scholarly journals Fast computation of a viscoelastic deformable Earth model for ice-sheet simulations

2007 ◽  
Vol 46 ◽  
pp. 97-105 ◽  
Author(s):  
Ed Bueler ◽  
Craig S. Lingle ◽  
Jed Brown
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Integral Formula ◽  
Mathematical Formulation ◽  
Ice Sheet ◽  
Earth Model ◽  
Ice Flow ◽  
Earth Models ◽  
New Formulation ◽  
Made In

AbstractThe model used by Lingle and Clark (1985) to approximate the deformation of the Earth under a single ice stream is adapted to the purposes of continent-scale ice-sheet simulation. The model combines a layered elastic spherical Earth (Farrell, 1972) with a viscous half-space overlain by an elastic plate lithosphere (Cathles, 1975). For the half-space model we identify a new mathematical formulation, essentially a time-dependent partial differential equation, which generalizes and improves upon the standard elastic plate lithosphere with relaxing asthenosphere model widely used in ice-sheet simulation. The new formulation allows a significantly faster numerical strategy, a spectral collocation method based directly on the fast Fourier transform. We verify this method by comparing to an integral formula for a disk load. We also demonstrate that the magnitudes of numerical errors made in approximating coupled ice-flow/Earth-deformation systems are significantly smaller than pairwise differences between several Earth models. Our implementation of the Lingle and Clark (1985) model offers important features of spherical, layered, self-gravitating, viscoelastic Earth models without the computational expense.

scholarly journals Comparing a thermo-mechanical Weichselian Ice Sheet reconstruction to reconstructions based on the sea level equation: aspects of ice configurations and glacial isostatic adjustment

Solid Earth ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 371-388 ◽  
Author(s):  
P. Schmidt ◽  
B. Lund ◽  
J-O. Näslund ◽  
J. Fastook
Keyword(s):  
Sea Level ◽  
Regional Scale ◽  
Ice Sheet ◽  
Earth Model ◽  
Model Parameters ◽  
Glacial Isostatic Adjustment ◽  
Isostatic Adjustment ◽  
Earth Models ◽  
Uplift Rates ◽  
Best Fit

Abstract. In this study we compare a recent reconstruction of the Weichselian Ice Sheet as simulated by the University of Maine ice sheet model (UMISM) to two reconstructions commonly used in glacial isostatic adjustment (GIA) modelling: ICE-5G and ANU (Australian National University, also known as RSES). The UMISM reconstruction is carried out on a regional scale based on thermo-mechanical modelling, whereas ANU and ICE-5G are global models based on the sea level equation. The three models of the Weichselian Ice Sheet are compared directly in terms of ice volume, extent and thickness, as well as in terms of predicted glacial isostatic adjustment in Fennoscandia. The three reconstructions display significant differences. Whereas UMISM and ANU includes phases of pronounced advance and retreat prior to the last glacial maximum (LGM), the thickness and areal extent of the ICE-5G ice sheet is more or less constant up until the LGM. During the post-LGM deglaciation phase ANU and ICE-5G melt relatively uniformly over the entire ice sheet in contrast to UMISM, which melts preferentially from the edges, thus reflecting the fundamental difference in the reconstruction scheme. We find that all three reconstructions fit the present-day uplift rates over Fennoscandia equally well, albeit with different optimal earth model parameters. Given identical earth models, ICE-5G predicts the fastest present-day uplift rates, and ANU the slowest. Moreover, only for ANU can a unique best-fit model be determined. For UMISM and ICE-5G there is a range of earth models that can reproduce the present-day uplift rates equally well. This is understood from the higher present-day uplift rates predicted by ICE-5G and UMISM, which result in bifurcations in the best-fit upper- and lower-mantle viscosities. We study the areal distributions of present-day residual surface velocities in Fennoscandia and show that all three reconstructions generally over-predict velocities in southwestern Fennoscandia and that there are large differences in the fit to the observational data in Finland and northernmost Sweden and Norway. These difference may provide input to further enhancements of the ice sheet reconstructions.

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

scholarly journals Site information and initial results from deep ice drilling on Law Dome, Antarctica

1997 ◽  
Vol 43 (143) ◽  
pp. 3-10 ◽  
Author(s):  
V.I. Morgan ◽  
C.W. Wookey ◽  
J. Li ◽  
T.D. van Ommen ◽  
W. Skinner ◽  
...  
Keyword(s):  
Ice Core ◽  
Ice Sheet ◽  
High Accumulation ◽  
Ice Flow ◽  
Ice Cap ◽  
Basal Ice ◽  
Inland Ice ◽  
The Last Glacial Maximum ◽  
Initial Results ◽  
The Last Glacial

AbstractThe aim of deep ice drilling on Law Dome, Antarctica, has been to exploit the special characteristics of Law Dome summit, i.e. low temperature and high accumulation near an ice divide, to obtain a high-resolution ice core for climatic/environmental studies of the Holocene and the Last Glacial Maximum (LGM). Drilling was completed in February 1993, when basal ice containing small fragments of rock was reached at a depth of 1196 m. Accurate ice dating, obtained by counting annual layers revealed by fine-detail δ18О, peroxide and electrical-conductivity measurements, is continuous down to 399 m, corresponding to a date of AD 1304. Sulphate concentration measurements, made around depths where conductivity tracing indicates volcanic fallout, allow confirmation of the dating (for Agung in 1963 and Tambora in 1815) or estimates of the eruption date from the ice dating (for the Kuwae, Vanuatu, eruption ~1457). The lower part of the core is dated by extrapolating the layer-counting using a simple model of the ice flow. At the LGM, ice-fabric measurements show a large decrease (250 to 14 mm2) in crystal size and a narrow maximum in c-axis vertically. The main zone of strong single-pole fabrics however, is located higher up in a broad zone around 900 m. Oxygen-isotope (δ18O) measurements show Holocene ice down to 1113 m, the LGM at 1133 m and warm (δ18O) about the same as Holocene) ice near the base of the ice sheet. The LGM/Holocene δ18O shift of 7.0‰, only ~1‰ larger than for Vostok, indicates that Law Dome remained an independent ice cap and was not overridden by the inland ice sheet in the Glacial.

scholarly journals Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model

2010 ◽  
Vol 56 (199) ◽  
pp. 805-812 ◽  
Author(s):  
Ying Ma ◽  
Olivier Gagliardini ◽  
Catherine Ritz ◽  
Fabien Gillet-Chaulet ◽  
Gaël Durand ◽  
...  
Keyword(s):  
Ice Sheet ◽  
Actual State ◽  
Polar Ice ◽  
Ice Flow ◽  
Ice Shelves ◽  
State Of Stress ◽  
Asymptotic Models ◽  
Enhancement Factors ◽  
Definition Of ◽  
Stress And Strain Rate

AbstractPolar ice is known to be one of the most anisotropic natural materials. For a given fabric the polycrystal viscous response is strongly dependent on the actual state of stress and strain rate. Within an ice sheet, grounded-ice parts and ice shelves have completely different stress regimes, so one should expect completely different impacts of ice anisotropy on the flow. The aim of this work is to quantify, through the concept of enhancement factors, the influence of ice anisotropy on the flow of grounded ice and ice shelves. For this purpose, a full-Stokes anisotropic marine ice-sheet flowline model is used to compare isotropic and anisotropic diagnostic velocity fields on a fixed geometry. From these full-Stokes results, we propose a definition of enhancement factors for grounded ice and ice shelves, coherent with the asymptotic models used for these regions. We then estimate realistic values for the enhancement factors induced by ice anisotropy for grounded ice and ice shelves.

scholarly journals Of isbræ and ice streams

2003 ◽  
Vol 36 ◽  
pp. 66-72 ◽  
Author(s):  
Martin Truffer ◽  
Keith A. Echelmeyer
Keyword(s):  
Ice Sheet ◽  
Shear Zones ◽  
West Antarctica ◽  
Ice Streams ◽  
Ice Flow ◽  
Bed Topography ◽  
Ice Stream ◽  
Fast Ice ◽  
Fast Flow ◽  
End Members

AbstractFast-flowing ice streams and outlet glaciers provide the major avenues for ice flow from past and present ice sheets. These ice streams move faster than the surrounding ice sheet by a factor of 100 or more. Several mechanisms for fast ice-stream flow have been identified, leading to a spectrum of different ice-stream types. In this paper we discuss the two end members of this spectrum, which we term the “ice-stream” type (represented by the Siple Coast ice streams in West Antarctica) and the “isbræ” type (represented by Jakobshavn Isbræ in Greenland). The typical ice stream is wide, relatively shallow (∼1000 m), has a low surface slope and driving stress (∼10 kPa), and ice-stream location is not strongly controlled by bed topography. Fast flow is possible because the ice stream has a slippery bed, possibly underlain by weak, actively deforming sediments. The marginal shear zones are narrow and support most of the driving stress, and the ice deforms almost exclusively by transverse shear. The margins seem to be inherently unstable; they migrate, and there are plausible mechanisms for such ice streams to shut down. The isbræ type of ice stream is characterized by very high driving stresses, often exceeding 200 kPa. They flow through deep bedrock channels that are significantly deeper than the surrounding ice, and have steep surface slopes. Ice deformation includes vertical as well as lateral shear, and basal motion need not contribute significantly to the overall motion. The marginal shear zone stend to be wide relative to the isbræ width, and the location of isbræ and its margins is strongly controlled by bedrock topography. They are stable features, and can only shut down if the high ice flux cannot be supplied from the adjacent ice sheet. Isbræs occur in Greenland and East Antarctica, and possibly parts of Pine Island and Thwaites Glaciers, West Antarctica. In this paper, we compare and contrast the two types of ice streams, addressing questions such as ice deformation, basal motion, subglacial hydrology, seasonality of ice flow, and stability of the ice streams.

Mathematical Formulation of the Global Coefficients of Transmission and Reflection of Ultrasonic Waves in Bi-Phase Porous Medium

2015 ◽  
Vol 1101 ◽  
pp. 471-479
Author(s):  
Georges Freiha ◽  
Hiba Othman ◽  
Michel Owayjan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Mathematical Formulation ◽  
Ultrasonic Waves ◽  
Ultrasonic Wave Propagation ◽  
Local Coefficients ◽  
Important Field ◽  
New Formulation ◽  
Transmission And Reflection

The study of signals propagation inside porous media is an important field especially in the biomedical research related to compact bones. The purpose of this paper is to determine a mathematical formulation of the global coefficients of transmission and reflection of nondestructive ultrasonic waves in any bi-phase porous medium. Local coefficients of transmission and reflection on the interface of the porous medium will be determined based on a study of boundary conditions. The behavior of different waves inside the porous medium will be developed so that we can derive a new formulation of global coefficients that takes interior phenomena into consideration. Results are found independently of the geometrical and physical characteristics of the medium. Note that this study is based on normal incident ultrasonic wave propagation.

scholarly journals Comparing a thermo-mechanical Weichselian ice sheet reconstruction to GIA driven reconstructions: aspects of earth response and ice configuration

2013 ◽  
Vol 5 (2) ◽  
pp. 2345-2388 ◽  
Author(s):  
P. Schmidt ◽  
B. Lund ◽  
J-O. Näslund
Keyword(s):  
Sea Level ◽  
Ice Sheet ◽  
Younger Dryas ◽  
Slow Phase ◽  
Glacial Isostatic Adjustment ◽  
Relative Sea Level ◽  
Isostatic Adjustment ◽  
Earth Models ◽  
Uplift Rates ◽  
Best Fit

Abstract. In this study we compare a recent reconstruction of the Weichselian ice-sheet as simulated by the University of Main ice-sheet model (UMISM) to two reconstructions commonly used in glacial isostatic adjustment (GIA) modeling: ICE-5G and ANU (also known as RSES). The UMISM reconstruction is carried out on a regional scale based on thermo-mechanical modelling whereas ANU and ICE-5G are global models based on the sea-level equation. The Weichselian ice-sheet in the three models are compared directly in terms of ice volume, extent and thickness, as well as in terms of predicted glacial isostatic adjustment in Fennoscandia. The three reconstructions display significant differences. UMISM and ANU includes phases of pronounced advance and retreat prior to the last glacial maximum (LGM), whereas the thickness and areal extent of the ICE-5G ice-sheet is more or less constant up until LGM. The final retreat of the ice-sheet initiates at earliest time in ICE-5G and latest in UMISM, while ice free conditions are reached earliest in UMISM and latest in ICE-5G. The post-LGM deglaciation style also differs notably between the ice models. While the UMISM simulation includes two temporary halts in the deglaciation, the later during the Younger Dryas, ANU only includes a decreased deglaciation rate during Younger Dryas and ICE-5G retreats at a relatively constant pace after an initial slow phase. Moreover, ANU and ICE-5G melt relatively uniformly over the entire ice-sheet in contrast to UMISM which melts preferentially from the edges. We find that all three reconstructions fit the present day uplift rates over Fennoscandia and the observed relative sea-level curve along the Ångerman river equally well, albeit with different optimal earth model parameters. Given identical earth models, ICE-5G predicts the fastest present day uplift rates and ANU the slowest, ANU also prefers the thinnest lithosphere. Moreover, only for ANU can a unique best fit model be determined. For UMISM and ICE-5G there is a range of earth models that can reproduce the present day uplift rates equally well. This is understood from the higher present day uplift rates predicted by ICE-5G and UMISM, which results in a bifurcation in the best fit mantle viscosity. Comparison of the uplift histories predicted by the ice-sheets indicate that inclusion of relative sea-level data in the data fit can reduce the observed ambiguity. We study the areal distributions of present day residual surface velocities in Fennoscandia and show that all three reconstructions generally over-predict velocities in southwestern Fennoscandia and that there are large differences in the fit to the observational data in Finland and northernmost Sweden and Norway. These difference may provide input to further enhancements of the ice-sheet reconstructions.

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