Past Mathematical Geoscience Seminar

20 June 2014
14:15
Tarje Nissen-Meyer
Abstract
Seismology currently undergoes rapid and exciting advances fueled by a simultaneous surge in recorded data (in both quality and quantity), realistic wave-propagation algorithms, and supercomputing capabilities. This enables us to sample parameter spaces of relevance for imaging the Earth's interior 3D structure with fully numerical techniques. Seismic imaging is the prime approach to illuminate and understand global processes such as mantle convection, plate tectonics, geodynamo, the vigorous interior of the Sun, and delivers crucial constraints on our grasp of volcanism, the carbon cycle and seismicity. At local scales, seismic Earth models are inevitable for hydrocarbon exploration, monitoring of flow processes, and natural hazard assessment. \\ \\ With a slight focus on global-scale applications, I will present the underlying physical model of realistic wave propagation, its numerical discretization and link such forward modeling to updating Earth models by means of inverse modeling. The associated computational burden to solve high-resolution statistical inverse problems with precise numerical techniques is however entirely out of reach for decades to come. Consequently, seismologists need to take approximations in resolution, physics, data and/or inverse methodology. I will scan a number of such end-member approximations, and focus on our own approach to simultaneously treat wave physics realistically across the frequency band while maximizing data usage and allow for uncertainty quantification. This approach is motivated by decisive approximations on the model space for typical Earth structures and linearized inverse theory.
  • Mathematical Geoscience Seminar
6 June 2014
14:15
Teresa Kyrke-Smith
Abstract
Ice sheets are among the key controls on global climate and sea-level change. A detailed understanding of ice sheet dynamics is crucial so to make accurate predictions of their mass balance into the future. Ice streams are the dominant negative component in this balance, accounting for up to 90$\%$ of the Antarctic ice flux into ice shelves and ultimately into the sea. Despite their importance, our understanding of ice-stream dynamics is far from complete. A range of observations associate ice streams with meltwater. Meltwater lubricates the ice at its bed, allowing it to slide with less internal deformation. It is believed that ice streams may appear due to a localization feedback between ice flow, basal melting and water pressure in the underlying sediments. I will present a model of subglacial water flow below ice sheets, and particularly below ice streams. This hydrologic model is coupled to a model for ice flow. I show that under some conditions this coupled system gives rise to ice streams by instability of the internal dynamics.
  • Mathematical Geoscience Seminar
16 May 2014
14:15
Roger Cropp
Abstract
The classical separate treatments of competition and predation, and an inability to provide a sensible theoretical basis for mutualism, attests to the inability of traditional models to provide a synthesising framework to study trophic interactions, a fundamental component of ecology. Recent approaches to food web modelling have focused on consumer-resource interactions. We develop this approach to explicitly represent finite resources for each population and construct a rigorous unifying theoretical framework with Lotka-Volterra Conservative Normal (LVCN) systems. We show that mixotrophy, a ubiquitous trophic interaction in marine plankton, provides the key to developing a synthesis of the various ways of making a living. The LVCN framework also facilitates an explicit redefinition of facultative mutualism, illuminating the over-simplification of the traditional definition. We demonstrate a continuum between trophic interactions and show that populations can continuously and smoothly evolve through most population interactions without losing stable coexistence. This provides a theoretical basis consistent with the evolution of trophic interactions from autotrophy through mixotrophy/mutualism to heterotrophy.
  • Mathematical Geoscience Seminar
9 May 2014
14:15
Andrew Nicholas
Abstract
Numerical models provide valuable tools for integrating understanding of riverine processes and morphology. Moreover, they have considerable potential for use in investigating river responses to environmental change and catchment management, and for aiding the interpretation of alluvial deposits and landforms. For this potential to be realised fully, such models must be capable of representing diverse river styles, and the spatial and temporal transitions between styles that can be driven by environmental forcing. However, while numerical modelling of rivers has advanced significantly over the past few decades, this has been accomplished largely by developing separate approaches to modelling different styles of river (e.g., meanders and braided networks). In addition, there has been considerable debate about what should constitute the ‘basic ingredients’ of river models, and the degree to which the environmental processes governing river evolution can be simplified in such models. This seminar aims to examine these unresolved issues, with particular reference to the simulation of large rivers and their floodplains.
  • Mathematical Geoscience Seminar
14 March 2014
14:15
Heather Viles
Abstract
Microbial biofilms grow on most rock and stone surfaces and may play critical roles in weathering. With climate change and improving air quality in many cities in Europe biofilms are growing rapidly on many historic stone buildings and posing practical problems for heritage conservation. With many new field and lab techniques available it is now possible to identify the microbes present and start to clarify their roles. We now need help modelling microbial biofilm growth and impacts in order to provide better advice for conservators.
  • Mathematical Geoscience Seminar
14 February 2014
14:15
Abstract
Hazardous geophysical mass flows, such as snow avalanches, debris-flows and pyroclastic flows, often spontaneously develop large particle rich levees that channelize the flow and enhance their run-out. Measurements of the surface velocity near an advancing flow front have been made at the United States Geological Survey (USGS) debris-flow flume, where 10m^3 of water saturated sand and gravel are allowed to flow down an 80m chute onto a run-out pad. In the run-out phase the flow front is approximately invariant in shape and advances at almost constant speed. By tracking the motion of surface tracers and using a simple kinematic model, it was possible to infer bulk motion as incoming material is sheared towards the front, over-run and shouldered to the side. At the heart of the levee formation process is a subtle segregation-mobility feedback effect. Simple models for particle segregation and the depth-averaged motion of granular avalanches are described and one of the first attempts is made to couple these two types of models together. This process proves to be non-trivial, yielding considerable complexity as well as pathologies that require additional physics to be included.
  • Mathematical Geoscience Seminar
31 January 2014
14:15
Mauro Werder
Abstract
Jakobshavn Isbrae and many other fast flowing outlet glaciers of present and past ice sheets lie in deep troughs which often have several overdeepened sections. To make their fast flow possible their bed needs to be slippery which in turn means high basal water pressures. I will present a model of subglacial water flow and its application to Jakobshavn. I find that, somewhat surprisingly, the reason for Jakobshavn's fast flow might be the pressure dependence of the melting point of ice. The model itself describes the unusual fluid dynamics occurring underneath the ice; it has an interesting mathematical structure that presents computational challenges.
  • Mathematical Geoscience Seminar
6 December 2013
14:15
Daniel Goldberg
Abstract
Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream. Distinct from stick-slip on northern hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be be controlled by fast processes at the bed and by tidally-induced stress. Modelling approaches to studying this phenomenon typically consider ice to be an elastically-deforming solid (e.g. Winberry et al, 2008; Sergienko et al, 2009). However, there remains a question of whether irreversible, i.e. viscous, deformation is important to the stick-slip process; and furthermore whether the details of stick-slip oscillations are important to ice stream evolution on longer time scales (years to decades). To address this question I use two viscoelastic models of varying complexity. The first is a modification to the simple block-and-slider models traditionally used to examine earthquake processes on a very simplistic fashion. Results show that the role of viscosity in stick-slip depends on the dominant stress balance. These results are then considered in the context of a continuum description of a viscoelastic ice stream with a rate-weakening base capable of exhibiting stick-slip behavior. With the continuum model we examine the spatial and temporal aspects of stick-slip, their dependence on viscous effects, and how this behavior impacts the mean flow. Different models for the evolution of basal shear stress are examined in the experiments, with qualitatively similar results. A surprising outcome is that tidal effects, while greatly affecting the spectrum of the stick-slip cycle, may have relatively little effect on the mean flow.
  • Mathematical Geoscience Seminar

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