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Introduction Volcanoes are the surface expression of heat-transfer processes taking place beneath the solid (or liquid) surface of a planet. For Earth, these processes involve convection of the hot interior and motion of the cold crust to bring a mixture of silicate liquids and solids, together with lower molecular weight gases, to the surface. This global-scale system is complex and difficult to observe, but understanding how volcanoes work provides a route for constraints.
Another good reason for understanding volcanoes is to enable forecasting of the hazards they present. Small-scale volcanic activity, for example strombolian eruptions, happens frequently. This short time period between events, when compared with the timescale of human endeavour, ensures that these eruptions pose only minor local hazard. As eruption magnitude increases, repose timescales lengthen to many times that of human endeavour and our experience of such events lies in the interpretation of the rock, and other, records. Between these two extremes lies a spectrum of complex primary and secondary volcanic processes for which data can be difficult to obtain; however, Information about volcanic process can be obtained from a number of approaches.
Geological record
Evidence of past volcanic processes is available from the geological record. This provides a rich source of observations and samples over time periods extending from the end of an eruption to, potentially, the planetary lifetime. The rock record represents an integration of all the processes that have produced the observed physical and chemical data at the time of measurement. Unravelling and interpreting all the processes to provide a unique sequence of events presents one of the great challenges of Earth Science.
Field observation
Measurements taken during eruptions provide a different view of volcanic activity. Because processes are underway, and can be measured, there is less uncertainty about the sequence of events that produce a particular physical or chemical feature in the rock record. Parameters such at temperature, ground motion, gas and magma chemistry, and atmospheric perturbation provide powerful tools with which to constrain volcanic processes, especially when combined. Growth in consumer technology has provided both quality and affordability of electronic devices, including communications, which have benefited much of science, volcanology included. Perhaps one of the most powerful tools has been the development of digital imaging. This has facilitated an explosion of readily available data on volcanic processes that can be interpreted in unprecedented detail. The challenge here is in linking these surface observations to a unique interpretation of sub-surface source processes.
Theoretical modelling
Volcanic processes should, like all else, follow the principles and laws of Physics. This enables the relationships between physical and chemical parameters to be related to both each other and to time and space. These theoretical relationships may be based on fundamental laws, but may also be empirical in nature, especially where complexity is high and understanding patchy. Levels of variability and uncertainty in the values of physical and chemical parameters may require a stochastic approach (e.g., Mader et al., 2006; Beven, 2009) to identify the most likely outcomes of particular sequences of events. Again, consumer technology has driven the availability of computer power that has lead to the exploration of theoretical problems that were unapproachable until recently. The power of theoretical modelling lies in its ability to quantify parameters that are either inaccessible by field measurement, or unmeasurable by any means, as a function of time and space. The challenges here lie in: (1) identification of the controlling physical and chemical parameters to model the correct process physics, and (2) quantification of parameter uncertainties to judge the plausibility of a range of possible outcomes.
Laboratory modelling
Laboratory experiments allow the investigation of processes in a controlled and repeatable environment. Experiments are fundamental to quantifying the physical and chemical properties of volcanic materials. One example is how experiments have quantified the response of volcanic materials to an applied force. The chemical and physical diversity of volcanic materials, combined with often rapidly changing applied force, makes this a difficult problem that has been studied for many decades. We now have some understanding of the complexity of behaviour generated by: (1) the degassing of volatiles, (2) changes in behaviour with strain rate (viscoelasticity), (3) the presence of solid particles (crystals), (4) the presence of bubbles, (5) changes of temperature, and (6) changes of pressure. Naturally, all there aspects are interlinked and processes commonly take place under dynamic conditions.
Another experimental approach is to use materials that are not volcanic. This is known as analogue modelling and forms the main focus here.
Combined tactics
None of these approaches operate in isolation, and the most insightful volcanology is often the result of combining these approaches to provide the strongest possible constraints. The geological record and field observation provide 'ground truth' data that theoretical and experimental approaches should be tested against. Theoretical and experimental approaches can provide information about processes that are difficult to unravel from the rock record and have not been subject to field observation. The contribution of analogue experimentation lies in: (1) giving qualitative insight into the controlling parameters and the range of processes that are possible in a particular system, and (2) providing quantitative data against which theoretical modelling can be tested.
Analogue experimentation
Field observation provides real volcano data, but is subject to certain challenges: (1) volcanic activity cannot be repeated at will, (2) there is no control over many of the variables, (3) the environment can be hostile and changeable, and (4) the processes creating the observation are often not themselves observable. Despite this, field observations are the most valuable source of volcanic data.
Analogue experimentation aims to complement some of these difficulties by making laboratory models of volcanic processes. The study of a laboratory model provides real data for the experimental system, i.e., you are observing the interactions of real atoms and molecules. The challenge for analogue experimentation is to make plausible links between laboratory processes that are readily observable and volcanic processes that are often only visible by their secondary or tertiary effects. Plausibility is gained by establishing that the laboratory system is likely to behave in an analogous way to the volcanic system, at least some of the time, by making similarity arguments or more rigorous scaling calculations.
Qualitative similarity
Here, we are looking for broad behavioural similarities that indicate our experiments may have some volcanic value. For example, if we were experimenting to try to understand aspects of lava flows, then we need to use an experimental material that has broadly similar properties but over temperature, pressure and size ranges readily employable in the laboratory. Lava shows a broad range of responses to an applied force that depends on time, position and history. Choosing a Newtonian liquid such as water that has a discrete solidification temperature is unlikely to give useful information about lava flow processes, although differences between systems can be useful in highlighting the roles of particular parameters. Ideally, the analogue 'lava' should change its behaviour from Newtonian liquid at high (< 100°C) temperature, through non-Newtonian fluid with yield strength, to a solid material at low (~ 20°C) temperature. In reality, ideal analogue materials rarely exist and compromise must be made. One analogue material used for lava flow experiments is polyethylene glycol or PEG (e.g., Cashman et al., 2006), a wax that solidifies at about 19°C. Although PEG is not strictly analogous to lava, the results of experiments give great insight into how lavas flow, and allow the testing of models applicable to lava flows. This is because well-designed PEG experiments can capture some of the controlling physics of lava flow.
Quantitative scaling
In addition to selecting an analogue material likely to mimic the behaviour of a volcanic system, experimental processes should be happening in the same (or similar) mode of behaviour. One example may be that a flow of volcanic material happens under laminar conditions, whereas experiments were carried out under turbulent conditions. It is then difficult to plausibly link the experimental results with the volcanic process, although useful data are still obtained should there be volcanic conditions under which turbulent flow could occur.
Assessment of this is usually a quantitative process that acts to link the laboratory scale to the volcanic scale through the use of a dimensional analysis (e.g., Palma et al., 2011). This analysis identifies dimensionless quantities (numbers) that indicate the balance of potential controlling factors within a particular system. There are many dimensionless quantities [e.g., see http://en.wikipedia.org/wiki/Dimensionless_quantity], and individual dimensionless quantities can be formulated in different ways for different applications. Perhaps the most well known dimensionless quantity assesses the balance between inertia and viscosity in a flowing fluid, and is known as the Reynolds number (Re), [e.g., see http://en.wikipedia.org/wiki/Reynolds_number]. The magnitude of the Reynolds number provides quantitative scaling between different fluid systems, for example, a low-density spherical particle rising (at terminal velocity) in water would drive similar water motion to the air motion driven by a spherical particle falling (at terminal velocity) in air. The dimensionless quantities for the two systems does not have to be identical, but to be quantitatively scaled they do need to both fall within a range associated with a particular behaviour.
The discussion of Re raises two general issues to highlight about the principle of analogue experimentation. Firstly, the specification of a spherical particle is often achieved during experiments, indeed such a particle shape is preferred because it reduces complexity and improves repeatability. There are also pragmatic reasons in that many different materials are available as spherical particles. However, spherical particles are rarely found volcanically, with the major exception being small beads from highly explosive events involving low viscosity magma. Secondly, terminal velocity was specified, i.e., the system was in equilibrium. Many volcanic systems are operating under highly dynamic conditions and this may act to modify quantitative scaling.
Identification of dimensionless quantities applicable to a specific experimental system can be undertaken using a dimensional analysis. The controlling variables will have dimensions that are a combination of the basic dimensional quantities: mass (M kg), length (L m), time (T s), temperature (
K), electric current (l A), number (N moles), luminous intensity (C candela). The number of basic dimensional quantities applicable to a specific experimental system (n) can be identified. The number of controlling variables (m) can also be identified, although this may vary dependent on the system behaviour, and may take some experimentation to determine.
Where m < or = n + 1 then the dimensionless combinations of the variables can be readily determined. Where
m > n + 1 then methods such as the Buckingham Pi theorem can be applied to identify dimensionless groups from combinations of the system variables. The dimensionless groups identified by this process then need to be understood in terms of there physical meaning. Scaling between experiment and volcano is then assessed by comparison of the dimensionless groups calculated for both. For experiment to give valuable insight the dimensionless groups may need to be equated, or need to fall within a certain range that defines a specific behavioural regime.
The references below provide more specific details of the scaling process and its application to specific processes.
Analogue experiments and other useful material in the literature
Below is a list of publications that incorporate analogue experimentation relevant to volcanology. The aim is for this to be as complete as possible. This is work in progress, but please notify any omissions to Steve Lane (s.lane@lancaster.ac.uk).
In Progress...
Acocella, V., F. Cifelli, R. Funiciello, (2000). Analogue models of collapse calderas and resurgent domes. Journal of Volcanology and Geothermal Research, 104(1–4), 81-96.
Acocella, V., F. Cifelli, R. Funiciello, (2001). The control of overburden thickness on resurgent domes: insights from analogue models. Journal of Volcanology and Geothermal Research, 111, 137–153.
Acocella, V., (2005). Modes of sector collapse of volcanic cones: insights from analogue experiments. Journal of Geophysical Research, 110, B02205.
Acocella, V., Neri, M. and Norini, G. (2013), An overview of experimental models to understand a complex volcanic instability: Application to Mount Etna, Italy. Journal of Volcanology and Geothermal Research, 251, 98-111.
Alidibirov, M., Panov, V., (1998). Magma fragmentation dynamics: experiments with analogue porous low-strength material. Bulletin of Volcanology, 59(7), 481-489.
Allen, S. R., Freundt, A., (2006). Resedimentation of cold pumiceous ignimbrite into water: facies transformations simulated in flume experiments. Sedimentology, 53(4), 1365-3091.
Allen, S.R., Freundt, A., Kurokawa, K., (2012). Characteristics of submarine pumice-rich density current deposits sourced from turbulent mixing of subaerial pyroclastic flows at the shoreline: field and experimental assessment. Bulletin of Volcanology, 74(3), 657-675.
Andrade, S.D. and van Wyk de Vries, B., (2010). Structural analysis of the early stages of catastrophic stratovolcano flank-collapse using analogue models. Bulletin of Volcanology, 72(7), 771-789.
Baas, J. H., Van Kesteren, W., Postma, G., (2004). Deposits of depletive high-density turbidity currents: a flume analogue of bed geometry, structure and texture. Sedimentology, 51(5), 1365-3091.
Bagdassarov, N., H. Pinkerton, (2004), Transient phenomena in vesicular lava flows based on laboratory experiments with analogue materials, Journal of Volcanology and Geothermal Research, 132(2-3), 115-136.
Belien, I. B., K. V. Cashman, A. W. Rempel, (2010). Gas accumulation in particle-rich suspensions and implications for bubble populations in crystal-rich magma, Earth and Planetary Science Letters, 297 (1–2), 133-140.
Berthelote, A., Prakash, A. and Dehn, J., (2008). An empirical function to estimate the depths of linear hot sources: Laboratory modeling and field measurements of lava tubes. Bulletin of Volcanology, 70(7), 813-824.
Beven, K., (2008), Environmental Modelling: An Uncertain Future? CRC Press, 978-0415457590.
Blake, S., B.C Bruno, (2000). Modelling the emplacement of compound lava flows. Earth and Planetary Science Letters, 184(1), 181-197.
Bonaccorso, A., G. Currenti, C. Del Negro, E. Boschi, (2010). Dike deflection modelling for inferring magma pressure and withdrawal, with application to Etna 2001 case. Earth and Planetary Science Letters, 293 (1–2), 121-129.
Cantelli, A., S. Johnson, J. D. L. White, G. Parker, (2008). Sediment Sorting in the Deposits of Turbidity Currents Created by Experimental Modeling of Explosive Subaqueous Eruptions. The Journal of Geology , 116(1), 76-93.
Caricchi, L., Pommier, A., Pistone, M., Castro, J., Burgisser, A., et al., (2011). Strain-induced magma degassing: insights from simple-shear experiments on bubble bearing melts. Bulletin of Volcanology, 73(9), 1245-1257.
Cashman, K. V., R. C. Kerr, R. W. Griffiths (2006), A laboratory model of surface crust formation and disruption on lava flows through non-uniform channels, Bull. Volcanol. 68: 753–770.
Castruccio, A., A. C. Rust, and R. S. J. Sparks (2010). Rheology and flow of crystal-bearing lavas: Insights from analogue gravity currents. Earth Planet. Sci. Lett., 297, 471-480.
Cimarelli, C., A. Costa, S. Mueller & H. M. Mader (2011). Rheology of magmas with bimodal crystal size and shape distributions: Insights from analog experiments,. Geochem. Geophys. Geosyst., 12, Q07024.
Del Gaudio, P., Ventura, G. and Taddeucci, J. (2013), The effect of particle size on the rheology of liquid-solid mixtures with application to lava flows: Results from analogue experiments. Geochemistry, Geophysics, Geosystems, Accepted, 2013.
Dioguardi, F., Dellino, P. and de Lorenzo, S. (2013), Integration of large-scale experiments and numerical simulations for the calibration of friction laws in volcanic conduit flows. Journal of Volcanology and Geothermal Research, 250, 75-90.
Donnadieu, F. & O. Merle (1998). Experiments on the indentation process during cryptodome intrusions: new insights into Mount St. Helens deformation. Geology, 26, 79–82.
Donnadieu, F. & O. Merle, (2001). Geometrical constraints of the 1980 Mount St. Helens intrusion from analogue models. Geophysical Research Letters, 28, 639–642.
Estep, J. and Dufek, J. (2013), Discrete element simulations of bed force anomalies due to force chains in dense granular flows. Journal of Volcanology and Geothermal Research, 254, 108-117.
Galland, O., P. Cobbold, E. Hallot, & J. de Bremond d'Ars, (2006). Use of vegetable oil and silca powder for scale modelling of magmatic intrusion in a deforming brittle crust. Earth and Planetary Science Letters, 243, 786–804.
Hailermariam, H. & G. Mulugeta, (1998). Temperature-dependent rheology of bouncing putties used as rock analogs. Tectonophysics, 294, 131–141.
Holasek, R. E., Andrew W. Woods, Stephen Self, (1996). Experiments on gas-ash separation processes in volcanic umbrella plumes. Journal of Volcanology and Geothermal Research, 70 (3–4), 169-181.
Hubbert, M. K. (1937) Theory of scale models as applied to the study of geologic structures. Bull Geol Soc Am 48:1459–1520.
James, M.R., Lane, S.J., Wilson, L. and Corder, S.B., (2009). Degassing at low magma-viscosity volcanoes: Quantifying the transition between passive bubble-burst and Strombolian eruption. Journal of Volcanology and Geothermal Research, 180(2-4), 81-88.
Kavanagh, J.L., Menand, T. and Daniels, K.A. (2013), Gelatine as a crustal analogue: Determining elastic properties for modelling magmatic intrusions. Tectonophysics, 582, 101-111.
Kervyn, M., Ernst, G.G.J., van Wyk de Vries, B., Mathieu, L. and Jacobs, P., (2009). Volcano load control on dyke propagation and vent distribution: Insights from analogue modeling. Journal of Geophysical Research - Solid Earth, 114, B03401.
Kueppers, U., Putz, C., Spieler, O. and Dingwell, D.B., (2012). Abrasion in pyroclastic density currents: Insights from tumbling experiments. Physics and Chemistry of the Earth, Part A, 45-46, 33-39.
Lane, S.J., Phillips, J.C. and Ryan, G.A., (2008). Dome-building eruptions: insights from analogue experiments. Geological Society, London, Special Publications, 307, 207-237.
Lane, S. J., James, M. R. and Corder, S. B. (2013), Volcano infrasonic signals and magma degassing: First-order experimental insights and application to Stromboli. Earth and Planetary Science Letters, 377–378, 169–179.
Lavallee, Y., Benson, P.M., Heap, M.J., Hess, K-U., Flaws, A., et al. (2013). Reconstructing magma failure and the degassing network of dome-building eruptions. Geology, 41(4), 515-518.
Mader, H. M., S. G. Coles, C. B. Connor, L. J. Connor, (2006), Statistics in Volcanology, GSL on behalf of IAVCEI, 978-1-86239-208-3.
Mastin, L.G., Spieler, O. and Downey, W.S., (2009). An experimental study of hydromagmatic fragmentation through energetic, non-explosive magma-water mixing. Journal of Volcanology and Geothermal Research, 180(2-4), 161-170.
Mathieu, L., B. van Wyk de Vries, M. Pilato, V. R. Troll, (2011). The interaction between volcanoes and strike-slip, transtensional and transpressional fault zones: Analogue models and natural examples. Journal of Structural Geology, 33 (5), 898-906.
Mathieu, L., B. van Wyk de Vries, (2011). The impact of strike-slip, transtensional and transpressional fault zones on volcanoes. Part 1: Scaled experiments. Journal of Structural Geology, 33 (5), 907-917.
Mauduit, T. & O. Dauteuil, (1996). Small-scale models of oceanic transform zones. Journal of Geophysical Research, 101, 20195–20209.
McLeod, P., S. Tait, (1999). The growth of dykes from magma chambers. Journal of Volcanology and Geothermal Research, 92 (3–4), 231-245.
Mcleod, P., Carey, S., Sparks, R. S. J., (1999). Behaviour of particle-laden flows into the ocean: experimental simulation and geological implications. Sedimentology, 46(3), 523-536.
Menand, T., Phillips, J. and Sparks, R.S.J., (2008). Circulation of bubbly magma and gas segregation within tunnels of the potential Yucca Mountain repository. Bulletin of Volcanology, 70(8), 947-960.
Merle, O. & A. Borgia, (1996). Scaled experiments of volcanic spreading. Journal of Geophysical Research, 101, 13805–13817.
Merle, O. & B. Vendeville, (1995). Experimental modelling of thin-skinned shortening around magmatic intrusions. Bulletin of Volcanology, 57, 33–43.
Merle, O, (1998). Internal strain within lava flows from analogue modelling. Journal of Volcanology and Geothermal Research, Volume 81 (3–4), 189-206.
Merle, O., N. Vidal & B. van Wyk de Vries, (2001). Experiments on vertical basement fault reactivation below volcanoes. Journal of Geophysical Research, 106, 2153–2162.
Middleton, G. V., P. R. Wilcock (1994) Mechanics in the Earth and environmental sciences. Cambridge University Press, Cambridge, ISBN: 9780521446693.
Nolesini, T., F. Di Traglia, C. Del Ventisette, S. Moretti & N. Casagli, (2013). Deformations and slope instability on Stromboli volcano: Integration of GBInSAR data and analog modeling, Geomorphology, 180–181, 242-254.
Norini, G. & V. Acocella, (2011). Analogue modeling of flank instability at Mount Etna: understanding the driving factors. Journal of Geophysical Research, 116, B07206.
Palma, J. L., S. Blake, E. S. Calder (2011), Constraints on the rates of degassing and convection in basaltic open-vent volcanoes, Geochem. Geophys. Geosyst., 12, Q11006.
Perret, F.A., (1950), Volcanological observations. Carnegie Institute of Washington, Publication 549. Washington D.C., William Byrd Press.
Perugini, D. and Kueppers, U., (2012). Fractal Analysis of Experimentally Generated Pyroclasts: A Tool for Volcanic Hazard Assessment. Acta Geophysica, 60(3), 682-698.
Phillips, J. C., A. W. Woods, (2001). Bubble plumes generated during recharge of basaltic magma reservoirs. Earth and Planetary Science Letters, 186(2), 297-309.
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Roche, O., Druitt, T. H., Merle, O., (2000). Experimental study of caldera formation. Journal of Geophysical Research: Solid Earth, 105(B1), 2156-2202.
Roche, O., B. van Wyk de Vries, T.H. Druitt, (2001). Sub-surface structures and collapse mechanisms of summit pit craters. Journal of Volcanology and Geothermal Research, 105(1–2), 1-18.
Roche, O., Montserrat, S., Niño, Y. and Tamburrino, A., (2008). Experimental observations of water-like behavior of initially fluidized, dam break granular flows and their relevance for the propagation of ash-rich pyroclastic flows. Journal of Geophysical Research, 113, B12203.
Roche, O., Montserrat, S., Niño, Y. and Tamburrino, A., (2010). Pore fluid pressure and internal kinematics of gravitational laboratory air-particle flows: Insights into the emplacement dynamics of pyroclastic flows. Journal of Geophysical Research, 115, B09206.
Roche, O., Gilbertson, M.A., Phillips, J.C., Sparks, R.S.J., (2004), Experimental study of gas-fluidized granular flows with implications for pyroclastic flow emplacement. Journal of Geophysical Research 109, paper B10201.
Ross, P.-S., White, J.D.L., Valentine, G.A., Taddeucci, J., Sonder, I., et al., (2013). Experimental birth of a maar-diatreme volcano. Journal of Volcanology and Geothermal Research, 260, 1-12.
Ross, P.-S., White, J.D.L., Zimanowski, B., Büttner, R., (2008), Multiphase flow above explosion sites in debris-filled volcanic vents: insights from analogue experiments. Journal of Volcanology and Geothermal Research 178, 104-112.
Ross, P.-S., White, J.D.L., Zimanowski, B., Büttner, R., (2008), Rapid injection of particles and gas into non-fluidized granular material: volcanological implications. Bulletin of Volcanology 70, 1151-1168.
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Seyfried, R., Freundt, A., (2000). Experiments on conduit flow and eruption behavior of basaltic volcanic eruptions. Journal of Geophysical Research: Solid Earth, 105(B10), 2156-2202.
Schipper, C.I., White, J.D.L., Zimanowski, B., Büttner, R., Sonder, I., Schmid, A., (2011), Experimental interaction of magma and "dirty" coolants. Earth andPlanetary Science Letters 303, 323-336.
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