"LPO Lite" : Representing Lattice Preferred Orientation and its Evolution Using Structured Basis Functions
Abstract
Current methods for calculating the evolution of flow-induced seismic anisotropy in the upper mantle describe Lattice Preferred Orientation (LPO) using ensembles of 103-104 individual grains, and are nowaday too computationally expensive to be incorporated into three-dimensional time-dependent convection models. We propose a much faster (by a factor ~ 103) method wherein LPO is described by a small number of 'structured basis functions' (SBFs.) The number of SBFs required is equal to the number of active slip systems (= 3 for olivine), and each SBF represents the 'virtual' LPO that would be produced by the action of just one of those systems. Analytical expressions for the SBFs are obtained using a simple 'single-slip' (SS) model, and are then tested against the predictions of the second-order (SO) self-consistent model of Ponte-Castaneda (J. Mech. Phys. Solids 50, 737-757, 2002) in which several slip systems act simultaneously. Remarkably, the SS model reproduces exactly (99.9% variance reduction) the orientation- dependence of the slip rate ·γ predicted by the SO model for each active slip system, once the overall amplitude of the SS expression for ·γ has been determined by least-squares fitting to the SO prediction. Having thus demonstrated that the analytical SBFs are physically realistic, we develop a scheme for representing an arbitrary LPO as a superposition of the SBFs and for determining the evolution equations satisfied by the expansion coefficients. We illustrate the method both for simple uniform deformations (uniaxial compression, simple shear) and for more geophysically realistic nonuniform deformation histories.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2008
- Bibcode:
- 2008AGUFMDI13A1688R
- Keywords:
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- 3902 Creep and deformation;
- 5112 Microstructure;
- 5120 Plasticity;
- diffusion;
- and creep;
- 8033 Rheology: mantle (8162);
- 8120 Dynamics of lithosphere and mantle: general (1213)