Numerical modeling of orbicular sctructures

Most commonly found in felsic plutonic rocks, orbicular structures represent repetitive concentric patterns consisting of continuous mafic and felsic layers that enclose the inner part of orbicules (Fig. 1). The inner parts of orbicules, or cores, can be a homogeneous spherical body of the same composition as of one of the layers, or a fragment of hosting parental rock or even a xenolith of wall rocks. The aggregates of alternating layer are referred to as shells. The mechanism of formation of the structure is still a puzzle for petrologists. Numerous papers (Eskola, 1938; Levenson, 1966; Elliston, 1984; and references therein) have been published on occurrences of orbicular rocks but all of them lack a quantifying explanation of their formation. For a large review on orbicular rocks see Elliston (1984).

Many authors describe orbicular structures observed in silica saturated (free silica) rocks like granodiorites, granites and monzogranodiorites (e.g., Decitre, et al., 2002; Grosse et al., 2010). However, silica-undersaturated rocks such as gabbro, diorites and even lamprophyres have been also reported (Levenson, 1966; Bryhni and Dons, 1975). It was widely emphasized that orbicular structures are most commonly observed in rocks of Precambrain age, especially in the Proterozoic. This fact can be attributed to inherent conditions existed on Earth in the Precambrian or can be explained by simply more advanced erosional level at Precambrian provinces that allows for exposure of deeper parts continental crust. In the field, orbicular structures are found to be spatially associated with the outermost parts of plutons. Bodies of orbicular rocks frequently form pockets with distinct boundaries between them and non-orbicular structured rocks. The most commonly observed shells of orbicular rocks consist of plagioclase-rich layers and biotite-rich layers. It was noted by many geologists that shells consist of alternating anhydrous and hydrous mineral assemblages. Apparently, orbicular structures are produced in presence of residual H₂O- and K₂O-rich melt (or fluid) interacting with preexisted solid particles .

Fig. 1. Orbicular structure in granite from Kangasala, Finnland. Adapted from Ellison, 1984. 

Using computational code written in MATLAB we present a model of orbicular structure formation in which the driving mechanisms are chemical oscillations and diffusion. In this paper, diffusion is considered to be a source of reactants that are concentrated at one place and spread outwards disturbing the local steady state causing the system to react. It is known that such mechanisms are responsible for producing so-called Turing pattern. After playing with diffusivity coefficients of different components, setting random concentrations of the components in the background and making initially high concentrations restricted to what subsequently became the cores of the orbicules, the code produces something that definitely resembles orbicular structure:

Fig. 2. Graphical output of the code. Warmer colors indicate higher concentrations. 

 

 The video!

This post is written based on my work in Geochemical Modeling class at the University of Oregon. I am grateful to Jim Watkins and Ben Shapiro for teaching me MATLAB and putting the code together that subsequently allowed me to play with it and produce the above described results. 

REFERENCES

1.    Bryhni, I. & Dons, J.A. (1975). Orbicular lamprophyre from Vestby, southeast Norway. Lithos, 9, 133-122.

2.   Decitre, S., Gasquet, D. & Marignac. C. (2002). Genesis of orbicular granitic rocks from the Ploumanac’h Plutonic Complex (Brittany, France): petrographical, mineralogical and geochemical constaints. Eur. J. Mineral., 14, 715-731.

3.  Elliston, J.N. (1984). Orbicules: an indication of the crystallization of hydrosilicates, I. Earth-Sci. Rev., 20, 265-344.

4.   Eskola, P. (1938). On the Esboitic crystallization of orbicular rocks. J. Geol., 46, 448-485.

5.  Grosse, P., Toselli, A.J. & Rossi, J.N. (2010). Petrology and geochemistry of the orbicular granitoid of Sierra de Velasco (NW Argentina) and implication for the origin of orbicular rocks. Geol. Mag., 147, 451-468.

6.  Levenson, D.J. (1966). Orbicular rocks: a review. Geol. Soc. Amer. Bull., 77, 409-426.