RICERCA ITALIANA     

CHAOTIC DYNAMICS AND FRACTAL GEOMETRY IN THE GENESIS AND MIXING OF MAGMAS

Università degli Studi di Perugia

Abstract

Compositional heterogeneities strongly characterize all the life stages of magmatic systems from the genesis of basaltic magmas in a geochemically heterogeneous upper mantle to successive evolutionary stages where magmas derived from both a single heterogeneous source and different sources interact.
The main goal of this research project is to study the processes acting during the genesis and evolution of magmas via magma mixing by analysing plutonic and volcanic rocks through a multidisciplinary approach involving petrology, geochemistry, and experimental petrology. Together with these classic petrologic techniques, also new methods of Chaos Theory and Fractal Geometry will be used. This approach will allow us to keep into account the non-linearity, the dependence upon initial conditions, and the scale-invariance of petrogenetic processes and, hence, to gain more in-depth knowledge about magmatic systems.
In detail, the project is mainly focused on:
i) understanding the nature of source regions and the length scale of upper mantle heterogeneities by focusing attention on OIB magmatism and by considering the compositional variability of basaltic melts from the length scale of oceans to single volcanoes;
ii) understanding the mechanisms acting during interaction of rheologically similar magmas by studying basaltic magmas generated by an heterogeneous mantle source and reconstructing the composition of end-members that were involved in the interaction process;
iii) understanding the initial stages of intrusion of mafic magmas in felsic magma chambers and the successive stages of the mixing process by studying plutonic and volcanic rocks with variable crystal contents, also using experimental petrology, to comprehend the role played by the dynamic evolution of mixing processes in determining the geochemical composition of igneous rocks at all length scales.
Researches will be carried out by studying intrusive rocks of the Adamello pluton (Italy), and plutons of coastal Maine (USA), and lava flows cropping out on the islands of Capraia (Italy), Lanzarote (Canary Islands), and Lesbos (Greece), and Monti Iblei and Mt. Etna (Italy).
Studies will be carried out by performing analyses of major and trace elements and isotopes (Sr, Nd, Pb, Hf) by using classical (SEM, EMPA, XRF, TIMS) and innovative (LAM e MC ICP-MS) analytical techniques, and the new techniques of Chaos Theory and Fractal Geometry. <<<

Principal Investigator

Giampiero POLI Università degli Studi di PERUGIA

Research Objectives

The main aim of this research project is the study of processes occurring during genesis and evolution via magma mixing of magmas using a multidisciplinary approach involving petrology, experimental petrology and geochemistry on selected and representative plutonic and volcanic rocks. Together with classic petrology, techniques based on Chaos Theory and Fractal Geometry will be used since these methods allow to keep into account the non-linearity, the variability connected to the initial conditions, and the scale invariance of magmatic processes.
This project will focus on understanding of:
- type and scale of the compositional heterogeneity of the upper mantle, by studying the geochemical variability of Oceanic Island Basalts (OIB);
- mixing processes among basaltic magmas during migration from their source, by studying compositional transects on representative samples;
- the early stages of the intrusion of mafic magmas into felsic magma chambers and successive evolution of mixing processes in time, by studying both plutonic rocks and lavas characterized also by variable crystallinity, and by performing experimental petrology experiments.

Regarding magma genesis, we will focus on partial melting processes through the study of basaltic rocks, mainly of OIB-type strictly correlated in space and time, to evaluate nature and dimensional length scale of the distribution of the upper mantle heterogeneities. The conceptual model is the "Statistical Upper Mantle Assemblage" (SUMA), in which the upper mantle would be characterized by a widespread small- to moderate- length scale heterogeneity, which can justify genesis of magmas with strong compositional variability even at the length scale of a single volcanoes. The mantle is thus regarded as a highly chaotic system, in which convective processes create dynamically active regions that may eventually host coherent and homogeneous domains. These domains propagate into the system according to a fractal distribution (2.2 Appendix) and can generate basaltic magmas with extremely variable chemical compositions.
To evaluate the degree and characteristic scale of the upper mantle heterogeneity, we will document the compositional variability observed in various regions of OIB magmatism. Different approaches will be used for each scale of observation:
i) the use of geochemical-statistical techniques will be applied to the study of mantle heterogeneity at the scale of oceans, using literature data. We will use an original method of plotting that allows a simultaneous evaluation of a high number of geochemical parameters, defining a limited number of end-members which contribute to identify the geochemical affinity of each basaltic sample. The application of this method is fundamental since mantle heterogeneities are the result of chaotic and fractal dynamics (2.2 Appendix), in which a large number of variables are non-linearly linked. Therefore the largest number of variables must be taken into account in order not to loose crucial information for understanding the evolution of the system in space and time;
ii) a petrological-geochemical approach will be used for analyzing the geochemical heterogeneity of upper mantle at the length scale of single oceanic islands (e.g. Lanzarote, Canary), and volcanic centres (e.g. recent alkaline basalts from Iblean Basin and Etna). The availability of dense spatial and temporal series of erupted products at Etna makes this volcano particularly suitable for a pilot study. In this case, both isotope and trace element ratios can be used as tracers in order to define the contribution of different mantle sources and their degree of partial melting to the chemical composition of lavas. These studies will be carried out by the Pisa Unit.

Since basaltic magmas during their migration from the source region can interact and, hence, mix chaotically (2.2 Appendix) we need to use analytical techniques that allow to highlight the occurrence of mixing processes and to constrain the geochemical features of magmas which have been involved in the mixing process. This will be done by analyzing compositional transects on representative basaltic samples and studying the correlation degree among the different chemical elements. This method has been proven very effective in detecting mixing events and to inferr the original composition of "end-members". These studies will be carried out in collaboration between the two Research Units.

Regarding the part of the project concerning magma mixing, it will focus on the study of basaltic melts which interact with crustal derived melts in magma chambers. In particular, we will study the early stages of injection of mafic magmas into felsic magmas which are characterized by the development of fractal interfaces. This geological configuration, still unclear, is fundamental to understand time evolution of magma mixing processes. For this reason, together with the study of plutonic rocks in Adamello pluton (Italian Alps) and in some plutons of coastal Maine (USA) in which it is possible to recognize such a process fossilized at the initial phase, we will carry out experimental petrology studies using a centrifuge that allows to follow in time the forced intrusion of a mafic magma into a felsic one. These experiments, in collaboration with Prof. D. Dingwell research group (Ludwig-Maximilians-Universität, Munich, Germany), are the first attempt to study this crucial stage of magma interaction from an experimental petrology point of view.
Evolution in time of magma interaction processes will be followed up studying chemical exchanges during mixing processes at the micrometric scale (‘micro-mixing') analyzing transect and melt inclusions on lavas cropping out at Monte Arci (Sardinia, Italy) and on the islands of Capraia (Italy) and Lesbos (Greece). This will give the opportunity to understand the influence of the different dynamic regions (AMR and CR; 2.2 Appendix) at such a length-scale and to evaluate the potential pitfalls in the usability of melt inclusions in petrological system characterised by mixing processes. Runs of experimental petrology will be performed by mixing natural mafic and felsic melts following chaotic mixing experimental protocols, the so-called ‘Journal Bearing Flow' constituted of two eccentric cylinders, where mixing is induced by rotating two cylinders in a time-periodic fashion. Experimental petrology runs will be carried out also by mixing mafic and felsic melts with different crystal contents, in order to understand their influence on chaotic mixing dynamics. Results will be compared with sampled plutonic and volcanic rocks in which the transfer of mineralogical phases among magmas has been observed. These studies will be carried out by Perugia Unit.

In order to understand the importance of the different extensive and intensive variables in magma mixing process, numerical simulations will be carried out to follow the evolution of this petrogenetic process in time. These studies will be carried out in collaboration between the two Research Units. <<<

Timescale

24 months

National and international background

There is a plethora of evidence that magmatic systems display compositional heterogeneities at many length-scales and that these heterogeneities play a very important role in the petrogenesis of igneous rocks [e.g. 1,2]. The causes of these heterogeneities are related to several processes acting on different spatial and temporal scales. A first process that can strongly influence the degree of heterogeneity of a magmatic system is partial melting of a source rock (e.g. the upper mantle); such a process can lead to the production of magma volumes with different geochemical composition depending on the degree of melting and the extent of compositional heterogeneity of the source rock [e.g. 3,4]. Single magma volumes generated by this process can coalesce during their migration from the source region to produce magmatic masses of larger dimensions which are constituted by several interacting sub-systems with variable compositions [e.g. 5]. Another process that is likely to form compositionally heterogeneous magmatic masses is interaction between magmas derived by partial melting of different source rocks [e.g. mantle-derived magmas which interact with crustal anatectic magmas; e.g. 6,7].
Recent studied have shown that the Earth mantle is highly heterogeneous in composition being constituted by regions having variable degrees of "fertility" which, potentially, can give basaltic melts with extremely different geochemical compositions. From a two layers upper mantle, separated by a seismic discontinuity at 660 Km and at the base of which "plumes" would originate [e.g., 8,9], recent studies proposed the concept of global convection [e.g. 10] in which oceanic slabs, penetrating the 660 Km discontinuity, induce contamination phenomena even in the lower mantle originating several geochemical reservoirs [M1, EM2, HIMU, PREMA, FOZO; e.g. 11,12,13,14]. The concept of geochemical reservoir is not able, however, to explain the compositional variations observed at both the length scale of chains of oceanic islands and within a single volcano [e.g. 15,16]. An alternative model to explain the heterogeneity of the mantle has been proposed by Meibom and Anderson in 2003 [Statistical Upper Mantle Assemblage; SUMA; 3]; according to this model the upper mantle would be characterized by a strong heterogeneity, from small to medium scale (10^2-10^5m), and it would be able to produce magmas with MORB and OIB affinity, arguing against the presence of several geochemical reservoirs separated by large scale discontinuities. Therefore the mantle would not be constituted by two separated layers interacting only occasionally, but it is considered as a highly chaotic system (Appendix), where convective processes create dynamically active regions which may contain coherent and homogenous domains [e.g. 2], propagating in the system according to a fractal distribution, and able to generate basaltic magmas with extremely variable compositions coexisting at short length scale.
Different approaches have been utilized to determine compositional characteristics of source regions and pressure conditions of partial melting. Results obtained in recent experimental studies [e.g. 17] by partial melting of pyroxenite sources have suggested a pressure of about 2 GPa as minimum value to obtain a thermal barrier, in the projection on Cats-Ol-Q plane of the basaltic system, between pyroxenite and peridotite derived melts. This approach could allow to identify the mineralogical characteristics of the source regions and the pressure conditions of the partial melting event.
Given the extremely large compositional heterogeneity of upper mantle, it has been necessary to find tracers able to discriminate among different geochemical domains. In particular, the use of isotope systematics such as Sr, Nd, Pb, Hf along with ratios of highly incompatible elements has been proven to discriminate both nature of source region and possible metasomatic enrichments due to either percolation of melts within the mantle itself and/or addition of materials deriving from recycling of subducted slabs and associated sediments [e.g. 3,9,13]
The different basaltic magmas, once generated in the mantle source, travel towards the Earth surface, and during their migration they can "collide" one with the other and, therefore, they can arrive on surface not as primary but partially mixed according to the chaotic and fractal dynamics discussed in Appendix [e.g. 14].
As introduced previously, magma interaction processes may occur also among magmas deriving from different sources. A crucial point of magma interaction is when magmas come initially into contact, for instance during the initial stages of intrusion of mafic magmas within felsic magma chambers. This geological condition is poorly known and only recently it has been suggested that this intrusion process would generate fractal interdigitate structures (Appendix) whose complexity would depend on the rheological differences between the two magmas [e.g. 18,19].
Several studies evidenced that the presence of chaotic dynamics within mixing systems strongly influences chemical exchanges between magmas [e.g. 2,20]. For instance, it has been widely documented that during chemical diffusion processes in AMR, the "sensitivity to initial conditions" of chaotic systems (Appendix), influences entirely diffusion processes generating in short times magma volumes with extremely variable correlation among chemical elements depending on their value of diffusion coefficient [e.g. 20]. On this respect it was suggested that, given the micrometric scale over which such processes occur, the analysis of melt inclusions in magma mixing systems could lead to misleading interpretations of the compositional variability of magmas present in the system [e.g. 20].
Even mineral phases are strongly influenced by the presence of chaotic dynamics and, in particular, their growth is strictly in relationship to the type of dynamic region (AMR or CR; Appendix) in which crystals grow. In detail, if crystals are inside AMR their growth is strongly favoured since within these regions chemical exchanges are very efficient [e.g. 21,22] whereas, if they are inside CR, their growth is inhibited because of low transfer of chemical elements in these regions [e.g. 21,22]. In such dynamical conditions, mineral phases record, through the development of compositional zonings, the type of dynamics experienced by the system and they become important tracers of the global dynamics of the magmatic system and of the petrogenetic process [e.g. 21,22].
Magma mixing has been recently reproduced in the laboratory by experimental petrology techniques [23] using real magmas, and results demonstrated that it is possible follow the evolution of mixing processes in space and time; this opens new fields of research for a more complete understanding of these natural phenomena.
From the above discussion it is evident that processes concurring in the genesis and evolution of magmas via magma mixing are in strict relationship to the length scale and the degree of compositional heterogeneity of the source region and of the magmatic masses. However, although many progresses have been made, several points remain still unclear and the most important are:
1) to establish the nature and the length scale of upper mantle geochemical heterogeneities and to understand the dynamical factors acting to produce them;
2) to reconstruct the mineralogical characteristics of the source region (e.g. pyroxenite/peridotite) and the pressure conditions of partial melting;
3) to understand the causes of extreme compositional variability of basaltic lavas erupted by a single volcano and if this variability is related to different degrees of partial melting of a single source or compositionally different source regions coexisting at short length scale;
4) to study the degree of interaction among mantle derived magmas with similar rheology but different composition and to reconstruct the geochemical composition of original basaltic end-members;
5) to understand the initial stages of intrusion of basaltic magmas within felsic magma chambers; given that magma interaction systems suffer the "sensitivity to initial conditions" because they are chaotic systems (Appendix), small variations in the initial conditions can lead to extremely different evolution of the mixing process;
6) to study in detail mixing processes at the micro-scale ("micro-mixing") and their influence on the compositional characteristics of melt inclusions and on their petrologic significance;
7) to understand the role played by mineral phases on the fluid-dynamics of magma mixing systems and their influence in restructuring the different dynamical regions (AMR and CR; Appendix) in space and time.

APPENDX
In the last years concepts and methods of the Chaos Theory and Fractal Geometry have been widely applied in all scientific fields [24]. These two disciplines are cross-related and their purpose is the analysis and comprehension of "complex dynamic systems". The development of Chaos Theory can be historically traced by starting from Edward N. Lorenz [25] who demonstrated, using computer assisted numerical techniques, that apparently simple systems may show a very complex behaviour. Lorenz analyzed the motion of particles in a convecting fluid and observed that arbitrary close particles diverged exponentially fast after a few calculus cycles and described completely different orbits. This feature is known as "sensitivity to initial conditions", and is a typical feature of chaotic systems (Fig. 2.2-1). In addition, Lorenz observed that orbits, even if diverging exponentially, were "attracted" toward a well-defined structure (Fig. 2.2-1). Particles within this structure were affected by continuous stretching and folding processes that generated patterns propagating at different length-scales (Fig. 2.2-1). The structure generated by the Lorenz's system was named "strange attractor" and it represented one of the first examples of chaotic systems. The occurrence of a "strange attractor" is required to classify a system as "chaotic". An important property of a "strange attractor", i.e. of a chaotic system, is that it shows the same patterns at different length-scales. This "scale invariance" (also known as "self-similarity") is a basic property of fractal structures [26]. Therefore, chaotic systems produce fractal structures and the use of concepts and techniques of Fractal Geometry is fundamental for the study of chaotic systems. By definition a "fractal" is a structure that, if divided in parts, each part is a statistically reduced-size copy of the whole structure. A fractal structure is quantified by measuring its "fractal dimension". Euclidean geometry deals with integer dimensions whereas Fractal Geometry deals with fractional dimensions. As an example, the fractal dimension of the Lorenz's strange attractor is 2.04 [e.g. 27]. The quantification of a chaotic system is made by calculating its fractal dimension. An important aspect of chaotic systems is that at similar values of fractal dimension correspond similar processes and dynamics, and this allows to compare different systems by using values of their fractal dimensions.
Another important aspect of chaotic and fractal dynamical systems is that they can be modelled numerically (Fig. 2.2-2) and that it is possible reproduce with very good approximation natural structures. This allows to replicate the behaviour of natural complex systems, such as magmatic systems [e.g. 2,21,22,28], and to follow their evolution in time, a possibility that is precluded by the exclusive study of rock outcrops that, in most cases, represent only single stages of evolution "frozen" in time.
Recent studies demonstrated that magma mixing processes are governed by chaotic dynamics [e.g. 20,28] that generate fractal structures. Such structures have been recognised within igneous bodies in both the volcanic and plutonic environment [e.g. 29,30] and their fractal analysis allowed to quantify several magmatic processes [e.g. 2,31] and, in some cases, to reconstruct the main characteristics of source rocks of magmas which took part in the mixing process. Magma mixing systems are chaotic because the mixing process is governed by "stretching and folding" dynamics of magmas and such dynamics are the basic "recipe" of Chaos [e.g. 32,33]. The evolution in time of "stretching and folding" dynamics generates different dynamical regions which are ubiquitous within the same system from the metric to the micrometric length-scale, and that have completely different geochemical and thermodynamical behaviours [Active Mixing Regions, AMR and Coherent Regions, CR; e.g. 2,34; Fig. 2.2-2]. The first type of regions (AMR) is characterised by efficient stretching and folding processes [e.g. 2,34] where mass transfer between magmas, liquid and crystals, are extremely efficient; such regions behave geochemically and thermodynamically as open systems. The second type of regions (CR) is characterised by weak stretching and folding processes [e.g. 2,34] where mass transfer, liquid and crystals, between magmas are inhibited; these regions behave geochemically and thermodynamically as closed systems.
The two types of dynamical regions occur within mixed magmatic systems as different structures. RAM are constituted by filament-like regions of magmas whereas CR appear as discrete portions of one of the two magmas recognisable on outcrops as globular enclaves [e.g. 2,28; Fig. 2.2-2]. The study of AMR and CR by the combined use of classical petrologic techniques and new methods developed by using concepts of Fractal Geometry and Chaos Theory allowed to extract important information about the role played by mixing dynamics in influencing the geochemical composition of end-members and to reconstruct their original compositions [e.g. 2,28,31].

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