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  • Oxford University Press  (3)
  • 2010-2014  (3)
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  • 1
    Publication Date: 2014-08-30
    Description: Theory has been long established for computing the elastic response of a spherically symmetric terrestrial planetary body to both body tide and surface loading forces. However, for a planet with laterally heterogeneous mantle structure, the response is usually computed using a fully numerical approach. In this paper, we develop a semi-analytic method based on perturbation theory to solve for the elastic response of a planetary body with lateral heterogeneities in its mantle. We present a derivation of the governing equations for our second-order perturbation method and use them to study the high-order tidal effects caused by mode coupling between degree-2 body tide forcing and the laterally heterogeneous elastic structure of the mantle. We test our method by applying it to the Moon in which small long-wavelength lateral heterogeneities are assumed to exist in the elastic moduli of the lunar mantle. The tidal response of the Moon is determined mode by mode, for lateral heterogeneities with different depth ranges within the mantle and different horizontal scales. Our perturbation method solutions are compared with numerical results, showing remarkable agreement between the two methods. We conclude that our perturbation method provides accurate results and can be adapted to address a variety of forward and inverse response problems.
    Keywords: Geodynamics and Tectonics
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 2
    Publication Date: 2013-01-11
    Description: We develop a 3-D finite-element model to study the viscoelastic response of a compressible Earth to surface loads. The effects of centre of mass motion, polar wander feedback, and self-consistent ocean loading are implemented. To assess the model's accuracy, we benchmark the numerical results against a semi-analytic solution for spherically symmetric structure. We force our model with the ICE-5G global ice loading history to study the effects of laterally varying viscosity structure on several glacial isostatic adjustment (GIA) observables, including relative sea-level (RSL) measurements in Canada, and present-day time-variable gravity and uplift rates in Antarctica. Canadian RSL observations have been used to determine the Earth's globally averaged viscosity profile. Antarctic GPS uplift rates have been used to constrain Antarctic GIA models. And GIA time-variable gravity and uplift signals are error sources for GRACE and altimeter estimates of present-day Antarctic ice mass loss, and must be modelled and removed from those estimates. Computing GIA results for a 3-D viscosity profile derived from a realistic seismic tomography model, and comparing with results computed for 1-D averages of that 3-D profile, we conclude that: (1) a GIA viscosity model based on Canadian relative sea-level data is more likely to represent a Canadian average than a true global average; (2) the effects of 3-D viscosity structure on GRACE estimates of present-day Antarctic mass loss are probably smaller than the difference between GIA models based on different Antarctic deglaciation histories and (3) the effects of 3-D viscosity structure on Antarctic GPS observations of present-day uplift rate can be significant, and can complicate efforts to use GPS observations to constrain 1-D GIA models.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 3
    Publication Date: 2011-03-09
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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