The three‐dimensional geometry of simulated porphyroblast inclusion trails: inert‐marker, viscous‐flow models

Abstract

A fluid dynamic model for a rigid spherical porphyroblast growing in a viscous fluid matrix undergoing simple shear deformation predicts an arrangement of captured inert inclusions that is remarkably similar to the spiral pattern observed in synkinematic 'rolled' garnets. The model assumes only creeping (Stokes) flow of the matrix and a kinetic model for the growth of the porphyroblast of the formwhere r is the crystal radius, Q is the amount of shear-induced rotation, and m and k are kinetic parameters.For rotation less than 180°, J. B. Thompson and J. L. Rosenfeld's simple ring-model provides a surprisingly accurate description of the three-dimensional geometry of the central inclusion surface in the simulated porphyroblasts. Although marker planes, originally parallel to the shear plane, are deflected around the porphyroblast, their intersections with its surface remain approximately circular for much larger amounts of rotation than anticipated by Rosenfeld.The polar coordinate equation, T(r, O ) , of the double spiral formed by the trace of the central inclusion surface in a section through the centre of simulated porphyroblasts, is also surprisingly simple, as follows:This relationship was observed over the complete range of rotation angles investigated, 0-720", and could form a reasonable basis for estimating the growth-rotation history of rolled garnets from the shape of their spiral inclusion trails.Two-dimensional sections through the simulated porphyroblasts, parallel to the rotation axis, yield 'clamshell' (Rosenfeld's term) inclusion geometries similar to the controversial 'millipede' patterns observed in many natural porphyroblasts.

Occurrence and growth history of texturally sector- and sigmoidal-zoned garnet in the San Lo renzo Schists in the Sierra Nevada de Santa Marta massif (Co lombia)

“…According to Ikeda et al (2002), the sigmoidal trends are commonly very similar in composition and show good continuation with the external foliation, suggesting that they represent foliation that has been incorporated within the garnet during its growth. They have traditionally been attributed to syn-growth rotation of the porphyroblast relative to the stretching axes of the instantaneous strain ellipse (e.g., Masuda and Mochizuki, 1989;Gray and Busa, 2007).…”

How useful are ‘millipede’ and other similar porphyroblast microstructures for determining synmetamorphic deformation histories?

“…Bell, 1981;Bell et id., 1986Bell et id., . 1992Vernon, 1989;Passchier et al, 1992;Gray & Busa, 1994;Johnson & Moore, 1996). This paper examines the formation of OCMs within and adjacent to porphyroblasts, classifying them into five nongenetic types.…”

“…Type 1 OCMs are found in sections parallel to spiral axes through porphyroblasts with spiral-shaped inclusion trails (e.g. Powell & Treagus, 1967;Rosenfeld, 1970;Schoneveld, 1979;Johnson, 1993a,b;Gray & Busa, 1994). They are commonly considered to form during single deformation events that are highly noncoaxial (e.g.…”

“…Recent critical discussions of 'millipede' OCMs (e.g. Passchier et al, 1992;Johnson, 1993a;Gray & Busa, 1994) have emphasized that theoretically they can form in a range of deformation histories.…”

“…They are commonly considered to form during single deformation events that are highly noncoaxial (e.g. Schoneveld, 1979;Brunel, 1986;Gray & Busa, 1994), and have played a fundamental role in developing specific models of porphyroblast growth during rotation relative to an (OCMs) in and adjacent to a porphyroblast (stippled). Individual S1 foliation surfaces can be followed from the matrix, through the porphyroblast and out into the matrix on the other side.…”