The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Proceedings of Computational Methods for Coupled Problems in Science and Engineering

Computational Methods for Coupled Problems in Science and Engineering

Study of the physical properties of metals and oxides at extreme pressure and temperature conditions

The high-pressure and temperature investigations on transition metals, metal doped-oxide system, nanocrystalline materials are presented in this dissertation. The metal-doped oxide systems are technologically important because of their applications, e.g. LSC, opto electronic applications, luminescence from lasers, etc., and from the earth sciences point of view, e.g. the study of trace elements in the MgO-SiO2 system, which accounts for 50% of the Earth's chondritic model. We have carried out thorough investigations on Cr2O3 and on chromium bearing oxides at high PT-conditions using in situ X-ray diffractometry and florescence spectroscopy techniques. Having obtained exciting results, an attempt to focus on the mechanism of the coordination of transition metals in oxides has been made. Additionally, the florescence from the metals in host oxides was found to be helpful to obtain information on structural variations like changes in the coordination of the doped element, formation of new phases, the diffusion processes. The possible reactions taking place at extreme conditions in the MgO-SiO2 system has been observed using florescence as markers. A new heating assemblage has been designed and fabricated for a precise determination of temperature at high pressures. An equation combining pressure shifts of ruby wavelength and temperature has been proposed. We observed that the compressibility of nanocrystalline material (MgO and Ni) is independent of crystallite size. A reduction in the transition pressure of nanocrystalline ceria at high-pressure has been observed as compare to the corresponding bulk material. ^

The study of silicates and refractory materials at high pressures and temperatures

To better understand high pressure behavior of solids, both silicates and oxides have been investigated to clarify the high pressure melting, phase transformations and thermal parameters as well as their size dependences, both theoretically and experimentally. ^ To judge the precision of data determined experimentally, the reliabilities of different high pressure techniques have been discussed. A thermodynamic model has been developed and demonstrated to be able to closely reproduce the melting of solids by comparison between results calculated and data obtained experimentally, including metals (Al, Ni and Pt), Silicates (Mg3Al 2Si3O12 and CaMgSi2O6), Halides (NaCl, CsCl and LiF) and Oxides (MgO, FeO and Al2O3). The melting data obtained have been discussed to address the dynamics of the Earth's interior. ^ Results obtained with Raman spectroscopy and x-ray diffraction show that solids including silicates (andradite and pyrope) and oxides (CeO2 and TiO2) undergo a series of pressure-induced phase transformations. The effects of particle size under high pressures have been investigated. The results obtained indicate that the reduction of particle size leads to the enhancement of the bulk modulus and a significant decrease of transition pressure in TiO2 (rutile) and CeO2. The pressure-induced amorphization in anatase also results from the size effects. ^ Combining the data obtained with global seismic tomography, the physics and chemistry of the Earth's mantle and the dynamics of the core-mantle interaction have been discussed. The high pressure phases of Al3+- and Fe3+-bearing minerals play important roles in the dynamics of the lower mantle. ^

Hydrological dynamics between a coastal aquifer and the adjacent estuarine system, Biscayne Bay, South Florida

Geochemical and geophysical approaches have been used to investigate the freshwater and saltwater dynamics in the coastal Biscayne Aquifer and Biscayne Bay. Stable isotopes of oxygen and hydrogen, and concentrations of Sr2+ and Ca2+ were combined in two geochemical mixing models to provide estimates of the various freshwater inputs (precipitation, canal water, and groundwater) to Biscayne Bay and the coastal canal system in South Florida. Shallow geophysical electromagnetic and direct current resistivity surveys were used to image the geometry and stratification of the saltwater mixing zone in the near coastal (less than 1km inland) Biscayne Aquifer. The combined stable isotope and trace metal models suggest a ratio of canal input-precipitation-groundwater of 38%–52%–10% in the wet season and 37%–58%–5% in the dry season with an error of 25%, where most (20%) of the error was attributed to the isotope regression model, while the remaining 5% error was attributed to the Sr2+/Ca2+ mixing model. These models suggest rainfall is the dominate source of freshwater to Biscayne Bay. For a bay-wide water budget that includes saltwater and freshwater mixing, fresh groundwater accounts for less than 2% of the total input. A similar Sr 2+/Ca2+ tracer model indicates precipitation is the dominate source in 9 out of 10 canals that discharge into Biscayne Bay. The two-component mixing model converged for 100% of the freshwater canal samples in this study with 63% of the water contributed to the canals coming from precipitation and 37% from groundwater inputs ±4%. There was a seasonal shift from 63% precipitation input in the dry season to 55% precipitation input in the wet season. The three end-member mixing model converged for only 60% of the saline canal samples possibly due to non-conservative behavior of Sr2+ and Ca2+ in saline groundwater discharging into the canal system. Electromagnetic and Direct Current resistivity surveys were successful at locating and estimating the geometry and depth of the freshwater/saltwater interface in the Biscayne Aquifer at two near coastal sites. A saltwater interface that deepened as the survey moved inland was detected with a maximum interpreted depth to the interface of 15 meters, approximately 0.33 km inland from the shoreline. ^

Thermodynamic description and phase transformation of highly symmetrical monoatomic structures

Based on theoretical considerations an explanation for the temperature dependence of the thermal expansion and the bulk modulus is proposed. A new equation state is also derived. Additionally a physical explanation for the latent heat of fusion is presented. These theoretical predictions are tested against experiments on highly symmetrical monatomic structures. ^ The volume is not an independent variable and must be broken down into its fundamental components when the relationships to the pressure and temperature are defined. Using zero pressure and temperature reference frame, the initial parameters, volume at zero pressure and temperature[V°], bulk modulus at zero temperature [K°] and volume coefficient of thermal expansion at zero pressure[α°] are defined. ^ The new derived EoS is tested against the experiments on perovskite and epsilon iron. The Root-mean-square-deviations (RMSD) of the residuals of the molar volume, pressure, and temperature are in the range of the uncertainty of the experiments. ^ Separating the experiments into 200 K ranges, the new EoS was compared to the most widely used finite strain, interatomic potential, and empirical isothermal EoSs such as the Burch-Murnaghan, the Vinet, and the Roy-Roy respectively. Correlation coefficients, RMSD's of the residuals, and Akaike Information Criteria were used for evaluating the fitting. Based on these fitting parameters, the new p-V-T EoS is superior in every temperature range relative to the investigated conventional isothermal EoS. ^ The new EoS for epsilon iron reproduces the preliminary-reference earth-model (PREM) densities at 6100-7400 K indicating that the presence of light elements might not be necessary to explain the Earth's inner core densities. ^ It is suggested that the latent heat of fusion supplies the energy required for overcoming on the viscous drag resistance of the atoms. The calculated energies for melts formed from highly symmetrical packing arrangements correlate very well with experimentally determined latent heat values. ^ The optical investigation of carhonado-diamond is also part of the dissertation. The collected first complete infrared FTIR absorption spectra for carhonado-diamond confirm the interstellar origin for the most enigmatic diamonds known as carbonado. ^

Effect of water on olivine single crystals plasticity, deformed under high pressure and high temperature

The Earth's upper mantle, mainly composed of olivine, is seismically anisotropic. Seismic anisotropy attenuation has been observed at 220km depth. Karato et al. (1992) attributed this attenuation to a transition between two deformation mechanisms, from dislocation creep above 220km to diffusion creep below 220km, induced by a change in water content. Couvy (2005) and Mainprice et al. (2005) predicted a change in Lattice Preferred Orientation induced by pressure, which comes from a change of slip system, from [100] slip to [001] slip, and is responsible for the seismic anisotropy attenuation. Raterron et al. (2007) ran single crystal deformation experiments under anhydrous conditions and observed that the slip system transition occurs around 8GPa, which corresponds to a depth of 260Km. Experiments were done to quantify the effects of water on olivine single crystals deformed using D-DIA press and synchrotron beam. Deformations were carried out in uniaxial compression along [110]c, [011]c, and [101]c, crystallographic directions, at pressure ranging from 4 to 8GPa and temperature between 1373 and 1473K. Talc sleeves about the annulus of the single crystals were used as source of water in the assembly. Stress and specimen strain rates were calculated by in-situ X-ray diffraction and time resolved imaging, respectively. By direct comparison of single crystals strain rates, we observed that [110]c deforms faster than [011]c below 5GPa. However above 6GPa [011]c deforms faster than [110]c. This revealed that [100](010) is the dominant slip system below 5GPa, and above 6GPa [001](010) becomes dominant. According to our results, the slip system transition, which is induced by pressure, occurs at 6GPa. Water influences the pressure where the switch over occurs, by lowering the transition pressure. The pressure effect on the slip systems activity has been quantified and the hydrolytic weakening has also been estimated for both orientations. Data also shows that temperature affects the slip system activity. The regional variation of the depth for the seismic anisotropy attenuation, which would depend on local hydroxyl content and temperature variations and explains the seismic anisotropy attenuation occurring at about 220Km depth in the mantle, where the pressure is about 6GPa. Deformation of MgO single crystal oriented [100], [110] and [111] were also performed. The results predict a change in the slip system activity at 23GPa, again induced by pressure. This explains the seismic anisotropy observed in the lower mantle.