Modèle d'anisotropie de susceptibilité magnétique induite par orientation préférentielle de forme de marqueurs paramagnétiques anisotropes dans une roche déformée

Abstract

Many rocks contain minerals with a significant paramagnetic anisotropy at room temperature. Quantitative relationships between preferred dimensional orientation (O.P.F.) and anisotropy of magnetic susceptibility (A.S.M.) constitute the bases of magnetic methods of structural analysis. These relationships are derived from strain response models, assuming that (1) a polymineralic rock is made of distinct groups of minerals dispersed in a non-magnetic deforming viscous matrix and (2) these groups are mechanically and magnetically independent. Accordingly, the partial magnetic contribution of each mineral may be deduced knowing the theoretical behaviour of one population of markers of that mineral. The bulk magnetic behaviour of the rock is obtained by weighting the contribution of each population by its volumic proportion in the rock. The mechanical behaviour of the rock is assumed to be described by Fernandez's O.P.F. model. Because of the magnetic properties of minerals and the magnetic and mechanical independence of each population, the bulk magnetic fabric may be described by the Relative Magnetic Susceptibility Tensor [S ij ]. We consider firstly the case of markers for which K 1 =K 2 ¬=K 3 (cylindrical symmetry). For isovolumic axial flattening or constriction on rocks containing one single family of magnetic markers a very simple analytical solution is derived showing that the tensor [S ij ] is related to the strain intensity and to two parameters: the first parameter (k) is a function of the shape of the markers; the second (r) is a function of the intrinsic magnetic anisotropy of the markers. The eigenvectors of [S ij ] coincide with the principal axes of the strain. It is expected that knowing the magnetic properties of the minerals constituting a rock experimental measurements of [S ij ] may be used to estimate the finite strain (λ 3 ). The «power law» derived by Rathore is not verified by our model. Rathore's model gives only approximate result