Geophysical implications of satellite determinations of the earth's gravitational field

Kaula, W. M.

doi:10.1007/bf00542895

Cited by 64 publications

(50 citation statements)

References 36 publications

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“…So the squashing of the earth by the glaciers of the Quarternary Ice Age accounts for between 13 per cent and 40 per cent of the present-day nonhydrostatic part of J 2 , with a preferred value of 22 per cent. Wang (1966) had suggested that glaciation might account for all of ^J 2 , but McKenzie (1966), Kaula (1967), and O'Conn ell (1971) indicated that glaciation accounts for an amount closer to the percentages given here. (For further discussion of AJ 2) see Goldreich and Toomre, 1969).…”

Section: U+mentioning

confidence: 56%

Postglacial rebound observed by lageos and the effective viscosity of the lower mantle

Rubincam¹

1984

J. Geophys. Res.

161

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Postglacial rebound appears to have been observed gravitationally by the Lageos satellite. Sixty‐four observations of the orbital node made over a 5‐year time interval reveal an acceleration of ( −8.1±1.8)×10−8 arc sec d−2 due to a source which is not presently modeled in the GEODYN orbit determination computer program. This acceleration cannot be explained by the ocean tide with an 18.6‐year period, assuming it to be an equilibrium tide. Instead it seems to be due to postglacial rebound, which changes the J2 coefficient in the spherical harmonic expansion of the earth's gravitational field at the rate of ( −8.2±1.8)×10−19 s−1 this, in turn, accelerates the node. This rate does not agree with the −32×10−19 s−1 predicted by Wu and Peltier's L2 model, which has upper and lower mantle effective viscosities of 1021 and 1022 Pa s, respectively. It does agree well with their L1 model, which gives about −10×10−19 s−1. Since the effective viscosity is 1021 Pa s throughout the entire mantle in the L1 model, the results support the contentions that (1) the effective viscosity is near 1021 Pa s everywhere in the mantle, and (2) this relatively low value for the effective viscosity may have permitted several degrees of polar wander due to glaciation during the Quaternary Ice Age.

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Section: U+mentioning

confidence: 56%

Postglacial rebound observed by lageos and the effective viscosity of the lower mantle

Rubincam¹

1984

J. Geophys. Res.

161

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“…Wang (1966) thought the excess flattening might be due to heavy glaciation at the poles, which would squeeze out a bulge due to the weight of the ice. This view was 13 criticized by McKenzie (1966), Kaula (1967), and O'Connell (1971); they indicated the ice caps would have to be unacceptably large to produce the extra flattening. Kahn and O'Keefe (1974), however, showed that glaciation in Antarctica probably produced the gravity field's large third harmonic, giving the earth its "pear shape. "…”

Section: Energy Of An Oblate Spheroidmentioning

confidence: 99%

“…Since the earth's gravitational potential energy has received . attention (and spherical harmonic treatments) in the past, particularly from MacDonald (1966), McKenzie (1966), and Kaula (1967), it should prove worthwhile to derive a general equation for the energy from the viewpoint of spherical harmonics.…”

Section: In'troducttionmentioning

confidence: 99%

Gravitational potential energy of the Earth: A spherical harmonic approach

Rubincam¹

1979

J. Geophys. Res.

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A spherical harmonic equation for the gravitational potential energy of the earth is derived for an arbitrary density distribution by conceptually bringing in mass‐elements from infinity and building up the earth shell upon spherical shell. The zeroth degree term in the spherical harmonic expansion agrees with the usual expression for the energy of a radial density distribution. The second degree terms give a maximum nonhydrostatic energy in the crust and mantle of −2.77×1029 ergs, an order of magnitude below McKenzie's (1966) estimate. McKenzie's result stems from mathematical error. Our figure is almost identical with Kaula's (1963) estimate of the minimum shear strain energy in the mantle, a not unexpected result on the basis of the virial theorem. If the earth is assumed to be a homogeneous viscous oblate spheroid relaxing to an equilibrium shape, then a lower limit to the mantle viscosity of 1.3×1020 P is found by assuming that the total geothermal flux is due to viscous dissipation of energy. This number is almost six orders of magnitude below MacDonald's (1966) estimate of the viscosity and removes his objection to convection. We have not determined where MacDonald's treatment diverges from our own. If the nonequilibrium figure is dynamically maintained by the earth acting as a heat engine at 1% efficiency, then the viscosity is 1022P, a number preferred by Cathles (1975) and Peltier and Andrew (1976) as the viscosity of the mantle.

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“…It is a degree variance (or its square root, degree-RMS) that has been often used to quantify the powers of signal and error in the gravity field estimates at various spatial wavelengths (Kaula 1967). In addition to admittance and correlation functions, it is useful to analyze and compare the global topography and (static) gravity to understand physical implications of their spatial variations for Earth and other planets' geodynamics (e.g., Kaula 1967;Wieczorek 2007).…”

Section: Introductionmentioning

confidence: 99%

Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions

Han

Ditmar

2007

J Geod

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A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused by great earthquakes such as the 2004 Sumatra-Andaman earthquake can be detected by the low-low tracking and the gradiometer data within the bandwidths of spherical degrees 15-30 and 25-100, respectively. However, the detection of terrestrial water storage variation by GOCE gradiometer is equivocal even after localization.

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Geophysical implications of satellite determinations of the earth's gravitational field

Cited by 64 publications

References 36 publications

Postglacial rebound observed by lageos and the effective viscosity of the lower mantle

Postglacial rebound observed by lageos and the effective viscosity of the lower mantle

Gravitational potential energy of the Earth: A spherical harmonic approach

Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions

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