Anthony D. Fowler

Supercooled rocks: development and significance of varioles, spherulites, dendrites and spinifex in Archaean volcanic rocks, Abitibi Greenstone belt, Canada

Abstract Many intriguing crystallization textures of Archaean volcanic rocks are ‘supercool’ in the sense that they are visually striking, and because they owe their origin to substantial undercooling of the silicate liquids from which they grew. Under conditions of high undercooling kinetic effects arise such that spherulitic, acicular or platy mineral habits are stabilized. The term variole refers to globular and spherical centimetre-scale, generally leucocratic masses visible on the weathered surfaces of mafic rock. At many localities the varioles can be shown to be plagioclase spherulites that grew near the quench margins of aphyric mafic lavas. Elsewhere, the varioles are droplets of felsic magma frozen into mafic magma as a result of magma mingling. Platy olivine spinifex in komatiites arises from a coupled process of hydrothermal cooling and constrained crystallization. Shrinkage of the komatiite crust during submarine cooling causes fracturing and sea water ingress such that a self-propagating vertically directed cooling/cracking-front develops. Within the magma below this front, forsterite crystals transport heat from the melt upwards to the hydrothermally cooled crust. Because of their higher thermal conductivity and greater transparency to near infrared thermal radiation, Mg-rich olivine crystals transfer heat more efficiently than the surrounding relatively Fe-rich liquid. The olivine forms vertically oriented platy crystals that cool the liquid directly in front of their tips and are thus self-propagating.

Organization of oscillatory zoning in zircon: analysis, scaling, geochemistry, and model of a zircon from Kipawa, Quebec, Canada

Abstract The character of oscillatory zoning within a zircon crystal from the syenite Kipawa Complex, Quebec, varies with scale of observation. Analysis of an scanning electron microscopy (SEM) back-scatter gray-scale traverse at a resolution of one pixel = 2.43 μm revealed 145 zones over 5130 μm, whereas a detailed high-resolution (one pixel = 0.195 μm) section near the crystal rim revealed 225 zones over 795 μm. In order to mathematically characterize the zoning pattern, wavelet, Fourier, and nonlinear analysis techniques were used on profiles of the SEM gray-scale data, and a series constructed was from the zone widths. Results demonstrate that the zircon oscillatory zoning preserves nonlinear and periodic components. Secondary ion mass spectrometry, electron microprobe, and SEM analyses of trace elements show the SEM back-scatter bright zones are enriched in U, Th, and rare earth elements (REE) in comparison to the darker zones. REE patterns are sharply heavy REE enriched and have negative Eu anomalies and prominent positive Ce anomalies. We model the oscillatory zoning, including a measure of its chemical variation, by use of a periodically forced nonlinear system. Results of this data-driven model are quantitatively similar to the natural data. We envisage that the small-scale oscillatory zoning was the result of a nonlinear feedback process wherein the crystal growth modified the adjacent melt, which in turn affected the crystal composition. The large-scale harmonic zones likely reflect changes in the bulk geochemistry of the system from which the zircon grew.

The origin of spinifex texture in komatiites

Komatiites are high-temperature, fluid, magnesium-rich lavas typically of Archaean age. A striking characteristic feature of such lavas is ‘spinifex’ texture—plate-like crystals of olivine ((Mg,Fe)2SiO4), millimetres to decimetres long, in a fine-grained matrix of spherulitic clinopyroxene (Ca(Mg,Fe,Al)(Si,Al)2O6), dendritic chromite ((Mg,Fe)(Cr,Al,Fe)2O4) and altered glass. Sheaves of olivine crystals can reach lengths exceeding one metre, even in komatiite flows less than 10 metres thick, in sharp contrast to the millimetre-scale post-eruption growth of crystals in more common volcanic rocks. Crystal growth of this magnitude might be a consequence of the high content of the constituent elements of olivine in komatiitic liquid, combined with the low viscosity and high chemical diffusivity of the lavas. But flows lacking spinifex texture are not uncommon, and those with such texture often contain substantial amounts of submillimetre olivine crystals of unremarkable appearance, so chemical considerations alone do not appear to provide a sufficient explanation. Here we present evidence that spinifex texture develops as a result of large thermal gradients, coupled with conductive and radiative heat transfer within olivine crystals fixed in the cool upper layers of the lava flows. This mode of growth has features in common with the high-temperature techniques used to grow large synthetic single crystals, but is rarely considered in geological contexts.

Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation

We present a nonlinear dynamical model for oscillatory zoning in plagioclase based on a simple isothermal constitutive undercooling mechanism. A phenomenological partitioning is introduced to relate the concentration of An in the melt at the interface with the concentration in the solid. The non-linearities in the model result from the coupling of the growth velocity with the local An concentration and from the boundary condition at the interface. The consideration of a nonlinear boundary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutions are possible via a Hopf bifurcation. As the system is driven further out of equilibrium, the model shows the development of chaotic solutions via a period-doubling sequence.

Modelling of igneous fractionation and other processes using Pearce diagrams

Geochemical data can be quantitatively modelled by means of Pearce diagrams. These are graphs of A/Z vs B/Z where A, B and Z are compositional abundances (e.g. wt.% SiO2, wt.% MgO, and ppm La) and Z has the additional property of having constant absolute abundance. In the terminology of igneous petrology, Z (the common denominator variable) could be an incompatible element. The numerators (A and B) may be complex algebraic combinations of elements, or even CIPW normative abundances. The utility of Pearce diagrams lies in the fact that slopes of data distributions equal the bulk A∶B ratio of minerals lost or gained from a suite of cogenetic rocks. There is no distortion because these plots correct for data closure. Terms of the form Ai·Z0/Zi (where Z0 is the abundance in a reference sample) remove the scaling to Ai caused by the abundance of a particular choice of Z. Subtraction of these terms for different samples (e.g. Ai·(Z0/Zi)-Aj· (Z0/Zj)) quantifies mineral losses and gains. Mathematical analysis shows that limited compatibility of the denominator variable is permitted. A bulk partition value (D) of 0.1 introduces an error of only 10% in values of Ai***-Z0/Zi, and 10° in slope-angle on Pearce diagrams over a crystallization interval of 50%. For D≤0.01 the error is minimal for a crystallization interval over 90%.

Dimensionality analysis of patterns: fractal measurements

Abstract Since the advent of Mandelbrots fractal geometry in 1975, many geological and geophysical patterns have been characterized by their fractal scaling properties. The purpose of this paper is to present and compare standard and new methods used to estimate the fractal dimension of random (natural) fractals. Examples demonstrate the relative limitations of the techniques, and the modifications necessary to more accurately estimate the scaling properties of certain types of fractals. Discussion and examples include branching diffusion-limited aggregates, fracture surfaces, and fractional Brownian surfaces.

The significance of europium anomalies in the REE spectra of granites and pegmatites, Mont Laurier, Quebec

Abstract Negative Eu anomalies in the REE spectra of granitic rocks are usually interpreted as evidence of earlier separation of a mineral phase such as plagioclase. Our study of the behaviour of the REE, and of U and Th, during late stage alteration of granites and the formation of pegmatites, suggests an alternative means for producing Eu anomalies. Albitization of earlier-formed plagioclase has depleted the granites in Eu and enriched the pegmatites in this element. This process is linked to the mobilization of U in the granites which is dependent on the oxidation state of the fluids. A systematic correlation between the ratios Eu Ce and U Th leads us to suggest a similar explanation for irregularities in the abundances of Ce and other rare-earths in the REE spectra of these rocks. We suggest that anomalous behavior of Eu in other environments or processes such as the alteration of basalt and the formation of certain ore deposit types may be caused partly by this mechanism.

Dimensionality analysis of time-series data: nonlinear methods

Abstract The field of nonlinear dynamics has resulted in the development of several techniques aimed at determining the dimensionality of strange attractors underlying time series outputs from chaotic systems. Knowledge of the system dimension allows estimation of the number of independent variables governing it. The techniques also allow one to distinguish between data sets produced through either random (i.e. high dimension) or deterministic processes (i.e. low dimension). Unlike physics and geophysics where data strings may be large ( n ∼ 1000s) those in geology are generally short ( n ∼ 100s), and there is associated noise. A new algorithm modeled after that of Sugihara and May is presented which in comparison to the correlation function technique works on short and discontinuous data strings.

Self-organized mineral textures of igneous rocks: the fractal approach

Abstract Many of the irregular patterns and textures that have been the subject of much recent scientific research are formed far from equilibrium, and are fractal in nature. Fractal structures are scale-invariant or self-similar. They appear the same, in a statistical sense, over large changes in scale. Silicate mineral crystals grown under conditions of disequilibrium frequently have a morphology composed of a hierarchy of similar branching parts. They are fractal objects and are self-organized on a macroscopic scale. The slopes of density-density correlation function plots are a measure of the fractal dimension. The plots show that some disequilibrium crystals exhibit a change from fractal to constant-density morphology. The growth of disequilibrium textures can be described in terms of the diffusion limited aggregation (DLA) algorithm. This is a stochastic model that mimics the Brownian motion of diffusing particles in the silicate liquid. It is an appropriate model as the disequilibrium crystals are known to have grown well below the liquidus under conditions of reduced atomic mobility. The simulations greatly resemble, and are quantitatively similar to naturally grown crystals. The branch growth is feedback-rich because the diffusing particles are not likely to cause growth anywhere, but near the branch tips.

Evidence for periodicity and nonlinearity in a high-resolution fossil record of long-term evolution

The application of new signal analysis techniques provides increased insight into the study of the fossil record and processes of evolution. The fossil record of 622 planktic foraminifera contains data from 200 stratigraphic stages of the past 127 m.y. Time-series analyses (wavelet and Fourier transform) of the planktic foraminifera fossil record were used to discern periodic components in long-term evolution. The correlation function analysis was used to distinguish between random and deterministic behavior of the fossil record. The analyses show that stationary ~30 m.y. periodicity and complex deterministic patterns occur in the long-term planktic foraminifera evolution, in particular in the extinction record. Our results suggest that the occurrence of intense diversity fluctuations with 3–10 m.y. periodicity after major extinction events may be attributed to nonlinear, self-organized evolutionary response to the availability of new ecospace. This coupled nonlinear-periodic scenario may explain the repetitive appearance of similar morphotypes in ~30 m.y. intervals.