditional approach for computing rotation perturbations driven by glacial isostatic adjustment significantly overestimates present-day true polar wander (TPW) speeds by underestimating the background oblateness on which the ice-age loading is superimposed. The underestimation has two contributions: the first originates from the treatment of the hydrostatic form and the second from the neglect of the Earth?s excess ellipticity supported by mantle convection. In Mitrovica et al. (2005), the second of these two contributions was computed assuming a biaxial nonhydrostatic form (i.e., the principal equatorial moments of inertia were assumed to be equal to their mean value). In this article we outline an extended approach that accounts for a triaxial planetary form. We show that differences in the TPW speed predicted using the Mitrovica et al. (2005) approach and our triaxial theory are relatively minor (∼0.1°/Myr) and are limited to Earth models with lower mantle viscosity less than ∼5 × 1021 Pa s. However, for this same class of Earth models, the angle of TPW predicted for a triaxial Earth is rotated westward (toward the axis of maximum equatorial inertia) by as much as ∼20° relative to the biaxial case. We demonstrate that these effects are a consequence of the geometry of the ice-age forcing, which has a dominant equatorial direction that is intermediate to the axes defining the principal equatorial moments of inertia of the planet. We complete the study by computing updated Frechet kernels for the TPW speed datum, which provide a measure of the detailed depth-dependent sensitivity of the predictions to variations in mantle viscosity. We show, in contrast to earlier efforts to explore this sensitivity based on the traditional rotation theory, that the datum does not generally have a sensitivity to viscosity that peaks near the base of the mantle.

Original language | English (US) |
---|---|

Journal | Journal of Geophysical Research: Space Physics |

Volume | 115 |

Issue number | 5 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science

### Cite this

*Journal of Geophysical Research: Space Physics*,

*115*(5). https://doi.org/10.1029/2009JB006564

**The rotational stability of a triaxial ice-age Earth.** / Matsuyama, Isamu M; Mitrovica, J. X.; Daradich, A.; Gomez, N.

Research output: Contribution to journal › Article

*Journal of Geophysical Research: Space Physics*, vol. 115, no. 5. https://doi.org/10.1029/2009JB006564

}

TY - JOUR

T1 - The rotational stability of a triaxial ice-age Earth

AU - Matsuyama, Isamu M

AU - Mitrovica, J. X.

AU - Daradich, A.

AU - Gomez, N.

PY - 2010

Y1 - 2010

N2 - Mitrovica et al. (2005), following calculations by Nakada (2002), demonstrated that the traditional approach for computing rotation perturbations driven by glacial isostatic adjustment significantly overestimates present-day true polar wander (TPW) speeds by underestimating the background oblateness on which the ice-age loading is superimposed. The underestimation has two contributions: the first originates from the treatment of the hydrostatic form and the second from the neglect of the Earth?s excess ellipticity supported by mantle convection. In Mitrovica et al. (2005), the second of these two contributions was computed assuming a biaxial nonhydrostatic form (i.e., the principal equatorial moments of inertia were assumed to be equal to their mean value). In this article we outline an extended approach that accounts for a triaxial planetary form. We show that differences in the TPW speed predicted using the Mitrovica et al. (2005) approach and our triaxial theory are relatively minor (∼0.1°/Myr) and are limited to Earth models with lower mantle viscosity less than ∼5 × 1021 Pa s. However, for this same class of Earth models, the angle of TPW predicted for a triaxial Earth is rotated westward (toward the axis of maximum equatorial inertia) by as much as ∼20° relative to the biaxial case. We demonstrate that these effects are a consequence of the geometry of the ice-age forcing, which has a dominant equatorial direction that is intermediate to the axes defining the principal equatorial moments of inertia of the planet. We complete the study by computing updated Frechet kernels for the TPW speed datum, which provide a measure of the detailed depth-dependent sensitivity of the predictions to variations in mantle viscosity. We show, in contrast to earlier efforts to explore this sensitivity based on the traditional rotation theory, that the datum does not generally have a sensitivity to viscosity that peaks near the base of the mantle.

AB - Mitrovica et al. (2005), following calculations by Nakada (2002), demonstrated that the traditional approach for computing rotation perturbations driven by glacial isostatic adjustment significantly overestimates present-day true polar wander (TPW) speeds by underestimating the background oblateness on which the ice-age loading is superimposed. The underestimation has two contributions: the first originates from the treatment of the hydrostatic form and the second from the neglect of the Earth?s excess ellipticity supported by mantle convection. In Mitrovica et al. (2005), the second of these two contributions was computed assuming a biaxial nonhydrostatic form (i.e., the principal equatorial moments of inertia were assumed to be equal to their mean value). In this article we outline an extended approach that accounts for a triaxial planetary form. We show that differences in the TPW speed predicted using the Mitrovica et al. (2005) approach and our triaxial theory are relatively minor (∼0.1°/Myr) and are limited to Earth models with lower mantle viscosity less than ∼5 × 1021 Pa s. However, for this same class of Earth models, the angle of TPW predicted for a triaxial Earth is rotated westward (toward the axis of maximum equatorial inertia) by as much as ∼20° relative to the biaxial case. We demonstrate that these effects are a consequence of the geometry of the ice-age forcing, which has a dominant equatorial direction that is intermediate to the axes defining the principal equatorial moments of inertia of the planet. We complete the study by computing updated Frechet kernels for the TPW speed datum, which provide a measure of the detailed depth-dependent sensitivity of the predictions to variations in mantle viscosity. We show, in contrast to earlier efforts to explore this sensitivity based on the traditional rotation theory, that the datum does not generally have a sensitivity to viscosity that peaks near the base of the mantle.

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U2 - 10.1029/2009JB006564

DO - 10.1029/2009JB006564

M3 - Article

VL - 115

JO - Journal of Geophysical Research

JF - Journal of Geophysical Research

SN - 0148-0227

IS - 5

ER -