The understanding of magma ascent dynamics is essential in forecasting the scale, style and timing of volcanic eruptions. The monitoring of near-field deformation is widely used to gain insight into these dynamics, and has been linked to stress changes in the upper conduit. The ascent of magma through the conduit exerts shear stress on the conduit wall, pulling up the surrounding edifice, whilst overpressure in the upper conduit pushes the surrounding edifice outwards. How much shear stress and pressure is produced during magma ascent, and the relative contribution of each to the deformation, has until now only been explored conceptually. By combining flow and deformation modeling using COMSOL Multiphysics, we for the first time present a quantitative model that links magma ascent to deformation. We quantify how both shear stress and pressure vary spatially within a cylindrical conduit, and show that shear stress generally dominates observed changes in tilt close to the conduit. However, the relative contribution of pressure is not insignificant, and both pressure and shear stress must be considered when interpreting deformation data. We demonstrate that significant changes in tilt can be driven by changes in the driving pressure gradient or volatile content of the magma. The relative contribution of shear stress and pressure to the tilt varies considerably depending on these parameters. Our work provides insight into the range of elastic moduli that should be considered when modeling edifice-scale rock masses, and we show that even where the edifice is modeled as weak, shear stress generally dominates the near field deformation over pressurization of the conduit. While our model addresses cyclic tilt changes observed during activity at Tungurahua volcano, Ecuador, between 2013 and 2014, it is also applicable to silicic volcanoes in general.

For optimal monitoring of the deformation of a volcano, instrumentation should be deployed at the location most sensitive to changes at the suspected deformation source. The topographic effect on tilt depends strongly on the orientation of the deformation field relative to the surface on which the instrument is deployed. This fact has long been understood and corrected for in tilt measurements related to body tides and referred to as "cavity" or "topographic effects" (Harrison, 1976). Despite this, and whilst topography at volcanoes is often significant, until now the topographic effect on tilt at volcanoes has not been systematically explored. Here, we investigate the topographic effect on tilt produced by either the pressurization of a reservoir or conduit, or shear stress as magma ascends through a conduit, using 2D axisymmetric and 3D finite element deformation modeling. We show that topography alone can amplify or reduce the tilt by more than an order of magnitude, and control the orientation of the maximum tilt. Therefore, a decrease in tilt can even be caused by an increase in deformation at the source. Hence, inverting for the source stress using simple analytical models that neglect topography could potentially lead to a misinterpretation of how the volcanic system is evolving. Since topographic features can amplify the tilt signal, they can be exploited when deciding upon an installation site.

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the h s Alamos National Laboratory &ANI,). The ocean is a very complex nonlinear system that exhibits turbulence on essentially all scales, multiple equilibria, and significant intrinsic variability. Modeling the Ocean's dynamics at mesoscales is of fundamental importance for long-time-scale climate predictions. A major goal of this project has been to coordinate, strengthen, and focus the efforts of applied mathematicians, computer scientists, computational physicists and engineers (at LANL and a consortium of Universities) in a joint effort addressing the issues in mesoscale Ocean dynamics. The project combines expertise in the core competencies of high performance computing and theory of complex systems in a new way that has great potential for improving ocean models now running on the Connection Machines CM-200 and CM-5 and on the Cray T3D.

<p>By modelling the magnitude and spatial distribution of surface displacement induced by different representations of magma conduits, more informed decisions can be made for the deployment of real-time monitoring devices, such as tiltmeters, and aid interpretations of stress changes within the subsurface. The existence of varying forms of magma conduit is widely known, despite this, the effect of laterally elongated conduits on magma flow processes and resulting surface deformation at volcanoes has not been systematically explored.</p><p>By varying the ellipticity of the volcanic conduit cross-section we assess the relative importance of laterally elongated conduits when considering flow processes and surface deformation. The scenario of magma ascent through a dyke that changes into a cylindrical conduit closer to the surface is also considered, herein referred to as a complex conduit. Both shear stress on the conduit walls due to viscous magma flow resistance and the pressurisation of conduits are used as source mechanisms.</p><p>When considering the pressurisation of different conduit geometries, the displacement field induced by an elongated conduit (where semi-axes a and b of the elliptical cross-section equal a=10b) is an order of magnitude larger than that of a cylindrical conduit. Moreover, for the case of the complex conduit, the displacement field is dominated by the dyke form of the deeper conduit, with little influence from the transition region between elongated and cylindrical conduit. When considering shear stress as a source mechanism, the displacement field induced is primarily vertical and radially symmetric even at the smallest spatial scales ($<1$ km), independent of ellipticity of conduit origin. The ellipticity of conduits with equal cross-sectional area has a significant control on the flow rate, and therefore, the magnitude of shear stress achieved under equal pressure gradients. The deformation resulting from shear stress on the conduit walls is also influenced by the depth of rheological changes within the magma and the inter-dependency with conduit geometry.</p>

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