Deformation of the South American Crust Estimated from Finite Element and Collocation Methods

Abstract

The present-day surface velocity field of the South American continent reflects the recent geodynamic features. It varies from quasi rigid body motion in the eastern part to mountain range deformation in the western Andes. Space geodetic observations provide velocities at discrete points only. To represent the continuous velocity field, an adequate deformation model has to be developed. Two different models are applied, the least squares collocation approach (LSC) and the finite element method (FEM). The input data are given by 329 velocities derived from continuously observing GPS stations and several GPS geodynamics projects. The different data sets are transformed to a common kinematic datum by deriving the rotation vector of the South American plate from station motions of the IGS Regional Network (RNAAC-SIR) in the rigid eastern part and reducing these plate motions from all the data sets. The resulting residual motions define the boundary conditions in the FEM and the input signals in the LSC. For the FEM a network of approximately 75000 linear elements is generated. The model theology is a homogeneous elastic material (Young’s modulus 70 GPa and Poisson ratio 0,3). For the LSC empirical covariance functions are derived from the observed velocity vectors. The comparison of both methods shows an agreement in the mm/a level. The result is a continuous surface velocity model for the South American continent which may be used for interpolation of point motions in geodetic networks and reference frames. A detailed geodynamic interpretation has not yet been done due to the simplicity of the model (homogeneous material, rough fault structures, no sophisticated dynamics).