48,06,2005misc 957 ANNALS OF GEOPHYSICS, VOL. 48, N. 6, December 2005 Key words lava domes – squeeze of magma – growth rates of domes – Hagen-Poiseuille Law – macroscopic viscosity 1. Introduction Lava domes are one of the significant features of volcanism at the earth surface and their defini- tions and classifications have been published by several researchers. However, the processes of their formation have not always been systemati- cally discussed. We know some examples of lava dome formations in historical times, which may give us fundamental knowledge on the move- ment of magmas in their formations. Yokoyama (2004) interpreted the formation processes of the 1909 Tarumai lava dome (an- desite) and the 1944 Usu lava dome (dacite), both in Hokkaido, Japan, as being squeezed from magma forced to flow through the vents. Ascending magmas became lower in tempera- ture, gas and water contents, with increased de- grees of crystallization. Accordingly their rheo- logic behavior changed from Newtonian vis- cous flows to Bingham plastic flows. In fact, these lava domes assumed different features of effusions such as growth process, its rate and fi- nal configurations, due to differences in vis- cosities of their magmas and other eruption pa- rameters. The stationary magma flows in formation of lava domes are governed by the Hagen- Poiseuille Law which relates the flow rates to size of conduits, driving pressure gradient and viscosity of magmas. Considering that meas- urements of viscosity of juvenile magma in situ are difficult, we will utilize the growth rates of Growth rates of lava domes with respect to viscosity of magmas Izumi Yokoyama Higashi 1-17-7-1304, Kunitachi, Tokyo 186-0002 Japan Abstract In the discussion of lava dome formation, viscosity of magma plays an important role. Measurements of viscos- ity of magmas in field and laboratory are briefly summarized. The types of lava dome emplacements are classi- fied into two, squeeze- and spine-type, by kinetic processes. The squeeze-type is the formation of a dome as a result of squeezes of magma through conduits and the latter is solidified magma forced to ascend by underlying fluid magma. An important parameter in the formation of such lava domes is their growth rates. Lava domes of squeeze-type are governed by the Hagen-Poiseuille Law which involves their viscosoties and other eruption pa- rameters. At present, the real viscosity of magmas at the site of lava dome is still inaccessible. In order to avoid uncertainty in viscosity of magmas, a conception of «macroscopic viscosity» is proposed, which involves effects of chemical components, mainly SiO2 and volatile material, crystals and temperature, and their changes with time. Lava dome formations during the 20th century are briefly examined and their growth rates are estimated. The relationship between the growth rates and the SiO2 content of the magma is statistically studied, and the macroscopic viscosity is empirically expressed as a function of SiO2 content. The linearity between the two pa- rameters is reasonably interpreted. This means that formation processes of lava domes are dominantly controlled by macroscopic viscosity of magma. Mailing address: Dr. Izumi Yokoyama, Higashi 1-17- 7-1304, Kunitachi, Tokyo 186-0002 Japan; e-mail: iyokoya@aol.com 958 Izumi Yokoyama various lava domes to estimate effective viscos- ity of their magmas from the macroscopic and statistic viewpoint. 2. Viscosity of magmas related to dome formation Knowledge on the physical properties of magma is fundamental to interpret the forma- tion of lava domes. The mode of formation is influenced by viscosity of magma, which strongly depends on contents of SiO2, water, bubbles and microlites and temperature. Of these factors, only temperature is determinable at the dome sites under some circumstances. In the following, temperature and viscosity of magmas shall be discussed briefly in relation to dome formation. 2.1. Temperature of magma Originally the temperature of magmas at reservoirs may be much higher than 1000°C. Basaltic magma may keep its original tempera- ture as far as vents due to its fluidity, while dacitic magma is viscous and moves slowly, and accordingly reaches vents at a lower tem- perature. Therefore, we may take the internal temperature of andestic and dacitic magmas during formation of lava domes to be lower than 1200°C, around 1000°C on the average as a whole. Field measurements of temperature of lavas are usually limited to those of basaltic lavas. For dacitic lavas, fumaroles on some dacitic domes are helpful. On the 1944 lava dome of Usu volcano, Hokkaido, whose formation was completed in 1945, there were a few strong fu- maroles issuing gases which transmit the deep temperature. Some of them became accessible around 1946. The temperature of one of the strong fumaroles has been periodically meas- ured by thermocouples. Its secular changes for 50 years (Yokoyama and Seino, 2000, fig. 13) indicate that the initial temperature of the fuma- role was approximately 1000°C. And accord- ingly, the original lava temperature should be higher than 1000°C. Huppert et al. (1982) suggested that the maximum temperature of the 1979 lava (basaltic andesite) of the Soufrière of St. Vin- cent was 800 ∼ 1100°C, by petrological studies. Murphy et al. (1998) applied the QUILF ther- mometer to the 1995-1997 Soufrière Hills an- desite and obtained a range of temperature of 810 ∼ 880°C. Nakada et al. (1999) estimated temperatures of the 1990-1992 Unzen dacite lavas at 850 ∼ 900°C with Fe-Ti oxides in groundmass. 2.2. Viscosity of magma In general, magmas at depths are higher than 1000°C in temperature, and may be vis- cous Newtonian fluids. As the magma ascends through conduits, its pressure lowers and its temperature drops gradually, and necessarily volatiles in the magma exsolve and crystalliza- tion progresses. Both the effects cause increas- es in magma viscosity. When they cool further, their viscosities in- crease exponentially and plastic behavior is greatly enhanced; they behave as plastic Bing- ham flows. Considering that glaciers, of which ice has a viscosity of the order of 1013 Pa⋅s around 0°C (Paterson, 1994), flow slowly, we may assume even dacitic lavas (roughly 107 Pa⋅s at 1000°C measured in laboratory by Goto, 1997) probably flow rather smoothly under en- dogenous or gravitational forces. In fact, Booth and Self (1973) measured viscosities of the 1971 basaltic lava of Etna volcano along its flows and obtained the viscosity range as 103∼ 107 Pa⋅s Field measurements – The measurements have usually been made at vents or along lava flows and rarely at lava lakes of basaltic lavas which scarcely form lava domes. Their results are more natural than those of dry melts. Here, we may mention a unique example of field measurement of dacitic lava flow on Santiguito volcano; Rose (1973) calculated viscosity of the 1932-1933 lava flow near the vent as 5×107 Pa⋅s, based on the equation of Nichols (1939). We have no information on the temperature of the lava flow, but it may have been a little lower than 1000°C because the site was near the vent. Growth rates of lava domes with respect to viscosity of magmas Huppert et al. (1982) theoretically estimat- ed the viscosity of the dome lava of the 1979 eruption of Soufrière of St. Vincent as 2 × 1011 Pa⋅s by observations of its lateral spreading. The lava dome was spread by different temper- atures at each part, cooled skin, disrupted blocks and a flow front, and consequently the viscosity was determined to deviate from the simple model. Huppert et al. (1982) called it «effective viscosity». Laboratory experiments – Since the 1930’s, the viscosities of silicate rock-forming minerals and igneous rock melts at the temperature range higher than 1150°C have been measured in the laboratory. Goto (1997) studied the viscosities of silicate melts from some Japanese volcanoes, including the 1944 lava dome of Usu volcano and the 1992 one of Unzen volcano (table I). He applied the fiber-elongation method for a vis- cosity range higher than 108 Pa⋅s (roughly tem- perature range lower than 950°C) and counter- balanced sphere method for a viscosity range lower than 105 Pa⋅s (roughly temperature range higher than 1150°C). At present, the viscosity range 105∼ 108 Pa⋅s is still left experimentally unsettled and only interpolation methods are applicable. In such viscosity ranges, magmas are half-solidified and usually common to the magmas forming lava domes. When we men- tion the viscosities of lavas in discussing dome formation in table I, they are reduced to the same temperature of 1000°C by interpolation. In this case, we refer to the experimental results obtained by Murase et al. (1985) and Goto (1997) that viscosities of melts of igneous rocks increase roughly 101 times with temperature de- crease of 100°C in a temperature range around 1000°C. 959 Table I. Growth rates of the lava domes and viscosities of the lavas measured in laboratory. Dome type, Lava type, SiO2 Growth rate Viscosity (a) Reference volcano dome volume (%) log (m3/day) logη (Pa·s) (Viscosity meas.) (×107 m3) (d) (e) Squeeze-type Soufrière S.V. (1979) BA 3.5 55 5.73 7.3 (b), 11.3 (c) Huppert et al. (1982) Colima (1998) A 0.04 59 5.58 Lamington (1951) A 6 59 6.20 (5.7) (6.3) Redoubt (1989) A 2 60 6.34 Soufrière Hills (1996) A 6.8 60 5.30 Tarumai (1909) A 1.5 60 6.58 (7.0) 6 Kani and Hosokawa (1936) Bezymianny (1956) A 4.2 60 6.15 (4.6) (5.2) Shiveluch (1980) A 1 61 5.27 (5.4) Pelée (1902) A 3.7 62 5.50 Mt. St. Helens (1980) D 1.0 63 5.92 (4.6) (4.6) ca. 6 Murase et al. (1985) Santiaguito (1922) D 20 64 5.20 (4.9) (4.6) 7.7 (c) Rose (1973) Popocatépetl (1996) A 1.1 64 5.26 Unzen (1992) D 5 66 5.70 6.0 Goto (1997) Usu (1944) D 4.4 69 5.05 (5) 6.8 Goto (1997) Novarupta (1912) D 0.5 73 4.40 (6) Spine-type Lamington (1951) A 0. 07 60 4.82 Pelée (1902) A 0.003 62 4.45 A – Andesite; D – Dacite; BA – Basaltic Andesite; (a) – reduced to 1000°C; (b) – deduced from petrology (Hup- pert et al., 1982); (c) – field data (temperature probably 1000°C); (d) – after Newhall and Melson (1983); (e) – after Swanson et al. (1987), for long-term formation. 960 Izumi Yokoyama Furthermore, viscosities of natural magmas are controlled by water, bubble and crystal con- tents which are not always easily determinable in situ. Recently viscosities of several volcanic rocks for a dissolved water content ranging from dry to 3 or 4% for wide temperature ranges were studied by Romano et al. (2003), Giordano and Dingwell (2003) and Giordano et al. (2004); hy- drations remarkably lower the viscosities of dry melts. Sparks (1997) discussed large increases in magma viscosity resulting from degassing and microlite growth as causes of pressurisation in lava dome eruptions. It is not easy for us to measure the proper- ties of actual magmas in situ such as viscosity, water and crystal contents, and laboratory measurements of rock viscosities remain ap- proximate for a certain viscosity range. In order to avoid uncertainty about the viscosities of as- cending magma, I later propose a conception of «macroscopic viscosity». 3. Classification of lava domes and modes of their formations 3.1. Classification of lava domes Lava domes have been defined in various ways. For example, Bardintzeff and McBirney (1998) define six principal types of domes based mainly on their morphological aspects: a) cryctodomes, b) plug domes, c) Peléan domes, d) spines, e) lava domes and f) Coulées. The present paper does not always adhere to such definitions. Cryptodomes are theoretically pos- sible, but I do not know of any examples geo- physically verified. In fact, as discussed by Yokoyama (2004), during the 1944 lava dome formation of Usu volcano, a 65 m high mound was caused by magma intrusion through a con- duit, but the magma top remained at a depth of 100 m. It is not always necessary to assume magma intrusion directly beneath the mounds. Peléan domes are defined as collapsed parts of plug domes. Some lava domes are formed by the spread of relatively fluid lava over squeezed domes. From the standpoint of formation mech- anism, plug domes and spines should be differ- ent from the others; they extrude through vents in an almost solidified state, even if the inner part remains soft. The possibility of formation of a lava dome and its morphology change with the viscosity of magmas. Lava domes are highly possible with dacitic compositions and rare with basaltic compositions in the order of silica contents. 3.2. Types of lava dome formation The substantial mode of lava dome forma- tion is squeezing, or forced extrusion, of mag- ma through a narrow opening similar to tooth- paste. Such a behavior is a characteristic of the Bingham fluids. This mode shows a wide vari- ation, such as the above-mentioned six types defined by final morphology. From the stand- point of magma movements at vents, we may classify two types: squeeze of fluidal or half-so- lidified magma (squeeze-type), and extrusion of solidified magma (spine-type). These two al- so include a variation according to the viscosi- ty of magma, endogenous pressure, size of vents and degrees of magma solidification. Squeeze-type – Usually magmas at high tem- perature are fluidal. As the magma ascends through a conduit as a viscous flow, it half solid- ifies due to lowering in temperature and pres- sure. The boundary viscosity between liquid and solid is approximately 1013 Pa⋅s (e.g., Huppert, 1982). Half-solidified magma behaves like a plastic Bingham body and piles up at the vent; this is a lava dome of squeeze-type. We assume magma movements of this type exactly or ap- proximately obey Hagen-Poiseuille Law. Spine-type – When magma lifts through a conduit, sometimes it solidifies totally or partly en route beneath the vent and extrudes as a sol- id spine, the interior of which may remain soft. Extrusions of solidified lava or lava spines are not similar to squeezes of fluidal or half-solidi- fied lavas but are displacements of solid lava bodies overcoming friction of the ground around conduits. The solid lavas are driven up by fluid magma beneath, whose viscosity ef- fects their displacements. As will be seen later, their growth rates are far smaller than the squeeze-type because of larger resistance be- tween solidified spines and conduit walls. Growth rates of lava domes with respect to viscosity of magmas Rare examples of the spine-type in the 20th century were found in the 1902-1903 eruption of Mt. Pelée and in the 1951 eruption of Lamington volcano. Both the spines may have been fluid flows at the early stage, and changed to plug flows, in which the central part had a uniform speed, before becoming solidified at the top part. In some cases, during formation of domes of squeeze-type, spinescent extrusives have ap- peared at the surface — the 1944 Usu dome (Yokoyama, 2004) and the 1996 Soufrière Hills dome (Watts et al., 2002), for example. Such apparent spines may be lava blocks solidified at or near the surface, and deeper parts must re- main fluidal. 3.3. Alternation of formation and destruction of lava domes The history of volcanic eruptions shows that dome formation and demolition have alternated, often being repeated several times. Shiveluch volcano, Kamchatska has finished five cycles of production and demolition since the 19th centu- ry and the last formed in 1980 (Dvigalo, 1988). In the case of Tarumai volcano, Hokkaido, the 1874 eruption destroyed the pre-existing lava dome (I), and the next eruption in 1909 produced the new lava dome (II) at the site of the previous lava dome (I) (Oinouye, 1909). In the following examples, the last eruptions demolished the pre- existing lava domes, and another production may be expected in the future. The 1982 eruption of El Chichon volcano, Chiapas – No historical eruptions of El Chi- chon volcano were known before 1982. Ac- cording to Duffield et al. (1984), growth of a la- va dome following excavation of a crater had occurred at least twice in the past. Before the 1982 eruption, there were two internal nested domes within the summit oval crater measuring 1900 × 900 m. The larger central dome was con- ical with a maximum relative height of approx- imately 200 m, and the other is the smaller flank dome. The 1982 eruption destroyed the central dome and caused pyroclastic flows at the last phase, leaving the 1982 crater which is approximately 1 km diameter and approximate- ly 240 m depth (Macias et al., 1997). The 1982 eruption of Galunggung volcano, Java – In the history of this volcano, the 1833 eruption produced lava dome (I) which was de- stroyed by the 1894 eruption, and the 1918 eruption produced lava dome (II) named Mt. Jadi, measuring 560 × 440 × 85 m on the crater lake. On April 5, 1982, a new activity took place and the pre-existing lava dome (II) was destroyed within one month. The activity stopped in January 1983 leaving a cinder cone on the crater floor (Katili and Sudradjat, 1984). 3.4. Examples of lava dome formations In the following, each type of dome forma- tions will be exemplified by the domes formed in the 20th century to estimate their growth rates. Later we apply the Hagen-Poiseuille Law to the dome formation under constraint that the dome is driven by liquid. 3.4.1. Lava domes of squeeze-type A few papers have compared growth rates of several lava domes. Newhall and Melson (1983) reviewed the dome growth of more than 70 volcanoes in historical times, and related it to their explosive activity. Among their data, duration of dome growth ranges from 0.3 to 2600 weeks. One of their conclusions is that the average rate of dome growth shows no system- atic relationship to the timing or character of explosions. Swanson et al. (1987) discussed the volu- metric growth of a composite dome during 1980 ∼ 1983 on Mt. St. Helens. Nine dominant- ly nonexplosive episodes of dome growth after 1981 were separately described. Furthermore, they compared the growth of four relatively long-lived contemporary lava domes at Mt. St. Helens for 1980∼ 1983 (3.2 years), Lamington for 1951∼ 1952 (1.4 years), Bezymianny 1956∼ ∼ 1982 (27.3 years) and Santiaguito 1922∼ 1982 (61.5 years). They remark that the dome, its feeding conduit and its magma reservoir are in a delicate balance, able to alternate over short periods of time between dominantly explosive and effusive activity. 961 962 Izumi Yokoyama During dome formations, magma move- ments fluctuate sometimes repeating the rise and fall in growth of lava domes. This may be attributed to changes in the driving pressure of magma from the standpoint of the Hagen- Poiseuille Law. On the other hand, Melnik and Sparks (1999) interpreted large changes in the dome extrusion rate and pulsatory patterns of dome growth observed during the 1995-1999 eruption of the Soufrière Hills, Montserrat by the nonlinear effects of crystallization and de- gassing in the ascending magma. As far as we assume Hagen-Poiseuille Law for magma flows in the formation of lava domes of squeeze-type, the following condi- tions are necessary in collecting the data. The flows must be stationary for a certain period, possibly a few weeks, and explosions and col- lapses of the dome have not intervened in the period. To assume stationary magma flows, it is desirable to select larger domes, such as larger than 107 m3, more or less in the final volume be- cause smaller domes can be formed even by un- stable processes. The following examples proved not to satis- fy the above conditions because their volumes are not sufficiently large. The 1989 dome of Lascar volcano, North- ern Chile – (The dome volume was roughly 106 m3 after Matthews et al., 1997), the 1990-1992 dome of Galeras volcano, Colombia (4 × 105 m3 after Calvache and Williams, 1997), the 1991 dome of Mount Pinatubo, Philippines (3∼ 6 × 105 m3 after Daag et al., 1996) and the 1992 dome of Merapi volcano, Java (2 × 106 m3 after Suban- driyo et al., 1992). In the following, lava dome formations for which quantitative data exist to estimate growth rates will be reviewed. The examples shall be mentioned in order of the sequence of erup- tions, and growth rates are expressed in m3/day for practice in field observations, not in the SI system, and accompanied with the error ranges, not probable errors. The 1902 dome of Mt. Pelée, Martinique – According to Lacroix (1904), the 1902 dome formed at the summit during the period from May to October 1902. The beginning of dome formation may be assumed as the day of the ca- tastrophe, May 8, and the dome may be as- sumed to have been completed on October 4, when a new spine began to extrude above the dome. The duration of dome formation is roughly 150 days and its volume as of October 4 is estimated in the sketches given by Lacroix (1904, fig. 28) as 3.7 × 107 m3, on the assump- tion that the dome is a circular cone. Then, the growth rate is Q = 3.7× 107 m3/120 days = 3.1× 105 m3/day. The error range in this estimate is derived from the errors in estimation of volume of the dome; it can be erroneous ±10%. Both the magmas of the 1902 dome and the 1902 spine of Mt. Pelée were andesite, but they manifested a large difference in their formation processes because the former was a squeeze flow and the latter was solidified at some depth beneath the vent before extrusion. The SiO2 content of the lava dome is 62% (Lacroix, 1904, p. 573). The 1909 dome of Tarumai volcano, Ok- kaido – The formation of this lava dome is dis- cussed in detail by Yokoyama (2004). The lava dome formed in the summit crater in 4 days in April 1909. The andesite magma was squeezed through the vent of 30 m diameter in a half-so- lidified state. Q=1.5 × 107 m3/4 days = 3.8 × 106 m3/day. The error range in this estimate is derived from the errors in estimation of duration and volume of the dome; the duration is 4 ± 2 days and the volume can be erroneous at ± 10%. Kani and Hosokawa (1936) measured the viscosity of the dry melt from the Tarumai lava dome, and the results are extrapolated to approx- imately 106 Pa⋅s at a temperature of 1000°C. The Reynolds number of the lava flow in the con- duit during the formation of the Tarumai dome was very small (2.2 × 10−3) and hence the flow was laminar (Yokoyama, 2004). The SiO2 con- tent of the dome lava is 60%. The 1912 dome of Novarupta dome, Kat- mai, Alaska – The 1912 eruption in the Valley of Ten Thousand Smokes was discussed in de- tail by Hildreth (1983) and Fierstein et al. (1997). In June 1912, magma of approximately Growth rates of lava domes with respect to viscosity of magmas 15 km3 erupted from the Novarupta caldera, and quasi simultaneously, at Mt. Katmai, 10 km E of Novarupta, a 600 m deep caldera formed. The Novarupta dome is blocky and a circular knoll of 380 m diameter and 65 m high is cen- tered within the 2 km diameter basin of subsi- dence that was the source of the 1912 ejecta. It apparently reached the final level of formation at the end of the eruptive sequence, possibly in several months after the last major pumice eruption. Its volume is approximately 5× 106 m3 which barely satisfies the condition upon the minimum volume of lava domes. If we take «several months» as 200 days, the growth rate is Q = 2.5× 104 m3/day. The error range in this estimate is derived from the errors in estimation of duration and volume of the dome; duration is 200 ± 50 days and the volume can be erroneous at ± 10%. The SiO2 content of this lava dome ranges 65∼77%, and is 73% on the average (Hildreth, 1983). The 1922-1925 Santiaguito dome, Guate- mala – According to Rose (1972, 1973), Santa Maria volcano erupted in 1902 for the first time in history, producing pyroclastics of 5.5 km3 and a large and deep crater was formed on its SW slope. In June 1922, a lava dome (Santia- guito) rose in the 1902 crater and grew to a rel- ative height of 400 m by the end of 1923. Rose (1973, figs. 1 and 7) showed a dia- gram of the estimate of the magma extrusion rate during the historic activities of the volcano. The highest rate for the period 1922∼1925 is given in annual rate as Q = 60 × 106 m3/yr = 1.6 × 105 m3/day. The error range in this estimate can be ± 20% of the value if we consider ambiguity in the origi- nal diagram. Rose (1973) calculated the viscosity of the 1932-1933 lava flow of Santiaguito near the vent as 5 × 107 Pa⋅s, as mentioned previously. The SiO2 content of the 1967 dome rock is 64% (Stoiber and Rose, 1969). The 1944 lava dome of Usu volcano, Hok- kaido – The formation of this lava dome was ful- ly discussed in the previous paper (Yokoyama, 2004). This dome is unique in that it was formed at the base of a volcano, flat ground, not within a crater. This is a variation of squeeze-type. The upward movement of magma was slow and the uppermost part was solidified in the course of up- heaval while the deeper part remained partly so- lidified and movable. The top part was succes- sively followed by emergence of solidified slab- like lavas, forming an onion structure. The vol- ume of the dome including the subsurface part was estimated at 4.4 × 107 m3 by Yokoyama (2004). The dome grew up rather uniformly for the early 13 months while the activity contin- ued for approximately 17 months in a combined total. Hence, the typical growth rate of the dome is obtained as Q = 4.4 × 107 m3/13 months = 1.1 × 105 m3/day. The error range in this estimate is derived from the errors in estimation of subsurface volume of the dome; it can be erroneous at −25%. As mentioned above, Goto (1997) measured the viscosity of dry melts from the lava dome as 106.8 Pa⋅s at a temperature of 1000°C. The mag- ma is dacite of SiO2 content 69%. The 1951 dome of Mt. Lamington, Papua – Our knowledge on the 1951 eruption of Lam- ington volcano entirely depends on the paper of Taylor (1958). A gigantic eruption occurred at the summit of the volcano on January 21, 1951. A lava dome began to extrude on January 25 and the first phase ended on March 5 when it reached a height of 450 m and the paroxysmal explosion shattered the dome causing pyroclas- tic flows. The growth curve of the dome in height is given by Taylor (1958, fig. 154) and the maxi- mum rate is 30 m/day between February 3 and 9. He states that this rate is probably the high- est recorded for the dome uplift. In the present paper, growth rates are defined as increases in volume of domes. Then, the growth rate is cal- culated for the period from January 25 to March 5 under the assumption that the dome was a cone with 730 m basal diameter (Taylor, 1958, fig. 4) and 450 m height. Then we have Q = π /4⋅7302× 450/3/40 days = 1.6×106 m3/day. 963 964 Izumi Yokoyama The error range in this estimate is derived from the error in estimation of volume of the dome; it can be + 20%. It is noticeable that a knife-edged spine emerged from the center of the dome on August 19, similarly to that at Mt. Pelée in 1902. This spine will be referred to later. The SiO2 content of the lava dome is 59% (after Taylor, 1958). The 1956 dome of Bezymianny volcano, Kamchatka – According to Gorshkov (1959), the first historical eruption of Bezymianny vol- cano began on October 22, 1955 after three- weeks’ earthquake swarm. The activity had de- veloped into the paroxysmal explosion on March 30, 1956 and the new crater had the shape of a semi-ring of 1.5 km by 2 km in size. Following the explosion of March 30, which produced large pyroclastic flows, an extrusive dome grew in the new crater. By early July, af- ter one month, the dome was mostly completed, approximately 320 m high above the crater floor and 340 m in average diameter. Its volume, the sum of the two trapezoids, is estimated at 4.2 ×107 m3. The growth rate of the dome is Q = 4.2×107 m3/30 days = 1.4×106 m3/day. The error range in this estimate is derived from the errors in estimation of duration and volume of the dome; the duration can be 40 days and the volume can be erroneous at ±10%. The activity continued till March 1957, and was repeated during March 1965 to March 1970 accompanying pyroclastic flows, and lat- er numerous explosive episodes took place with lava extrusion. The lava of the 1956 dome is an- desite and 59.9 in SiO2 percentage (Gorshkov, 1959). The 1979 dome of the Soufrière of St. Vin- cent, West Indies – The 1979 eruption of Soufrière volcano was first discussed by Shep- herd et al. (1979). The eruption began on April 13 and a series of strong explosions continued until April 26. The extrusion of lava was ob- served from about May 6 until its final em- placement after 5 months. Huppert et al. (1982) applied a theoretical analysis to the radial spreading of the lava extrusion accumulated in the crater, and estimated the «effective» viscos- ity at 2×1011 Pa⋅s. On the other hand, the 1909 Tarumai dome did not deform noticeably after the emplace- ment (Yokoyama, 2004) though its formation was not observed quantitatively. It is probably because the Tarumai lava is andesite and was plastic after the squeeze. Huppert et al. (1982) also estimated the viscosity at 2.1×107 Pa⋅s at 1000°C from the petrological model assuming a phenocryst content of 45% and dacitic liquid phase. Huppert et al. (1982, table II and fig. 11) published the growth data of the Soufrière dome during the period May to October 1979 when the growth rate had gradually decreased. They interpreted that the lava ascended under a decreasing hydrostatic driving pressure. The growth rate at the early stage for 65 days (May 7∼July 10) is obtained as Q = 3.5 × 107 m3/65 days = 5.4 × 105 m3/day. In table II of Huppert et al. (1982), the highest rate is 6.3 × 105 m3/day for 19 days (May 7 to 25); the error range in the above estimate can be indicated by this value.The SiO2 content of the 1979 lava is 55.0% (basaltic andesite, Huppert et al., 1982). The 1980 domes of Mt. St. Helens, Washing- ton – The great eruption of Mt. St. Helens on May 18, 1980 was followed by formation and collapse of lava domes in the newly formed crater 1.5× 3 km across. Moore and Albee (1981) presume the bulge at the summit just before the outburst as a cryptodome of 0.11 km3 in volume directly beneath the summit. I already remarked that such a bulge could be formed by upward thrust of ascending magma. Swanson et al. (1987, table 2 ) obtained the average growth rate as 0.014 km3/yr (3.8 × 104 m3/day) for the period of 1981∼1983. During the period, lavas extruded step by step and a composite dome continued to grow. The present paper selects the relatively short-lived magma extrusions, 4 steps in 1980 and 5 steps in 1981 (Swanson et al., 1987, table 1). These domes were partly destroyed by subsequent explosions one after another. The average growth rate of the 9 steps for 34 days is obtained as Q = 28.5 × 106 m3/34 days = 8.4 × 105 m3/day. Growth rates of lava domes with respect to viscosity of magmas On the other hand, Moore et al. (1981, table 58) compared dimensions, volume, growth periods etc. of three domes in June, August and October 1981. The mean growth rate of the three domes is estimated as 9.6 ×105 m3/day. This estimate indicates the error range. Murase et al. (1985) measured viscosity of the dome lava (melt) in the laboratory. The vis- cosity reduced to 1000°C is approximately 106 Pa⋅s. The SiO2 content of the dome materials on Mt. St. Helens ranges from 61 to 64% (after Swanson et al., 1987). The 1980 lava dome of Shiveluch volcano, Kamchatka – The volcano has produced lava domes 5 times in the explosion crater since the 19th century. During the 1980-1981 eruption, a new lava dome of approximately 150 m height formed. Dvigalo (1988) observed the growth of the dome with a photogrammetric method for the period from July 1980 to March 1982. The growth rate was the maximum for the first sur- vey period (July to October 1980) amounting to Q=1.86 × 105 m3/day. In this estimate, the volume can be erroneous at ± 10%. The SiO2 content of the lava dome is 61%. The 1989-1990 lava dome of Redoubt vol- cano, Alaska – During six months of the 1989- 1990 eruption, the volcano repeated a dome- growth and -destructive phase in which 14 short- lived andesite domes were formed and 13 subse- quently destroyed. Miller (1994) estimates the cumulative volume of the domes dividing the pe- riod of six months into three segments, I, II and III, and calculates the growth rate of each seg- ment: segment I produced the largest dome with the highest growth rate. The lava domes in seg- ments II and III were not sufficiently large in vol- ume to show stable growth rates. The growth rate in segment I is given by Miller (1994, table 3) as Q = 20×106 m3/9 days = 2.2 × 106 m3/day. The volume of the dome is erroneous at ± 5×106 m3. The SiO2 content of the dome lava is 59.8% on the average (Miller, 1994, table 2). The 1990-1992 lava domes of Unzen vol- cano, Kyushu – Unzen volcano reawoke at the summit crater in November 1990 after 198 years’ quiescence. On May 20, 1991, magma extruded in the summit crater, forming lobes and domes which flowed very gently and showed elongated forms. Thereafter, magma was continuously supplied to form successive domes. Seven lava domes were formed at the summit during May 1991 to April 1992. New domes pushed and partly overrode the preexist- ing domes to form an onion structure that re- sulted from squeeze processes, similar to the 1944 lava dome of Usu volcano (Yokoyama, 2004): the Unzen lava domes belong to the squeeze-type of half-solidified magma. After- wards the domes repeatedly collapsed to form pyroclastic flows along the slope. According to Nakada (1996), the magma ef- fusion rate was highest in September 1991 amounting to Q = (4 ∼ 6) × 105 m3/day. Thereafter it decreased with time before stop- ping in 1995. The error range in the above esti- mate is ambiguity of growth periods. Goto (1997) measured the viscosity of dry melts of the 1992 Unzen lava dome as 106.0 Pa⋅s at 1000°C. The SiO2 content of the dome lava is 66% on an average (after Yanagi et al., 1992). The 1995-1997 lava domes of Soufrière Hills volcano, Montserrat – Phreatic explosions began in July 1995 at this volcano, and were followed by a continuous eruption of andestic magma in the form of a lava dome in Novem- ber 1955. The eruptions have been monitored and discussed from various standpoints. The growth patterns of the lava dome during the pe- riod of November 1995 to December 1997 are illustrated and the growth rate are graphically reported: Sparks et al. (1998, fig. 2) present the extrusion rates as a function of time and Watts et al. (2002, fig. 3) present the change in dome volume. We search the periods of monotonous growth to estimate growth rates of the lava dome. Considering the change in dome height given by Melnik and Sparks (2002, fig. 1), we select two periods from February 17 to Septem- ber 30, 1996 (Stage III), and October 1, 1996 to May 13, 1997 (Stages IV and V). The latter pe- riod is selected on the condition that the higher 965 966 Izumi Yokoyama growth rate is preferable. The growth rate through Stages IV and V is graphically deter- mined in the diagram of change in dome vol- ume given by Watts et al. (2002, fig. 3b) Q = 68 × 106 m3/340 days = 2.0 × 105 m3/day. Naturally this roughly agrees with the values given by Sparks et al. (1998, fig. 2) and the er- ror range is given by the growth rate in Stage III. The SiO2 content of the dome lava is 59.5% on an average (Murphy et al., 1998). The 1996 lava dome of Popocatépetl vol- cano, Central México – The summit of Popo- catépetl volcano is 5450 m a.s.l. and located ap- proximately 50 km distant from México City. Popocatépetl had repeated small explosive eruptions in 1920-1922 and produced a small lava plug in the summit crater, but no lava flows. The present activity began in 1994. After the first outburst on December 24, 1994, lava domes formed several times in the elliptical summit crater, which measures 600 m by 400 m, and is approximately 330 m deep, measured from the lower crater rim. According to Global Volcanism Network (1996) and S. De la Cruz-Reyna (personal com- munication), dome A in the summit crater was found first on March 25, 1996 from the air and had grown to 1.1 × 107 m3 by May 25 when the growing stopped. Then the growth rate is Q = 1.1 × 107 m3/61 days = 1.8 × 105 m3/day. The error range in this estimate is derived from the errors in estimation of volume of the dome; it may be erroneous at ±10%. The bulk of dome A had been demolished by repeated explosions by August 1996. The SiO2 content of the lava is 64% (Robin and Boudal, 1987). The 1998 lava dome of Colima volcano, Western México – Colima volcano (3850 m a.s.l.) has experienced at least 50 eruptions since 1560. The 1913 summit eruption pro- duced disastrous pyroclastic flows. After that, lava rose through the vent, and block lavas gradually filled the 200-m-wide summit crater by 1957. The latest series of eruptions began in March 1991, and lavas extruded onto the sum- mit crater resulted in block flows and ash flows on the south flank of the volcano. Navarro-Ochoa (2002) reports on the em- placement of the November 1998-February 1999 lava flows. On November 20, 1998, a la- va dome grew rapidly at a rate of 4.4 m3/s inside the summit crater and its volume amounted to 3.8 × 105 m3 in 24 h. On the following day, the lava dome began to collapse, causing the largest pyroclastic flows on November 25-26, and thereafter, block-lava flows went down in three branches. Their volume is estimated at approx- imately 3.9 × 107m3. In this case, the dome is small in volume but may be assumed to have been formed by Hagen-Poiseuille Law because its growth rate is rather high and it was shortly followed by a large amount of lava flows. We take the growth rate as Q = 3.8 × 105 m3/day. The error range in this estimate is derived from the errors in estimation of duration and volume of the dome; both of them can be erroneous at ±10%. The SiO2 content of the lava is 59% (Na- varro-Ochoa, 2002). 3.4.2. Lava domes of spine-type There are only two examples of this type that have been monitored quantitatively, as far as the present author knows. One is the 1912 la- va spine of Mt. Pelée, and the other is the 1951 lava spine of Lamington volcano. They were solidified lavas driven by underlying magmas through conduits, and met with resistance at the conduit walls. Hence, their growth rates do not obey Hagen-Poiseuille Law. The 1902 lava spine of Mt. Pelée – This la- va dome is characterized as an extrusion of a huge solidified spine. A lava dome formed at the summit of Mt. Pelée from May to October 1902. During this period, on May 8, pyroclastic flows occurred, devastating the town of St. Pierre along the sea. According to Lacroix (1904), a spine extruded above the top of the dome after the dome was completed. The extru- sion of the spine first began on the night of No- vember 3-4, 1902. It may have ascended Growth rates of lava domes with respect to viscosity of magmas through the vent of the preceding lava dome. The 1902∼1903 lava spine of Mt. Pelée meas- ured 190 m high above the terrace in March 1903 and approximately 60 m across at its base; some parts were partially hollow. It is different from the 1944 lava dome of Usu, which grew laterally after the lava reached the surface and completed an onion structure. The spine repeat- ed noticeable growths 3 times, and small col- lapses with short steps, during the period from November 1902 to September 1903, as illus- trated and sketched by Lacroix (1904, figs. 29 ∼ 35). The total amount of extrusion is esti- mated at approximately 620 m. Lacroix (1904) reported that the maximum growth rate of the spine was 10 m/day for No- vember 3∼ 4. If we assume the section of the spine as a 60 m-diameter-circle (Lacroix, 1904, fig. 55), the rate of magma flow to cause the rise of the spine is approximately Q = π /4⋅602×10 m3/day = 2.8 × 104 m3/day. The error range in this estimate is derived from the errors in estimation of sectional diameter and ascending velocity of the spine; both of them may be erroneous at ±10%. The upward movement of the solidified spine through the conduit may have met with more fric- tion than fluidal flows. The lava is andesite with SiO2 content of 62% (Lacroix, 1904). The 1951 lava spine of Lamington volcano – The 1951 eruption of Lamington volcano was accompanied by extrusion of a spine. A lava dome began to extrude after the gigantic erup- tion in March 1951. When the dome reached a height of approximately 450 m in March, it was partly destroyed. In July a lava spine began to extrude at the center of the dome. Its growth curve is given by Taylor (1958, fig. 4). The up- lift rate of the spine is estimated at 83 m/10 days by the growth curve, and the spine is assumed to be a cone with roughly 175 m basal diameter (Taylor, 1958, fig. 140) and 83 m height. Then we have Q = π /4⋅1752× 83 × 1/3 m3/10 days = = 6.6 × 104 m3/day. The error range in this estimate is derived from the errors in estimation of sectional diameter of the spine, and it may be erroneous at ±10%. According to Taylor (1958), this monolith showed neither plastic deformation nor slicken- sides. The SiO2 content of the spine is 60% (af- ter Taylor, 1958). 4. Growth rate of lava domes of the squeeze- type and macroscopic viscosity We select the 15 lava domes of the squeeze- type formed in the 20th century with reliable observational data, and we can discuss their growth rates statistically. Lava flows may be modeled as viscous or plastic fluids. Flows of dome-forming lava are usually laminar, as confirmed by the 1909 lava dome of Tarumai volcano (Yokoyama, 2004). If we know the growth rates of lava domes, it is possible to find a relationship among the phys- ical parameters of lava dome formation, such as viscosity of magmas, conduit dimension and driving pressure, by Hagen-Poiseuille Law which is conditioned for fluids to flow through a narrow space. In the present case, the growth rate Q of lava dome is expressed as (4.1) where r denotes the radius of the vent, ∆p driving pressure, ∆p/l pressure gradient, l vertical length of the vent, ρ density of lava, g gravity accelera- tion and η viscosity of lava. Among these factors, ∆p is liable to fluctuate due to degassing and crystallization in the magma. The viscosity η de- termined by eq. (4.1) involves the effects of chemical components (mainly SiO2 and water), crystallization and temperature averaged for the period of dome formation, and their changes with time and space. Actually the temperature may be around 1000°C. We may call such η «macroscop- ic viscosity». From eq. (4.1) we obtain (4.2) where (4.3).logK r l p g 8 4 $= - r t ∆ c m log logQ K= - h Q r l p g 8 4 = - r h t ∆ c m 967 968 Izumi Yokoyama The growth rates of the lava domes described in the previous chapter are tabulated in table I where those estimated by Newhall and Melson (1983) and Swanson et al. (1987) are addition- ally shown for reference. The growth rates are also plotted in logarithmic scale against SiO2% of lavas in fig. 1, where some of the growth rates (ordinate) have a rather high degree of un- certainty and their error ranges are calculated and indicated by the bars attached to the plots. The growth rates of the spines of Lamington and Pelée volcanoes are indicated by star sym- bols in fig. 1 for reference, and are significant- ly smaller than those of their domes, respective- ly, because solidified or half-solidified spines may meet with higher resistance through con- duits. Their formation processes do not obey Hagen-Poiseuille Law, and they are excepted from the following discussion. As shown in fig. 1, the relationship between the logQ and the SiO2% is roughly linear though the plots are rather scattered, and classi- fication of the plots into two groups, upper and lower, is not justified because of their inaccura- cy. We may assume that logη can be replaced by SiO2% in eq. (4.2) and that K does not vary with the volcano. Their relationship is deter- mined by the least squares method as (4.4) where the correlation coefficient is − 0.68. From eqs. ((4.2) and (4.4)), we obtain approximately (4.5) Hence, we may label 104.3, 105.2 and 106.1 Pa⋅s in macroscopic viscosity for 50, 60 and 70 in SiO2%, respectively on the abscissa of fig. 1. As the data increase in number, the parameters in eq. (4.4) should change necessarily. At present, macroscopic viscosities calculat- ed by eq. (4.5) are not directly comparable with the lava viscosities experimentally determined at 1000°C. However, the former is usually lower than the latter as shown in table I. This is reason- able if we consider the effects of volatile materi- al and crystallization in real lavas. The growth rate Q most strongly depends on r and next on η, ∆p, l and ρ in eq. (4.1). The linearity of the diagram (logQ ∼ SiO2%) sug- gests that Q changes in logarithmic proportion to SiO2 percentage. Constant term K in eq. (4.2) proves to be roughly common in logarith- mic scale among various volcanoes. This is plausible when we consider that both too- small-radius and too-large-radius conduits are not favorable for lava dome formation and that too shallow and too deep magma positions are not probable. Radii of the conduits feeding la- va domes must be a few tens of meters in com- mon. Driving pressure is liable to fluctuate as observed in some dome forming eruptions . ( %) .log SiO0 087 2]h . . ( %)log SiOQ 11 04 0 087 2= - Fig. 1. Logarithm of Q (growth rate of lava dome) versus SiO2%. The two domes of spine-type (star symbols) are excepted from the least squares to de- termine the best fit line. The bars attached to the plots indicate the ranges of errors. η along the abscis- sa denotes «macroscopic viscosity» with exponents in round figures. MSH – Mt. St. Helens; Souf SV – Soufrière of St. Vincent; Souf HM – Soufrière Hills, Montserrat. Growth rates of lava domes with respect to viscosity of magmas (Melnik and Sparks, 1999) and must have its limit because lava domes have a limit of their heights, a few hundred meters at maximum above the surface. The result shown by eq. (4.5) is simple, but not a result of oversimplification. We should take into account that the growth rates may be correct in order of magnitude and the log-linear diagram is rather limited in resolvability. It means that growth rates in some eruptions may be affected by unsteadiness in driving pressure. 5. Concluding remarks Firstly physical properties of magmas, tem- perature and viscosity, are examined in relation to lava dome formation. Growth rates of lava domes are expected to undergo the strongest ef- fect by viscosity of magmas. Modes of dome formation are classified into two, squeeze- and spine-types, from the standpoint of the mecha- nism of magma movements. The majority of the lava domes mentioned in the present paper belongs to the squeeze-type. Squeezes of vis- cous and plastic magmas through conduits should satisfy Hagen-Poiseuille Law, by which growth rates are related to the viscosity of mag- mas. The viscosity involved in the law should be different from the normal viscosity of lavas, and is defined as macroscopic viscosity on the assumption that the temperature is around 1000°C during dome formation. Growth rates of the 15 lava domes formed in the 20th centu- ry are determined with reference to the pub- lished quantitative data. The relationship be- tween the macroscopic viscosity and SiO2 con- tent of lavas is statistically obtained through the agency of growth rates of the domes. Formation processes of lava domes of squeeze-type are strongly controlled by macroscopic viscosity of magma. 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