Vertical deformation and absolute gravity

Fang, Ming; Hager, Bradford H.

doi:10.1046/j.0956-540x.2001.01483.x

Cited by 15 publications

(13 citation statements)

References 23 publications

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“…This ratio was studied by FANG and HAGER (2001) who confirmed that it is independent of the radial viscosity profile of the Earth, which is due to the nearly incompressible viscous response of a Maxwell Earth. Using the ICE-3G history of TUSHINGHAM and PELTIER (1991) to model the GIA in Antarctica, JAMES and IVINS (1998) numerically found a ratio of -0.16 lGal/mm, close to ratio (3).…”

Section: Viscoelastic and Elastic Gravity And Uplift Ratesmentioning

confidence: 88%

Separation of the Geodetic Consequences of Past and Present Ice-Mass Change: Influence of Topography with Application to Svalbard (Norway)

Mémin

Hinderer

Rogister

2011

Pure Appl. Geophys.

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Polar regions such as Greenland, Svalbard and Antarctica are deforming today because of both the present-day ice-mass (PDIM) change of glaciers and the glacial isostatic adjustment (GIA) following the Pleistocene deglaciation. Observations handled in these areas contain both the contributions from the PDIM change and GIA. This study aims at separating them by considering two specific gravity variation-to-vertical displacement ratios. We first review the case of the viscoelastic rebound (GIA) subsequent to the Pleistocene deglaciation leading to a ratio C v . The outcome of previous studies is that C v is approximately equal to -0.15 lGal/mm and almost independent of the deglaciation history, ice geometry and viscosity profile of the mantle. Similarly we consider the elastic deformation resulting from PDIM change which leads to a second ratio C e,N . Several studies have shown that C e;N % À0:26 lGal/mm if one assumes that the changing glaciers are thin layers over the surface of a spherical Earth model. In this case, we show that the separation between the contributions from PDIM change and GIA is unique if both gravity and height changes observations are available at the same station. Next, we focus on C e,N and show that according to the deglaciation/glaciation context and from colocated gravity variation and ground vertical velocity measurements one can deduce a range of possible values for C e,N . Studying the influence of the topography on C e,N we first show that it tends to positive values if most of surrounding ice-mass changes above the altitude of the observation site and to values lower than -0.26 lGal/mm if changes are below. We next apply our general formalism to the case of the past and PDIM changes in Svalbard, Norway. We compute the ratio C e,N at the geodetic observatory at Ny-Å lesund and show the influence of the topography of the surrounding glaciers on the measured gravity and uplift rates. We show that if the ice-mass change is spatially uniform, C e, N does not depend on the speed of ice-mass change, and hence the separation of the contributions from PDIM changes and GIA can still be done univocally. However, if the ice-mass change is not spatially uniform, C e, N depends on both the speed of ice-mass change and the volume of ice-change rate.

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Section: Viscoelastic and Elastic Gravity And Uplift Ratesmentioning

confidence: 88%

Separation of the Geodetic Consequences of Past and Present Ice-Mass Change: Influence of Topography with Application to Svalbard (Norway)

Mémin

Hinderer

Rogister

2011

Pure Appl. Geophys.

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“…The discovery leads them to propose that absolute-gravity measurements could be used to remove the GIA contribution from observedḣ to leave only the elastic part due to contemporary ice balance. Fang and Hager (2001) found that such a Bouguer ratio is almost independent of the radial viscosity profile, as the viscous response of a Maxwell earth is nearly incompressible. Peltier (2004) points out that (as a consequence of an approximate relationship between viscoelastic load Love numbers) g ≈ (−2g/a + g/a)ḣ = (−g/a)ḣ; the ratio −g/a then equals the number of Wahr et al (1995) cited above.…”

Section: Expected Relationship Between Gravity Change and Vertical Momentioning

confidence: 94%

Absolute gravimetry in Antarctica: Status and prospects

Mäkinen

Amalvict

Shibuya

et al. 2007

Journal of Geodynamics

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“…Fang & Hager (2001) have carefully studied the response of a viscoelastic Maxwell Earth. They found that the viscoelastic load Love numbers of a compressible model with a Maxwell rheology can be related to each other through a pseudo‐surface density depending on n .…”

Section: Asymptotic Limit Of Ge/umentioning

confidence: 99%

A search for the ratio between gravity variation and vertical displacement due to a surface load

Linage

Hinderer

Rogister

2007

Geophysical Journal International

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S U M M A R YWe study the ratio between the gravity variation and vertical displacement at the surface of a self-gravitating spherical elastic earth model when a load is applied at the surface. By expanding both the gravity variation and vertical displacement in series of spherical harmonics, we investigate the spectral behaviour of the ratio of the harmonic components of the gravity variation and vertical displacement. Special attention is paid to the asymptotic limit, that is, for large degrees, and to the mean value for a given degree range, without considering the spectral properties of the load itself. First, we split the gravity variation into two parts: the first term stems from the direct attraction of the load, the second one is due to the elastic deformation of the model. The origin of the second term is twofold: the surface is displaced in the Earth's gravity field and the position of the Earth's mass particles is changed. The ratio between the gravity variation associated to the displacement of the surface and this displacement is the well-known free-air gradient of −0.30 μGal mm −1 . We show, by considering different earth models, that the ratio between the harmonic components of the elastic gravity variation (i.e. mass redistribution and free-air effect) and the corresponding components of the vertical displacement tends to the Bouguer corrected gradient of −0.20 μGal mm −1 when both the harmonic degree n of the components is very large and the top layer of the earth model is incompressible. Second, we compute, for each n, the ratio of the components of the gravity variation and those of the vertical displacement omitting the local Newtonian attraction term. Whereas it weakly depends on n for n < ∼ 6, it is nearly constant for n > ∼ 6. By defining an average value for those ratios, we obtain a fairly good approximation of the ratio between the total gravity variation and vertical displacement, only valid outside the loaded area, which is −0.26 μGal mm −1 . Finally, to check out our spectral result, we consider the loading effect of spherical caps of various angular apertures. We find a mean value of −0.21 μGal mm −1 outside the loaded area which is by 20 per cent in agreement with our spectral result.

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Vertical deformation and absolute gravity

Cited by 15 publications

References 23 publications

Separation of the Geodetic Consequences of Past and Present Ice-Mass Change: Influence of Topography with Application to Svalbard (Norway)

Separation of the Geodetic Consequences of Past and Present Ice-Mass Change: Influence of Topography with Application to Svalbard (Norway)

Absolute gravimetry in Antarctica: Status and prospects

A search for the ratio between gravity variation and vertical displacement due to a surface load

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