scholarly journals A Transient Temperature Solution for Bore-Hole Model Testing

1987 ◽  
Vol 33 (114) ◽  
pp. 140-148 ◽  
Author(s):  
Brian Hanson ◽  
Robert E. Dickinson
Keyword(s):  
Response Time ◽  
Time Scale ◽  
Numerical Models ◽  
Ice Sheet ◽  
Energy Balance Equation ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Small Scale ◽  
Transient Temperature ◽  
Vertical Column

AbstractTransient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hypergeometric function. This solution shows that advection and diffusion have clearly separated areas of dominance, with diffusion being a sufficient approximation for small-scale perturbations in the temperature profile and advection placing an upper limit on the response time of the ice sheet as a whole. This solution is useful for analysis and testing of numerical models, for evaluation of the response time of an ice sheet and for exploratory analysis of real bore-hole data. The lowest eigenvalue of the solution determines the time-scale for transient decay of temperature anomalies. The time-scale can be determined for more general strain-rates using a finite-difference approximation to the linearized energy-balance equation.

scholarly journals A Transient Temperature Solution for Bore-Hole Model Testing

1987 ◽  
Vol 33 (114) ◽  
pp. 140-148 ◽  
Author(s):  
Brian Hanson ◽  
Robert E. Dickinson
Keyword(s):  
Response Time ◽  
Time Scale ◽  
Numerical Models ◽  
Ice Sheet ◽  
Energy Balance Equation ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Small Scale ◽  
Transient Temperature ◽  
Vertical Column

AbstractTransient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hypergeometric function. This solution shows that advection and diffusion have clearly separated areas of dominance, with diffusion being a sufficient approximation for small-scale perturbations in the temperature profile and advection placing an upper limit on the response time of the ice sheet as a whole. This solution is useful for analysis and testing of numerical models, for evaluation of the response time of an ice sheet and for exploratory analysis of real bore-hole data. The lowest eigenvalue of the solution determines the time-scale for transient decay of temperature anomalies. The time-scale can be determined for more general strain-rates using a finite-difference approximation to the linearized energy-balance equation.

scholarly journals Past ice-sheet behaviour: retreat scenarios and changing controls in the Ross Sea, Antarctica

2016 ◽  
Vol 10 (3) ◽  
pp. 1003-1020 ◽  
Author(s):  
Anna Ruth W. Halberstadt ◽  
Lauren M. Simkins ◽  
Sarah L. Greenwood ◽  
John B. Anderson
Keyword(s):  
High Resolution ◽  
Continental Shelf ◽  
Drainage Basin ◽  
Ross Sea ◽  
Numerical Models ◽  
Ice Sheet ◽  
Small Scale ◽  
Antarctic Ice Sheet ◽  
Grounding Line ◽  
Western Ross Sea

Abstract. Studying the history of ice-sheet behaviour in the Ross Sea, Antarctica's largest drainage basin can improve our understanding of patterns and controls on marine-based ice-sheet dynamics and provide constraints for numerical ice-sheet models. Newly collected high-resolution multibeam bathymetry data, combined with two decades of legacy multibeam and seismic data, are used to map glacial landforms and reconstruct palaeo ice-sheet drainage. During the Last Glacial Maximum, grounded ice reached the continental shelf edge in the eastern but not western Ross Sea. Recessional geomorphic features in the western Ross Sea indicate virtually continuous back-stepping of the ice-sheet grounding line. In the eastern Ross Sea, well-preserved linear features and a lack of small-scale recessional landforms signify rapid lift-off of grounded ice from the bed. Physiography exerted a first-order control on regional ice behaviour, while sea floor geology played an important subsidiary role. Previously published deglacial scenarios for Ross Sea are based on low-spatial-resolution marine data or terrestrial observations; however, this study uses high-resolution basin-wide geomorphology to constrain grounding-line retreat on the continental shelf. Our analysis of retreat patterns suggests that (1) retreat from the western Ross Sea was complex due to strong physiographic controls on ice-sheet drainage; (2) retreat was asynchronous across the Ross Sea and between troughs; (3) the eastern Ross Sea largely deglaciated prior to the western Ross Sea following the formation of a large grounding-line embayment over Whales Deep; and (4) our glacial geomorphic reconstruction converges with recent numerical models that call for significant and complex East Antarctic ice sheet and West Antarctic ice sheet contributions to the ice flow in the Ross Sea.

scholarly journals 250 000 years in the history of Greenland’s ice sheet

1996 ◽  
Vol 23 ◽  
pp. 359-363
Author(s):  
Magnus Weis ◽  
K. Hutter ◽  
Reinhard Calov
Keyword(s):  
Video Clip ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Atmospheric Temperature ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Heat Conducting ◽  
The South ◽  
Climate History ◽  
Ice Dynamics

Calculations have been conducted for the geometric evolution of the Greenland ice sheet through the last 250 000 years of its climate history. An extended version of Calov’s three-dimensional ice-sheet model is used, i.e. ice is modelled as a viscous thermomechanically coupled fluid with power-law rheology underlain by a heat-conducting lithosphere susceptible to bedrock sinking. The shallow-ice approximation is imposed and the simplified equations are numerically integrated by finite-difference approximation using a centred staggered Arakawa grid. This system is driven by data obtained from the European Greenland Ice Core Project (GRIP). The parameterization of the atmospheric temperature is based on data from Ohmura, precipitation data are taken from Ohmura and Reeh and implemented as shown by Calov. Topographic data for the present observed conditions are those of Letréguilly. The resultant 250 kyear model integrated topography is quite close to that obtained from a steady-state calculation under present conditions. For the calculations presented, Greenland’s north dome seems to be more sensitive to changes in precipitation than its south dome. While the height of the north dome is directly related to the atmospheric temperature, the height of the south dome is inversely related to this variable. In the south, changes in ice dynamics due to a change in ice temperature oppose changes in precipitation. The calculations are visualized in a short video clip that is kept on file with the authors.

scholarly journals 250 000 years in the history of Greenland’s ice sheet

1996 ◽  
Vol 23 ◽  
pp. 359-363 ◽  
Author(s):  
Magnus Weis ◽  
K. Hutter ◽  
Reinhard Calov
Keyword(s):  
Video Clip ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Atmospheric Temperature ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Heat Conducting ◽  
The South ◽  
Climate History ◽  
Ice Dynamics

Calculations have been conducted for the geometric evolution of the Greenland ice sheet through the last 250 000 years of its climate history. An extended version of Calov’s three-dimensional ice-sheet model is used, i.e. ice is modelled as a viscous thermomechanically coupled fluid with power-law rheology underlain by a heat-conducting lithosphere susceptible to bedrock sinking. The shallow-ice approximation is imposed and the simplified equations are numerically integrated by finite-difference approximation using a centred staggered Arakawa grid. This system is driven by data obtained from the European Greenland Ice Core Project (GRIP). The parameterization of the atmospheric temperature is based on data from Ohmura, precipitation data are taken from Ohmura and Reeh and implemented as shown by Calov. Topographic data for the present observed conditions are those of Letréguilly. The resultant 250 kyear model integrated topography is quite close to that obtained from a steady-state calculation under present conditions. For the calculations presented, Greenland’s north dome seems to be more sensitive to changes in precipitation than its south dome. While the height of the north dome is directly related to the atmospheric temperature, the height of the south dome is inversely related to this variable. In the south, changes in ice dynamics due to a change in ice temperature oppose changes in precipitation. The calculations are visualized in a short video clip that is kept on file with the authors.

scholarly journals The Effectiveness of Ensemble-Neural Network Techniques to Predict Peak Uplift Resistance of Buried Pipes in Reinforced Sand

2021 ◽  
Vol 11 (3) ◽  
pp. 908
Author(s):  
Jie Zeng ◽  
Panagiotis G. Asteris ◽  
Anna P. Mamou ◽  
Ahmed Salih Mohammed ◽  
Emmanuil A. Golias ◽  
...  
Keyword(s):  
Neural Network ◽  
Numerical Models ◽  
Correlation Coefficients ◽  
Network Models ◽  
Small Scale ◽  
Offshore Platforms ◽  
Neural Network Models ◽  
Buried Pipes ◽  
Ensemble Techniques ◽  
Uplift Resistance

Buried pipes are extensively used for oil transportation from offshore platforms. Under unfavorable loading combinations, the pipe’s uplift resistance may be exceeded, which may result in excessive deformations and significant disruptions. This paper presents findings from a series of small-scale tests performed on pipes buried in geogrid-reinforced sands, with the measured peak uplift resistance being used to calibrate advanced numerical models employing neural networks. Multilayer perceptron (MLP) and Radial Basis Function (RBF) primary structure types have been used to train two neural network models, which were then further developed using bagging and boosting ensemble techniques. Correlation coefficients in excess of 0.954 between the measured and predicted peak uplift resistance have been achieved. The results show that the design of pipelines can be significantly improved using the proposed novel, reliable and robust soft computing models.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

scholarly journals A new bedrock and surface elevation dataset for modelling the Greenland ice sheet

2003 ◽  
Vol 37 ◽  
pp. 351-356 ◽  
Author(s):  
Jonathan L. Bamber ◽  
Duncan J. Baldwin ◽  
S. Prasad Gogineni
Keyword(s):  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Detailed Comparison ◽  
Radar Data ◽  
The Arctic ◽  
Small Scale ◽  
Surface Model ◽  
Rock Outcrops ◽  
Bed Topography ◽  
Elevation Model

AbstractA new digital elevation model of the surface of the Greenland ice sheet and surrounding rock outcrops has been produced from a comprehensive suite of satellite and airborne remote-sensing and cartographic datasets. The surface model has been regridded to a resolution of 5 km, and combined with a new ice-thickness grid derived from ice-penetrating radar data collected in the 1970s and 1990s. A further dataset, the International Bathymetric Chart of the Arctic Ocean, was used to extend the bed elevations to include the continental shelf. The new bed topography was compared with a previous version used for ice-sheet modelling. Near the margins of the ice sheet and, in particular, in the vicinity of small-scale features associated with outlet glaciers and rapid ice motion, significant differences were noted. This was highlighted by a detailed comparison of the bed topography around the northeast Greenland ice stream.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

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