Geodynamics Group, **Machine** VP, CM

Research School of Earth Sciences

**Three-Dimensional Modelling of Crustal Deformation Coupled to Surface
Processes and Temperature Calculations**

The lithosphere is the Earth's solid-like outer shell. It is subject to large forces that arise from convective flow in the underlying mantle. In response to these forces, large lithospheric plates collide and rift apart leading to shortening and extension along the plate boundaries and sometimes within the plate interiors.

The study of lithospheric deformation is a rather complex, non-linear problem. Rocks behave as brittle and power-law viscous materials depending on their pressure and temperature. Tectonic events usually lead to very large deformation that cannot be properly described by infinitesimal strains. The boundary conditions at the base and top surface of the lithosphere are complex: contact with a viscous fluid at the lithosphere-asthenosphere boundary and erosion/sedimentation at the lithosphere/atmosphere boundary.

We have developed in the last few years a series of numerical models to study the processes at play during lithospheric deformation. These include:

* a three-dimensional model of the brittle/viscous lithosphere which properly represents large strains, finite rotations and the loading/unloading due to surface processes;

* a three-dimensional model of heat transfer by advection/conduction to accurately predict the evolution of the temperature field in a deforming tectonic province; the model predictions are used to interpret geo-thermo-chronological data that provides direct constraints on rates of deformation;

* a surface processes model to predict erosion/sedimentation by long-range river transport and short-range diffusive processes.

These numerical models are based on new techniques such as the EBE iterative method to solve large algebraic systems, Delaunay triangulation to form adaptive numerical meshes, Natural Neighbour interpolation to obtain accurate estimates of high order derivatives on irregular meshes and local iterative methods to compute river networks from complex topographic surfaces.

Most numerical codes have been designed to run efficiently on the VP2200 and the CM-5.

**What are the basic questions addressed?**

What is a good representation of the Earth's lithosphere rheology? What are the forces responsible for crustal deformation? What is the most important aspect of the dynamics of crustal deformation, the rheology of rocks or the nature and geometry of boundary conditions? How is the morphology of crustal structures influenced by surface processes such as erosion and sedimentation?

**What are the results to date and future of the work?**

So far, we have looked at the dynamics of compressional, strike-slip and transpressive plate boundaries. We have defined the temperature anomaly produced by lithospheric deformation in compressional orogens and used it to better interpret geo-chronological data. We are now working on an algorithm to properly couple surface erosion/sedimentation with lithospheric deformation and thermal evolution.

**What computational techniques are used and why is a supercomputer
required?**

The finite element method is used to discretize the equations of lithosphere dynamics; the EBE (element-by-element) method is used to solve the resulting large system of algebraic equations. We have also developed the Dynamical Lagrangian Remeshing (DLR) concept that allows us to model the large deformation of solid materials in a Lagrangian framework. We have developed the Natural Element Method (NEM) to solve problems of fluid-structure interactions. The geomorphological model is based on a local approach to solve a complex network problem. All methods are local and are therefore perfectly suited for parallelization/vectorization.

**Publications**

*Three-dimensional numerical simulations of crustal-scale wrenching
using a non-linear failure criterion,* J Braun, Journal of Structural
Geology, **16**, 1173-1186 (1994).

*Three-dimensional numerical experiments of strain partitioning at oblique
plate boundaries: implications for contrasting tectonic styles in California
and South Island, New Zealand*, J Braun and C Beaumont, Journal of
Geophysical Research, in press.

*Dynamical Lagrangian Remeshing: a new algorithm for solving large strain
deformation problems and its application to fault-propagating folding*, J
Braun and M Sambridge, Earth and Planetary Science Letters, **124**, 211-220
(1994).

*Geophysical Parameterization and interpolation of irregular data using
natural neighbours*, M Sambridge and J Braun, Geophysical Journal
International, in press.

*A physical explanation for apparent accelerating uplift in collisional
orogens*, G Batt and J Braun, Geology, submitted.

*The Natual Element Method (NEM)*, J Braun and M Sambridge, Nature,
submitted.