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The postglacial rebound signal of Fennoscandia - observed by absolute gravimetry, GPS, and tide gauges Bjørn Ragnvald Pettersen Department of Mathematical Sciences and Technology University of Environmental and Life Sciences P O Box 5003, N-1432 Ås, Norway E-mail: bjorn.pettersen@umb.no

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Vertical uplift derived from leveling and GPS Courtesy:H.-G. Scherneck et al. (2003)

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Vertical uplift of Fennoscandian far-field J.-M. Nocquet, E. Calais, B. Parsons (2005). GRL 32,L06308.

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NGOS-Nordic Geodetic Observing System

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Absolute gravity stations in Fennoscandia

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Tromsø, Norway Gravity change = -0.2 ± 0.2 μGal/year Sea level change = 0.1 ± 0.4 mm/year GPS vertical change = 2.5 0.2 mm/year

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Stavanger, Norway Gravity change = -0.2 ± 0.2 μGal/year Sea level change = 0.6 ± 0.4 mm/year GPS vertical change = 1.3 ± 0.2 mm/year

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Trysil, Norway Gravity change = -1.13 ± 0.07 μGal/year GPS vertical change = 10.3 0.2 mm/year

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Skellefteå, Sweden Gravity change = -1.8 ± 0.2 μGal/year GPS vertical change = 9.6 ± 0.2 mm/yearSea level change = -8.5 ± 0.3 mm/year

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Data sources GPS –Lidberg et al. (2006), Journal of Geodesy –Kaniuth & Vetter (2005), GPS Solutions 9, 32. Tide gauges –www.pol.ac.uk/psmsl/datainfo/rlr.trends Absolute gravimetry –Engfeldt et al. (2006), 1st symp. IGFS. –Bilker-Koivula et al. (2006), 1st symp. IGFS. –Wilmes et al. (2004), IAG symp. 129.

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Parameters derived from observations Site namedg/dt (AG)dh/dt (GPS)dh/dt (TG) Tromsø-0.44 W -0.2 E2.30 L 1.8 KV 0.05 P Stavanger -0.1 E1.18 L 0.6 KV-0.27 P -0.2 e Trysil-1.15 W -1.1 E9.2 k Onsala AN-0.9 W -0.8 E2.66 L 2.6 KV 1.42 P Onsala AS -0.7 E Mårtsbo-1.3 W -1.2 E6.74 L 6.05 P 5.9 e Skellefteå-1.82 W -1.8 E9.61 L 8.54 P 8.8 e Kiruna-1.1 W -0.8 E6.2 L Sodankylä-1.6 M -1.6 E7.12 L Vaasa AA-2.1 M -2.2E8.62 L 8.1 KV 7.34 P 7.6 e Vaasa AB-1.7 M -1.7 E Metsähovi-0.5 M -0.5 E4.26 L 3.9 KV 2.44 P 2.3 e Joensuu-2.1 M -1.7 E4.06 L

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Gravity change versus height change dg= - 0.17 (±0.04)·dh – 0.17 (±0.23) dg= - 0.19 (±0.02)·dh – 0.24 (±0.08) Note: TG is more precise than GPS!

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East-west traverse of relative gravity J. Mäkinen et al. (2004). The Fennoscandian Land Uplift Gravity Lines. Proceedings GGSM2004, Porto. dg=-1.07 ± 0.24 μGal/year +0.91 ± 0.09 μGal/year dh= 6.9 ± 0.5 mm/year -4.7 ± 0.5 mm/year dg/dh= -0.16 ± 0.1 -0.19 ± 0.08 μGal/mm

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Postglacial rebound in North America A. Lambert, N. Courtier, T. S. James (2006). J Geodynamics 41, 307-317.

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The Bouguer plate The vertical component (in P) of the attraction force from mass element is rdr dd h dh P l Mass element: m=rd dr dh = mass density Newtonian attraction in P from mass element is

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Integrating the Bouguer plate We thus need to integrate from 0 to 360 degrees, r from 0 to , and h from 0 to a height h which represents the vertical displacement. A free air uplift produces reduction in gravity of -0.31 Gal/mm. The Bouguer plate adds gravity to the effect of +0.14 Gal/mm due to the attraction of its mass. The net effect is -0.31 + 0.14 = -0.17 Gal/mm.

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Uplift model of a viscoelastic earth - mathematical formulation Initial condition: a spherically symmetric, three-layered, self-gravitating planet in hydrostatic equilibrium at the onset of ice melting. The surface mass load is represented by a spherical harmonic expansion: (L = load function; Y=surface spherical harmonics) ▪ Responses of earth model are expressed using Love numbers h, l, and k. ▪ Responses are radial and tangential (geometry), and in the gravity potential. ▪ In the time domain, Love numbers have elastic and non-elastic components

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Uplift model of a viscoelastic earth - mathematical formulation Vertical uplift ▪ Gravity perturbation due to change in mass distribution The first term describes the elastic response The second term contains the viscous component, represented by a superposition of exponential decay modes ▪ Time histories may be derived by differentiating these equations

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Uplift model of a viscoelastic earth - model results Numerical experiments show that for each l there is a single viscoelastic mode that dominates the sum over j (85-90% of the signal). This mode is caused by buoyancy forces acting on the depressed lithosphere. J. Wahr, Han, D., A. Trupin (1995). GRL 22, 977-980. ▪ Numerical experiments show that this ratio ≈ -0.15 for all values of l and a wide range of viscosity profiles and lithospheric thicknesses. l +: x:

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Conclusions A preliminary confrontation of observations and theory reveals general agreement. The basic model concept is correct. Improved empirical relationships are needed to restrain theoretical parameters, e.g. mantel viscosities (upper and lower), lithosphere thickness, etc.

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Conclusions This may be achieved by - extending the time series (AG, GPS, etc.) - improved understanding of local effects on observational results e.g. hydrological variability, seasonal meteorology, reference frame realisations, etc. - map and understand the effects of local geology, The present approach of considering Fennoscandia as one rigid uplift region may be insufficient or incorrect. The physics may be the same overall, but faults etc. may require a fractioned end model.

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