Alexander A. Proussevitch

Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling

We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2–4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R∼t1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R∼log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water-saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates >1–5 m s−1.

Dynamics of coupled diffusive and decompressive bubble growth in magmatic systems

Bubble growth in an ascending parcel of magma is controlled both by diffusion of oversaturated volatiles and decompression as the magma rises. We have developed a numerical model which explores the processes involved in water exsolution from basaltic and rhyolitic melts rising at a constant rate from magma chamber depths of 4 and 1 km. While the model does not attempt to simulate natural eruptions, it sheds light on the processes which control eruptive behavior under various conditions. Ascent rates are defined such that a constant rate of decompression dP/dt is maintained. A variety of initial ascent rates are considered in the model, from 1 m/s to 100 m/s for basalts, and from a few centimeters per second to 10 m/s for rhyolite, at the base of the conduit. The model results indicate that for any reasonable ascent rate, basaltic melt degasses at a rate sufficient to keep the dissolved volatile concentration at equilibrium with the decreasing ambient pressure. Rhyolitic melt reaches the surface at equilibrium if its ascent rate is less than 1 m/s, but it can erupt with high oversaturation at greater ascent rates. The latter may lead to explosive eruptions. If the ascent rate of rhyolite is 10 m/s or more, then melt barely degasses at all in the conduit and erupts with the highest oversaturation possible. For the case of slow magma rise, bubble growth is limited by decompression. For the case of rapid magma rise, bubble growth is limited by diffusion. The results of our simple model do not accurately simulate natural volcanic eruptions, but suggest that subsequent, more complex models may be able to simulate eruptions using the insights regarding diffusive and decompressive bubble growth processes explored in this study. Numerical modeling of volcanic degassing may eventually lead to better prediction of eruption timing, energetics and hazards of active volcanoes.

Stability of foams in silicate melts

Bubble coalescence and the spontaneous disruption of high-porosity foams in silicate melts are the result of physical expulsion of interpore melt (syneresis) leading to bubble coalescence, and diffusive gas exchange between bubbles. Melt expulsion can be achieved either along films between pairs of bubbles, or along Plateau borders which represent the contacts between 3 or more bubbles. Theoretical evaluation of these mechanisms is confirmed by experimental results, enabling us to quantify the relevant parameters and determine stable bubble size and critical film thickness in a foam as a function of melt viscosity, surface tension, and time. Foam stability is controlled primarily by melt viscosity and time. Melt transport leading to coalescence of bubbles proceeds along inter-bubble films for smaller bubbles, and along Plateau borders for larger bubbles. Thus the average bubble size accelerates with time. In silicate melts, the diffusive gas expulsion out of a region of foam is effective only for water (and even then, only at small length scales), as the diffusion of CO2 is negligible. The results of our analyses are applicable to studies of vesicularity of lavas, melt degassing, and eruption mechanisms.

Recongnition and separation of discrete objects with in complex 3D voxelized structures

Abstract 3D voxelized images can be manipulated if their component parts can be identified, cataloged, and measured. To accomplish this, it is necessary to separate individual convex objects from the complex structures that result from digital observation techniques such as X-ray tomography. Toward this end, we have developed schemes that peel away sequential layers of voxels from complex structures until narrow waists that connect individual objects disappear, and each component object can be identified. These peeling schemes provide the most uniform possible cumulative thickness of removed layers regardless of the orientation of the voxel grid pattern. Consequently, they lead to the most accurate application regarding inter-object interfaces, medial axis analysis, and individual object statistics such as volumes, orientations and interconnectivity. Peeling schemes can be categorized by the number of steps involved in each peeling iteration. Each step removes voxels according to three possible criteria for defining the exterior of a voxel: exposed faces, edges, or corners. Each of these ultimately causes an initial sphere, for example, to evolve into a cube, dodecahedron, or octahedron, respectively. Combinations of steps can be used to create more complex polyhedra (tetrahexadra, trisoctahedra, trapezohedra, and hexoctahedra). The resulting polyhedron that most closely resembles a starting sphere depends on the appropriate definition of “sphericity”. Using a metric based on the standard deviation of the polyhedral surface from that of a concentric sphere of equal volume, the optimal scheme is peeling by faces 7 times, by edges 3 times, and by corners 4 times. This leads to a hexoctahedron with Miller indices (14 7 4) and a standard deviation of 0.025. Using a metric based on minimizing surface area, the optimal scheme is peeling by faces 9 times, by edges 6 times, and by corners 5 times, leading to a hexoctahedron with Miller indices (20 11 5). In the past, only 1-step peeling has been used (by faces or corners). If computational or conceptual constraints limit peeling to 1-step, the criterion of edges should be used, as the dodecahedron that results deviates from a sphere by only half the amount of either the cube or octahedron resulting from 1-step peeling of faces or corners, respectively. We also determined the best criteria for 2-step and 3-step peeling. The peeling schemes we identify can be used to separate objects from complex structures for application to a number of geological and other problems. Information that emerges from the analysis includes object volumes, which can be used for determining grain- or bubble-size distributions in volcanologic, petrologic, and sedimentary applications, among others.

Thermal effects of magma degassing

Abstract The thermodynamics of diffusive bubble growth is dominated by latent heat of water exsolution (vaporization) and the work of gas expansion (P dV work). A numerical assessment of the effects of these on cooling of bubbly magma (water in albite) indicates that a magma can exsolve volatiles at equilibrium, or with varying degrees of oversaturation, depending on decompression history and degassing kinetics. Heat of water exsolution (vaporization) from magmatic melts has not previously been experimentally or analytically determined, and we have evaluated it from others thermodynamic functions known for the albite-water system. Heat of exsolution is small for pressures over 100 MPa, but can reach 20 kJ/mole at 1–2 MPa (10–20 bar). Oversaturation degassing at 10–20 bar can cause cooling of albite by 8 K/wt.% of exsolved water. The thermal effect of equilibrium degassing depends on the starting pressure of decompression because it follows the solubility curve. For a saturated melt at 100 MPa (4 wt.% water), it can cool a magma at least by 35 K before it disrupts into spray as gas volume fraction exceeds 0.8. Although we do not specifically consider the dynamics of bubble interactions in this study, our results suggest that the dynamic cooling rate could be significant at the vent of an erupting magma column, and under extreme eruption conditions, can lead to glass formation around fast growing bubbles of magmatic foam. This could cause fragmentation into fine ash by brittle failure. Conversely, bubble wall cooling (even before glass formation) can serve to reduce diffusive volatile flux into bubbles, decreasing the overall cooling of the system, and lead to solidification of oversaturated magmas, as occasionally observed in eruption products.

Analysis of Vesicular Basalts and Lava Emplacement Processes for Application as a Paleobarometer/Paleoaltimeter

We have developed a method for determining paleoelevations of highland areas on the basis of the vesicularity of lava flows. Vesicular lavas preserve a record of paleopressure at the time and place of emplacement because the difference in internal pressure in bubbles at the base and top of a lava flow depends on atmospheric pressure and lava flow thickness. At the top of the flow, the pressure is simply atmospheric pressure, while at the base, there is an additional contribution of hydrostatic lava overburden. Thus the modal size of the vesicle (bubble) population is larger at the top than at the bottom. This leads directly to paleoatmospheric pressure because the thickness of the flow can easily be measured in the field, and the vesicle sizes can now be accurately measured in the lab. Because our recently developed technique measures paleoatmospheric pressure, it is not subject to uncertainties stemming from the use of climate‐sensitive proxies, although like all measurements, it has its own sources of potential error. Because measurement of flow thickness presupposes no inflation or deflation of the flow after the size distribution at the top and bottom is “frozen in,” it is essential to identify preserved flows in the field that show clear signs of simple emplacement and solidification. This can be determined by the bulk vesicularity and size distribution as a function of stratigraphic position within the flow. By examining the stratigraphic variability of vesicularity, we can thus reconstruct emplacement processes. It is critical to be able to accurately measure the size distribution in collected samples from the tops and bottoms of flows because our method is based on the modal size of the vesicle population. Previous studies have used laborious and inefficient methods that did not allow for practical analysis of a large number of samples. Our recently developed analytical techniques involving high‐resolution x‐ray computed tomography (HRXCT) allow us to analyze the large number of samples required for reliable interpretations. Based on our ability to measure vesicle size to within 1.7% (by volume), a factor analysis of the sensitivity of the technique to atmospheric pressure provides an elevation to within about ±400 m. If we assume sea level pressure and lapse rate have not changed significantly in Cenozoic time, then the difference between the paleoelevation “preserved” in the lavas and their present elevation reflects the amount of uplift or subsidence. Lava can be well dated, and therefore a suite of samples of various ages will constrain the timing of epeirogenic activity independent of climate, erosion rates, or any other environmental factors. We have tested our technique on basalts emplaced at known elevations at the base, flanks, and summit of Mauna Loa. The results of the analysis accurately reconstruct actual elevations, demonstrating the applicability of the technique. The tool we have developed can subsequently be applied to problematic areas such as the Colorado and Tibetan Plateaus to determine the history of uplift.

The size range of bubbles that produce ash during explosive volcanic eruptions

Volcanic eruptions can produce ash particles with a range of sizes and morphologies. Here we morphologically distinguish two textural types: Simple (generally smaller) ash particles, where the observable surface displays a single measureable bubble because there is at most one vesicle imprint preserved on each facet of the particle; and complex ash particles, which display multiple vesicle imprints on their surfaces for measurement and may contain complete, unfragmented vesicles in their interiors. Digital elevation models from stereo-scanning electron microscopic images of complex ash particles from the 14 October 1974 sub-Plinian eruption of Volcán Fuego, Guatemala and the 18 May 1980 Plinian eruption of Mount St. Helens, Washington, U.S.A. reveal size distributions of bubbles that burst during magma fragmentation. Results were compared between these two well-characterized eruptions of different explosivities and magma compositions and indicate that bubble size distributions (BSDs) are bimodal, suggesting a minimum of two nucleation events during both eruptions. The larger size mode has a much lower bubble number density (BND) than the smaller size mode, yet these few larger bubbles represent the bulk of the total bubble volume. We infer that the larger bubbles reflect an earlier nucleation event (at depth within the conduit) with subsequent diffusive and decompressive bubble growth and possible coalescence during magma ascent, while the smaller bubbles reflect a relatively later nucleation event occurring closer in time to the point of fragmentation. Bubbles in the Mount St. Helens complex ash particles are generally smaller, but have a total number density roughly one order of magnitude higher, compared to the Fuego samples. Results demonstrate that because ash from explosive eruptions preserves the size of bubbles that nucleated in the magma, grew, and then burst during fragmentation, the analysis of the ash-sized component of tephra can provide insights into the spatial distribution of bubbles in the magma prior to fragmentation, enabling better parameterization of numerical eruption models and improved understanding of ash transport phenomena that result in pyroclastic volcanic hazards. Additionally, the fact that the ash-sized component of tephra preserves BSDs and BNDs consistent with those preserved in larger pyroclasts indicates that these values can be obtained in cases where only distal ash samples from particular eruptions are obtainable.

Sizing up the bubbles that produce very fine ash during explosive volcanic eruptions

] Explosive volcanic eruptions emit large proportions ofvery fine ash (<30 mm) into the atmosphere, posing hazardsto aviation, infrastructure, and human health. Here wepresent an analysis of bubble size distributions at the pointof fragmentation during the 18 May 1980 eruption of MSHthrough the examination of simple ash particles in distallydeposited fall samples. The external surfaces of individualfine ash grains preserve the morphology of the bubbles thatburst to form the ash, so bubble sizes can be measuredusing stereo-scanning electron microscopy. Simple ashparticles are those that allow the measurement of a singlevesicle imprint per individual grain. These simple ashparticles are the finest component of the tephra, and canthus travel great distances from the source volcano.Analyses of samples provided bubble volume distributionswith a dominant peak between 560 and 5600 mm

Vesiculation and fragmentation history in a submarine scoria cone-forming eruption, an example from Nishiizu (Izu Peninsula, Japan)

An uplifted, >50-m-thick, half-dissected, submarine-emplaced (below wave-base) scoria cone occurs as dipping beds in coastal outcrops at Nishiizu, on the Izu Peninsula in Japan. Concentrically outward-dipping, weakly stratified, ungraded, framework-supported thin-to-very thick beds consist of brown coarse tuff to scoria lapilli-tuff, with outsized fluidal bombs throughout; accessory lithic clasts chiefly occur in the lowermost visible beds. Scoria bombs have quenched margins, weak bread-crust textures and their vesicle number densities decrease inward, which is indicative of fast surface cooling. Composite textures in the scoria bombs indicate recycling and agglutination of quenched and semi-molten pyroclasts at the submarine vent. In contrast to weak concentric gradations in vesicle size distribution in the bombs, lapilli have asymmetrical gradients in vesicle size distribution, indicating that they are fragments of coarser, quenched lumps. Three grain-size modes characterise the Nishiizu brown scoria, with coarse magma lumps ejected during magmatic fragmentation and quench-jointed upon contact with seawater, to be subsequently fragmented into lapilli and coarse ash by various styles of fragmentation where seawater plays a critical role. The cone was constructed by slow-moving fallout-fed granular flow/creep, fed directly by suspension settling focused at the crater rim but extending onto the cone flanks, with only minor resedimentation by granular flows. Nishiizu deposits yield an exceptional record of eruption and sedimentation dynamics during submarine cone-building activity, and in this study we compare their vesiculation and fragmentation mechanisms with those of potential subaerial analogues.

Submarine deposits from pumiceous pyroclastic density currents traveling over water : an outstanding example from offshore Montserrat (IODP 340).

Pyroclastic density currents have been observed to both enter the sea, and to travel over water for tens of kilometers. Here, we identified a 1.2-m-thick, stratified pumice lapilli-ash cored at Site U1396 offshore Montserrat (Integrated Ocean Drilling Program [IODP] Expedition 340) as being the first deposit to provide evidence that it was formed by submarine deposition from pumice-rich pyroclastic density currents that traveled above the water surface. The age of the submarine deposit is ca. 4 Ma, and its magma source is similar to those for much younger Soufriere Hills deposits, indicating that the island experienced large-magnitude, subaerial caldera-forming explosive eruptions much earlier than recorded in land deposits. The deposit’s combined sedimentological characteristics are incompatible with deposition from a submarine eruption, pyroclastic fall over water, or a submarine seafloor-hugging turbidity current derived from a subaerial pyroclastic density current that entered water at the shoreline. The stratified pumice lapilli-ash unit can be subdivided into at least three depositional units, with the lowermost one being clast supported. The unit contains grains in five separate size modes and has a >12 phi range. Particles are chiefly subrounded pumice clasts, lithic clasts, crystal fragments, and glass shards. Pumice clasts are very poorly segregated from other particle types, and lithic clasts occur throughout the deposit; fine particles are weakly density graded. We interpret the unit to record multiple closely spaced (<2 d) hot pyroclastic density currents that flowed over the ocean, releasing pyroclasts onto the water surface, and settling of the various pyroclasts into the water column. Our settling and hot and cold flotation experiments show that waterlogging of pumice clasts at the water surface would have been immediate. The overall poor hydraulic sorting of the deposit resulted from mixing of particles from multiple pulses of vertical settling in the water column, attesting to complex sedimentation. Slow-settling particles were deposited on the seafloor together with faster-descending particles that were delivered at the water surface by subsequent pyroclastic flows. The final sediment pulses were eventually deflected upon their arrival on the seafloor and were deposited in laterally continuous facies. This study emphasizes the interaction between products of explosive volcanism and the ocean and discusses sedimentological complexities and hydrodynamics associated with particle delivery to water.