2D Shape Optimization Based on a NURBS Surface Velocity Field

Author(s):  
Luiz Oliveira ◽  
Pablo Andrés Muñoz Rojas
2019 ◽  
Vol 220 (3) ◽  
pp. 1700-1716
Author(s):  
Sean M Langemeyer ◽  
Julian P Lowman ◽  
Paul J Tackley

SUMMARY Previous geodynamic studies have indicated that the presence of a compositionally anomalous and intrinsically dense (CAID) mantle component can impact both core heat flux and surface features, such as plate velocity, number and size. Implementing spherical annulus geometry mantle convection models, we investigate the influence of intrinsically dense material in the lower mantle on core heat flux and the surface velocity field. The dense component is introduced into a system that features an established plate-like surface velocity field, and subsequently we analyse the evolution of the surface velocity as well as the interior thermal structure of the mantle. The distribution and mobility of the CAID material is investigated by varying its buoyancy ratio relative to the ambient mantle (ranging from 0.7 to 1.5), its total volume (3.5–10 per cent of the mantle volume) and its intrinsic viscosity (0.01–100 times the ambient mantle viscosity). We find at least three distinct distributions of the dense material can occur adjacent to the core–mantle boundary (CMB), including multiple piles of varying topography, a core enveloping layer and two diametrically opposed provinces (which can on occasion break into three distinct piles). The latter distribution mimics the morphology of the seismically observed large low shear wave velocity provinces (LLSVPs) and can occur over the entire range of CAID material viscosities. However, diametrically opposed provinces occur primarily in cases with CAID material buoyancy numbers of 0.7–0.85 (corresponding to contrasts in density between ambient and CAID material of 130 and 160 kg m−3, respectively) in our model (with an effective Rayleigh number of order 106). Steep and high topography piles are also obtained for cases featuring buoyancy ratios of 0.85 and viscosities 10–100 times that of the ambient mantle. An increase in relative density, as well as larger volumes of CAID material, lead to the development of a core enveloping layer. Our findings show that when two provinces are present core heat flux can be reduced by up to 50 per cent relative to cases in which CAID material is absent. Surface deformation quantified by Plateness is minimally influenced by variation of the properties of the dense material. Surface velocity is found to be reduced in general but mostly substantially in cases featuring high CAID material viscosities and large volumes (i.e. 10 per cent) or buoyancy ratios.


2014 ◽  
Vol 60 (222) ◽  
pp. 735-742 ◽  
Author(s):  
Yuande Yang ◽  
Bo Sun ◽  
Zemin Wang ◽  
Minghu Ding ◽  
Cheinway Hwang ◽  
...  

AbstractKnowledge of the surface topography, velocity field and strain field at an ice-core site is critical to the accurate interpretation of ice-core records. At Dome Argus (Dome A), where a Chinese deep ice-core drilling project is being carried out, we have produced an accurate surface digital elevation model from GPS measurements in January 2013 at 47 sites. We identify two peaks at Dome A, with the northern peak ~7 cm higher than the southern peak. Repeat GPS measurements at 12 sites in 2008 and 2013 provide a surface velocity field around the dome. The surface velocity ranges from 3.1±2.6 to 29.4±1.2 cm a–1, with a mean of 11.1 ~2.4 cm a–1. The surface flow directions are near perpendicular to the surface elevation contours. Velocities from GPS are lower than derived from satellite radar interferometry (InSAR). From GPS velocities, the accuracy of velocity from the existing InSAR velocity field is determined, resulting in a standard deviation of 0.570 m a–1 in speed and 117.5º in direction. This result is consistent with the reported accuracy of InSAR, showing the value of in situ GPS measurements for assessing and correcting remote-sensing results. A surface strain field for the drilling site over Dome A is calculated from 24 strain triangles, showing north–south extension, east– west compression and vertical layer thinning.


1996 ◽  
Vol 23 ◽  
pp. 364-373 ◽  
Author(s):  
Jonathan L. Bamber ◽  
Philippe Huybrechts

This paper presents improved geometric boundary conditions (surface elevation and ice thickness) required as inputs to calculations of the surface-velocity field for the Antarctic ice sheet. A comparison of the two-dimensional horizontal velocity field obtained on the basis of conservation of mass (balance velocity) with the diagnostic velocity field calculated with an ice-sheet model (dynamic velocity) may yield information on shortcomings in the way the ice-sheet model describes the ice flow. Here, the surface-elevation grid is described in detail, as it has been generated specifically for such a study and represents a new standard in accuracy and resolution for calculating surface slopes. The digital-elevation model was generated on a 10 km grid size from over 20 000 000 height estimates obtained from eight 35 d repeat cycles of ERS-1 radar-altimeter data. For surface slopes less than 0.4°, the accuracy is better than 1.5 m. In areas of high surface slope (coastal and mountainous regions), the altimeter measurements have been supplemented with data taken from the Antarctic Digital Database. South of 81.5°, data from the SPRI folio map have been used. The ice-thickness grid was produced from a combination of a redigitization of the SPRI folio and the original radio-echo-sounding flight lines. For areas of grounded ice, the elevation of the bed was estimated from surface elevation and ice thickness. Significant differences (in excess of 25% of ice thickness) were obtained between an earlier digitization of the folio bed-elevation map and the data set derived here. Furthermore, a new value of 25.6 × 106 km3 was obtained for the total volume of the ice sheet and ice shelves, which is a reduction of 12% compared with the original estimate derived during the compilation of the SPRI folio. These differences will have an important influence on the results obtained by numerical ice-sheet models.


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