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2 Volcanic Plume Height Measured by Seismic Waves Based on a Mechanical Model
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4 Stephanie G. Prejean1 and Emily E. Brodsky2
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6 1. USGS Alaska Volcano Observatory
7 4210 University Ave., Anchorage AK 99508
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9 2. University of California, Santa Cruz
10 Department of Earth and Planetary Sciences
11 Santa Cruz, CA 95064
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23 Submitted to Journal of Geophysical Research, 4-4-10 24 Abstract
25 In August 2008 an unmonitored, largely unstudied Aleutian volcano, Kasatochi,
26 erupted catastrophically. Here we use seismic data to infer the height of large eruptive
27 columns, like those of Kasatochi, based on a combination of existing fluid and solid
28 mechanical models. In so doing, we propose a connection between a common observable,
29 short-period seismic wave amplitude and the physics of an eruptive column. To construct
30 a combined model we estimate the mass ejection rate of material from the vent based on
31 the plume height, assuming that the height is controlled by thermal buoyancy for a
32 continuous plume. Using the calculated mass ejection rate, we then derive the equivalent
33 vertical force on the Earth through a momentum balance. Finally, we calculate the far-
34 field surface waves resulting from the vertical force. Physically, this single force reflects
35 the counter force of the eruption as material is discharged into the atmosphere. In contrast
36 to previous work, we explore the applicability to relatively high frequency seismic waves
37 recorded at ~ 1 s. The model performs well for the 2008 eruption of Kasatochi volcano
38 and the 2006 eruption of Augustine volcano. The consistency between the seismically
39 inferred and measured plume heights indicates that in these cases the far-field 1 s seismic
40 energy radiated by fluctuating flow in the volcanic jet during eruption is a useful
41 indicator of overall mass ejection rates. Use of the model holds promise for
42 characterizing eruptions and evaluating ash hazards to aircraft in real time based on far-
43 field short-period seismic data.
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2 47 1. Introduction and Motivation
48 Empirical studies have suggested that the amplitude of high frequency or
49 broadband seismic waves radiated during large volcanic eruptions generally scales with
50 the height of an eruption column [McNutt 1994]. However, a direct calculation of the
51 expected seismic wave amplitude based on physical models has not yet been successful.
52 Connecting commonly observable data, like seismic wave amplitudes, to a model of the
53 flow in the eruptive jet would provide a new tool to test and improve our understanding
54 of eruptive physics. For instance, small-scale turbulence is thought to play a major role in
55 entrainment of hot particles and gases and hence buoyancy of eruptive columns, yet there
56 are few measurements of the strength or distribution of small-scale features in real
57 eruptive columns [Andrews and Gardner, 2009]. Using seismic data to provide
58 observational constraints on eruption column flow processes is particularly attractive as
59 seismic data is often available even in remote settings. Thus use of the seismic database
60 would greatly increase the number and type of eruptions amenable to study.
61 Pragmatically, a physical model connecting plume height and seismic data would
62 allow the use of seismology as a remote sensing technology to determine volcanic plume
63 height. It would be a particularly useful tool for exploring eruption dynamics in remote
64 environments where direct observation is not possible, such as the volcanoes of the
65 northern Pacific Ocean. Although many volcano observatories world-wide are gradually
66 replacing short-period seismometers with broadband seismometers, we still largely rely
67 on short-period instruments for forecasting, monitoring and analyzing eruptions. These
68 realities motivate the development of the model described below.
3 69 In this study we build on previous work to develop a physical model for the
70 expected amplitude of seismic waves from an eruption that generates a plume of a given
71 height. As a cautionary note we describe situations where the model is not applicable,
72 such as small eruptions or eruptions where most mass ejected is not entrained in the
73 plume. After reviewing previous work on co-eruptive seismology and the characteristics
74 of the Kasatochi and Augustine eruptions, we use the connection between plume height
75 and thermal ejection rate to predict the momentum ejection rate that generates the seismic
76 waves and then compare the model to the data for the Kasatochi eruption as well as the
77 2006 Augustine eruption. We show that for a reasonable range of parameters the model
78 performs well.
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80 2. Background
81 2.1 Co-eruptive Seismology
82 Volcanic activity produces seismic waves. These waves, which include brittle
83 failure earthquakes, long period and very long period events, and volcanic tremor,
84 generally result from movement of fluid in the Earth’s subsurface, directly and indirectly
85 [see Chouet 1996, McNutt, 2005, for reviews]. Seismology also directly senses magma
86 leaving the Earth in the form of both eruption tremor and discrete eruption earthquakes
87 [eg. Nishimura and Hamaguchi, 1993; Nishimura, 1995]. Such co-eruptive seismicity has
88 been documented in scientific literature since Omori’s early studies of Usu-san and
89 Asama volcanoes [1911-1913] and is the subject of this study.
90 By analyzing long period surface waves radiated by the May 18, 1980 eruption of
91 Mount St. Helens, Kanamori and Given [1982] show that the co-eruptive seismic source
4 92 can be represented kinematically by a near-vertical downward single force. This single
93 force represents the counter force of eruption [Kanamori et al., 1984]. This model has
94 been used to investigate eruption source properties of volcanic eruption earthquakes at
95 other volcanoes including Mount Tokachi and Mount Asama, Japan [Nishimura, 1995;
96 Nishimura and Hamaguchi, 1993]. Brodsky et al. [1999] calculated vertical mass
97 discharge rates for the May 18, 1980 eruption of Mount St. Helens based on this model.
98 Our work follows these studies.
99 Other models for the source of co-eruption seismicity exist. For example, Uhira
100 and Takeo [1994] show that in the case of 1986 eruptions of Sakurajima volcano, Japan,
101 a single force model cannot explain long period (several seconds) seismic radiation
102 patterns as well as a model containing volumetric components of expansion and
103 contraction of rock around the source. Chouet et al. [in press] and Chouet et al. [in prep]
104 suggest that in the case of Kilauea volcano, explosive degassing bursts associated with
105 Strombolian eruptions are best modeled by a single force at the lowest frequencies (VLP
106 band) followed by higher frequency oscillations in the conduit and short-period energy
107 from the slug burst itself.
108 Overall the source of low-frequency energy radiated co-eruptively has been more
109 thoroughly studied than high-frequency energy radiated co-eruptively. McNutt and
110 Nishimura [2008] model co-eruptive tremor as resulting from radial oscillations of
111 conduit walls, but do not connect the amplitudes to the plume dynamics. Here we take a
112 different approach and model the seismic wave generation as resulting directly from the
113 mass discharge of the erupting column.
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5 115 2.2 The 2008 Eruption of Kasatochi Volcano
116 Kasatochi volcano is a 3 km wide island with a large crater lake in the Andreanof
117 Islands in the Aleutian Arc (figure 1). Though the volcano’s summit is 314 m in
118 elevation, the volcanic vent is near sea level. Prior to its 2008 eruption, little was known
119 about this volcano. Kasatochi volcano is not seismically or geodetically monitored. The
120 nearest seismometers are a short-period network operated by the Alaska Volcano
121 Observatory (AVO) at Great Sitkin volcano, 40 km west of Kasatochi (figure 1). The
122 nearest broadband station functioning at the time of the eruption, ATKA operated by the
123 Alaska Earthquake information Center (AEIC), is 80 km southeast of Kasatochi on Atka
124 Island.
125 After a brief but powerful earthquake swarm with earthquakes as large as M 5.8
126 [Ruppert et al., submitted] Kasatochi volcano had three large ash producing eruptions
127 with satellite-detectable plumes to 18 km above sea level (22:01 UTC 7 August 2008,
128 01:50 and 04:35 UTC 8 August 2008) [Carn et al., submitted; Waythomas et al.,
129 submitted; Webley et al., submitted]. Co-eruptive tremor associated with each of these
130 three explosions was readily apparent in real-time seismic data for at least 20 minutes
131 (Figure 2). Infrasound and seismic data indicate that two additional smaller explosions
132 occurred in the following 5 hours during the episode of continuous ash emissions
133 [Arnoult et al., submitted]. Satellite data indicate that the third large explosion was
134 significantly more ash-rich and had a higher plume than the first two [Waythomas et al.,
135 submitted, Fee et al., submitted]. Seismic data support this observation as the far field
136 amplitude of the third explosion was more energetic than the previous explosions.
137 Following the third explosion, ash vented continuously for roughly 16 hours. Satellite
6 138 data indicate that the continuous ash emission phase had a decreasing density of ash
139 emission with time [Waythomas et al., submitted]. This observation is consistent with
140 seismic data, as the prolonged continuous ash emission phase radiated less seismic
141 energy than the initial 10 minutes of the third explosion .
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143 2.3 The 2006 Eruption of Augustine Volcano
144 The 2006 eruption of Augustine Volcano was far better monitored than the 2008
145 eruption of Kasatochi, in part because the volcano erupted previously in 1971, 1976, and
146 1986. Augustine, a volcano located in the lower Cook Inlet with summit at 1260 m above
147 sea level (figure 1), is instrumented with both broadband and short-period seismometers.
148 Increasing seismicity and deformation was noted months before the eruption onset
149 [Power and Lalla, in press]. The Augustine pre-eruptive seismic swarm was notably less
150 intense than that of Kasatochi. The largest earthquake associated with the eruption was M
151 2.1. The explosive phase of the eruption began on 11 January and continued through 28
152 January [see Power and Lalla, in press]. The ash producing eruptions of Augustine,
153 though numerous, were shorter in duration and lower in altitude that the Kasatochi
154 eruption. Augustine produced 13 ash plumes ranging in altitude from 9 to 14 km above
155 sea level. The co-eruptive tremor durations for these explosions, as determined from far-
156 field seismic data, ranged from 3 – 7 minutes. The co-eruptive seismicity associated with
157 the Augustine eruption plumes was observed at a maximum distance of ~ 200 km,
158 whereas Kasatochi co-eruptive seismicity was visible to over 350 km distance.
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7 161 3. Relating Plume Height to Seismic Wave Amplitudes
162 Here we develop a composite model that combines existing fluid and solid
163 mechanical models to connect observable seismic wave amplitudes to volcanic plume
164 height. We test the model on the 2008 eruption of Kasatochi volcano and the 2006
165 eruption of Augustine volcano. The model consists of three distinct steps as illustrated in
166 Figure 3: 1) Relate maximum ash plume height to mass ejection rate of material from the
167 volcanic vent. 2) Relate mass ejection rate to a single downward force acting on the solid
168 Earth. 3) Calculate far-field seismic wave amplitudes resulting from the single force.
169 Each step is described in detail below.
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171 3.1 Step 1: Relate Plume Height to Mass Ejection Rate
172 We begin by assuming that plume height is controlled by thermal buoyancy for a
173 continuous ash-rich plume with dense rock equivalent volumetric ejection rate Q. This
174 fundamental physics for column height has its origins in studies of forest fire plumes
175 [Morton et al., 1956] and has been verified using eruption data [Carey and Sigurdsson,
176 1989; Sparks et al., 1997]. Slightly different relationships between Q and plume height
177 exist in the literature depending on the datasets used for calibration. We use the widely
178 cited Sparks et al. [1997], equation 5.1
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180 H=1.67 Q0.259 (1)
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182 where H is the column height in km above the vent and Q is measured in m3/s. Equation
183 (1) is an empirical regression with its form is motivated by analytic models of thermally
8 184 buoyant continuous plumes in a stratified atmosphere [equation 4.15 of Sparks et
185 al.,1997; Wilson et al, 1978]. Observations used to constrain Equation 1 include
186 uncertainties both in plume height and ejecta volumes as discussed in Mastin et al. [2009]
187 and Sparks et al. [1997]. We use the term continuous to describe a plume where the
188 volcano is still activity venting at the time the plume reaches its maximum height. This is
189 often referred to as an attached plume.
190 An alternative model is a rapid ejection eruption where all of the mass is released
191 so quickly that the bottom of the plume has left the vent before the top of the plume
192 reaches its maximum height. Though this may have been the case for the first two
193 Kasatochi explosions, satellite data show that this was not likely the case for the third
194 explosion, as that explosion was the beginning of a 13 hour phase of continuous ash
195 emission [Waythomas et al., submitted]. Nonetheless, it is useful to realize that even in
196 this extreme case, the scaling in equation (1) is preserved and the only major
197 modification is the inclusion of the ejection duration. Morton et al. [1956] also developed
198 a relationship for a quickly released plume and found,
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200 H=1.87 x 10-3 E1/4 (2)
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202 where H is height in kilometers and E is thermal energy in Joules. The thermal energy is
203 primarily carried by the solid particles and E=cp ρ ΔT Q τ where cp is the heat capacity, ρ
204 is the density of the solid rock, ΔT is the temperature difference between the plume and
205 the ambient air and τ is the duration of the ejection phase. Substituting in reasonable
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9 3 3 207 values of the parameters (cp = 1 KJ/kg/K, ρ = 3000 kg/m , ΔT = 10 K, τ=100 s), yields
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209 H=1.4 Q1/4 (3)
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211 which is nearly identical to the protracted source result (equation 1). Thus, the model is
212 insensitive to the assumed relative duration of the source.
213 We next relate the thermal ejection rate to the mass ejection rate, as the later
214 quantity is most directly associated with the momentum flux which ultimately generates
215 seismic waves. If dense rock equivalent density is ρ, then
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• 217 M = Qρ (4)
• 218 where M is the mass ejection rate.
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220 3.2 Step 2: Relate Mass Ejection Rate to Single Force
221 We assume that the force system acting on the Earth during eruption can be
222 represented as a single force following the work of Kanamori and Given [1982],
223 Kanamori et al. [1984], and Brodsky et al. [1999]. Due to a lack of quality broadband
224 seismic data and poor coverage of the focal sphere typical of Aleutian eruptions, we are
225 not able to invert the seismic radiation field of co-eruptive Kasatochi for an equivalent
226 force system. Thus we cannot directly demonstrate that a single force is the most
227 appropriate source model for Kasatochi. Instead we start with this simple seismic source
228 model and test its applicability.
10 229 Using the mass ejection rate from (4), we can derive the equivalent vertical force
230 F on the Earth using a momentum balance following Brodsky et al. [1999].
• 231 d(Momentum) dt = M v = F (5)
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233 where v is the velocity of material exiting the vent. This is sometimes termed the rocket
234 equation [Thompson, 1972]. In the case of a rocket the force propelling a rocket upward
235 is equal to the momentum discharge rate of the fuel behind it. In the case of a volcano the
236 rocket is inverted, as it discharges momentum upward.
237 To use equation 5, we need to estimate v. For large-scale eruptions, the extreme
238 overpressures at the vent require supersonic flow. In steady-state the flow is choked at the
239 vent with the vent velocity equal to the sound speed of the erupting material [Kieffer,
240 1981; Woods, 1995; Mastin, 2007]. The mixture of ash and gas in a plume has a greatly
241 depressed sound velocity relative to either the solid or gas end member [Rudinger, 1980].
242 For instance, the May 18, 1980 blast of Mount St. Helens is thought to have a sound
243 speed of ~100-250 m/s based on the temperature and relative mass fraction of gas and
244 solid phases [Kieffer, 1981; Brodsky et al., 1999]. Kieffer and Sturtevant [1984] argue
245 that the low sound velocity of particulate-laden flows allows vent velocities as low as
246 meters per second. Alternative derivations of the vent velocity based on conduit flow
247 models also arrive at the range of 100-250 m/s [Papale and Longo, 2008]. McNutt and
248 Nishimura [2008] summarize vent velocities for a large number of eruptions globally and
249 arrive at a range of 28-420 m/s with the caveat that the lowest end of the range is likely
250 an underestimate due to the neglect of the coupled gas flow. We consider vent velocities
11 251 within either the observational or theoretical ranges, i.e., 28-420 m/s, reasonable and
252 consistent with prior work.
253 The simplest application of equation 5 would be using data with periods of
254 minutes, consistent with the time it takes to evacuate the magma chamber, following
255 Kanamori et al. [1984]. We lack data at those frequencies, so we explore the possibility
256 that the higher frequency seismic waves radiated by turbulence in the volcanic jet scale
257 with energy radiated at low frequencies. This requires some discussion of the role of
258 turbulence in the volcanic jet and its effect on seismic waves.
259 As the generation of seismic waves is a linear process, the observed seismic
260 spectrum is a product of the propagation spectrum in the elastic medium (see equation 6
261 below) and the spectrum of momentum ejection from the vent (source spectrum). The
262 spectrum at the source can reflect the spectrum of vent velocities, which in turn are
263 controlled by properties of the flow. In a turbulent flow fluid velocity generally fluctuates
264 with well-defined statistical properties. For instance, for homogeneous, isotropic
265 turbulence in an incompressible flow, the energy density spectrum, S, of the flow is
266 related to frequency S ~ f -5/3, and the integral of the energy spectrum over all
267 wavenumbers is proportional to the autocorrelation of the velocity field [Kolmogorov,
268 1954; Matthieu and Scott, 2000]. A volcanic eruption involves transient, compressible
269 flow that has multiple origins of velocity fluctuations including the turbulent field,
270 internally generated periodic collapses and evolving vent shape [Ogden et al., 2009]. For
271 simplicity, in this initial study we assume that the vent velocity spectrum is flat and the
272 spectral amplitude is constant for all frequencies. We also do not consider here the
273 influence of density fluctuations on the source spectrum. These assumptions are difficult
12 274 to evaluate in the absence of direct observations of the turbulent structure of plumes and
275 thus can only be justified by testing the consistency of the seismic data with the model.
276 We use the spectral simplifications as a starting place to explore the link between plume
277 height and seismic waves. For future studies infrasound data from large eruptions could
278 potentially be used to provide constraints on the true turbulence spectrum of volcanic jets
279 [eg. Matoza et al., 2009; Fee et al., submitted].
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281 3.3 Step 3: Relate Single Force to Far-Field Seismic Waves
282 Finally, we calculate the far-field surface waves resulting from a single force. For
283 a vertical single force F, the displacement amplitude of a fundamental mode Rayleigh
284 wave with wavenumber k traveling in a half-space is
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0.07F k 286 u = (6) μ r
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288 where μ is the shear modulus and r is the distance from the source [Aki and Richards,
289 1980]. Equivalently, equation 6 describes the propagation spectrum as a function of
290 wavenumber k.
291 Equation 6 is applicable for a single mode. For real data, we apply a narrow
292 bandpass that captures multiple modes. Since the modal spectrum is dense near 1 s, it is
293 difficult to analytically add all of the relevant modes together to construct the amplitude.
294 Instead, we generate synthetic seismograms using a wavenumber-frequency summation
295 method and bandpassed the synthetics to obtain a correction for the finite band-pass
296 (Figure 4) [Herrmann, 1987]. Empirically, we find that an impulse source for a given F
13 297 bandpassed at 0.5-1.5 Hz at the regional distances studied here produces an amplitude 2.4
298 times greater than that predicted by equation 6 for a half-space homogenous velocity
299 model. This correction factor also holds for a more realistic velocity model like AK135
300 [Kennett et al., 1995; Montaigner and Kennett, 1995]. Therefore, we apply this factor of
301 2.4 correction to our predicted amplitude found using equation 6. A potential
302 complication to this seismic model is the dominance of scattering at high-frequencies.
303 For this initial study, we confine the calculation to the direct energy.
304 By assuming values for μ, v, and ρ, we can calculate ground displacement as a
305 function of column height and observed wavenumber k. Combining equations 1 with 4-6
306 with the finite band-pass correction yields
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0.17ρv k 308 u = ()H /1.67 1/0.259 (7) μ r
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310 Equation 7 predicts the amplitude of the seismic waves resulting from a certain column
311 height based entirely on known physics. The column height is an observed quantity and
312 the wavenumber and epicentral distance r are generally well-resolved for seismic data as
313 is the dense rock density ρ and the shear modulus μ. Therefore, utilizing Equation 7
314 requires estimating only one relatively poorly constrained eruptive quantity, the vent
315 velocity v.
316
317 3.4 Model Applicability
318 We now discuss the range of conditions and eruption styles for which this model
319 is appropriate. Because multiple physical processes produce seismic waves at a variety of
14 320 frequencies during large ash producing volcanic eruptions, it is sometimes difficult to
321 connect broadband seismic amplitudes with eruptive properties directly, particularly in
322 the near field and for small eruptions. For example, local processes including rock falls
323 and pyroclastic flows can dominate seismic recordings local to the volcano.
324 Because the calculated mass ejection rate only accounts for erupted material that
325 provides energy for buoyant ascent of ash-rich plumes, our model is not applicable for
326 phreatic eruptions or eruptive phenomenon apart from the plume such pyroclastic flows
327 and lava fountaining. In the case of eruptions where the majority of the mass ejected is
328 not entrained in the plume, the model may overestimate plume height for a given
329 amplitude of ground shaking.
330 The model is also only appropriate for plumes that rise to altitudes of 5 km or
331 higher for three reasons: 1) The empirical regression in Sparks et al. [1997] is not
332 constrained for plume heights below 5 km. 2) The assumption that the upward mobility
333 of the plume is thermally driven may not be correct at heights where material can travel
334 ballistically. The maximum ballistic height of a projectile with initial velocity v occurs
335 when the initial kinetic energy equals the gravitational potential energy, i.e., ½ M v2 = M
336 gh, where M is mass, g is the acceleration due to gravity, and h is ballistic height. Thus,
337 the maximum ballistic height is ½ v2 / g. Assuming v = 300 m/s or less, ballistics could
338 be ejected to 4.5 km. 3) The gas thrust region can be dominated by the dynamics of the
339 compressible flow rather than the thermal buoyancy [Ogden et al., 2009]. In the case of
340 small eruptions at Tungurahua and Santiaguito volcanoes Johnson et al [2004] and
341 Johnston et al. [2005] show that amplitudes of co-eruptive seismic waves scale poorly
15 342 with eruption intensity. In both cases however, eruption plumes analyzed were less than 4
343 km in height.
344 This model is also not appropriate in cases where the source of co-eruptive
345 volcanic tremor is not the volcanic vent, but elsewhere in the system. For example during
346 the 2008 eruption of Okmok volcano, co-eruptive tremor amplitude correlated poorly
347 with volcanic plume height after the opening phase of the eruption. Haney [submitted]
348 estimates that the VLP tremor occurred along the length of a dike at 2 km depth. Thus in
349 the case of Okmok, Haney concludes that the primary tremor source likely reflected the
350 flux of magma from the shallow magma chamber into the dike rather than mass ejection
351 at the vent directly.
352 Similarly, we must avoid performing this analysis on time series where the
353 seismic data is dominated by earthquakes sourced from deeper in the system. In the case
354 of the Kasatochi eruption, for example, the far-field seismic energy radiated by pre-
355 eruptive earthquakes was up to 4 times larger in amplitude than the co-eruptive tremor
356 itself at the distances we consider when seismic energy is averaged over 10 minute
357 windows. For this reason, we limit our analysis at Kasatochi to a time period free of large
358 earthquakes.
359 The model is only applicable when the volcanic vent is open and freely emitting
360 material. Therefore, caution must be used when considering the initial stages of eruption.
361 During this time frame a large portion of the seismic energy may be related to “throat
362 clearing” or removing the lid that caps the magma body. For example, the first large ash
363 producing explosion during the 2006 eruption of Augustine volcano produced stronger
16 364 ground shaking than the subsequent 20 ash producing explosions, although the plume
365 height of the first explosion was similar to that of many later explosions.
366 Finally, atmospheric effects should be considered when applying our model. For
367 example, the model is most appropriate for large eruptions with strong plumes where
368 tropospheric wind shear and other atmospheric instabilities are minimal. In addition,
369 because the buoyancy of volcanic ash plumes can increase significantly if atmospheric
370 water vapor is entrained in the plume [Woods, 1993; Tupper et al., 2009], our model is
371 more applicable in dry sub-polar environments such as Alaska than in moist tropical
372 environments. However, in all environments atmospheric humidity does not have an
373 appreciable effect on large eruption columns greater than 15 km in height [Woods, 1993].
374
375 4. Data Analysis and Results
376 4.1 Kasatochi
377 To apply our model to the eruption of Kasatochi, we begin by measuring co-
378 eruptive ground displacement after correcting for instrument response at short-period and
379 broad-band seismometers primarily located west of the volcano. Stations analyzed are
380 shown in Figure 1. The geometry of the Aleutian Islands provides us with a nearly linear
381 array. We are not able to use data recorded at Great Sitkin volcano because co-eruptive
382 seismic waves are clipped there (Figure 2). We also do not use data east of Atka Island
383 because seismic waves generated by Kasatochi volcano would likely be contaminated by
384 those generated by the simultaneous eruption of Okmok volcano, roughly 350 km east of
385 Kasatochi.
17 386 This use of far field data is an advantage because far field data is not
387 contaminated by energy radiated from secondary surficial processes such as the huge
388 pyroclastic and block and ash flows which left the island inundated in up to 15 meters of
389 tephra. Secondary seismic sources such as rock falls and pyroclastic flows decay more
390 quickly with distance than a single force source associated with magma removal because
391 these secondary sources: 1) transport a small percentage of mass compared to the total
392 mass ejected, 2) are multi-pole sources distributed in time and space on the volcano’s
393 flank in contrast to the concentrated single force mono-pole associated with overall mass
394 ejection [Kanamori et al., 1984, Appendix A], and 3) are largely surficial sources. Jolly et
395 al. [2002] show that in the case of Soufriere Hills Volcano, Monstserrat, seismic waves
396 generated by pyroclastic flows are highly attenuated (Q=20) due to their surficial travel
397 paths.
398 We focus our study on the initial pulse of energy radiated by the third and most
399 ash rich explosion at Kasatochi (22:01 UTC, 7 Aug 2008) (Figure 5), as this explosion
400 began a 13 hour phase of continuous venting and is not contaminated by earthquakes.
401 The strongest phase of this energy packet is several minutes in duration and can be
402 clearly identified as it moves out appropriately with distance away from Kasatochi
403 (Figure 2). We measure the peak amplitude of ground displacement at 1 second period by
404 bandpass filtering data between 0.5 and 1.5 Hz (Figure 5). We choose 1 second period
405 because it is well within the response range of short-period instruments, it is below the
406 frequency range generally radiated by pyroclastic flows [eg. Zobin et al., 2009], yet it is
407 low enough to minimize site effects. At higher frequencies site effects cause significant
408 scatter in our measurements. Figure 6 shows that the relative amplitude of the observed
18 409 seismic waves fall off with distance as 1 r 1/2, where r is radius from the source, as would
410 be expected for Rayleigh waves. This fall-off with distance is a helpful corroboration of
411 the direct Rayleigh wave interpretation of the co-eruptive seismicity in equation 6. To
412 evaluate fit of our model, we fit a line to our data points by forward modeling, varying v.
413 We assume a shear modulus of μ = 3 x1010 Pa, and specify k = 2π f c , where the
414 frequency in the middle of the observed bandpass f = 1 s and c = 3x 103 m/s. Dense rock
415 equivalent, ρ, is 2700 kg/m3.
416 Figure 6 shows ground displacement measurements for the Kasatochi eruption
417 and predicted ground displacement with distance. In our preferred model (black line) v =
418 80 m/s in the case of an 18 km plume. This velocity is in the range of those predicted by
419 Kieffer and Sturevant [1984] and observational estimates for vent velocity of specific
420 eruptions as summarized in McNutt and Nishimura [2008]. However, this vent velocity is
421 at the lower end of the previously established ranges. The data therefore is consistent
422 with either the flat spectrum source model as proposed above, or may accommodate an
423 increase in spectral amplitude of the source with increasing period as would be expected
424 from turbulence models [Kolmogorov, 1941; Matthieu and Scott, 2000; Matoza et al.,
425 2009].
426
427 4.2 Augustine
428 In order to investigate the robustness of the model to a different eruptive setting,
429 we test its applicability for the 2006 eruption of Augustine volcano. Although Augustine
430 is locally instrumented, for our analysis we use the short-period seismometer, OPT,
431 located 37 km from the erupting vent. This is required since our model uses far-field
19 432 surface waves and because we do not want the tephra ejection signal contaminated by
433 more surficial local processes that dominate the short-period signals on the island, such as
434 rockfalls and pyroclastic flows. In the case of the 2006 eruption of Augustine McNutt
435 [submitted] shows that pyroclastic flows were only visible seismically on stations near
436 the flow travel path and were not visible on the volcano flanks opposite the flow path.
437 Figure 7 shows the 2 s – 1.5 Hz displacement amplitudes at OPT for explosions at
438 01:40 UTC 14 January and 16:57 UTC 17 January 2006, which had plume heights of
439 10.5 and 13 km above sea level respectively based on radar and pilot reports [Power and
440 Lalla, in press]. The far-field short-period amplitudes of these two explosions are similar
441 to other explosions in the sequence (with the exception of the initial 11 January
442 explosion). We select these explosions to analyze because they are representative of the
443 entire eruption. Because the initial explosions from the 2006 eruption of Augustine
444 volcano may have included energy from brittle failure vent clearing processes, we do not
445 analyze data from 11 January 2006. In the case of Augustine, the volcanic vent is well
446 above sea level at ~1260 m altitude. Thus, when applying our model we correct for the
447 difference between vent altitude and the reported plume heights, which are defined with
448 respect to sea level.
449 As in the Kasatochi case, we assume a shear modulus of μ = 3 x1010 Pa, and
450 specify k = 2π f c , where the observed frequency is f= 1 s and c = 3x 103 m/s. Dense
451 rock equivalent, ρ, is 2700 kg/m3. In the case of the 13 km plume at Augustine on 17
452 January 2008, our model performs well, as it estimates the correct plume height for vent
453 velocities of 78 m/s based on seismic data. In the case of the 10.5 km plumes on 14
454 January 2008, our model estimates the correct plume height if the velocity at the vent is
20 455 95 m/s. These velocities are within the previously defined range of reasonable values (28-
456 420 m/s), but as in the case of Kasatochi, they are at the lower end of the expected values.
457 Once again, there is ambiguity between the appropriateness of the flat spectrum and the
458 possibility of a decrease in spectral amplitude with increasing frequency.
459
460 5. Dynamical Implications
461 Because our model fits the data, the single force model appears to be an
462 appropriate force system in the case of the two eruptions we consider. The most
463 surprising aspect of the model’s success is the fact that we can relate plume height to
464 seismic wave amplitude using ~1 s radiated waves assuming a reasonable v of 78-95 m/s.
465 This consistency implies that the high-frequency fluctuations of the plume are
466 comparable in magnitude to the long-period eddies. The fact that our v estimates are at
467 the low-end of the expected range allows that the source spectral amplitude may be
468 decreasing with frequency. This finding is not surprising as turbulent flows commonly
469 have stronger eddies at long-periods than short-periods [Kolmogorov, 1941; Matthieu
470 and Scott, 2000; Fee et al., submitted]. The spectrum can also be modified by additional
471 processes like supersonic flow [Smits and Dussauge, 2006]. The length scale of turbulent
472 eddies in a volcanic plume has only recently been measured in plumes [Andrews and
473 Gardner, 2009] and thus far there is little independent constraint on the relative strength
474 of various frequencies in the plumes. The seismic measurements presented in this paper
475 suggest that future work on the seismic source spectrum of plumes would be a fruitful
476 avenue into the fluid dynamics of erupting jets.
477
21 478 6. Practical Implications
479 For the Aleutian Islands and many other remote volcanoes in the North Pacific the
480 primary safety concern is the threat of ash clouds to aircraft. Airlines are most concerned
481 about ash clouds that reach aircraft cruising altitudes. Estimating volcanic plume heights
482 in remote environments in real-time (and even in retrospect) is always challenging,
483 particularly when clouds are obscuring activity and the timing of satellite passes is not
484 optimal. With further development this model could potentially be used to constrain
485 plume heights in near-real-time. In the case of the Kasatochi eruption, we would have
486 estimated plume heights of 13-19 km using our model based on seismic data alone,
487 potentially giving airlines notice that the eruption was large enough to be dangerous. To
488 narrow this range in height, we would need more accurate estimates of v and its spectrum
489 or a larger empirical database of v measurements from similar eruptions. These estimates
490 could possibly be obtained through other data sources such as infrasound or radar or by
491 studying a range of eruptions with our model and establishing a range of possible
492 velocities observationally.
493 To illustrate the potential utility of the approach, we examine our ability to
494 characterize future eruptions at Kasatochi Volcano using the nearest seismic stations,
495 incorporating some of the uncertainty in the free parameter, v. Figure 8 shows calculated
496 ground displacement at Great Sitkin stations estimated for eruptions of Kasatochi with a
497 variety of reasonable v values. We assume a detection threshold of 0.4 μm, as AVO
498 short-period seismometers in the Aleutian arc often have noise below this threshold for
499 raw unfiltered data. This is a conservative estimate for eruption detection provided the
500 recording environment is relatively quiet and the seismometers are functioning optimally.
22 501 Figure 8 shows that generally, we can expect to detect co-eruption seismicity for
502 explosive eruptions with plumes that reach 9 – 12 km height above sea level or higher at
503 Kasatochi volcano.
504 This same approach allows us to estimate detection capability for eruptions at
505 other unmonitored volcanoes. For instance, Bogoslof and Seguam volcanoes are small
506 unmonitored Aleutian Islands, like Kasatochi (Figure 1). Bogoslof most recently erupted
507 in 1992 and had 7 additional historic eruptions. Seguam most recently erupted in 1993
508 and had 5 additional historic eruptions. The nearest seismometers to Bogoslof and
509 Seguam are those of the Okmok and Korovin seismic networks respectively, ~50 km and
510 ~100 km distant. Using figure 9, we estimate that large continuous ash producing
511 eruptions at Bogolof and Seguam would be visible in high frequency data at the nearest
512 seismic stations if the plumes reached roughly 12 km in altitude, in the conservative case
513 where v=200 m/s. Again, however, a better understanding of vent velocity is needed, as
514 reasonable variation in v (50 – 200 m/s) leads to scatter in predicted plume heights over a
515 4 km range.
516 With better constraints on v and its spectrum,, our model could provide a plume
517 height estimate independent of remote sensing techniques that could be considered along
518 with estimates from other sources. To do this more work would need to be done to
519 constrain errors, explore applicability to different eruptions, and test velocity model
520 assumptions. Another consideration is that several physical processes cause seismic
521 tremor in the Earth’s crust, so other data are needed to confirm that tremor observed is
522 co-eruptive tremor before applying our model. Uncertainties in tremor source process
23 523 would likely lead to far more false positives than false negatives. Thus our model could
524 be used as a conservative indicator of threats to aviation from volcanic ash.
525
526 7. Conclusions
527 Our model is generally successful in relating plume height to ground shaking in
528 the 2008 eruption of Kasatochi volcano and the 2006 eruption of Augustine volcano. This
529 suggests that using plume height to calculate the mass ejection rate and interpreting the
530 resulting force system as a single force are appropriate techniques. The single force
531 model appropriate at low frequencies also fits measurements reasonably well at
532 frequencies of ~ 1 s. This surprising observation suggests that force resulting from the
533 high frequency turbulence in volcanic jets can be a useful indicator of plume height.
534 The success and applicability of the model to other vulcanian and plinian
535 eruptions globally remains to be evaluated. However, the results from Kasatochi and
536 Augustine volcanoes are sufficiently encouraging that more work in this field is
537 warranted. Future studies should focus on other eruptions to explore errors and the range
538 of applicability of the model, consider more complicated velocity structures and indirect
539 wave arrivals, consider atmospheric effects, and further investigate frequency variations
540 in energy radiated by the volcanic jet. Further development of this model may give us a
541 means to better understand the relationship of ground shaking to plume height and
542 explore eruption dynamics of the turbulent jet. In the best case scenario, this avenue of
543 research may lead us to constraining plume height based on seismic wave amplitudes in
544 near-real-time.
545
24 546
547 Acknowledgements
548 Review by Larry Mastin, Darcy Ogden, David Schneider, David Hill, and David Fee
549 significantly improved this manuscript. Seismic stations used in this study were originally
550 installed with funding from the Federal Aviation Administration.
551
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731
732 Figure Captions
733
734 Figure 1 – Map of central Aleutian arc showing locations of Augustine volcano,
735 Kasatochi Island and neighboring islands and volcanoes. Seismic stations used in this
736 study are shown with triangles. Red are short-period instruments. Green are broadband
737 instruments. Great Sitkin volcano had a functioning seismic network at the time of the
738 Kasatochi eruption. However, those data were clipped and not used in this study.
739
740 Figure 2 - Waveform of third ash producing explosion of Kasatochi as recorded on
741 short-period stations, GSMY, ETKA, KIKV, TASE, and GANE. Line shows moveout of
742 surface wave energy packets at 3.4 km/s.
743
744 Figure 3 – Cartoon depicting processes associated with the three calculation steps in our
745 model. Step 1 relates plume height to mass ejection rate. Step 2 relates mass ejection rate
746 to a downward acting sngle force. Step 3 calculates seismic waves radiated by the single
747 force.
748
33 749 Figure 4 - Synthetic seismograms from an impulse source of the same strength as
750 inferred for the Kasatochi eruption. The synthetics are bandpassed using the same filter as
751 the observed seismograms (0.5-1.5 Hz) to measure the amplitude in the narrow band-pass
752 corresponding to equation 7. The synthetics were produced using a regional f-k
753 integration and the ak135 model [Hermann, 1987; Kennett et al., 1995; Montaigner and
754 Kannett, 1995]. Synthetics are calculated for distances to stations GSMY, ETKA, KIKV,
755 TASE, and GANE. The resulting phase velocity matches the observations in Figure2.
756
757
758 Figure 5 – a) Raw waveform of third large ash producing explosion of Kasatochi, as
759 recorded at short-period station TASE at Tanaga Volcano, 177 km distant from
760 Kasatochi. b) First distinct burst of energy, which we analyze by bandpass filtering raw
761 waveform between 0.5 and 1.5 Hz and measure maximum displacement. c) Spectrogram
762 of energy recorded at TASE.
763
764 Figure 6 – Ground displacement at 1 s period of co-eruptive seismicity with distance
765 from Kasatochi volcano for the large ash producing explosion at 2008. Large dots are
766 broadband stations ATKA and AMKA. Small dots are short-period stations. Preferred
767 forward model fit shown with solid line (v=80m/s).
768
769 Figure 7- Ground displacement at 0.5 - 2 s period of co-eruptive seismicity with distance
770 from Augustine volcano for the large ash producing explosions on January 14 and 17,
771 2006. Model fits for velocities of 78 m/s and 95 m/s are shown with lines.
34 772
773 Figure 8 – Expected ground displacement at 1 s period due to a plume observed at Great
774 Sitkin, 40 km distant from Kasatochi, for three vent velocities, 50 m/s (dashed), 100 m/s
775 (solid), and 200 m/s (dotted). Vertical line indicates average noise level at Great Sitkin
776 seismic stations.
777
778 Figure 9 – Minimum detectable plume heights with distance, assuming a conservative
779 detection threshold of 0.4e-6 m at 1 second period and vent velocities of 50 m/s (dashed),
780 100 m/s (solid), and 200 m/s (dotted).
35 0 400 km Alaska
Bogoslof Seguam Augustine
180 -178 -176 53
Kasatochi Atka Great Sitkin 52 Tanaga Kanaga Gareloi
Amchitka Island 51
Figure 1 elocity (nm/s)
V
Moveout 3.4 km/s
100 200 300 400 500 600 700 time (s)
Figure 2 Figure 3 40 km 70 km
118 km
177 km
227 km
3.4 km/s
Figure 4 5000 a
0
-5000 20000 40000 60000 80000
5000 x 10 b V e l o c i t y ( n m / s ) 0
-5000 22000 26000 30000 34000
1 c 0.5 F r e q u n c y 0 0 10000 20000 30000 40000 Time (s)
Figure 5 2 10 Short period seismometer Broadband seismometer 1 10
0 10
-1 10 D i s p l a c e m n t 1 r o d ( µ )
-2 10 2 3 10 10 Distance from Kasatochi (km)
Figure 6 16
15 v = 78 m/s 14 v = 95 m/s 13 17 Jan. 2006
12
11 Plume Height (km) 10
9 14 Jan. 2006
8 0 0.5 1 1.5 2 2.5 3 Displacement at OPT, 37 km Distance (mm)
Figure 7 20 v = 50 18 v = 100 16
v = 200 14
12 P l u m e H i g h t ( k )
10
8 0 0.5 1 1.5 2 2.5 3 Displacement (µm)
Figure 8 18
16 v = 200 m/s
14 v = 100 m/s 12 v = 50 m/s
10 Plume Height (km) Height Plume
8
6
10 1 10 2 103 10 4 Distance (km)
Figure 9