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Journal of Volcanology and Geothermal Research 178 (2008) 10–18

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Volcanic tremor during eruptions: Temporal characteristics, scaling and constraints on conduit size and processes

Stephen R. McNutt a,⁎, Takeshi Nishimura b a Alaska Volcano Observatory, Geophysical Institute, University of Alaska, Fairbanks, Alaska, USA, 99775-7320 b Department of Geophysics, Graduate School of Science, Tohoku University, Sendai 980-77, Japan

ARTICLE INFO ABSTRACT

Article history: We investigated characteristics of eruption tremor observed for 24 eruptions at 18 volcanoes based on Received 1 June 2007 published reports. In particular, we computed reduced displacements (DR) to normalize the data and Accepted 7 March 2008 examined tremor time histories. We observed: (a) maximum DR is approximately proportional to the square Available online 26 March 2008 root of the cross sectional area of the vent, however, with lower than expected slope; (b) about one half of the cases show approximately exponential increases in D at the beginnings of eruptions, on a scale of minutes to Keywords: R hours; (c) one half of the cases show a sustained maximum level of tremor; (d) more than 90% of the cases volcanic tremor eruptions show approximately exponential decay at the ends of eruptions, also on a scale of minutes to hours; and (e) conduit radius exponential increases, if they occur, are commonly associated with the first large stage of eruptions. We explosions estimate the radii of the vents using several methods and reconcile the topographic estimates, which are scaling systematically too large, with those obtained from DR itself and theoretical considerations. We compare scaling of tremor DR with that for explosions and find that explosions have large absolute pressures and scale with vent radius squared, whereas tremor consists of pressure fluctuations that have lower amplitudes than the absolute pressure of explosions, and the scaling is different. We explore several methods to determine the appropriate scaling. This characteristic helps us to distinguish the type of eruptions: explosive (Vulcanian or Strombolian) eruptions versus sustained or continuous ash (e.g. Plinian) eruptions. Average eruption discharge, estimated from the total volume of tephra and the total duration of eruption tremor, is well correlated with peak discharge calculated from cross sectional area of the vent and velocity of volcanic ejecta. These results suggest similar scaling between different eruption types and the overall usefulness of monitoring tremor for evaluating volcanic activity. © 2008 Elsevier B.V. All rights reserved.

1. Introduction 1986; Mori et al., 1989; Nishimura et al., 1990; Chouet, 1996; Neuberg et al., 2000). As a result, many characteristics of tremor have been Volcanic tremor that occurs during eruptions (hereinafter termed identified and quantified. Examples include: ambiguous onset and eruption tremor) is associated with the upward migration of magma unclear phases with a predominant frequency of about 1–3 Hz, and an and gases through the vent, and includes much information on overall frequency range of 0.5–10 Hz; various duration times from a eruption dynamics and kinematics of magma movement under- few tens of seconds (so called isolated tremor) to 10 days or more; and ground. Hence, source processes of eruption tremor are important to hypocenter depths ranging from the surface down to 60 km understand eruption mechanisms, and monitoring tremor is useful to (summarized in McNutt, 1994b). To explain these features of tremor, determine eruption parameters quantitatively. Tremor in general, especially the predominant frequencies, numerous theoretical models including eruption tremor, has been documented at more than 160 have been proposed. These include resonance of a magma body under volcanoes worldwide (McNutt, 1994a,b). In this paper we investigate the ground (e.g., Crosson and Bame, 1985; Chouet, 1986, 1996), fluid systematic relations between tremor reduced displacement, a normal- movement in volcanic conduits or channels (e.g., Ferrick et al., 1982; ized amplitude metric, and factors such as vent radius, erupted Honda and Yomogida, 1993), bubble growth and collapse in magma or volume, and tremor time history with the purpose of deducing gen- water (e.g., Leet, 1988), and non-linear excitations caused by magma eral scaling relationships. flow (Julian, 1994). However, these proposed models do not always The source processes of volcanic tremor, which is not always explain well the characteristics of all volcanic tremor, because dif- “eruption tremor”, have been investigated at many volcanoes around ferent types of tremor are observed associated with varying magma the world for several decades (e.g., Aki and Koyanagi, 1981; McNutt, properties, vent geometries, volcano structures, and eruption styles. In the present study, we focus only on eruption tremor to avoid fi ⁎ Corresponding author. dif culties arising from analysis of tremor from unknown sources. The E-mail address: [email protected] (S.R. McNutt). merits of this approach are as follows: (1) discrimination of eruption

0377-0273/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jvolgeores.2008.03.010 Author's personal copy

S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 11 tremor from other types is comparatively simple because eruption (1995) inferred that the source mechanism of eruption tremor at Mt. tremor is associated with the surface phenomena of eruptions; (2) Tokachi can be represented as a counter force of the eruption (single data for many eruptions are available, with comparatively large seis- force). Nishimura (1998) extended this work to a suite of explosion mic signal amplitudes, hence good signal-to-noise ratios; (3) the earthquakes at 11 volcanoes and determined scaling relationships. general physical environments for generating eruption tremor are From a comparison of tremor at different eruptions, McNutt (1994a, similar, since all tremor accompanies the common phenomena of 2004) showed a linear relation between log10(reduced displacement) eruptions; and (4) measured surface phenomena help us to constrain (DR) of maximum sustained amplitude of eruption tremor and the realistic source processes. Volcanic Explosivity Index (VEI; Newhall and Self, 1982) as: Several detailed studies on eruption tremor have been reported. ¼ : VEI þ : ð1Þ For example, Eaton et al. (1987) showed that the amplitude of tremor log10DR 0 46 0 08 increases with heights of lava fountains at Kilauea Volcano. Yamasato et al. (1988) investigated the temporal characteristics of eruption In this paper, we examine systematic behavior of temporal variations tremor associated with the 1986 Oshima eruption. Nishimura et al. and scaling laws for the amplitude of eruption tremor. To describe the

Table 1 Observed parameters of volcanic eruption tremor. Notes: El Chichon total vol=370; 200 assumed in Apr 4 eruption. Kilauea total dur Jan 83=99 h, we used Jan 5 part=34 h, thus vol 1/3. Usu total volume=80, 20 per eruption. Nyiragongo Nov 94 Vt insignificant (lava lake). type: c (central vent); f (fissure);ph (phreatomagmatic explosion); lk (lava lake). Izu Oshima (event 2) had a central vent at the surface but an inferred fissure at depth. Times for stages I, II, and III: h=hours, d=days, m=minutes. Under Vent, radius is given for circular vents and length for fissures (see r or l column). ⁎Usu did not decay exp; concave downward

Event no., volcano Date Type Vt Height VEI Duration DR Freq. References

6 2 (start) ×10 m3 (km) (h) (cm ) (Hz) 1 El Chichon 82.Apr.4 c 200 17 5 1.08 278 1 (Sigurdsson et al. 1984; McClelland et al. 1989; Havskov et al. 1993) 2 Izu Oshima 86.Nov.15 c (f) 4.4 5 2 72 1230 0.8 Yamasato et al. (1988); Endo et al. (1988) 3 Izu Oshima 86.Nov.21 f 24 16 3 10 2380 0.8 Yamasato et al. (1988); Endo et al. (1988) 4 Kilauea 83.Jan.5 f 5 2 2 38 18 1–10 Koyanagi et al. (1988); McClelland et al. (1989)) 5 Kilauea 83.Oct.2 c 14 2 2 64 16 2 Koyanagi et al. (1988); McClelland et al. (1989) 6 Kilauea 83.Nov.5 f 12 2 2 43 16 2 Koyanagi et al. (1988); McClelland et al. (1989) 7 Miyake 83.Oct.3 f 7.4 10 3 15.25 65 1.4 Uhira et al. (1984); McClelland et al. (1989) 8 Nyamuragira 81.Dec.25 f 28 6 3 480 120 2 Hamaguchi (1983); Ueki (1983); McClelland et al. (1989) 9 Nyamuragira 86.Jul.16 f 12 5 2 52 – 2 Kasahara et al. (1988) 10 Nyiragongo 94.Nov lk 0.001 1 1 120 4 2 Hamaguchi pers comm 1996; GVN 1994 11 Pavlof 80.Nov.12 c 6 11 3 30 11 1.5 McNutt (1987); McClelland et al. (1989); McNutt (1994a,b) 12 Pavlof 83.Nov.14 c 12.5 7.5 3 48 16 1.5 McNutt (1987); McClelland et al. (1989); McNutt (1994a,b) 13 Pinatubo 91.Jun.15 c 9000 30 6 16.8 1070 1 Pin. Volc. Obs. Team (1991); White (1992); Wolfe (1992) 14 Piton de la Four. 85.Jun.14 f 1 2 1 24 8? 2? McClelland et al. (1989) 15 Raoul Island 64.Nov.20 ph – 111.2491Adams and Dibble (1966) 16 Redoubt 89.Dec.15 c 13 12 3 0.67 39 1.6 Power et al. (1994); McNutt (1994a,b) 17 Shiveluch 64.Nov.12 c 300 15 4 1 152 2 Gorshkov and Dubik (1970); Belousov (1995) 18 Spurr 92.Jun.27 c 44 14.5 3 4.05 16 2 McNutt et al. (1995); Neal et al. (1995) 19 Spurr 92.Aug.18 c 52 18 3 3.47 30 2 McNutt et al. (1995); Neal et al. (1995) 20 St. Helens 80.May.18 c 400 24 5 5.5 260 1 Scandone and Malone (1985); McClelland et al. (1989) 21 Tokachi 62.Jun.29 c 71 12 3 2 49 3 Yokoyama (1964); Katsui et al. (1978) 22 Unzen 90.Nov.17 ph – 1 1 18 7.6 2.5 Shimizu et al. (1992) 23 Usu 77.Aug.7 c 20 12 3 2.1 58 2 Suzuki and Kasahara (1979); Niida et al. (1980) 24 Veniaminof 83.Jun.4 c 9.8 8 3 432 17 1 McClelland et al. (1989); McNutt (1994a,b)

Event no., volcano Type Stage I Stage II Stage III Vent Area r or l Velocity Density τb τe V0

2 3 3 τI τII τIII (m) (m ) (m/s) (g/cm )(m) 1 El Chichon c 5 m 50 m 15 m 300 2.80E+05 r 300 1.4 5 m 15 m 5.90E +10 2 Izu Oshima c 1d 2d none 150 7.00E+04 r 100 2.5 8.1 h –– 3 Izu Oshima f b1 h 5 h 4 h? 2000 2.00E+03 l 178 2.5 – 4 h 4.00E+09 4 Kilauea f 8 h 27 h 3 h 1000 1.00E+03 l 61 2.5 4 h 1.5 h 2.57E+08 5 Kilauea c 7 h 55 h 2 h 4 5.00E+01 r 77 2.5 8 h 1 h 1.08E+07 6 Kilauea f none none 43 h 700 7.00E+02 l 28 2.5 – 7 h 3.85E+08 7 Miyake f none none 15 h 4500 4.50E+03 l 90 2.5 – 3.4 h 3.87E+09 8 Nyamuragira f 1d? 16d 3d 1200 1.20E+03 l 100 2.5 – 1.4d 1.13E + 10 9 Nyamuragira f none 12 h 40 h 20 4.00E+02 l 100 2.5 – 24 h 2.70E+09 10 Nyiragongo lk none none 5d 10 3.10E+02 r 20 2.5 – 4d 1.67E+09 11 Pavlof c 12 h 16 h 2 h 50 7.90E+03 r 77 2.5 7.5 h 1 h 1.71E+09 12 Pavlof c 14 h 20 h 14 h 50 7.90E+03 r 77 2.5 7.1 h 4.8 h 8.20E+09 13 Pinatubo c 20 m 2.7 h 13.8 h 1000 3.10E+06 r 420 1.4 20 m 3 h 1.10E+13 14 Piton de la Four. f none none 24 h 1000 1.00E+03 l 45 2.5 – 6 h 7.58E+08 15 Raoul Island ph none none 1.2 h 50 7.90E+03 r 141 2.5 – 16 m 8.34E+08 16 Redoubt c 20 m none 20 m 200 1.30E+05 r 100 2.5 10 m 15 m 9.13E+09 17 Shiveluch c 52 m none 8 m 875 2.40E+06 r 300 1.4 12.5 m 4 m 1.35E+11 18 Spurr c 3.3 h none 43 m 109 3.70E+04 r 283 2.5 2.2 h 22 m 1.08E+10 19 Spurr c 16 m 3 h 15 m 109 3.70E+04 r 400 2.5 16 m 15 m 1.04E+10 20 St. Helens c 3.6 h 0.63 h 1.3 h 600 1.10E+06 r 380 1.4 54 m 8 m 1.56E+11 21 Tokachi c 47 m 14 m 64 m 75 1.77E+04 r 100 2.5 16 m 10 m 8.28E+08 22 Unzen ph none none 18 h 10 2.00E+01 l 45 1.0 – 5.5 h 1.39E+07 23 Usu c 63 m none ⁎62 m 50 7.90E+03 r 105 1.4 19 m – 0.00E+00 24 Veniaminof c 1d 2d 14d 250 2.00E+05 r 71 2.5 – 9d 8.61E+12 Author's personal copy

12 S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 average features, we investigate eruption tremor from many eruptions at different volcanoes around the world on the basis of published studies and reports. First, we examine amplitude, estimates of vent size and general characteristics of temporal variations of tremor amplitude. Second, we compare the eruption tremor with explosion earthquakes that accompanied Vulcanian or strong Strombolian eruptions. Subse- quently, we examine the discharge rate of volcanic materials from the vent, based on the data of eruption tremor and other geological evi- dence. Finally, we discuss the source mechanisms of eruption tremor in light of our new interpretations.

2. Observed characteristics of eruption tremor

We investigate 24 examples of eruption tremor at 18 volcanoes on the basis of published reports. In Table 1, parameters of eruption tremor analyzed in the present paper are summarized with information on eruption type, tephra volume, ash column height, and other parameters. Height of ash column and volume of tephra are followed by references. Most of the VEI values are determined by Simkin and Siebert (1994),but some of the VEIs are estimated by us from heights of ash columns and volumes of tephra. For descriptive purposes, we classified eruptions into four types; (1) eruptions from a central circular vent, (2) fissure eruptions, (3) lava lake activity, and (4) phreatic or phreatomagmatic eruptions. Vents are characterized by either radius (r)orfissure length

(l), and the area (cross sectional area) of the vent is calculated from the Fig. 1. Comparison of cross sectional area of the vent with the observed tremor reduced 2 formula of either πr or l×1m(fissures are assumed to have a thickness displacement. Numbers in the figure correspond to each eruption in Table 1. Square of 1 m; this may slightly underestimate some values). We use the symbols represent fissure eruptions, and circles are eruptions from circular vents. maximum fissure length and do not adjust for temporal variations in the portion of the fissure erupting. Radii of vents and fissure lengths are estimated from topographic maps, photographs of eruptions and publishedpffiffiffiffiffiffiffiffi reports. Flow velocity v is estimated by using the relation abruptly when the eruption started. After reaching a maximum level, v 2gh,whereh is the height of fountaining, ballistics, or plume, and g is the tremor amplitude decreased approximately exponentially, and the gravitational acceleration. Because this formulation neglects the eventually returned to the noise level. Fig. 2(b) is an example from the momentum of entrained fluid flow, it may slightly underestimate the November 1964 eruption of Raoul Island that produced a phreatomag- velocity. We have used the best and highest resolution data available for matic explosion (Adams and Dibble, 1966). Like Miyake, the tremor most of these estimates, however, as in any study using published data amplitude at Raoul Island increased suddenly as the eruption began, (instead of original data), some prudence must be exercised in inter- followed by approximately exponential decay (the amplitude also shows preting the measurements. a small perturbation in the middle of the decay sequence at about 18 h We first discuss the amplitude of eruption tremor. Fig. 1 shows a 30 m). Fig. 2(c) shows an example of tremor observed during the June 27, relation between reduced displacement and cross sectional area of 1992 eruption of Mt. Spurr (McNutt et al., 1995). This case is slightly the vent as measured at the ground surface. Reduced displacement different from the former two cases. Tremor amplitude showed an

(DR)(Aki and Koyanagi, 1981; Fehler, 1983) represents a normalized approximately exponential increase for about 3.5 h after the eruption amplitude (DR is equal to rms amplitude times distance), which is started, and reached a maximum. Then, the amplitude decayed corrected for geometric spreading and instrument gain. Note that the approximately exponentially over about 43 m. Scandone and Malone reduced displacement in the present study is estimated from the (1985) show the temporal variation of tremor accompanying the 1980 maximum amplitude of eruption tremor; distances to stations are eruptions of Mt. St. Helens (Fig. 2(d)). On May 18, continuous tremor given in maps or tables in the various papers cited. Most of the reduced started 3 h after the beginning of the initial gigantic explosion. The displacements were determined by us and the others were previously amplitude increased approximately exponentially for about 4 h and determined by McNutt (1994a).Wefind that the reduced displacement reached a maximum. After the tremor sustained this maximum level for is roughly proportional to the cross sectional area of the vent or fissure, about 1 h, during which small fluctuations were observed, the amplitude although some of the tremor from fissures shows very large reduced decayed. For the later eruptions at Mt. St. Helens (May 25, June 12, July displacements (e.g., events 2, 3 and 8). The slope of the best fit 22, 1980 (Fig. 2(d)) and later), we find that for all the cases eruption regression line is 0.3, with a regression coefficient of 0.52. This can be tremor increased abruptly, then decayed approximately exponentially. written as log10(DR)=log10(0.29×cross sectional area)+0.52. We infer Note that we have been careful to state the curve shapes as that the maximum reduced displacement is approximately propor- “approximately exponential”.Thisreflects the fact that we have not tional to the square root of the area of vents, that is, the reduced performed formal curve fitting to all the data. However, several cases for displacement linearly increases with crater radius when vents form a which curve fitting have been done are indeed exponential (e.g. Pavlof – circular crater. This correlation suggests that the area of the vent (crater 1996 eruption; J. Benoit, writt. comm.; Shishaldin – 1999 eruption; G. or conduit) plays an important role in controlling the amplitude of Thompson, writt. comm.). Benoit et al. (2003) showed that scaling eruption tremor, which is similar to the relation for volcanic explo- relationships between tremor amplitudes and durations for tremor at sion earthquakes (Nishimura and Hamaguchi, 1993; Nishimura, 1995, nine volcanoes were exponential, further supporting this generalization. 1998). The implications of this are explained below. In the remainder of the Next, we examine temporal variations of eruption tremor amplitude. paper, however, we use the terms “gradual increase” and “gradual Fig. 2(a) shows the observed variation of eruption tremor amplitude decrease” with the implicit understanding that these are approxima- during the October 1983 eruption of Mt. Miyake, which produced lava tions. In all cases but one the tremor time histories are concave upwards fountaining (Uhira et al., 1984). We see that the amplitude increased for the increasing and decreasing segments. Author's personal copy

S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 13

Fig. 2. Examples of temporal variations of eruption tremor: (a) Miyake, October, 1983; (Uhira et al., 1984) (b) Raoul Island, November, 1964; (Adams and Dibble, 1966) (c) Spurr, June, 1992, (McNutt et al., 1995) (d) Mt. St. Helens, May, June, and July, 1980, (Scandone and Malone, 1985).

A detailed analysis of the events in Table 1 showed three main of a maximum level also have similar problems for other tremor characteristics in the temporal variation of tremor amplitude: (1) an episodes. Hence, our classification in Table 1 is judged by which pro- exponential increase [which we call stage I], (2) maintenance of a cesses are dominant in the sequence of tremor. To evaluate each stage, maximum level [stage II], and (3) an exponential decrease [stage III]. we measure total duration times for each stage, τI, τII, τIII, which are Durations of the exponential increase and decrease usually differ, the times from the start of eruption to peak amplitude, time of flat or with the increase having a longer time constant. We also observe fluctuating part, and time from peak until end, respectively. If these that small fluctuations and perturbations are common during these three stages are added together, we obtain the total duration of the stages and that some of the tremor has slightly more complicated eruption. Table 1 also shows τb and τe, for an exponential increase at time histories. However, fluctuations are usually smaller than the the beginning and an exponential decrease at the end of eruption, variations of the three main characteristics, and some of the respectively, which are measured from the peak to 36% of the peak complicated shapes (time histories) can be explained by a super- (=1/e). These are not durations, but instead are characteristic times for position of several exponential increases and decreases (e.g., tremor exponential increases or decreases in amplitude. We did not measure on February 4, 1989, at Mt. Tokachi; see Fig. 7 of Nishimura et al., the time constants τb and τe, for a few examples of tremor that were 1990). Therefore, we conclude that an exponential increase, the not matched with the three stages (e.g., concave downward decay of maintenance of a maximum level, and an exponential decrease are the 1977 eruption of Usu). the three most basic stages of eruption tremor. The durations of the We find that the occurrence of an exponential increase (58% of three characteristics are displayed for each event in Table 1: 58% of cases) is less likely than that of an exponential decrease (92% of cases), the events clearly show an exponential increase, 58% show the although exponential increases are clearly observed at the May 18 maintenance of a maximum level, and 92% show an exponential eruption of Mt. St. Helens, at the first eruption of Mt. Spurr, June 27, decrease. 1992, and at the November 1964 event of Mt. Shiveluch. As in the 1980 The occurrence ratio for each stage in this analysis is approximate. eruption sequence of Mt. St. Helens (Fig. 2(d)), the exponential Because our data were selected from figures in previously published increase often occurs accompanying the first main eruption, but reports, our classification depends on the resolution of the figures for seems to be less frequently observed before the second and later each eruption. For example, it is difficult to judge whether or not an eruptions. Hence, we infer that the exponential increases are mainly exponential increase occurred in cases of rapid increase as shown in associated with the first paroxysmal phase, or in the early stages of an Fig. 2(a) and (b). The criteria of exponential decrease and maintenance eruption sequence at a volcano. Author's personal copy

14 S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18

The main characteristics of eruption tremor are summarized as follows; (a) the maximum reduced displacement is approximately proportional to the square root of the cross sectional area of the vent, (b) the eruption tremor shows three basic stages: a gradual increase, maintenance of a maximum level, and a gradual decrease, and (c) the gradual increase observed for the first big eruption of a volcano is generally very clear.

3. Comparison of the eruption tremor to explosion earthquakes

Volcano seismologists have classified volcanic explosion earth- quakes and eruption tremor mainly based on the following points. Explosion earthquakes produce simple waveforms with short dura- tions of less than a few tens of seconds, often accompanied by an air- shock wave that is superimposed on the seismograms or is recorded by a micro-phone or infrasound meter. On the other hand, eruption tremor generally has a long duration (e.g. minutes to hours) with emergent onsets, and is not accompanied by large air-shock waves. These two types of signals are generally associated with different types of eruptions, such as brief Strombolian or Vulcanian-type ex- plosions and sustained ash or lava emissions, respectively. Hence systematic differences between eruption tremor and explosion earth- quakes reflect differences in the dynamics of eruption in these erup- tion styles. In Fig. 3 we plotted explosions and tremor magnitudes as func- tions of the radius on the same axes. Here we covert DR to magnitude (Tuboi, 1954; Watanabe, 1971; see Nishimura, 1998 for details) so we can use the same base plot as Nishimura (1998). Explosions scale with r2, so the slope is 2 in Fig. 3. Explosions require a high absolute pressure; that is, pressure builds up under a sealed cap and rupture occurs quickly when the pressure exceeds the strength of the cap. For Vulcanian eruptions the cap is solid rock, whereas for Strombolian eruptions the upper slug of magma serves the same purpose. This

Fig. 4. Comparison of different kinds of the volume discharge rate. a) discharge estimated from column height versus average discharge rate. Average discharge is obtained from dividing the total tephra volume by the total duration of eruption. Note that units are volume per sec on the vertical axis and mass per sec on the horizontal axis. b) Peak discharge rate versus average discharge rate. Peak or instantaneous discharge is obtained from the product of cross sectional area of vent and flow velocity. Numbers and symbols are the same as Fig. 3.

Fig. 3. Seismic magnitudes for explosions and tremor versus vent radius. Round black symbols are explosions from Nishimura (1998). Numbers in the figure correspond to pressure is estimated to be 1–10 MPa (Nishimura, 1998; Nishimura each eruption in Table 1 for tremor and from Table 1 of Nishimura (1998) for explosions. and Uchida, 2005). Eruption tremor, by contrast, occurs under open Square symbols represent fissure eruptions; open circles are eruptions from circular fl vents. Fitted lines are for 10 m and larger radius for explosions, and for all data for vent conditions. Tremor is generated by pressure uctuations from tremor. turbulence within the conduit, and the amplitude of these fluctuations Author's personal copy

S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 15 must be less than the absolute pressure of explosions. Further, tremor expressed by e.g., Chouet (1996) in the xyz coordinate (z axis is the is a sustained signal, so the fluctuating pressures persist for periods of vertical direction): minutes to hours or longer, in contrast to explosions, which have a 0 1 k þ A times scale measured in seconds to minutes. Even though we do not 00 M ¼ @ k þ A AD : ð2Þ know the exact source mechanics for eruption tremor, such a 0 0 V 00A difference as can be recognized in Fig. 3 is quite useful to empirically distinguish the styles of eruption: explosive (Vulcanian or Strombo- where λ and μ are the Lame constants, ΔV the volume change of the lian) or continuous ash emissions (e.g. Plinian). One case of the source. We use the far field expression for Rayleigh waves from this “ ” eruption tremor, for Izu Ohshima 1986 (square symbol labelled 3 in seismic moment tensor (e.g., Aki and Richards, 1980; Eq. (7.149) on Fig. 3), plots almost on the scaling relation for explosion earthquakes. page 316) as the displacement of eruption tremor: Note that this tremor is twice as strong as that from the 1991 eruption rffiffiffiffiffiffiffiffi of Pinatubo (tremor point labelled “13” in Fig. 3). Although the Izu ðÞ j j¼r2 0 2 ðÞþdr2 j ð3Þ Oshima eruption was a basaltic type eruption, this tremor behaved u 2kr1 h i h M0 8cUI1 pkr dz more like an explosion earthquake and not like typical eruption tremor from the view point of seismic wave generation. This where r2 (z) is the fundamental mode of the eigen function (we determination is also supported by phenomenological observations neglect higher modes), c the phase velocity, U the group velocity, I1 of a very high eruption column reaching 16 km a.s.l. and by the the energy integral, k the wavenumber, and r the epicentral distance. λ μ μΔ generation of visible shock waves from the active vent. Additionally Here we assume = so that M0 = V. For simplicity, we assume a the eruption may have broken fresh rock to form a new fissure, which semi-infinite medium, so we obtain: would contribute to stronger tremor by a geometric effect as shown in ðÞ¼ 0:8475kh : 0:3933kh Fig. 1. r1 h e 0 5773e ðÞ¼ : 0:8475kz : 0:3933kz r2 z 0 8475e 1 4679e ð4Þ I ¼ 1:2049q=k 4. Discharge rate of eruptions 1 c ¼ U ¼ 0:9194b

Our systematic measurements in Table 1 permit an additional where h is the source depth, ω is the angular frequency of tremor, β comparison to be made. Fig. 4(a) shows a comparison of two kinds of the S-wave velocity, ρ the density of medium, and the units are MKS. discharge rates of tephra. The first is the average discharge rate Qt As a result, the reduced displacement is written as: estimated by dividing the total tephra volume by the total duration pffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffi of the eruption estimated from tremor duration. The second is j j ðÞ ¼ upffiffiffiLr ¼ 2r2 0 : 0:85kh : 0:39kh ; ð5Þ discharge rate Q obtained from the column height (Morton et al., DR 1 23e 0 58e M0 H 2 8cUI1 1956; see also below). In Fig. 4(b), the discharge rate in the vertical axis is calculated as the product of the vent area and the estimated where L represents the wavelength. ε peak flow velocity QSv; this is the peak or maximum instantaneous The seismic moment M0 can be expressed by using the strain in discharge. Note that the units of the horizontal and vertical axes are the radial direction at the conduit wall: not the same, the former is kg/s and the latter is m3/s. We find that ¼ pA 2e: ð6Þ the two peak discharge rates are highly correlated with the average M0 2 LcR discharge rate. The flow velocity varies over about one order of Alternatively, we can express the M by the pressure disturbance magnitude (20–420 m/s) and the vent area across five orders (5 ×101 0 in the flow, ΔP: to 3.1 ×106 m3), therefore, we conclude that cross sectional area is a more important parameter in controlling the mass flux. Because 2 M0 ¼ pLcR DP: ð7Þ tremor amplitude is proportional to the square root of the cross sectional area, we can in principle quantitatively evaluate the These relations are quite important for estimating the conduit discharge rate of eruption by monitoring tremor amplitude. It is radius R because the eruption dynamics and the magnitude of noteworthy to mention that Qt is strongly proportional to QSv,which eruptions are closely related to the cross sectional area of the enables us to roughly evaluate an average discharge rate by conduit. However, Eqs. (5) and (7) indicate that we cannot extract measuring only the cross sectional area of the vent and assuming a the radius from DR without determining Lc and Δ P (or ε ) representative flow velocity. independently. We can use a fixed Lc of 500 m, and assume a maximum value of ΔP at 1 MPa to determine a minimum conduit 5. Discussion radius under the assumption of cylindrical geometry. Assuming β =1.5 km/s, ω=2π×2 rad/s, h=250 m, and ρ=2500 kg/m3, we plot We wish to compare quantitatively the differences between these values versus the radius determined from surface topography tremor and explosion earthquakes, so that we can infer some of the in Fig. 5 and list the values in Table 2. For comparison we also physical factors that govern tremor occurrence during eruptions. To determined the radius for spherical geometry (a point source) which do so we present a straightforward model of tremor generation. First, is the minimum possible radius that can be determined using we suppose that the eruption tremor is generated by pressure seismic data. This is of course physically unreasonable because there fluctuations in a cylindrical conduit due to volcanic flows. The conduit is no way for the magma to move, however it provides some insight shape is not critical here and a cylindrical conduit is mathematically into the limiting case. These values are quite small and are also convenient. We envision that expanding gases and flow of magma shown in Table 2. push against the wall rocks as magma moves towards the surface to We now need to link the conduit radii determined from seismic erupt. We then quantitatively represent a source of eruption tremor. data to those determined from topography and to use these data to Eruption tremor consists mainly of surface waves (McNutt, 1994b), so bring together the constraints from both explosions and eruption the source is presumed to be located at a shallow portion of the tremor. Three of our cases have data for both explosions and tremor: volcanic conduit. We use a cylindrical conduit with a radius of R and a Pavlof, St. Helens and Tokachi. These cases are especially useful to length of Lc as a source configuration, and the tremor represents determine how much lower the pressure fluctuations are for tremor radial oscillations of the conduit wall in and out from its neutral compared to the absolute pressure of the explosions. In each case the position. In this case, the moment tensor of the source, M,is seismic magnitude of the explosions is larger than the tremor by 1–4 Author's personal copy

16 S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 orders of magnitude as seen in Fig. 3. Thus the relative sizes of ex- Table 2 plosions versus tremor appear to be correct in terms of the pressure Estimates of vent radii using several methods. Numbers in brackets are equivalent radii for fissures arguments in Section 3 above; high absolute pressure for explosions and lower pressure for tremor. Volcano Date DR radius radius radius We next attempt to reconcile the systematic errors in measuring (spherical) (cylindrical) (topo) the vent/conduit radius. We observe in Fig. 3 that the explosion and (cm2) (m) (m) (m) tremor data have different slopes, which imply fundamentally dif- 1 El Chichon 82.Apr.4 278 8.3 46.9 300 ferent scaling relations and different underlying processes. But we 2 Izu Oshima 86.Nov.15 1230 17.5 98.6 150 must first consider whether the measurements of vent radius (seen 3 Izu Oshima 86.Nov.21 2380 24.4 137.1 [25.2] 4 Kilauea 83.Jan.5 18 2.1 11.9 [17.8] at the surface) and conduit radius (what we infer acts to produce 5 Kilauea 83.Oct.2 16 2 11.2 4 tremor at depth) can be improved or corrected. We explored three 6 Kilauea 83.Nov.5 16 2 11.2 [14.9] correction schemes. First, we used Mount St. Helens as a reference 7 Miyake 83.Oct.3 65 4 22.7 [37.8] value of 50 m because it has constraints based on several different 8 Nyamuragira 81.Dec.25 120 5.5 30.8 [19.5] methods (Carey and Sigurdsson, 1985; Chadwick et al., 1988), and 9 Nyamuragira 86.Jul.16 0.0 [11.3] 10 Nyiragongo 94.Nov 4 1 5.6 10 shifted tremor data to the left to agree with the same slope as 11 Pavlof 80.Nov.12 11 1.7 9.3 50 explosions and the observed offset of Mount St. Helens. This 12 Pavlof 83.Nov.14 16 2 11.2 50 scheme is the most restrictive and assumes that the scaling of 13 Pinatubo 91.Jun.15 1070 16.4 91.9 1000 explosions is correct. Second, we used the conduit radius 14 Piton de la Four. 85.Jun.14 8 1.4 8.0 [17.8] 15 Raoul Is 64.Nov.20 49 3.5 19.7 50 determined from D (cylindrical geometry in Table 2) to rotate R 16 Redoubt 89.Dec.15 39 3.1 17.6 200 the data, again using Mount St. Helens at 50 m as a reference value. 17 Shiveluch 64.Nov.12 152 6.2 34.7 875 This gives the same slope as explosions but preserves the scatter of 18 Spurr 92.Jun.27 16 2 11.2 109 the data; we presume the scatter has physical meaning. A third 19 Spurr 92.Aug.18 30 2.7 15.4 109 scheme, sliding the data to the left but retaining the slope of the 20 St. Helens 80.May.18 260 8.1 45.3 600 21 Tokachi 62.Jun.29 49 3.5 19.7 75 tremor data, was rejected because it moves the leftmost points 22 Unzen 90.Nov.17 7.6 1.4 7.7 [2.5] (smallest R) unrealistically too far to the left. Of the three methods 23 Usu 77.Aug.7 58 3.8 21.4 50 we prefer method 2 as being best grounded in the observations and 24 Veniaminof 83.Jun.4 17 2.1 11.6 250 also agreeing reasonably well with the theory. However, none of the various correction methods we considered can satisfactorily explain the offset and scatter of tremor data with respect to explosion data without invoking parameters that cannot be directly measured. Since Q =velocity× cross sectional area, for circular conduits this We considered other factors that contribute to our understand- implies H is proportional to R0.5.InFig. 6 we plot R determined ing and assessment of appropriate values for the vent/conduit radii. from H (using data from Table 1) versus R from DR. We assumed For example, plume rise theory based on Morton et al. (1956) velocity in Table 1 andweusedtheR determined from DR with suggests that H =1.67Q0.259 where H is height and Q is discharge. cylindrical geometry (Table 2). We observe that the slope is approximately 1.0 for values of R determined from H greater than 100 m hence we consider this to be the range where observations are most reliable. Smaller values give extremely low R estimates (lower part of Fig. 6). We also note that all the values of R based on H are very small. In fact they agree better with the radii determined

from DR using a point source (Table 2; spherical geometry), which is the minimum possible size using seismic data. This suggests again that the main part of the flow during eruptions is concen- trated near the center of the conduits so that the effective radius is indeed quite small. The choice of R for various modeling schemes depends very strongly on the conditions of the eruptions and the constraints allowed by the data. Why would explosions scale differently than volcanic tremor? We suggest that explosions actually form the craters, so the size necessarily scales with the strength of the explosion, assuming that the strength of the rock is constant (Sato and Taniguchi, 1997; Nishimura, 1998). Tremor, on the other hand, apparently occurs associated with sustained eruptions that use only a portion of the available conduit, generally the central part, and does not modify the conduit significantly during the course of the eruption, except perhaps at the vent. We were surprised to see so little obvious difference between basalt and andesite/dacite composition (different symbols in Fig. 3). We had anticipated an effect because basalt is less viscous and may have a lower gas content, whereas andesite/dacite is more viscous and has higher gas content. The lack of a difference suggests that the physics of sustained explosive eruptions are not very sensitive to magma composition, but depend more strongly on parameters such as conduit size, ascent velocity, etc. Fig. 5. Vent size estimated from DR versus vent size estimated from topography. The vent sizes estimated from topographic maps, photographs, etc. Numbers and symbols are the same as Fig. 3. Note that radius estimated from DR is effective radius. See text and Table 2 for details. are known to be too large, for several reasons. First, the radius is Author's personal copy

S.R. McNutt, T. Nishimura / Journal of Volcanology and Geothermal Research 178 (2008) 10–18 17 measured at the ground surface, whereas the eruption tremor signal Table 3 originates at depths of a few hundred meters or more. Geological Variations of parameters for each stage of eruption tremor investigations generally show that volcanic vents are flared at the Stage Area size Velocity and Magma Tremor tops, hence surface values are always maxima. Second, geologic of vent density of flow supply amplitude evidence at Mule Creek (Stasiuk et al., 1996) shows breccia, vitrophyre, I Increase Constant with Yes or no Exponential and degassed magma near the wall rocks, suggesting that the part of fluctuation Increase the magma that moves, or the effective size, is smaller than the full II Constant Constant with Yes Maintenance of a fl fl fl uctuation Maximum Level size measured to the wall rocks. Third, ow models for viscous uids III Constant Decrease with No Exponential such as magma (Poiseuille type flow or plug flow) show that the flow fluctuation Decrease velocity is high near the center of a conduit and very slow near the edges, hence the part of the conduit involved in the main magma flow is again smaller than the full conduit dimensions. This implies that only a small part of the flow processes contribute to volcanic tremor These changes of the radius, density, flow velocity, etc. for each stage generation. This would be the parts near the walls, suggesting that the are summarized in Table 3. central maximum flow part is decoupled or does not transmit its energy very efficiently to the adjacent material that is closer to the 6. Conclusions wall. All these factors likely contribute to the scatter in plots of vent size versus seismic amplitude, and also affect the slope of scaling We investigated characteristics of 24 cases of eruption tremor at 18 relations. volcanoes based on published reports. Detailed analyses of reduced Based on the characteristics of eruption tremor, we infer the displacements and temporal variations of eruption tremor with geo- behavior of the vent and flow as follows. In stage I, either the effective logical data such as areas of vents, flow velocities of ejecta, and tephra size of vent is enlarged by the flow of volcanic ejecta, or the fluctuation volumes, reveal the following basic characteristics of the tremor: (1) of pressure in the volcanic flow systematically increases, or both. The reduced displacement is approximately proportional to the square root distribution of gasses in the magma may contribute to the exponential of the cross sectional area of the vent; (2) temporal variation of tremor increase, with low gas at first and more gas later, because the upper amplitude shows an exponential increase at the beginning of eruption, portion would be partially degassed to the surroundings during slow followed by maintenance of a maximum level, and exponential decay ascent (e.g. Jaupart, 1998). New magma may gradually be supplied at the end; (3) exponential increase is often observed at the first big from deeper regions. These factors may increase amplitude of tremor eruption of a sequence. exponentially. In stage II, the cross sectional area of the vent has To explain these characteristics, we investigated scaling relations reached a maximum size and remains roughly constant. The velocity between tremor amplitude, cross sectional area of the vent (conduit), and density of flow do not change because magma supplied to the velocity and density of volcanic flow, and other parameters. From the reservoir and magma withdrawn through the vent are almost equal. comparison of these parameters with the characteristics of the erup- Hence, the amplitude of tremor keeps a maximum level. In stage III, tion tremor, we find that cross sectional area of the conduit or vent is the cross sectional area of the vent remains almost at the maximum an important parameter controlling the amplitude of tremor and its level, but the velocity of flow decreases as the pressure of the reservoir temporal variation, despite measurement problems. Explosions are becomes lower due to cessation of magma supply from deeper stronger than tremor at the same volcano, reflecting the fact that reservoirs. As a result, tremor eventually ceases at the end of eruption. explosions require a high absolute pressure to break the cap rock, whereas tremor consists of lower magnitude fluctuations of pressure in a sustained eruption from an open vent. The observed features of eruption tremor may help us to better understand temporal changes in the magnitude of volcanic eruptions.

Acknowledgments

We are grateful to H. Hamaguchi for providing us the unpublished data of Volcano Nyiragongo and to K. Uhira for giving us information on tremor data of Mt. Miyake. An earlier draft of the paper was reviewed by J. Benoit, M. Garces, H. Shimozuru and B. Sturtevant. Matthias Hort and Silvio de Angelis kindly provided comments on the current draft. This study was partly supported by the foreign scientist invitation program of the Japan Society for Promoting Science, by the U.S. National Science Foundation under grant EAR-9418219, by the 21COE Program of Tohoku University, and by the U.S. Geological Survey as part of the Volcano Hazards Program, and by additional funds from the State of Alaska to the Alaska Volcano Observatory.

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