Finite and incremental deformations recorded by planar subfabrics in S-tectonites

Abstract

Analysis of relative componental movements in foliated rocks is formulated in terms of space-continuous deformations assuming that a portion of the strain recorded by planar subfabrics results from differential movements on closely spaced shear surfaces (i.e. fiducial planes). Continuous and discontinuous velocity boundary conditions controlling deformation patterns within subdomains of folded layers are analyzed by combining the spatial velocity and finite deformation gradients. Within each subdomain internal rotations cause material elements oblique to the principal strain rate directions to undergo a series of complex strain transfers resulting in their compensatory lengthening and shortening during finite intervals. Equations are derived which continuously monitor successive variations in the logarithmic strain rates, ≐( N, t), for fabrics whose rotation axes are parallel to an intermediate principal axis. Values of ≐( N, t) at an angle N to the shear plane are numerically equal at time t, to the magnitude of the Hencky strain rate vector ( dh i dt ) referred to natural strain coordinates and used in conjunction with e ̈ (N,t) and the finite stretch, evaluate contemporary strain profiles for groups of planar fabrics replacing passive material planes. Applications to rectilinear shearing modes reveal that the most significant changes in local extensional rates are located between the maximum shearing and principal stretching directions. Assuming sectional continuity and constant material properties of the subfabrics and their matrix, these variations are correlated with systematic spacings between boudin structures suggesting that recognition of multiple orders of boudinage with respect to a potential shear surface in natural S-tectonites can be useful in deciphering local finite and incremental deformation coefficients as well as differentiate continuous ( dh i dt = ƒ(t) or constant) from pulsatory ( dh i dt is undefined at t) overprinting of the subdomain.