Beschreibung: A key to understand many geodynamic processes is studying the associated large deformation fields. Finite deformation can be measured in the field by using geological strain markers giving the logarithmic strain f = log 10 ( R ), where R is the ellipticity of the strain ellipse. It has been challenging to accurately quantify finite deformation of geodynamic models for inhomogeneous and time-dependent large deformation cases. We present a new formulation invoking a 2-D marker-in-cell approach. Mathematically, one can describe finite deformation by a coordinate transformation to a Lagrangian reference frame. For a known velocity field the deformation gradient tensor, F , can be calculated by integrating the differential equation D t F ij = L ik F kj , where L is the velocity gradient tensor and D t the Lagrangian derivative. The tensor F contains all information about the minor and major semi-half axes and orientation of the strain ellipse and the rotation. To integrate the equation centrally in time and space along a particle's path, we use the numerical 2-D finite difference code FDCON in combination with a marker-in-cell approach. For a sufficiently high marker density we can accurately calculate F for any 2-D inhomogeneous and time-dependent creeping flow at any point for a deformation f up to 4. Comparison between the analytical and numerical solution for the finite deformation within a Poiseuille–Couette flow shows an error of less than 2 per cent for a deformation up to f  = 1.7. Moreover, we determine the finite deformation and strain partitioning within Rayleigh–Taylor instabilities (RTIs) of different viscosity and layer thickness ratios. These models provide a finite strain complement to the RTI benchmark of van Keken et al. Large finite deformation of up to f  = 4 accumulates in RTIs within the stem and near the compositional boundaries. Distinction between different stages of diapirism shows a strong correlation between a maximum occurring deformation of f  = 1, 3 and 4, and the early, intermediate and late stages of diapirism, respectively. Furthermore, we find that the overall strain of a RTI is concentrated in the less viscous regions. Thus, spatial distributions and magnitudes of finite deformation may be used to identify stages and viscosity ratios of natural cases.

Beschreibung: SUMMARY Formation of salt diapirs has been described to be due to upbuilding (i.e. Rayleigh–Taylor like instability of salt diapirs piercing through a denser sedimentary overburden) or syndepositional down-building process (i.e. the top of the salt diapir remains at the surface all the time). Here we systematically analyse this second end-member mechanism by numerical modelling. Four parameters are varied: sedimentation rate  v sed , salt viscosity η salt , amplitude δ of the initial perturbation of the sedimentation layer and the wavenumber  k  of this perturbation. The shape of the resulting salt diapirs strongly depends on these parameters. Small diapirs with subvertical side walls are found for small values of  v sed and η salt or large values of δ, whereas taller diapirs with pronounced narrow stems build for larges values of  v sed and η salt or small values of δ. Two domains are identified in the four-parameter space, which separates successful down-building models from non-successful models. By applying a simple channel flow law, the domain boundary can be described by the non-dimensional law , where is the sediment density scaled by the density contrast Δρ between sediment and salt, the wavelength is scaled by the salt layer thickness  h salt , and velocity is scaled by η salt /( Δ ρg ), where η salt is the salt viscosity and  g  is the gravitational acceleration. From the numerical models, the constants  C 1 and  C 2 are determined as 0.0283 and 0.1171, respectively.

Beschreibung: In geodynamic models of mid-ocean ridges hydrothermal cooling processes are important to control the temperature and thus the rheological behaviour of the crust. However, the characteristic time scale of hydrothermal convection is considerably shorter than that of viscous flow of mantle material or cooling of the oceanic lithosphere and can hardly be addressed in a conjoined model. To overcome this problem we present an approach to mimic hydrothermal cooling by an equivalent, increased thermal conductivity. First the temperature and pressure dependence of crack related porosity and permeability are derived based on composite theory. A characteristic pore closure depth as a function of pressure, temperature and pore aspect ratio is defined. 2-D porous convection models are used to derive scaling laws for parameterized convection including a Rayleigh–Nusselt number relation for a permeability exponentially decreasing with depth. These relations are used to derive an equivalent thermal conductivity to account for consistently evolving hydrothermal heat transport in thermally evolving systems. We test our approach using a 1-D model for cooling of the oceanic lithosphere. Within the context of our modelling parameters we found a pronounced effect for young lithosphere (younger than 10 Ma) down to about 20 km. Significant deviations of the heat flux versus age from the 1/ $\sqrt t $ law may occur due to hydrothermal convection. For the bathymetry versus age curves slopes steeper than 1/ $\sqrt t $ slopes already occur for very young lithosphere. Hydrothermal convection leads to an increase of the total heat flux and heat loss with respect to the classical purely conductive cooling model. Comparison of the total heat flow and its conductive contribution with observations confirm previous suggestions that for young lithosphere heat flow measurements represent only the conductive part, while at older ages the total heat flow is observed. Within their scatter and uncertainties heat flow and bathymetry data are in general agreement with our hydrothermally enforced cooling model suggesting that hydrothermal convection may be important even up to high ages.