Eleonora Rivalta's home page

My interests

• Crustal deformation : Dislocation theory is one of my main interests. Maurizio Bonafede and I derived analytical formulas for the displacement and stress field generated by 2D tensile, dip-slip and screw Volterra dislocations in elastic and viscoelastic layered media (see Publications ). We then integrated the elementary dislocation kernels to obtain more realistic crack models, with prescribed stress on crack plane rather than constant displacement. We obtained that layer discontinuities act as stress concentrators and modify the directions of principal stresses, potentially changing the trajectories of propagating cracks. This phenomenon is particularly enhanced in the case of dikes (tensile cracks).
  
  More recently, Paul Segall and I looked into the problem of volume budget during magma transfer from chambers to dikes. Inversion of geodetic data show that often dikes result to be up to 4 or 5 larger in volume than volume loss at magma chambers. Applying mass conservation and taking into account magma compressibility and shape effects (dikes result to have a much more compressible shape than ellipsoidal chambers) we demonstrate that volume gains up to one order of magnitude may be explained without appealing to additional non-detected magma sources.
  
  
• Volcanology : I am interested in all aspects related to the physics of volcanic processes, focusing in particular to what happens inside the volcanic edifice. This includes the modelling of dikes and other magma-filled sources (magma chambers, sills) and the study of other geophysical phenomena related to magma propagation: magma-induced seismicity and deformation, magma transport, magma chambers - dikes interaction. I use a broad range of modelling techniques: analytic, numerical (boundary elements mainly) and also analogue experiments at this aim.
  
  
• Laboratory Experiments : Torsten Dahm and I, with the very professional technical help of Michael Boettinger, started to do analogue modelling a few years ago (see Rivalta et al., 2005, and Rivalta and Dahm, 2006). In our first series of experiments we concentrated on two questions: How do layering interfaces affect dike propagation? And how does the free surface influence the velocity of propagating dikes? We looked for an answer to these questions employing the same kind of analogue modelling already D. Pollard, A. Takada, Ito and Martel, Menand and Tait and others had already used to investigate other dike-related issues. We injected fluids in homogeneous and layered gelatin stiffened at fridge temperature in a perspex container. We then recorded the experiments with videocameras. In homogeneous gelatin a fluid-filled fracture propagates with constant velocity. We changed the concentration of gelatin powder in water to obtain a less stiff gelatin on top of a stiffer one, and then we tried with the opposite situation, with a stiffer layer lying on a more compliant one. When fluid-filled fractures, driven by buoyancy, come closer to the interface with a less stiff medium, they accelerate. Ones entirely contained in the upper layer, they reach a new constant velocity motion, until they come close to the free surface, when they start to accelerate until "eruption". When the propagating cracks approach the interface with a stiffer medium, they decelerate and depending on a series of factors, sometimes they stop. Injecting further fluid leads sometimes to the creation of a sill. For further infos on the experiments, you can visit this page.
  
  
• Dike induced seismicity and Fracture Mechanics : I started my work on fracture mechanics and seismology modelling disclocation sources and looking into dike-related processes.

  Propagation of fluid-filled cracks: A possible way to model the propagation of magma-filled dikes in the solid brittle crust is to use the Weertman model. When a fluid (magma or other) is injected in a brittle solid (e.g. rock), a penny-shaped crack forms. If the crack is long enough so that the stress intensity factor at its upper tip overcomes the fracture toughness of the solid, it will start to propagate to the surface (if the rock is denser than the fluid, so that it will be buoyant) or downwards (if the fluid is denser than the rock). The Weertman model agrees well with experimental results obtained injecting fluids in gelatine. Torsten Dahm and I observed during gelatine experiments that fractures accelerate in proximity of the free surface (see Rivalta and Dahm, 2006 ), as predicted by Pollard and Holzhausen. We modelled our observations using Weertman theory and Pollard considerations.

  Relationship between dike-induced deformation and seismicity: Torsten and I looked at what happens if a dike is injected in a fractured material (see Rivalta and Dahm (2004) ). Using a boundary element approach and applying Effective Media theories, we reached the conclusion that a dike which is not propagating produces seismicity and deformation related by a very simple relationship: The logarithm of deformation is directly proportional to the cumulative number of earthquakes induced. We tested successfully this hipothesis with data from the 2000 dike injection at Izu Islands. My current interest is to compare our results to what other authors find for deformation and seismicity caused by large earthquakes.