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.

Introduction to Special issue on the Symposium on the Application of Neural Networks to the Earth Sciences

Papers in this issue of Natural Resources Research are from the “Symposium on the Application of Neural Networks to the Earth Sciences,” held 20–21 August 2002 at NASA Moffet Field, Mountain View, California. The Symposium represents the Seventh International Symposium on Mineral Exploration (ISME-02). It was sponsored by the Mining and Materials Processing Institute of Japan (MMIJ), the US Geological Survey, the Circum-Pacific Council, and NASA. The ISME symposia have been held every two years in order to bring together scientists actively working on diverse quantitative methods applied to the earth sciences. Although the title, International Symposium on Mineral Exploration, suggests exclusive focus on mineral exploration, interests and presentations always have been wide-ranging—talks presented at this symposium are no exception.

Enhancing student performance through cooperative learning in physical sciences

Students in a physical sciences course were introduced to cooperative learning at the University of Queensland, Gatton Campus. Groups of four to five students worked together in tutorial and practical sessions. Mid-term and practical examinations were abolished and 40% of total marks were allocated to the cooperative learning activities. A peer- and self-assessment system was successfully adapted to account for individual performance in cooperative learning group assignments. The results suggest that cooperative learning was very well received by students, and they expressed willingness to join cooperative learning groups in other courses. In addition, cooperative learning offered many benefits to students in terms of graduate attributes such as teamwork, communication, lifelong learning and problem-solving.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Rare earth element geochemistry of Late Devonian reefal carbonates, canning basin, Western Australia: Confirmation of a seawater REE proxy in ancient limestones

Rare earth element and yttrium (REE+Y) concentrations were determined in 49 Late Devonian reefal carbonates from the Lennard Shelf, Canning Basin, Western Australia. Shale-normalized (SN) REE+Y patterns of the Late Devonian samples display features consistent with the geochemistry of well-oxygenated, shallow seawater. A variety of different ancient limestone components, including microbialites, some skeletal carbonates (stromatoporoids), and cements, record seawater-like REE+Y signatures. Contamination associated with phosphate, Fe-oxides and shale was tested quantitatively, and can be discounted as the source of the REE+Y patterns. Co-occurring carbonate components that presumably precipitated from the same seawater have different relative REE concentrations, but consistent REE+Y patterns. Clean Devonian early marine cements (n = 3) display REE+Y signatures most like that of modern open ocean seawater and the highest Y/Ho ratios (e.g., 59) and greatest light REE (LREE) depletion (average Nd-SN/Yb-SN = 0.413, SD = 0.076). However, synsedimentary cements have the lowest REE concentrations (e.g., 405 ppb). Non-contaminated Devonian microbialite samples containing a mixture of the calcimicrobe Renalcis and micritic thrombolite aggregates in early marine cement (n = 11) have the highest relative REE concentrations of tested carbonates (average total REE = 11.3 ppm). Stromatoporoid skeletons, unlike modern corals, algae and molluscs, also contain well-developed, seawater-like REE patterns. Samples from an estuarine fringing reef have very different REE+Y patterns with LREE enrichment (Nd-SN/Yb-SN > 1), possibly reflecting inclusion of estuarine colloidal material that contained preferentially scavenged LREE from a nearby riverine input source. Hence, Devonian limestones provide a proxy for marine REE geochemistry and allow the differentiation of co-occurring water masses on the ancient Lennard Shelf. Although appropriate partition coefficients for quantification of Devonian seawater REE concentrations from out data are unknown, hypothetical Devonian Canning Basin seawater REE patterns were obtained with coefficients derived from modern natural proxies and experimental values. Resulting Devonian seawater patterns are slightly enriched in LREE compared to most modem seawaters and suggest higher overall REE concentrations, but are very similar to seawaters from regions with high terrigenous inputs. Our results suggest that most limestones should record important aspects of the REE geochemistry of the waters in which they precipitated, provided they are relatively free of terrigenous contamination and major diagenetic alteration from fluids with high, non-seawater-like REE contents. Hence, we expect that many other ancient limestones will serve as seawater REE proxies, and thereby provide information on paleoceanography, paleogeography and geochemical evolution of the oceans. Copyright (C) 2004 Elsevier Ltd.

Stirring in 3-d spherical models of convection in the Earth's mantle

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convection. We review observational constraints, and investigate stirring properties of numerical models of mantle convection. Conditions in the early Earth may have supported layered convection with rapid stirring in the upper layers. Material that has been altered near the surface is transported downwards by small-scale convection. Thereby a layer of homogeneous depleted material develops above pristine mantle. As the mantle cools over Earth history, the effects leading to layering become reduced and models show the large-scale convection favoured for the Earth today. Laterally averaged, the upper mantle below the lithosphere is least affected by material that has experienced near-surface differentiation. The geochemical signature obtained during the previous episode of small-scale convection may be preserved there for the longest time. Additionally, stirring is less effective in the high viscosity layer of the central lower mantle [1, 2], supporting the survival of medium-scale heterogeneities there. These models are the first, using 3-d spherical geometry and mostly Earth-like parameters, to address the suggested change of convective style. Although the models are still far from reproducing our planet, we find that proposal might be helpful towards reconciling geochemical and geophysical constraints.