Bubble coalescence in basalt flows: comparison of a numerical model with natural examples

Gas accumulation in magma may be aided by coalescence of bubbles because large coalesced bubbles rise faster than small bubbles. The observed size distribution of gas bubbles (vesicles) in lava flows supports the concept of post-eruptive coalescence. A numerical model predicts the effects of rise and coalescence consistent with observed features. The model uses given values for flow thickness, viscosity, volume percentage of gas bubbles, and an initial size distribution of bubbles together with a gravitational collection kernel to numerically integrate the stochastic collection equation and thereby compute a new size spectrum of bubbles after each time increment of conductive cooling of the flow. Bubbles rise and coalesce within a fluid interior sandwiched between fronts of solidification that advance inward with time from top and bottom. Bubbles that are overtaken by the solidification fronts cease to migrate. The model predicts the formation of upper and lower vesicle-rich zones separated by a vesicle-poor interior. The upper zone is broader, more vesicular, and has larger bubbles than the lower zone. Basaltic lava flows in northern California exhibit the predicted zonation of vesicularity and size distribution of vesicles as determined by an impregnation technique. In particular, the size distribution at the tops and bottoms of flows is essentially the same as the initial distribution, reflecting the rapid initial solidification at the bases and tops of the flows. Many large vesicles are present in the upper vesicular zones, consistent with expected formation as a result of bubble coalescence during solidification of the lava flows. Both the rocks and model show a bimodal or trimodal size distribution for the upper vesicular zone. This polymodality is explained by preferential coalescence of larger bubbles with subequal sizes. Vesicularity and vesicle size distribution are sensitive to atmospheric pressure because bubbles expand as they decompress during rise through the flow. The ratio of vesicularity in the upper to that in the lower part of a flow therefore depends not only on bubble rise and coalescence, but also on flow thickness and atmospheric pressure. Application of simple theory to the natural basalts suggests solidification of the basalts at 1.0±0.2 atm, consistent with the present atmospheric pressure. Paleobathymetry and paleoaltimetry are possible in view of the sensitivity of vesicle size distributions to atmospheric pressure. Thus, vesicular lava flows can be used to crudely estimate ancient elevations and/or sea level air pressure.     

Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns

Three models for the dynamics of seismic airgun‐generated bubbles and their associated far‐field signals are developed and compared with geophysical data. The first model of an airgun‐generated bubble uses a spherical approximation, the second is an approximate Lagrangian model which allows for small deformations from a spherical shape, whilst the final model is an axisymmetric boundary‐integral method which permits the bubble to evolve into highly non‐spherical geometries. The boundary‐integral method also allows both geometric interference and strong dynamic interactions in multi‐bubble studies. When comparing the spherical model to experimental data there are three apparent, significant differences: the magnitude of the primary pressure peak, which is greater in the model; the subsequent decay of the pressure peaks and motion – the experimental data demonstrating greater decay and a slower rise rate; and the frequency of oscillation, which is slower in the experimental data. It is believed that the first discrepancy is due to the initial stages of expansion where the compressed air is forced to sparge through the airgun ports. The other differences indicate that there is some other energy‐loss mechanism which is not accounted for in the spherical bubble model. Non‐spherical bubble behaviour is investigated through the use of two different deformable many‐bubble codes and their predictions are compared with the spherical model and experimental data. The Lagrangian model predicts the formation of a buoyancy‐driven liquid jet on the first collapse of a typical airgun bubble; however, the model breaks down when the bubble becomes significantly deformed, due to a low‐order spherical‐harmonic approximation for the potential. The axisymmetric boundary‐integral code models the jet shape accurately and it is found that these bubbles evolve to toroidal geometries when the jet impacts on the opposite surface of the bubble. This highly non‐spherical behaviour is readily observed on high‐speed films of airgun bubbles, and is one key source of energy loss; it damps the pulsations of the bubble and slows its rise speed. Inter‐bubble interactions are investigated using the two deformable bubble models, and the predictions are compared to field data. It was found that as the bubbles approach each other, their periods of oscillation increase in accordance with observations, and jets are formed in the direction of motion upon collapse.     

The influence of gas bubbles on sediment acoustic properties: in situ, laboratory, and theoretical results from Eckernförde Bay, Baltic sea

Acoustic turbidity caused by the presence of gas bubbles in seafloor sediments is a common occurrence worldwide,but is as yet poorly understood. The Coastal Benthic Boundary Layer experiment in the Baltic off northern Germany was planned to better characterize the acoustic response of a bubbly sediment horizon. In this context, in situ measurements of compressional wave speed and attenuation were made over the frequency range of 5–400 kHz in gassy sediments of Eckernförde Bay. Dispersion of compressional speed data was used to determine the upper limit of the frequency of methane bubble resonance at between 20 and 25 kHz. These data, combined with bubble size distributions determined from CT scans of sediments in cores retained at ambient pressure, yield estimates of effective bubble sizes of 0.3–5.0 mm equivalent radius. The highly variable spatial distribution of bubble volume and bubble size distribution is used to reconcile the otherwise contradictory frequency-dependent speed and attenuation data with theory. At acoustic frequencies above resonance (>25 kHz) compressional speed is unaffected by bubbles and scattering from bubbles dominates attenuation. At frequencies below resonance (<1 kHz) ‘compressibility effects’ dominate, speed is much lower (250 m s^-1) than bubble-free sediments, and attenuation is dominated by scattering from impedance contrasts. Between 1.5 and 25 kHz bubble resonance greatly affects speed and attenuation. Compressional speed in gassy sediments (1100–1200 m s^-1) determined at 5–15 kHz is variable and higher than predicted by theory (<250 m s^-1). These higher measured speeds result from two factors: speeds are an average of lower speeds in gassy sediments and higher speeds in bubble-free sediments; and the volume of smaller-sized bubbles which contribute to the lower observed speeds is much lower than total gas volume. The frequency-dependent acoustic propagation is further complicated as the mixture of bubble sizes selectively strips energy near bubble resonance frequencies (very high attenuation) allowing lower and higher frequency energy to propagate. It was also demonstrated that acoustic characterization of gassy sediments can be used to define bubble size distribution and fractional volume.     

A simple field-portable rainfall simulator for difficult terrain

A small portable rainfall simulator is described which is inexpensive to construct and use and which requires relatively little water. Although drops are produced by drop-formers a satisfactory drop-size distribution is obtained by allowing the drops to break-up by falling onto a 3 mm wire mesh. The kinetic energy of the simulated rain is lower than that of natural rainfall because of the low fall height. Characteristics of the simulated rain are described and the use of the simulator briefly illustrated by results obtained from forested areas in Luxembourg.     

The Density Distributions and the Correlations of an Earthquake's Source Parameters

The data analysis of the source parameters of five sets of earthquake sequences, aftershocks and earthquakes scattered in a region shows that the scalar seismic moment is correlated with the linear size of the fault and the static stress drop. We tentatively imply that a correlation also exists between the radius of the faults and the static stress drops and it is suggested that the static stress drop may be decreasing with increasing radius of the source. It is shown that the density distribution of the source radius, calculated through the source rupture duration obtained from the body wave pulse (Boatwright, 1980) using the time T between the P-wave onset and the first zero crossing on the seismogram, may be represented by a power law as the density distribution of the stress drops and of the moment which are also computed. It is also suggested, and tentatively verified, that the density distribution of the areas of the broken barriers on the faults is similar to that of the density distribution of the static stress drops. It is finally suggested that the seismicity of a region may be studied two-dimensionally as a function of the stress drop and the radius of the source instead of the classic b and b₀ values. Concerning the discussion on the range of the values of the static stress drop, whether it is almost constant in a seismic region and varies only from one region to another, it is seen that in the aftershocks of the 1994 Northridge earthquake it covers a range of almost 5 orders of magnitudes. Finally it is ascertained that the density distribution of the source parameters does not give equipartition of seismic moment release.     

Bubble growth in rhyolitic melts: experimental and numerical investigation

 Bubble growth controlled by mass transfer of water from hydrated rhyolitic melts at high pressures and temperatures was studied experimentally and simulated numerically. Rhyolitic melts were hydrated at 150 MPa, 780–850  °C to uniform water content of 5.5–5.3 wt%. The pressure was then dropped and held constant at 15–145 MPa. Upon the drop bubbles nucleated and were allowed to grow for various periods of time before final, rapid quenching of the samples. The size and number density of bubbles in the quenched glasses were recorded. Where number densities were low and run duration short, bubble sizes were in accord with the growth model of Scriven (1959) for solitary bubbles. However, most results did not fit this simple model because of interaction between neighboring bubbles. Hence, the growth model of Proussevitch et al. (1993), which accounts for finite separation between bubbles, was further developed and used to simulate bubble growth. The good agreement between experimental data, numerical simulation, and analytical solutions enables accurate and reliable examination of bubble growth from a limited volume of supersaturated melt. At modest supersaturations bubble growth in hydrated silicic melts (3–6 wt% water, viscosity 10⁴–10⁶ Pa·s) is diffusion controlled. Water diffusion is fast enough to maintain steady-state concentration gradient in the melt. Viscous resistance is important only at the very early stage of growth (t<1 s). Under the above conditions growth is nearly parabolic, R²=2Dtρ_m(C₀–C_f)/ρ_g until the bubble approaches its final size. In melts with low water content, viscosity is higher and maintains pressure gradients in the melt. Growth may be delayed for longer times, comparable to time scales of melt ascent during eruptions. At high levels of supersaturation, advection of hydrated melt towards the growing bubble becomes significant. Our results indicate that equilibrium degassing is a good approximation for modeling vesiculation in melts with high water concentrations (C₀>3 wt%) in the region above the nucleation level. When the melt accelerates and water content decreases, equilibrium can no longer be maintained between bubbles and melt. Supersaturation develops in melt pockets away from bubbles and new bubbles may nucleate. Further acceleration and increase in viscosity cause buildup of internal pressure in the bubbles and may eventually lead to fragmentation of the melt. Received: 19 June 1995 / Accepted: 27 December 1995     

Vesiculation path of ascending magma in the 1983 and the 2000 eruptions of Miyakejima volcano, Japan

The vesiculation of magma during the 1983 eruption of Miyakejima Volcano, Japan, is discussed based on systematic investigations of water content, vesicularity, and bubble size distribution for the products. The eruption is characterized by simultaneous lava effusion and explosive sub-plinian (‘dry’) eruptions with phreatomagmatic (‘wet’) explosions. The magmas are homogeneous in composition (basaltic andesite) and in initial water content (H₂O = 3.9±0.9 wt%), and residual groundmass water contents for all eruption styles are low (H₂O <0.4 wt%) suggestive of extensive dehydration of magma. For the scoria erupted during simultaneous ‘dry’ and ‘wet’ explosive eruptions, inverse correlation was observed between vesicularity and residual water content. This relation can be explained by equilibrium exsolution and expansion of ca. 0.3 wt% H₂O at shallow level with different times of quenching, and suggests that each scoria with different vesicularity, which was quenched at a different time, provides a snapshot of the vesiculation process near the point of fragmentation. The bubble size distribution (BSD) varies systematically with vesicularity, and total bubble number density reaches a maximum value at vesicularity Φ ∼ 0.5. At Φ  ∼ 0.5, a large number of bubbles are connected with each other, and the average thickness of bubble walls reaches the minimum value below which they would rupture. These facts suggest that vesiculation advanced by nucleation and growth of bubbles when Φ < 0.5, and then by expansion of large bubbles with coalescence of small ones for Φ > 0.5, when bubble connection becomes effective. Low vesicularity and low residual water content of lava and spatter (Φ  < 0.1, H₂O  < 0.1 wt%), and systematic decrease in bubble number density from scoria through spatter to lava with decrease in vesicularity suggest that effusive eruption is a consequence of complete degassing by bubble coalescence and separation from magma at shallow levels when magma ascent rate is slow.

地球等离子体片中磁泡对地面磁场的扰动

观测到的爆发流（Busty Bulk Flows,简称为BBFs）有很多主要特征都可以用磁泡图像描述 . 磁泡模型认为电离层中绝大部分电势降落都发生在磁泡中,据此可以估算它周围的霍尔电 流及其在地面引起的地磁扰动. 将本文结果与SMA（Scandinavian Magnetometer Array）雷 达阵列观测的BBFs的特征进行比较之后,发现二者符合得很好. 这表明BBFs与磁泡在引起地 面磁场扰动上的表征是一样的,暗示BBFs很可能就是磁泡.     

Coupled degassing and crystallization: experimental study at continuous pressure drop, with application to volcanic bombs

 Experiments on degassing of water-saturated granite melts with a pressure drop from 100 and 450 MPa to 40 and 120 MPa, respectively, at temperatures close to feldspar liquidus (750–700  °C), were carried out to determine the modality of water exsolution and vesicle formation at the liquidus temperature. Pressure-drop rates as small as approximately 100 bar/day were used. Uniform space distributions of bubbles of exsolved water were obtained with starting glass containing a small fraction (≈0.5 vol.%) of trapped air bubbles. Volume crystallization of feldspar was observed in degassed melts supplied with seeds. Bubble size distributions (BSD) measured in granite glasses after degassing are presented. Data on vesicle characteristics (number, radius, area, elongation) were acquired on images digitized with standard software, while the reconstruction of size distributions was performed with the Schwartz-Saltikov "unfolding" procedure. Bubble size distributions of size classes in the range 5–1000 μm were acquired with proper magnification and satisfactory statistical reliability of determined number densities. The BSDs of the experimental samples are compared with the results of measurements of rapidly degassed products of Mt. Etna and Vulcano Island. Many particular features of the bubble nucleation and growth can be distinguished in an individual BSD. However, the general BSD of the whole data set, including natural ones, can be relatively well described with linear regression in bilogarithmic coordinates. The slope of this regression is approximately 2.8±0.1. This dependence is in striking contrast with distributions theoretically predicted with classical nucleation models based on homogeneous nucleation of vesicles. The theoretical distribution requires the occurrence of strong maxima that are not observed in our experimental and natural samples, thus arguing for heterogeneous nucleation mechanisms. Received: 1 October 1998 / Accepted: 25 June 1999     

Permeability development in vesiculating magmas: implications for fragmentation

 Fragmentation, or the "coming apart" of magma during a plinian eruption, remains one of the least understood processes in volcanology, although assumptions about the timing and mechanisms of fragmentation are key parameters in all existing eruption models. Despite evidence to the contrary, most models assume that fragmentation occurs at a critical vesicularity (volume percent vesicles) of 75–83%. We propose instead that the degree to which magma is fragmented is determined by factors controlling bubble coalescence: magma viscosity, temperature, bubble size distribution, bubble shapes, and time. Bubble coalescence in vesiculating magmas creates permeability which serves to connect the dispersed gas phase. When sufficiently developed, permeability allows subsequent exsolved and expanded gas to escape, thus preserving a sufficiently interconnected region of vesicular magma as a pumice clast, rather than fully fragmenting it to ash. For this reason pumice is likely to preserve information about (a) how permeability develops and (b) the critical permeability needed to insure clast preservation. We present measurements and calculations that constrain the conditions (vesicularity, bubble size distribution, time, pressure difference, viscosity) necessary for adequate permeability to develop. We suggest that magma fragments explosively to ash when and where, in a heterogeneously vesiculating magma, these conditions are not met. Both the development of permeability by bubble wall thinning and rupture and the loss of gas through a permeable network of bubbles require time, consistent with the observation that degree of fragmentation (i.e., amount of ash) increases with increasing eruption rate. Received: 5 July 1995 / Accepted: 27 December 1995     

Simulation of the size distribution and erosivity of raindrops and throughfall drops

This paper presents a model that simulates the size distribution and erosivity of raindrops and throughfall drops. It utilizes existing models of rainfall drop size distribution and fall velocity and combines them with newly collated evidence of throughfall drop size distributions. A sensitivity analysis reveals that the model is sensitive to parameters that are easily measured or estimated: rainfall intensity, the mean volume drop diameter of the intercepted throughfall, canopy cover, and canopy height. The results of the model may be used at two levels. Firstly, to calculate specifically the size and fall velocity of individual drops, parameters that are needed in studies examining the response of soil surfaces to forces applied by rainfall. Secondly, to produce erosivity indices, based on rainfall intensity but which take account of the effects of a vegetation canopy. The paper shows that while the kinetic energy of rainfall (E(0), J mm^?1 m^?2) may be calculated from an equation of the familiar form: the kinetic energy of throughfall under any canopy may be calculated by combining this equation with another that relates the energy of drops under a 100 per cent canopy cover (E(100)) and the canopy height: .     

Controls on magma permeability in the volcanic conduit during the climactic phase of the Kos Plateau Tuff eruption (Aegean Arc)

X-ray computed microtomography (μCT) was applied to pumices from the largest Quaternary explosive eruption of the active South Aegean Arc (the Kos Plateau Tuff; KPT) in order to better understand magma permeability within volcanic conduits. Two different types of pumices (one with highly elongated bubbles, tube pumice; and the other with near spherical bubbles, frothy pumice) produced synchronously and with identical chemical composition were selected for μCT imaging to obtain porosity, tortuosity, bubble size and throat size distributions. Tortuosity drops on average from 2.2 in frothy pumice to 1.5 in tube pumice. Bubble size and throat size distributions provide estimates for mean bubble size (~93–98 μm) and mean throat size (~23–29 μm). Using a modified Kozeny-Carman equation, variations in porosity, tortuosity, and throat size observed in KPT pumices explain the spread found in laboratory measurements of the Darcian permeability. Measured difference in inertial permeability between tube and frothy pumices can also be partly explained by the same variables but require an additional parameter related to the internal roughness of the porous medium (friction factor f ₀ ). Constitutive equations for both types of permeability allow the quantification of laminar and turbulent gas escape during ascent of rhyolitic magma in volcanic conduits.     

Bubble size distribution in magma chambers and dynamics of basaltic eruptions

In the shallow magma chambers of volcanoes, the CO₂ content of most basaltic melts is above the solubility limit. This implies that the chamber contains gas bubbles, which rise through the magma and expand. Thus, the volume of the chamber, its gas volume fraction and the gas flux into the conduit change with time in a systematic manner as a function of the size and number of gas bubbles. Changes in gas flux and gas volume are calculated for a bubble size distribution and related to changes in eruption regimes. Fire fountain activity, only present during the first quarter of the eruption, requires that the bubbles are larger than a certain size, which depends on the gas flux and on the bubble content[1]. As the chamber degasses, it loses its largest gas bubbles and the gas flux decreases, eventually suppressing the fire fountaining activity. Ultimately, an eruption stops when the chamber contains only a few tiny bubbles. More generally, the evolution of basaltic eruptions is governed by a dimensionless number, τ * ≈ τgΔρa_O²/(18μh_c), where τ = a characteristic time for degassing; a₀ = the initial bubble diameter; μ = the magma viscosity; and h_c = the thickness of the degassing layer. Two eruptions of the Kilauea volcano, Mauna Ulu (1969–1971) and Puu O'o (1983—present), provide data on erupted gas volume and the inflation rate of the edifice, which help constrain the spatial distribution of bubbles in the magma chamber: bubbles come mainly from the bottom of the reservoir, either by in situ nucleation long before the eruption or within a vesiculated liquid. Although the gas flux at the roof of the chamber takes similar values for both eruptions, the duration of both the fire fountaining activity and the entire eruption was 6 times shorter at Mauna Ulu than during the Puu O'o eruption. The dimensionless analysis explains the difference by a degassing layer 6 times thinner in the former than the latter, due to a 2 year delay in starting the Mauna Ulu eruption compared to the Puu O'o eruption.     

Drop shape and erosivity part II: Splash detachment,transport and erosivity indices

The relevance of drop shape for erosivity was tested for different combinations of drop sizes and fall heights. For all test combinations together the introduction of the observed drop shape in erosivity parameters only produces minor improvements in the relation between erosivity and detachment and transport by splash. This result is attributed to the dominance of oblate shapes in high velocity conditions. Using small fall heights and low fall velocities as in many rainfall simulators and drop tests it is shown that prolate drops produce a splash detachment which is 2 to 3 times higher than that produced by drops with an oblate shape at impact. As drop production in rainulators or for aggregate stability drop tests may result in more or less uncontrolled variations of drop shape, it is concluded that in addition to other test conditions drop shape should be specified. Moreover it is noted that the erosive capability of prolate drops can explain partly the high splash erosion amounts below vegetation.     

Distribution and enrichment patterns of selenium in the Ediacaran and early Cambrian strata in the Yangtze Gorges area,South China

The distribution and enrichment patterns of selenium(Se) in the E-?1 strata in the Yangtze Gorges area of South China were obtained. The geochemical characteristics of the significantly and non-significantly enriched strata of Se were analyzed.The observed enrichment factor(EF, relative to the upper continental crust) and concentration coefficient(CC, relative to the similar lithology in Eastern China) both suggest that Se is the most enriched/concentrated(SeEF=26.97, SeCC=48.04) among the analyzed23 trace elements the E-?1 strata. The normalized enrichment factor(EF′, EF after Al or Th normalized) shows Se is secondly enriched(SeEF′=218.73), which is slightly lower than cadmium(CdEF′=288.46) but significantly higher than the third enriched trace element arsenic(AsEF′=97.49). Se concentrations in the E-?1 strata vary from 10.5 to 30.08 ppm with an arithmetic mean value of 1.35 ppm. Compared to the Nantuo Formation, Se increased 11.78 times in the whole E-?1 strata and the average EF values are displayed as Shuijingtuo(92.58)Yanjiahe(54.45)Doushantuo(24.72)Dengying(2.48)Shipai(1.95)lower Tianheban(1.24)Formations. Se concentrations in the E-?1 strata are best displayed on natural logarithm normal quantile-quantile(Q-Q) plots and shown as a positive-skewed distribution pattern. The Se significantly enriched(EF10) strata sequences mainly include the lower and upper Doushantuo member II(DST-II), top DST-III, DST-IV, the basal and upper Yanjiahe Formation, and lower and upper Shuijingtuo Formation. Geochemical characteristics indicate that Se concentrations in the significantly enriched strata were generally influenced by terrigenous detrital as well as the combined action of single or multiple factors, such as hydrotherm,volcanic debris and deep source. Moreover, pyrite and organic matter promoted the enrichment of Se in the upper DST-II, DST-IV,upper Shuijingtuo Formation and lower DST-II, upper Shuijingtuo Formation, respectively. The Se concentrations in the not significantly enriched strata(except for DST-I, middle Shuijingtuo Formation, Shipai Formation and lower Tianheban Formation)were also influenced by terrigenous detrital, but other enrichment activities(e.g., hydrothermal, volcanic debris, and deep source)were generally insignificant.     

Bubble growth in highly viscous melts: theory, experiments, and autoexplosivity of dome lavas

We examine the physics of growth of water bubbles in highly viscous melts. During the initial stages, diffusive mass transfer of water into the bubble keeps the internal pressure in the bubbles close to the initial pressure at nucleation. Growth is controlled by melt viscosity and supersaturation pressure and radial growth under constant pressure is approximately exponential. At later stages, internal pressure falls, radial growth decelerates and follows the square-root of time. At this stage it is controlled by diffusion. The time of transition between the two stages is controlled by the decompression, melt viscosity and the Peclet number of the system. The model closely fit experimental data of bubble growth in viscous melts with low water content. Close fit is also obtained for new experiments at high supersaturation, high Peclet numbers, and high, variable viscosity. Near surface, degassed, silicic melts are viscous enough, so that viscosity-controlled growth may last for very long times. Using the model, we demonstrate that bubbles which nucleate shortly before fragmentation cannot grow fast enough to be important during fragmentation. We suggest that tiny bubbles observed in melt pockets between large bubbles in pumice represent a second nucleation event shortly before or after fragmentation. The presence of such bubbles is an indicator of the conditions at fragmentation. The water content of lavas extruded at lava domes is a key factor in their evolution. Melts of low water content (<0.2 wt%) are too viscid and bubbles nucleated in them will not grow to an appreciable size. Bubbles may grow in melts with 0.4 wt% water. The internal pressure in such bubbles may be preserved for days and the energy stored in the bubbles may be important during the disintegration of dome rocks and the formation of pyroclastic flows.     

四川长宁地区地震震源参数的时空分布特征

使用谱比法计算得到四川长宁地区2018年12月至2019年7月期间442个地震的震源参数,并进一步分析了震源参数之间的相互关系及应力降的时空分布特征.研究区的地震活动主要集中在长宁背斜核部和南部建武向斜页岩气开采区.研究结果显示,该地区ML1.3～4.7地震的应力降位于0.02～7.26MPa范围内,超过90％的地震应...     

Measurement of bubble size distributions in vesiculated rocks with implications for quantitative estimation of eruption processes

This paper outlines methods for determining a bubble size distribution (BSD) and the moments of the BSD function in vesiculated clasts produced by volcanic eruptions. It reports the results of applications of the methods to 11 natural samples and discusses the implications for quantitative estimates of eruption processes. The analysis is based on a quantitative morphological (stereological) method for 2-dimensional imaging of cross-sections of samples. One method determines, with some assumptions, the complete shape of the BSD function from the chord lengths cut by bubbles. The other determines the 1st, 2nd and 3rd moments of distribution functions by measurement of the number of bubbles per unit area, the surface area per unit volume, and the volume fraction of bubbles. Comparison of procedures and results of these two distinct methods shows that the latter yields rather more reliable results than the former, though the results coincide in absolute and relative magnitudes. Results of the analysis for vesiculated rocks from eleven subPlinian to Plinian eruptions show some interesting systematic correlations both between moments of the BSD and between a moment and the eruption column height or the SiO₂ content of magma. These correlations are successfully interpreted in terms of the nucleation and growth processes of bubbles in ascending magmas. This suggests that bubble coalescence does not predominate in sub-Plinian to Plinian explosive eruptions. The moment-moment correlations put constraints on the style of the nucleation and growth process of bubbles. The scaling argument suggests that a single nucleation event and subsequent growth with any kind of bubble interaction under continuous depressurization, which leads to an intermediate growth law between the diffusional growth ( ) at a constant depressurization rate and the Ostwald ripening ( ) under a constant pressure, where R_m and t are the mean radius of bubble and the effective time of diffusion respectively, occurred in the eruptions. It is emphasized that the BSD in vesiculated rocks from terrestrial volcanoes can be used to estimate quantitatively eruption processes such as the initial saturation pressure and magma ascent velocity in a volcanic conduit.     

Ein Spektrograph für Niederschlagstropfen mit automatischer Auswertung

Summary A new spectrometer which gives a continuous record of the size distribution of raindrops is described. The basic principe is the automatic compensation of the force, produced by a raindrop falling upon the rigid receiving system.The spectrometer is able to record the drop-size distribution of very weak as well as very heavy showers (more than 200 mm/h). Up to 200 drops per second with diameters ranging from 0.3 to 5.3 mm sorted into 20 groups can be recorded.An analog computer calculates and integrates simultaneously the rain intensityR, the water content in the airW and the radar reflectivityZ. The precision of the radar reflectivityZ, calculated from the raindrop spectrum, depends on the rain intensity, the receiving area and the timet during exposure. The precision ofZ is calculated for different timest as a function of the rain intensity.