Presentday secular variations in the zonal harmonics of Earth's geopotential
Abstract
We develop a new formalism for the prediction of secular variations in the gravitational potential field of a spherically symmetric, selfgravitating, (Maxwell) viscoelastic planetary model subjected to an arbitary surface load which may include a gravitationally selfconsistent ocean loading component. The theory is applied to generate the most accurate predictions to date, of the presentday secular variations in the zonal harmonics of the geopotential (the socalled \Jdot_{l} for degree l) arising as a consequence of the late Pleistocene glacial cycles. In this respect, we use the very recent ICE3G reconstruction of the last late Pleistocene deglaciation event (Tushingham and Peltier, 1991). A comparison of these predictions with those generated using simplified disk models of the ice sheets, which have been used in all previous studies of the \Jdot_{l} harmonics (l>2), (indicates that the disk model approximation introduces unacceptably large errors at all spherical harmonic degrees except perhaps l=2. Predictions have also been made using a eustatic loading approximation (also used in previous studies) in place of a gravitationally selfconsistent ocean loading component, and we have found that the resulting discrepancy is largest at degrees 2, 8 and 10. In the case of \Jdot_{2} the magnitude of the error incurred using the eustatic approximation can be as large as order 1015% of the predicted value. We have attributed this discrepancy to the present day net flux of water away from the equatorial regions arising from the remanant presentday adjustment associated with the late Pleistocene glacial cycles. The effect represents a heretofore unrecognized contribution to the \Jdot_{l} harmonics, or alternatively the nontidal acceleration of Earth's axial rate of rotation. In terms of the later, the maximum anormaly in the length of day is approximately 1.7 μs/yr.
We also consider the sensitivity of the \Jdot_{l} data to variations in the radial mantle viscosity profile by using a suite of forward calculations and an examination of Fréchet kernls. The theory required for the computation of those kernls is described herein. We find that the radial variation in sensitivity can be a strong function of the viscosity model used in the calculations. For models with a uniform upper mantle viscosity (v_{um}) of 10^{21} Pa s, forward predictions of the \Jdot_{l} harmonics exhibit a pronounced peak when a wide enough range of lower mantle viscosities (v_{LM}) are considered (we denote the v_{LM} value at this peak as v̂^{l}_{LM}). At the lowest degrees (l<=4), Fréchet kernels computed for a series of increasing v_{LM} values (10^{2}^{1} Pa s<=v_{LM}<10^{2}^{4} Pa s) indicate a migration of the dominant sensitivity of the \Jdot_{l} data to variations in viscosity from regions below approximately 1200 km depth (for v_{LM}<=v̂^{l}_{LM}) to regions above this depth in the lower mantle (for v_{LM}>=v̂^{l}_{L}_{M}). The sensitivity of the \Jdot_{l} data to variations in the viscosity profile in the shallowest parts of the lower mantle, for the case v_{LM}<=v̂^{l}_{LM}, is also reflected in a set of forward calculations described herein. As an example, \Jdot_{l} predictions made using Earth models in which the viscosity above 1200 km depth is constrained to be 10^{2}^{1} Pa s, do not exhibit the multiple solutions characteristic of the v_{UM}=10^{2}^{1} Pa s calculations.
The same is true of Earth models in which the upper mantle viscosity is weakened an order of magnitude to 10^{2}^{0} Pa s. The theory described herein is also applied to commute the \Jdot_{l} signal (l<=10) arising from the retreat of small ice sheets and glaciers described by Meier (1984) and also from any potential variations in the mass of the Antarctic and Greenland ice sheets. The present day \Jdot_{l} signal due to the late Pleistocene glacial cycles dominates the signal from Meier's sources at all degrees except l=3. In contrast, the \Jdot_{l} signal arising from mass variations in the Antarctic and Greenland ice sheets is potentially comparable to the former. A comparison of observational constraints on the J_{l} data with predictions of the postglacial rebound signal described in this paper, in order to infer mantle rheology, cannot proceed until constraints are placed on the presentday mass flux of these large polar ice sheets. We show that the constraints required are weakest at degrees l=2 and 4. Finally, we outline a potentially important procedure for incorporating predictions of the \Jdot_{l} signal due to the late Pleistocene glacial cycles and Meier's sources, with an observational constraint on the \Jdot_{g} datum, to yield bounds on the presentday net mass flux from the Antarctic and Greenland ice sheets. A rigorous application of this procedure must wait until observational constraints on \JdotSUB>2 are reestablished in the literature.
 Publication:

Journal of Geophysical Research
 Pub Date:
 March 1993
 DOI:
 10.1029/92JB02700
 Bibcode:
 1993JGR....98.4509M
 Keywords:

 Geopotential;
 Planetary Evolution;
 Planetary Gravitation;
 Secular Variations;
 Zonal Harmonics;
 Earth Mantle;
 Glaciology;
 Ocean Models;
 Viscosity;
 Geophysics;
 Geodesy and Gravity: Geopotential theory and determination;
 Geodesy and Gravity: Rotational variations;
 Tectonophysics: Rheologygeneral