Skip to main content
SpringerLink
Log in

A virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations: a new approach for understanding spatial and temporal complexity of magma dynamics

  • Original Article
  • Published:
Visual Geosciences

Abstract

In this contribution, we present a virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations with the aim to highlight the power of 3D representations in the understanding of this geological phenomenon. In particular, samples of mixed juveniles from Salina island (Southern Italy) are reconstructed in 3D by serial lapping and digital montage and numerical simulations are performed by using a 3D chaotic dynamical system. Natural and simulated magma mixing structures are visualized by using several multimedia tools including animations and “virtual reality” models. It is shown that magma interaction processes can generate large spatial and temporal compositional heterogeneities in magmatic systems. The same topological structures are observed in both 3D reconstructed rock samples and chaotic numerical simulations, indicating that the mixing of magmas is governed by chaotic dynamics. The use of 3D multimedia models gives the opportunity to penetrate into magma mixing structures and to understand their significance in the context of magma dynamics. Such an approach is very powerful since multimedia tools can strongly capture the attention of the reader bringing him/her into an interactive and memorable geological experience.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

References

  • Abraham ER, Bowen MM (2002) Chaotic stirring by a mesoscale surface-ocean flow. Chaos 12:373–381

    Article  Google Scholar 

  • Addison PS (1997) Fractals and chaos: an illustrated course. Institute of Physics Publishing, Bristol, pp 256

  • Aref H, El Naschie MS (1995) Chaos applied to fluid mixing. Pergamon, reprinted from Chaos, solutions and fractals. Exeter, GB, 4(6):380

  • Bacon CR (1986) Magmatic inclusions in silicic and intermediate volcanic rocks. J Geophys Res 91:6091–6112

    Article  Google Scholar 

  • Bateman R (1995) The interplay between crystallization, replenishment and hybridization in large felsic magma chambers. Earth Sci Rev 39:91–106

    Article  Google Scholar 

  • Binson J (1996) Chaotic advection by Rossby–Haurwitz waves. Fluid Dyn Res 18:1–16

    Article  Google Scholar 

  • Blake S, Fink JH (2000) On the deformation and freezing of enclaves during magma mixing. J Volcanol Geotherm Res 95:1–8

    Article  Google Scholar 

  • Bresler L, Shinbrot T, Metcalfe G, Ottino JM (1997) Isolated mixing regions: origin, robustness and control. Chem Eng Sci 52:1623–1636

    Article  Google Scholar 

  • Calanchi N, De Rosa R, Mazzuoli R, Ricci Lucchi F, Rossi PL, Santacroce R (1987) L’attivita’ del centro di Pollara (Salina, Isole Eolie). Boll. GNV, pp 187–213

  • Calanchi N, De Rosa R, Mazzuoli R, Rossi PL, Santacroce R, Ventura G (1993) Silicic magma entering a basaltic magma chamber: eruptive dynamics and magma mixing—an example from Salina (Aeolian Islands, Southern Tyrrhenian Sea). Bull Volcanol 55:504–522

    Article  Google Scholar 

  • Cartwright JHE, Feingold M, Piro O (1994) Passive scalars and three-dimensional Liouvillian maps. Physica D 76:22–33

    Article  Google Scholar 

  • Cerbelli S, Zalc JM, Muzzio FJ (2000) The evolution of material lines curvature in deterministic chaotic flows. Chem Eng Sci 55:363–371

    Article  Google Scholar 

  • Collet P, Eckman JP (1980) Iterated maps on the interval as dynamical systems. Progress in physics. Birkhauser, Basel, pp 256

    Google Scholar 

  • Crank J (1975) The mathematics of diffusion. Clarendon, Oxford, pp 424

    Google Scholar 

  • De Campos CP, Dingwell DB, Fehr KT (2004) Decoupled convection cells from mixing experiments with alkaline melts from Phlegrean fields. Chem Geol 213:227–251

    Article  Google Scholar 

  • De Rosa R (1999) Compositional modes in the ash fraction of some modern pyroclastic deposits: their determination and significance. Bull Volcanol 3:162–173

    Article  Google Scholar 

  • De Rosa R, Mazzuoli R, Rossi PL, Santacroce R, Ventura G (1989) Nuovi dati ed ipotesi per la ricostruzione della storia eruttiva dell’Isola di Salina (Isole Eolie). Boll GNV-CNR 2:791–809

    Google Scholar 

  • De Rosa R, Donato P, Ventura G (2002) Fractal analysis of mingled/mixed magmas: an example from the Upper Pollara eruption (Salina Island, southern Tyrrhenian Sea, Italy). Lithos 65:299–311

    Article  Google Scholar 

  • De Rosa R, Guillou H, Mazzuoli R, Ventura G (2003) New Unspiked K-Ar ages of volcanic rocks of the central and western sector of the Aeolian Islands: reconstruction of the volcanic stages. J Volcanol Geotherm Res 120:161–178

    Article  Google Scholar 

  • Denison C, Carlson WD (1997) Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography: part II. Application to natural samples. J Met Geol 15:45–58

    Article  Google Scholar 

  • Didier J, Barbarin B (1991) Enclaves and granite petrology, developments in petrology, 13. Elsevier, Amsterdam, pp 625

    Google Scholar 

  • Eichelberger JC (1990). Vesiculation of mafic magma during replenishment of silicic magma reservoir. Nature 288:446–450

    Article  Google Scholar 

  • Flinders J, Clemens JD (1996) Non-linear dynamics, chaos, complexity and enclaves in granitoid magmas. Trans R Soc Edinburgh Earth Sci 87:225–232

    Article  Google Scholar 

  • Fountain GO, Khakhar DV, Ottino JM (1998) Visualization of three-dimensional chaos. Science 281:683–686

    Article  Google Scholar 

  • Galluccio S, Vulpiani A (1994) Stretching of material lines and surfaces in systems with Lagrangian chaos. Physica A 212:75–98

    Article  Google Scholar 

  • Gillot PY (1987) Histoire volcanique des Iles Eoliennes: arc insulaire or complexe orogenique anulaire? DT IGAL 11:35–42

    Google Scholar 

  • Gonnermann HM, Manga M (2005) Flow banding in obsidian: a record of evolving textural heterogeneity during magma deformation. Earth Planet Sci Lett 236:135–147

    Article  Google Scholar 

  • Haller G (2001) Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149:248–277

    Article  Google Scholar 

  • Keller J (1980) The Island of Salina. Rend Soc It Miner Petrol 36:489–524

    Google Scholar 

  • Lesher CE (1994) Kinetics of Sr and Nd exchange in silicate liquids: theory, experiments, and application to uphill diffusion, isotopic equilibration, and irreversible mixing of magmas. J Geophys Res 99:9585–9604

    Article  Google Scholar 

  • Liu M, Muzzio FJ, Peskin RL (1994a) Quantification of mixing in aperiodic chaotic flows. Chaos Solitions Fractals 4:869–893

    Article  Google Scholar 

  • Liu M, Peskin RL, Muzzio FJ, Leong CW (1994b) Structure of the stretching field in chaotic cavity flows. Am Inst Chem Engin AIChE J 40:1273–1286

    Article  Google Scholar 

  • Lorenz E (1963) Deterministic non-periodic flow. J Atm Sci 20:130–141

    Article  Google Scholar 

  • Mandelbrot BB (1982) The fractal geometry of nature. W.H. Freeman, New York, pp 480

    Google Scholar 

  • Marschallinger R (1998) A method for three-dimensional reconstruction of macroscopic features in geological materials. Comp Geosci 24:875–883

    Article  Google Scholar 

  • McCauley JL (1993) Chaos, dynamics and fractals: an algorithmic approach to deterministic chaos. Cambridge University Press, Cambridge, p 347

    Book  Google Scholar 

  • Metcalfe G, Bina CR, Ottino JM (1995) Kinematic considerations for mantle mixing. Geophys Res Lett 22:743–746

    Article  Google Scholar 

  • Ottino JM (1990) Mixing, chaotic advection and turbulence. Ann Rev Fluid Mech 22:207–254

    Article  Google Scholar 

  • Ottino JM, Leong CW, Rising H, Swanson PD (1988) Morphological structures produced by mixing in chaotic flows. Nature 333:419–425

    Article  Google Scholar 

  • Ottino JM, Muzzio FJ, Tjahjadi M, Franjione JG, Jana SC, Kusch HA (1993) Chaos, symmetry, and self-similarity: exploiting order and disorder in mixing processes. Science 257:754–760

    Article  Google Scholar 

  • Paterson SR, Pignotta, Geoffrey S, Vernon RH (2004) The significance of microgranitoid enclave shapes and orientations. J Struct Geol 26:1465–1481

    Article  Google Scholar 

  • Perugini D, Poli G, Gatta G (2002) Analysis and simulation of magma mixing processes in 3D. Lithos 65:313–330

    Article  Google Scholar 

  • Perugini D, Poli G, Mazzuoli R (2003a) Chaotic advection, fractals and diffusion during mixing of magmas: evidence from lava flows. J Volcanol Geotherm Res 124:255–279

    Article  Google Scholar 

  • Perugini D, Poli G, Christofides G, Eleftheriadis G (2003b) Magma mixing in the Sithonia Plutonic complex, Greece: evidence from mafic microgranular enclaves. Mineral Petrol 78:173–200

    Article  Google Scholar 

  • Perugini D, Ventura G, Petrelli M, Poli G (2004) Kinematic significance of morphological structures generated by mixing of magmas: a case study from Salina Island (Southern Italy). Earth Planet Sci Lett 222:1051–1066

    Article  Google Scholar 

  • Perugini D, Poli G, Valentini L (2005) Strange attractors in plagioclase oscillatory zoning: petrological implications. Contrib Mineral Petrol 149:482–497

    Article  Google Scholar 

  • Petford N, Bryon D, Atherton MP, Hunter RH (1993) Fractal analysis in granitoid petrology—a means of quantifying irregular grain morphologies. Eur J Mineral 5:593–598

    Article  Google Scholar 

  • Petrelli M, Perugini D, Poli G (2005) Time-scales of hybridisation of magmatic enclaves in regular and chaotic flow fields: petrologic and volcanologic implications. Bull Volcanol 68(3):285–293

    Article  Google Scholar 

  • Pierrehumbert RT (1995) Tracer microstructures in the large-eddy dominated regime. In: Aref H, El Naschie MS (eds) Chaos applied to fluid mixing. Pergamon, reprinted from Chaos, solutions and fractals 4, 6, Exeter, G.B, pp 347–366

  • Poli G Perugini D (2002) Strange attractors in magmas: evidence from lava flows. Lithos 65:287–297

    Article  Google Scholar 

  • Poli G, Tommasini S, Halliday AN (1996) Trace elements and isotopic exchange during acid-basic magma interaction processes. Trans R Soc Edinb Earth Sci 87:225–232

    Article  Google Scholar 

  • Pugliese S, Petford N (2001) Reconstruction and visualisation of melt topology in veined microdiorite enclaves. Electron Geosci 6, 1 (vol 6, article no. 3)

  • Snyder D (2000) Thermal effects of the intrusion of basaltic magma into a more silicic magma chamber and implications for eruption triggering. Earth Planet Sci Lett 175:257–273

    Article  Google Scholar 

  • Tang XZ, Boozer AH (1999) A Lagrangian analysis of advection-diffusion equation for a three dimensional chaotic flow. Phys Fluids 11:1418–1434

    Article  Google Scholar 

  • Turcotte DL (1992) Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge, p 412

    Google Scholar 

  • Ventura G (2004) The strain path and kinematics of lava domes: an example from Lipari (Aeolian Islands, Southern Tyrrhenian Sea, Italy). J Geophys Res 109 No.B1 doi:B0120310.1029 /2003JB002740

  • Wada K (1995) Fractal structure of heterogeneous ejecta from the Me-akan volcano, eastern Hokkaido, Japan: implications for mixing mechanism in a volcanic conduit. J Volcanol Geotherm Res 66:69–79

    Article  Google Scholar 

  • Welander P (1955) Studies on the general development of motion in a twodimensional, ideal fluid. Tellus 7:141–156

    Article  Google Scholar 

Download references

Acknowledgments

Editorial handling of J. D. Clemens and N. Petford are gratefully acknowledged. This work was funded by MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) and Università degli Studi di Perugia grants.

Author information

Authors and Affiliations

  1. Department of Earth Sciences, University of Perugia, Piazza Università, 06100, Perugia, Italy

    Diego Perugini, Maurizio Petrelli & Giampiero Poli

Authors
  1. Diego Perugini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maurizio Petrelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giampiero Poli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diego Perugini.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material, approximately 58.5 MB.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perugini, D., Petrelli, M. & Poli, G. A virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations: a new approach for understanding spatial and temporal complexity of magma dynamics. Vis Geosci 13, 1–24 (2008). https://doi.org/10.1007/s10069-006-0004-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10069-006-0004-x

Keywords

Search

Navigation