Applied Mathematics Seminar

Geodynamics is the study of the fundamental processes which drive the evolution of the Earth and other planets. In recent years it has become apparent that knowledge of the large-scale, long time behaviour of the Earth can dramatically improve the way we understand and model smaller scale geological processes, such as crustal deformation and long-term sea-level change. Partly due to the availability of high-speed workstations at relatively low cost, a new brand of 3-D geodynamic models is being developed that include mantle convection, the history of plate motions, changing plate geometries through time and a more realistic crust. These models come closer to modelling the "real Earth" than ever before. Geodynamic modelling and visualisation provides both industry and academia with tools to better understand the formation of ore deposits, the occurrence of fossil fuels, and the formation and evolution of Australia's continental margins and surrounding ocean basins.
Alliances between academia and industry, fostered in particular in Australia, have resulted in the emergence of a relatively new field of applied research which may be called "Exploration Geodynamics" - the focusing of geodynamic modeling on resource exploration. The exploration industry is beginning to make use of dynamical modeling on a crustal scale to improve their understanding of the formation of natural resources. To do so requires the integration of models which span a very large range of time and space scales - length scales ranging from convection cells and plates (10000km) down to the size of structures in resource deposits; time scales ranging from the age of the Earth to the time for an individual sedimentary basin to subside.
We have extended the two-dimensional particle-in-cell (PIC) finite element code "Ellipsis", written by Louis Moresi from Monash University, to three-dimensions for application to problems in geodynamics. The particle in cell scheme is a hybrid method which combines a fixed mesh of computational points and a dense arrangement of mobile material points. The fixed Eulerian mesh allows very fast computation (performed in Ellipsis via a multigrid iteration method) whereas the Lagrangian particle reference frame allows the tracking of material interfaces and history dependent properties such as strain history for strain-softening materials. The PIC method is exceptionally useful in very large deformation analyses where purely Lagrangian approaches would be severely hampered by the need for remeshing to minimize element distortion.
We apply the Ellipsis particle-in-cell finite element code to a series of problems involving extension of the continental lithosphere. This constitutes one of the first applications of 3D particle-in-cell technology to a problem of geodynamic importance. Specifically, we model a 3 layer lithosphere (with upper and lower crust and upper mantle components), and incorporate phase changes via decompression melting. The extension proceeds in multiple steps, including orientations normal to and oblique to predefined weak zones that serve to aid the onset of localization. The rheological model is viscoplastic (work is continuing on the 3D code's elastic aspect), where the plastic part of the rheology is set to mimic brittle deformation and the viscosity is temperature-dependent. We show examples of the distribution of brittle deformation patterns in the upper crust, as well as the distribution of melt in the system for realistic parameter values, to improve our understanding of volcanism associated with basin and continental margin formation.