• Exact and numerical solutions for stokes flow in glaciers

      Mitchell, William H. (2012-08)
      We begin with an overview of the fluid mechanics governing ice flow. We review a 1985 result due to Balise and Raymond giving exact solutions for a glaciologically-relevant Stokes problem. We extend this result by giving exact formulas for the pressure and for the basal stress. This leads to a theorem giving a necessary condition on the basal velocity of a gravity-induced flow in a rectangular geometry. We describe the finite element method for solving the same problem numerically. We present a concise implementation using FEniCS, a freely-available software package, and discuss the convergence of the numerical method to the exact solution. We describe how to fix an error in a recent published model.
    • Strategies for applying active seismic subglacial till characterization methods to valley glaciers

      Zechman, Jenna M.; Truffer, Martin; Larsen, Christopher F.; Coakley, Bernard J.; Amundson, Jason M. (2017-05)
      Subglacial materials play an important role in glacier dynamics. High pore-pressure, high porosity (dilatant) tills can contribute to high basal motion rates by deforming. Amplitude Variation with Angle (AVA) analysis of seismic reflection data uses the relationship between basal reflectivity and reflection incidence angle to characterize the subglacial material. This technique can distinguish between dilatant tills and less-porous, non-deforming (dewatered) tills due to their distinctive reflectivity curves. However, noise from crevasses and glacier geometry effects can complicate reflectivity calculations, which require a source amplitude derived from the bed reflection multiple. We use a forward model to produce synthetic seismic records, including datasets with and without visible bed reflection multiples. The synthetic data are used to test source amplitude inversion and crossing angle analysis, which are amplitude analysis techniques that do not require absolute reflectivity calculations. We and that these alternative methods can distinguish subglacial till types, as long as reflections from crevasses do not obscure the bed reflection. The forward model can be used as a planning tool for seismic surveys on glaciers, as it can predict AVA success or failure based on crevasse geometries from remote sensing data and glacier bed geometry from radar or from a worst-case-scenario assumption of glacier bed shape. Applying lessons from the forward model, we perform AVA on a seismic dataset collected from Taku Glacier in Southeast Alaska in March 2016. Taku Glacier is a valley glacier thought to overlay thick sediment deposits. It has been the subject of numerous studies focusing on its ice-sediment interactions. Our analysis indicates that Taku Glacier overlies unconsolidated tills with porosity values greater than 33 %, though because of uncertainties due to the lack of a bed reflection multiple, it is possible that the tills are not dilatant.