2 volcanic plume height measured by seismic waves based...
TRANSCRIPT
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Volcanic Plume Height Measured by Seismic Waves Based on a Mechanical Model 2
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Stephanie G. Prejean1 and Emily E. Brodsky2 4
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1. USGS Alaska Volcano Observatory 6
4210 University Ave., Anchorage AK 99508 7
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2. University of California, Santa Cruz 9
Department of Earth and Planetary Sciences 10
Santa Cruz, CA 95064 11
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Submitted to Journal of Geophysical Research, 4-4-10 23
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Abstract 24
In August 2008 an unmonitored, largely unstudied Aleutian volcano, Kasatochi, 25
erupted catastrophically. Here we use seismic data to infer the height of large eruptive 26
columns, like those of Kasatochi, based on a combination of existing fluid and solid 27
mechanical models. In so doing, we propose a connection between a common observable, 28
short-period seismic wave amplitude and the physics of an eruptive column. To construct 29
a combined model we estimate the mass ejection rate of material from the vent based on 30
the plume height, assuming that the height is controlled by thermal buoyancy for a 31
continuous plume. Using the calculated mass ejection rate, we then derive the equivalent 32
vertical force on the Earth through a momentum balance. Finally, we calculate the far-33
field surface waves resulting from the vertical force. Physically, this single force reflects 34
the counter force of the eruption as material is discharged into the atmosphere. In contrast 35
to previous work, we explore the applicability to relatively high frequency seismic waves 36
recorded at ~ 1 s. The model performs well for the 2008 eruption of Kasatochi volcano 37
and the 2006 eruption of Augustine volcano. The consistency between the seismically 38
inferred and measured plume heights indicates that in these cases the far-field 1 s seismic 39
energy radiated by fluctuating flow in the volcanic jet during eruption is a useful 40
indicator of overall mass ejection rates. Use of the model holds promise for 41
characterizing eruptions and evaluating ash hazards to aircraft in real time based on far-42
field short-period seismic data. 43
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1. Introduction and Motivation 47
Empirical studies have suggested that the amplitude of high frequency or 48
broadband seismic waves radiated during large volcanic eruptions generally scales with 49
the height of an eruption column [McNutt 1994]. However, a direct calculation of the 50
expected seismic wave amplitude based on physical models has not yet been successful. 51
Connecting commonly observable data, like seismic wave amplitudes, to a model of the 52
flow in the eruptive jet would provide a new tool to test and improve our understanding 53
of eruptive physics. For instance, small-scale turbulence is thought to play a major role in 54
entrainment of hot particles and gases and hence buoyancy of eruptive columns, yet there 55
are few measurements of the strength or distribution of small-scale features in real 56
eruptive columns [Andrews and Gardner, 2009]. Using seismic data to provide 57
observational constraints on eruption column flow processes is particularly attractive as 58
seismic data is often available even in remote settings. Thus use of the seismic database 59
would greatly increase the number and type of eruptions amenable to study. 60
Pragmatically, a physical model connecting plume height and seismic data would 61
allow the use of seismology as a remote sensing technology to determine volcanic plume 62
height. It would be a particularly useful tool for exploring eruption dynamics in remote 63
environments where direct observation is not possible, such as the volcanoes of the 64
northern Pacific Ocean. Although many volcano observatories world-wide are gradually 65
replacing short-period seismometers with broadband seismometers, we still largely rely 66
on short-period instruments for forecasting, monitoring and analyzing eruptions. These 67
realities motivate the development of the model described below. 68
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In this study we build on previous work to develop a physical model for the 69
expected amplitude of seismic waves from an eruption that generates a plume of a given 70
height. As a cautionary note we describe situations where the model is not applicable, 71
such as small eruptions or eruptions where most mass ejected is not entrained in the 72
plume. After reviewing previous work on co-eruptive seismology and the characteristics 73
of the Kasatochi and Augustine eruptions, we use the connection between plume height 74
and thermal ejection rate to predict the momentum ejection rate that generates the seismic 75
waves and then compare the model to the data for the Kasatochi eruption as well as the 76
2006 Augustine eruption. We show that for a reasonable range of parameters the model 77
performs well. 78
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2. Background 80
2.1 Co-eruptive Seismology 81
Volcanic activity produces seismic waves. These waves, which include brittle 82
failure earthquakes, long period and very long period events, and volcanic tremor, 83
generally result from movement of fluid in the Earth’s subsurface, directly and indirectly 84
[see Chouet 1996, McNutt, 2005, for reviews]. Seismology also directly senses magma 85
leaving the Earth in the form of both eruption tremor and discrete eruption earthquakes 86
[eg. Nishimura and Hamaguchi, 1993; Nishimura, 1995]. Such co-eruptive seismicity has 87
been documented in scientific literature since Omori’s early studies of Usu-san and 88
Asama volcanoes [1911-1913] and is the subject of this study. 89
By analyzing long period surface waves radiated by the May 18, 1980 eruption of 90
Mount St. Helens, Kanamori and Given [1982] show that the co-eruptive seismic source 91
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can be represented kinematically by a near-vertical downward single force. This single 92
force represents the counter force of eruption [Kanamori et al., 1984]. This model has 93
been used to investigate eruption source properties of volcanic eruption earthquakes at 94
other volcanoes including Mount Tokachi and Mount Asama, Japan [Nishimura, 1995; 95
Nishimura and Hamaguchi, 1993]. Brodsky et al. [1999] calculated vertical mass 96
discharge rates for the May 18, 1980 eruption of Mount St. Helens based on this model. 97
Our work follows these studies. 98
Other models for the source of co-eruption seismicity exist. For example, Uhira 99
and Takeo [1994] show that in the case of 1986 eruptions of Sakurajima volcano, Japan, 100
a single force model cannot explain long period (several seconds) seismic radiation 101
patterns as well as a model containing volumetric components of expansion and 102
contraction of rock around the source. Chouet et al. [in press] and Chouet et al. [in prep] 103
suggest that in the case of Kilauea volcano, explosive degassing bursts associated with 104
Strombolian eruptions are best modeled by a single force at the lowest frequencies (VLP 105
band) followed by higher frequency oscillations in the conduit and short-period energy 106
from the slug burst itself. 107
Overall the source of low-frequency energy radiated co-eruptively has been more 108
thoroughly studied than high-frequency energy radiated co-eruptively. McNutt and 109
Nishimura [2008] model co-eruptive tremor as resulting from radial oscillations of 110
conduit walls, but do not connect the amplitudes to the plume dynamics. Here we take a 111
different approach and model the seismic wave generation as resulting directly from the 112
mass discharge of the erupting column. 113
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2.2 The 2008 Eruption of Kasatochi Volcano 115
Kasatochi volcano is a 3 km wide island with a large crater lake in the Andreanof 116
Islands in the Aleutian Arc (figure 1). Though the volcano’s summit is 314 m in 117
elevation, the volcanic vent is near sea level. Prior to its 2008 eruption, little was known 118
about this volcano. Kasatochi volcano is not seismically or geodetically monitored. The 119
nearest seismometers are a short-period network operated by the Alaska Volcano 120
Observatory (AVO) at Great Sitkin volcano, 40 km west of Kasatochi (figure 1). The 121
nearest broadband station functioning at the time of the eruption, ATKA operated by the 122
Alaska Earthquake information Center (AEIC), is 80 km southeast of Kasatochi on Atka 123
Island. 124
After a brief but powerful earthquake swarm with earthquakes as large as M 5.8 125
[Ruppert et al., submitted] Kasatochi volcano had three large ash producing eruptions 126
with satellite-detectable plumes to 18 km above sea level (22:01 UTC 7 August 2008, 127
01:50 and 04:35 UTC 8 August 2008) [Carn et al., submitted; Waythomas et al., 128
submitted; Webley et al., submitted]. Co-eruptive tremor associated with each of these 129
three explosions was readily apparent in real-time seismic data for at least 20 minutes 130
(Figure 2). Infrasound and seismic data indicate that two additional smaller explosions 131
occurred in the following 5 hours during the episode of continuous ash emissions 132
[Arnoult et al., submitted]. Satellite data indicate that the third large explosion was 133
significantly more ash-rich and had a higher plume than the first two [Waythomas et al., 134
submitted, Fee et al., submitted]. Seismic data support this observation as the far field 135
amplitude of the third explosion was more energetic than the previous explosions. 136
Following the third explosion, ash vented continuously for roughly 16 hours. Satellite 137
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data indicate that the continuous ash emission phase had a decreasing density of ash 138
emission with time [Waythomas et al., submitted]. This observation is consistent with 139
seismic data, as the prolonged continuous ash emission phase radiated less seismic 140
energy than the initial 10 minutes of the third explosion . 141
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2.3 The 2006 Eruption of Augustine Volcano 143
The 2006 eruption of Augustine Volcano was far better monitored than the 2008 144
eruption of Kasatochi, in part because the volcano erupted previously in 1971, 1976, and 145
1986. Augustine, a volcano located in the lower Cook Inlet with summit at 1260 m above 146
sea level (figure 1), is instrumented with both broadband and short-period seismometers. 147
Increasing seismicity and deformation was noted months before the eruption onset 148
[Power and Lalla, in press]. The Augustine pre-eruptive seismic swarm was notably less 149
intense than that of Kasatochi. The largest earthquake associated with the eruption was M 150
2.1. The explosive phase of the eruption began on 11 January and continued through 28 151
January [see Power and Lalla, in press]. The ash producing eruptions of Augustine, 152
though numerous, were shorter in duration and lower in altitude that the Kasatochi 153
eruption. Augustine produced 13 ash plumes ranging in altitude from 9 to 14 km above 154
sea level. The co-eruptive tremor durations for these explosions, as determined from far-155
field seismic data, ranged from 3 – 7 minutes. The co-eruptive seismicity associated with 156
the Augustine eruption plumes was observed at a maximum distance of ~ 200 km, 157
whereas Kasatochi co-eruptive seismicity was visible to over 350 km distance. 158
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3. Relating Plume Height to Seismic Wave Amplitudes 161
Here we develop a composite model that combines existing fluid and solid 162
mechanical models to connect observable seismic wave amplitudes to volcanic plume 163
height. We test the model on the 2008 eruption of Kasatochi volcano and the 2006 164
eruption of Augustine volcano. The model consists of three distinct steps as illustrated in 165
Figure 3: 1) Relate maximum ash plume height to mass ejection rate of material from the 166
volcanic vent. 2) Relate mass ejection rate to a single downward force acting on the solid 167
Earth. 3) Calculate far-field seismic wave amplitudes resulting from the single force. 168
Each step is described in detail below. 169
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3.1 Step 1: Relate Plume Height to Mass Ejection Rate 171
We begin by assuming that plume height is controlled by thermal buoyancy for a 172
continuous ash-rich plume with dense rock equivalent volumetric ejection rate Q. This 173
fundamental physics for column height has its origins in studies of forest fire plumes 174
[Morton et al., 1956] and has been verified using eruption data [Carey and Sigurdsson, 175
1989; Sparks et al., 1997]. Slightly different relationships between Q and plume height 176
exist in the literature depending on the datasets used for calibration. We use the widely 177
cited Sparks et al. [1997], equation 5.1 178
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H=1.67 Q0.259 (1) 180
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where H is the column height in km above the vent and Q is measured in m3/s. Equation 182
(1) is an empirical regression with its form is motivated by analytic models of thermally 183
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buoyant continuous plumes in a stratified atmosphere [equation 4.15 of Sparks et 184
al.,1997; Wilson et al, 1978]. Observations used to constrain Equation 1 include 185
uncertainties both in plume height and ejecta volumes as discussed in Mastin et al. [2009] 186
and Sparks et al. [1997]. We use the term continuous to describe a plume where the 187
volcano is still activity venting at the time the plume reaches its maximum height. This is 188
often referred to as an attached plume. 189
An alternative model is a rapid ejection eruption where all of the mass is released 190
so quickly that the bottom of the plume has left the vent before the top of the plume 191
reaches its maximum height. Though this may have been the case for the first two 192
Kasatochi explosions, satellite data show that this was not likely the case for the third 193
explosion, as that explosion was the beginning of a 13 hour phase of continuous ash 194
emission [Waythomas et al., submitted]. Nonetheless, it is useful to realize that even in 195
this extreme case, the scaling in equation (1) is preserved and the only major 196
modification is the inclusion of the ejection duration. Morton et al. [1956] also developed 197
a relationship for a quickly released plume and found, 198
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H=1.87 x 10-3 E1/4 (2) 200
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where H is height in kilometers and E is thermal energy in Joules. The thermal energy is 202
primarily carried by the solid particles and E=cp ρ ΔT Q τ where cp is the heat capacity, ρ 203
is the density of the solid rock, ΔT is the temperature difference between the plume and 204
the ambient air and τ is the duration of the ejection phase. Substituting in reasonable 205
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values of the parameters (cp = 1 KJ/kg/K, ρ = 3000 kg/m3, ΔT = 103 K, τ=100 s), yields 207
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H=1.4 Q1/4 (3) 209
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which is nearly identical to the protracted source result (equation 1). Thus, the model is 211
insensitive to the assumed relative duration of the source. 212
We next relate the thermal ejection rate to the mass ejection rate, as the later 213
quantity is most directly associated with the momentum flux which ultimately generates 214
seismic waves. If dense rock equivalent density is ρ, then 215
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ρQM =•
(4) 217
where •
M is the mass ejection rate. 218
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3.2 Step 2: Relate Mass Ejection Rate to Single Force 220
We assume that the force system acting on the Earth during eruption can be 221
represented as a single force following the work of Kanamori and Given [1982], 222
Kanamori et al. [1984], and Brodsky et al. [1999]. Due to a lack of quality broadband 223
seismic data and poor coverage of the focal sphere typical of Aleutian eruptions, we are 224
not able to invert the seismic radiation field of co-eruptive Kasatochi for an equivalent 225
force system. Thus we cannot directly demonstrate that a single force is the most 226
appropriate source model for Kasatochi. Instead we start with this simple seismic source 227
model and test its applicability. 228
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Using the mass ejection rate from (4), we can derive the equivalent vertical force 229
F on the Earth using a momentum balance following Brodsky et al. [1999]. 230
FvMdtMomentumd ==•
)( (5) 231
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where v is the velocity of material exiting the vent. This is sometimes termed the rocket 233
equation [Thompson, 1972]. In the case of a rocket the force propelling a rocket upward 234
is equal to the momentum discharge rate of the fuel behind it. In the case of a volcano the 235
rocket is inverted, as it discharges momentum upward. 236
To use equation 5, we need to estimate v. For large-scale eruptions, the extreme 237
overpressures at the vent require supersonic flow. In steady-state the flow is choked at the 238
vent with the vent velocity equal to the sound speed of the erupting material [Kieffer, 239
1981; Woods, 1995; Mastin, 2007]. The mixture of ash and gas in a plume has a greatly 240
depressed sound velocity relative to either the solid or gas end member [Rudinger, 1980]. 241
For instance, the May 18, 1980 blast of Mount St. Helens is thought to have a sound 242
speed of ~100-250 m/s based on the temperature and relative mass fraction of gas and 243
solid phases [Kieffer, 1981; Brodsky et al., 1999]. Kieffer and Sturtevant [1984] argue 244
that the low sound velocity of particulate-laden flows allows vent velocities as low as 245
meters per second. Alternative derivations of the vent velocity based on conduit flow 246
models also arrive at the range of 100-250 m/s [Papale and Longo, 2008]. McNutt and 247
Nishimura [2008] summarize vent velocities for a large number of eruptions globally and 248
arrive at a range of 28-420 m/s with the caveat that the lowest end of the range is likely 249
an underestimate due to the neglect of the coupled gas flow. We consider vent velocities 250
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within either the observational or theoretical ranges, i.e., 28-420 m/s, reasonable and 251
consistent with prior work. 252
The simplest application of equation 5 would be using data with periods of 253
minutes, consistent with the time it takes to evacuate the magma chamber, following 254
Kanamori et al. [1984]. We lack data at those frequencies, so we explore the possibility 255
that the higher frequency seismic waves radiated by turbulence in the volcanic jet scale 256
with energy radiated at low frequencies. This requires some discussion of the role of 257
turbulence in the volcanic jet and its effect on seismic waves. 258
As the generation of seismic waves is a linear process, the observed seismic 259
spectrum is a product of the propagation spectrum in the elastic medium (see equation 6 260
below) and the spectrum of momentum ejection from the vent (source spectrum). The 261
spectrum at the source can reflect the spectrum of vent velocities, which in turn are 262
controlled by properties of the flow. In a turbulent flow fluid velocity generally fluctuates 263
with well-defined statistical properties. For instance, for homogeneous, isotropic 264
turbulence in an incompressible flow, the energy density spectrum, S, of the flow is 265
related to frequency S ~ f -5/3, and the integral of the energy spectrum over all 266
wavenumbers is proportional to the autocorrelation of the velocity field [Kolmogorov, 267
1954; Matthieu and Scott, 2000]. A volcanic eruption involves transient, compressible 268
flow that has multiple origins of velocity fluctuations including the turbulent field, 269
internally generated periodic collapses and evolving vent shape [Ogden et al., 2009]. For 270
simplicity, in this initial study we assume that the vent velocity spectrum is flat and the 271
spectral amplitude is constant for all frequencies. We also do not consider here the 272
influence of density fluctuations on the source spectrum. These assumptions are difficult 273
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to evaluate in the absence of direct observations of the turbulent structure of plumes and 274
thus can only be justified by testing the consistency of the seismic data with the model. 275
We use the spectral simplifications as a starting place to explore the link between plume 276
height and seismic waves. For future studies infrasound data from large eruptions could 277
potentially be used to provide constraints on the true turbulence spectrum of volcanic jets 278
[eg. Matoza et al., 2009; Fee et al., submitted]. 279
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3.3 Step 3: Relate Single Force to Far-Field Seismic Waves 281
Finally, we calculate the far-field surface waves resulting from a single force. For 282
a vertical single force F, the displacement amplitude of a fundamental mode Rayleigh 283
wave with wavenumber k traveling in a half-space is 284
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u =0.07F
μk
r (6) 286
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where μ is the shear modulus and r is the distance from the source [Aki and Richards, 288
1980]. Equivalently, equation 6 describes the propagation spectrum as a function of 289
wavenumber k. 290
Equation 6 is applicable for a single mode. For real data, we apply a narrow 291
bandpass that captures multiple modes. Since the modal spectrum is dense near 1 s, it is 292
difficult to analytically add all of the relevant modes together to construct the amplitude. 293
Instead, we generate synthetic seismograms using a wavenumber-frequency summation 294
method and bandpassed the synthetics to obtain a correction for the finite band-pass 295
(Figure 4) [Herrmann, 1987]. Empirically, we find that an impulse source for a given F 296
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bandpassed at 0.5-1.5 Hz at the regional distances studied here produces an amplitude 2.4 297
times greater than that predicted by equation 6 for a half-space homogenous velocity 298
model. This correction factor also holds for a more realistic velocity model like AK135 299
[Kennett et al., 1995; Montaigner and Kennett, 1995]. Therefore, we apply this factor of 300
2.4 correction to our predicted amplitude found using equation 6. A potential 301
complication to this seismic model is the dominance of scattering at high-frequencies. 302
For this initial study, we confine the calculation to the direct energy. 303
By assuming values for μ, v, and ρ, we can calculate ground displacement as a 304
function of column height and observed wavenumber k. Combining equations 1 with 4-6 305
with the finite band-pass correction yields 306
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u =0.17ρv
μk
rH / 1.67( )1/0.259
(7) 308
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Equation 7 predicts the amplitude of the seismic waves resulting from a certain column 310
height based entirely on known physics. The column height is an observed quantity and 311
the wavenumber and epicentral distance r are generally well-resolved for seismic data as 312
is the dense rock density ρ and the shear modulus μ. Therefore, utilizing Equation 7 313
requires estimating only one relatively poorly constrained eruptive quantity, the vent 314
velocity v. 315
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3.4 Model Applicability 317
We now discuss the range of conditions and eruption styles for which this model 318
is appropriate. Because multiple physical processes produce seismic waves at a variety of 319
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frequencies during large ash producing volcanic eruptions, it is sometimes difficult to 320
connect broadband seismic amplitudes with eruptive properties directly, particularly in 321
the near field and for small eruptions. For example, local processes including rock falls 322
and pyroclastic flows can dominate seismic recordings local to the volcano. 323
Because the calculated mass ejection rate only accounts for erupted material that 324
provides energy for buoyant ascent of ash-rich plumes, our model is not applicable for 325
phreatic eruptions or eruptive phenomenon apart from the plume such pyroclastic flows 326
and lava fountaining. In the case of eruptions where the majority of the mass ejected is 327
not entrained in the plume, the model may overestimate plume height for a given 328
amplitude of ground shaking. 329
The model is also only appropriate for plumes that rise to altitudes of 5 km or 330
higher for three reasons: 1) The empirical regression in Sparks et al. [1997] is not 331
constrained for plume heights below 5 km. 2) The assumption that the upward mobility 332
of the plume is thermally driven may not be correct at heights where material can travel 333
ballistically. The maximum ballistic height of a projectile with initial velocity v occurs 334
when the initial kinetic energy equals the gravitational potential energy, i.e., ½ M v2 = M 335
gh, where M is mass, g is the acceleration due to gravity, and h is ballistic height. Thus, 336
the maximum ballistic height is ½ v2 / g. Assuming v = 300 m/s or less, ballistics could 337
be ejected to 4.5 km. 3) The gas thrust region can be dominated by the dynamics of the 338
compressible flow rather than the thermal buoyancy [Ogden et al., 2009]. In the case of 339
small eruptions at Tungurahua and Santiaguito volcanoes Johnson et al [2004] and 340
Johnston et al. [2005] show that amplitudes of co-eruptive seismic waves scale poorly 341
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with eruption intensity. In both cases however, eruption plumes analyzed were less than 4 342
km in height. 343
This model is also not appropriate in cases where the source of co-eruptive 344
volcanic tremor is not the volcanic vent, but elsewhere in the system. For example during 345
the 2008 eruption of Okmok volcano, co-eruptive tremor amplitude correlated poorly 346
with volcanic plume height after the opening phase of the eruption. Haney [submitted] 347
estimates that the VLP tremor occurred along the length of a dike at 2 km depth. Thus in 348
the case of Okmok, Haney concludes that the primary tremor source likely reflected the 349
flux of magma from the shallow magma chamber into the dike rather than mass ejection 350
at the vent directly. 351
Similarly, we must avoid performing this analysis on time series where the 352
seismic data is dominated by earthquakes sourced from deeper in the system. In the case 353
of the Kasatochi eruption, for example, the far-field seismic energy radiated by pre-354
eruptive earthquakes was up to 4 times larger in amplitude than the co-eruptive tremor 355
itself at the distances we consider when seismic energy is averaged over 10 minute 356
windows. For this reason, we limit our analysis at Kasatochi to a time period free of large 357
earthquakes. 358
The model is only applicable when the volcanic vent is open and freely emitting 359
material. Therefore, caution must be used when considering the initial stages of eruption. 360
During this time frame a large portion of the seismic energy may be related to “throat 361
clearing” or removing the lid that caps the magma body. For example, the first large ash 362
producing explosion during the 2006 eruption of Augustine volcano produced stronger 363
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ground shaking than the subsequent 20 ash producing explosions, although the plume 364
height of the first explosion was similar to that of many later explosions. 365
Finally, atmospheric effects should be considered when applying our model. For 366
example, the model is most appropriate for large eruptions with strong plumes where 367
tropospheric wind shear and other atmospheric instabilities are minimal. In addition, 368
because the buoyancy of volcanic ash plumes can increase significantly if atmospheric 369
water vapor is entrained in the plume [Woods, 1993; Tupper et al., 2009], our model is 370
more applicable in dry sub-polar environments such as Alaska than in moist tropical 371
environments. However, in all environments atmospheric humidity does not have an 372
appreciable effect on large eruption columns greater than 15 km in height [Woods, 1993]. 373
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4. Data Analysis and Results 375
4.1 Kasatochi 376
To apply our model to the eruption of Kasatochi, we begin by measuring co-377
eruptive ground displacement after correcting for instrument response at short-period and 378
broad-band seismometers primarily located west of the volcano. Stations analyzed are 379
shown in Figure 1. The geometry of the Aleutian Islands provides us with a nearly linear 380
array. We are not able to use data recorded at Great Sitkin volcano because co-eruptive 381
seismic waves are clipped there (Figure 2). We also do not use data east of Atka Island 382
because seismic waves generated by Kasatochi volcano would likely be contaminated by 383
those generated by the simultaneous eruption of Okmok volcano, roughly 350 km east of 384
Kasatochi. 385
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This use of far field data is an advantage because far field data is not 386
contaminated by energy radiated from secondary surficial processes such as the huge 387
pyroclastic and block and ash flows which left the island inundated in up to 15 meters of 388
tephra. Secondary seismic sources such as rock falls and pyroclastic flows decay more 389
quickly with distance than a single force source associated with magma removal because 390
these secondary sources: 1) transport a small percentage of mass compared to the total 391
mass ejected, 2) are multi-pole sources distributed in time and space on the volcano’s 392
flank in contrast to the concentrated single force mono-pole associated with overall mass 393
ejection [Kanamori et al., 1984, Appendix A], and 3) are largely surficial sources. Jolly et 394
al. [2002] show that in the case of Soufriere Hills Volcano, Monstserrat, seismic waves 395
generated by pyroclastic flows are highly attenuated (Q=20) due to their surficial travel 396
paths. 397
We focus our study on the initial pulse of energy radiated by the third and most 398
ash rich explosion at Kasatochi (22:01 UTC, 7 Aug 2008) (Figure 5), as this explosion 399
began a 13 hour phase of continuous venting and is not contaminated by earthquakes. 400
The strongest phase of this energy packet is several minutes in duration and can be 401
clearly identified as it moves out appropriately with distance away from Kasatochi 402
(Figure 2). We measure the peak amplitude of ground displacement at 1 second period by 403
bandpass filtering data between 0.5 and 1.5 Hz (Figure 5). We choose 1 second period 404
because it is well within the response range of short-period instruments, it is below the 405
frequency range generally radiated by pyroclastic flows [eg. Zobin et al., 2009], yet it is 406
low enough to minimize site effects. At higher frequencies site effects cause significant 407
scatter in our measurements. Figure 6 shows that the relative amplitude of the observed 408
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seismic waves fall off with distance as r1 1/2, where r is radius from the source, as would 409
be expected for Rayleigh waves. This fall-off with distance is a helpful corroboration of 410
the direct Rayleigh wave interpretation of the co-eruptive seismicity in equation 6. To 411
evaluate fit of our model, we fit a line to our data points by forward modeling, varying v. 412
We assume a shear modulus of μ = 3 x1010 Pa, and specify cfk π2= , where the 413
frequency in the middle of the observed bandpass f = 1 s and c = 3x 103 m/s. Dense rock 414
equivalent, ρ, is 2700 kg/m3. 415
Figure 6 shows ground displacement measurements for the Kasatochi eruption 416
and predicted ground displacement with distance. In our preferred model (black line) v = 417
80 m/s in the case of an 18 km plume. This velocity is in the range of those predicted by 418
Kieffer and Sturevant [1984] and observational estimates for vent velocity of specific 419
eruptions as summarized in McNutt and Nishimura [2008]. However, this vent velocity is 420
at the lower end of the previously established ranges. The data therefore is consistent 421
with either the flat spectrum source model as proposed above, or may accommodate an 422
increase in spectral amplitude of the source with increasing period as would be expected 423
from turbulence models [Kolmogorov, 1941; Matthieu and Scott, 2000; Matoza et al., 424
2009]. 425
426
4.2 Augustine 427
In order to investigate the robustness of the model to a different eruptive setting, 428
we test its applicability for the 2006 eruption of Augustine volcano. Although Augustine 429
is locally instrumented, for our analysis we use the short-period seismometer, OPT, 430
located 37 km from the erupting vent. This is required since our model uses far-field 431
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surface waves and because we do not want the tephra ejection signal contaminated by 432
more surficial local processes that dominate the short-period signals on the island, such as 433
rockfalls and pyroclastic flows. In the case of the 2006 eruption of Augustine McNutt 434
[submitted] shows that pyroclastic flows were only visible seismically on stations near 435
the flow travel path and were not visible on the volcano flanks opposite the flow path. 436
Figure 7 shows the 2 s – 1.5 Hz displacement amplitudes at OPT for explosions at 437
01:40 UTC 14 January and 16:57 UTC 17 January 2006, which had plume heights of 438
10.5 and 13 km above sea level respectively based on radar and pilot reports [Power and 439
Lalla, in press]. The far-field short-period amplitudes of these two explosions are similar 440
to other explosions in the sequence (with the exception of the initial 11 January 441
explosion). We select these explosions to analyze because they are representative of the 442
entire eruption. Because the initial explosions from the 2006 eruption of Augustine 443
volcano may have included energy from brittle failure vent clearing processes, we do not 444
analyze data from 11 January 2006. In the case of Augustine, the volcanic vent is well 445
above sea level at ~1260 m altitude. Thus, when applying our model we correct for the 446
difference between vent altitude and the reported plume heights, which are defined with 447
respect to sea level. 448
As in the Kasatochi case, we assume a shear modulus of μ = 3 x1010 Pa, and 449
specify cfk π2= , where the observed frequency is f= 1 s and c = 3x 103 m/s. Dense 450
rock equivalent, ρ, is 2700 kg/m3. In the case of the 13 km plume at Augustine on 17 451
January 2008, our model performs well, as it estimates the correct plume height for vent 452
velocities of 78 m/s based on seismic data. In the case of the 10.5 km plumes on 14 453
January 2008, our model estimates the correct plume height if the velocity at the vent is 454
21
95 m/s. These velocities are within the previously defined range of reasonable values (28-455
420 m/s), but as in the case of Kasatochi, they are at the lower end of the expected values. 456
Once again, there is ambiguity between the appropriateness of the flat spectrum and the 457
possibility of a decrease in spectral amplitude with increasing frequency. 458
459
5. Dynamical Implications 460
Because our model fits the data, the single force model appears to be an 461
appropriate force system in the case of the two eruptions we consider. The most 462
surprising aspect of the model’s success is the fact that we can relate plume height to 463
seismic wave amplitude using ~1 s radiated waves assuming a reasonable v of 78-95 m/s. 464
This consistency implies that the high-frequency fluctuations of the plume are 465
comparable in magnitude to the long-period eddies. The fact that our v estimates are at 466
the low-end of the expected range allows that the source spectral amplitude may be 467
decreasing with frequency. This finding is not surprising as turbulent flows commonly 468
have stronger eddies at long-periods than short-periods [Kolmogorov, 1941; Matthieu 469
and Scott, 2000; Fee et al., submitted]. The spectrum can also be modified by additional 470
processes like supersonic flow [Smits and Dussauge, 2006]. The length scale of turbulent 471
eddies in a volcanic plume has only recently been measured in plumes [Andrews and 472
Gardner, 2009] and thus far there is little independent constraint on the relative strength 473
of various frequencies in the plumes. The seismic measurements presented in this paper 474
suggest that future work on the seismic source spectrum of plumes would be a fruitful 475
avenue into the fluid dynamics of erupting jets. 476
477
22
6. Practical Implications 478
For the Aleutian Islands and many other remote volcanoes in the North Pacific the 479
primary safety concern is the threat of ash clouds to aircraft. Airlines are most concerned 480
about ash clouds that reach aircraft cruising altitudes. Estimating volcanic plume heights 481
in remote environments in real-time (and even in retrospect) is always challenging, 482
particularly when clouds are obscuring activity and the timing of satellite passes is not 483
optimal. With further development this model could potentially be used to constrain 484
plume heights in near-real-time. In the case of the Kasatochi eruption, we would have 485
estimated plume heights of 13-19 km using our model based on seismic data alone, 486
potentially giving airlines notice that the eruption was large enough to be dangerous. To 487
narrow this range in height, we would need more accurate estimates of v and its spectrum 488
or a larger empirical database of v measurements from similar eruptions. These estimates 489
could possibly be obtained through other data sources such as infrasound or radar or by 490
studying a range of eruptions with our model and establishing a range of possible 491
velocities observationally. 492
To illustrate the potential utility of the approach, we examine our ability to 493
characterize future eruptions at Kasatochi Volcano using the nearest seismic stations, 494
incorporating some of the uncertainty in the free parameter, v. Figure 8 shows calculated 495
ground displacement at Great Sitkin stations estimated for eruptions of Kasatochi with a 496
variety of reasonable v values. We assume a detection threshold of 0.4 μm, as AVO 497
short-period seismometers in the Aleutian arc often have noise below this threshold for 498
raw unfiltered data. This is a conservative estimate for eruption detection provided the 499
recording environment is relatively quiet and the seismometers are functioning optimally. 500
23
Figure 8 shows that generally, we can expect to detect co-eruption seismicity for 501
explosive eruptions with plumes that reach 9 – 12 km height above sea level or higher at 502
Kasatochi volcano. 503
This same approach allows us to estimate detection capability for eruptions at 504
other unmonitored volcanoes. For instance, Bogoslof and Seguam volcanoes are small 505
unmonitored Aleutian Islands, like Kasatochi (Figure 1). Bogoslof most recently erupted 506
in 1992 and had 7 additional historic eruptions. Seguam most recently erupted in 1993 507
and had 5 additional historic eruptions. The nearest seismometers to Bogoslof and 508
Seguam are those of the Okmok and Korovin seismic networks respectively, ~50 km and 509
~100 km distant. Using figure 9, we estimate that large continuous ash producing 510
eruptions at Bogolof and Seguam would be visible in high frequency data at the nearest 511
seismic stations if the plumes reached roughly 12 km in altitude, in the conservative case 512
where v=200 m/s. Again, however, a better understanding of vent velocity is needed, as 513
reasonable variation in v (50 – 200 m/s) leads to scatter in predicted plume heights over a 514
4 km range. 515
With better constraints on v and its spectrum,, our model could provide a plume 516
height estimate independent of remote sensing techniques that could be considered along 517
with estimates from other sources. To do this more work would need to be done to 518
constrain errors, explore applicability to different eruptions, and test velocity model 519
assumptions. Another consideration is that several physical processes cause seismic 520
tremor in the Earth’s crust, so other data are needed to confirm that tremor observed is 521
co-eruptive tremor before applying our model. Uncertainties in tremor source process 522
24
would likely lead to far more false positives than false negatives. Thus our model could 523
be used as a conservative indicator of threats to aviation from volcanic ash. 524
525
7. Conclusions 526
Our model is generally successful in relating plume height to ground shaking in 527
the 2008 eruption of Kasatochi volcano and the 2006 eruption of Augustine volcano. This 528
suggests that using plume height to calculate the mass ejection rate and interpreting the 529
resulting force system as a single force are appropriate techniques. The single force 530
model appropriate at low frequencies also fits measurements reasonably well at 531
frequencies of ~ 1 s. This surprising observation suggests that force resulting from the 532
high frequency turbulence in volcanic jets can be a useful indicator of plume height. 533
The success and applicability of the model to other vulcanian and plinian 534
eruptions globally remains to be evaluated. However, the results from Kasatochi and 535
Augustine volcanoes are sufficiently encouraging that more work in this field is 536
warranted. Future studies should focus on other eruptions to explore errors and the range 537
of applicability of the model, consider more complicated velocity structures and indirect 538
wave arrivals, consider atmospheric effects, and further investigate frequency variations 539
in energy radiated by the volcanic jet. Further development of this model may give us a 540
means to better understand the relationship of ground shaking to plume height and 541
explore eruption dynamics of the turbulent jet. In the best case scenario, this avenue of 542
research may lead us to constraining plume height based on seismic wave amplitudes in 543
near-real-time. 544
545
25
546
Acknowledgements 547
Review by Larry Mastin, Darcy Ogden, David Schneider, David Hill, and David Fee 548
significantly improved this manuscript. Seismic stations used in this study were originally 549
installed with funding from the Federal Aviation Administration. 550
551
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Figure Captions 732
733
Figure 1 – Map of central Aleutian arc showing locations of Augustine volcano, 734
Kasatochi Island and neighboring islands and volcanoes. Seismic stations used in this 735
study are shown with triangles. Red are short-period instruments. Green are broadband 736
instruments. Great Sitkin volcano had a functioning seismic network at the time of the 737
Kasatochi eruption. However, those data were clipped and not used in this study. 738
739
Figure 2 - Waveform of third ash producing explosion of Kasatochi as recorded on 740
short-period stations, GSMY, ETKA, KIKV, TASE, and GANE. Line shows moveout of 741
surface wave energy packets at 3.4 km/s. 742
743
Figure 3 – Cartoon depicting processes associated with the three calculation steps in our 744
model. Step 1 relates plume height to mass ejection rate. Step 2 relates mass ejection rate 745
to a downward acting sngle force. Step 3 calculates seismic waves radiated by the single 746
force. 747
748
34
Figure 4 - Synthetic seismograms from an impulse source of the same strength as 749
inferred for the Kasatochi eruption. The synthetics are bandpassed using the same filter as 750
the observed seismograms (0.5-1.5 Hz) to measure the amplitude in the narrow band-pass 751
corresponding to equation 7. The synthetics were produced using a regional f-k 752
integration and the ak135 model [Hermann, 1987; Kennett et al., 1995; Montaigner and 753
Kannett, 1995]. Synthetics are calculated for distances to stations GSMY, ETKA, KIKV, 754
TASE, and GANE. The resulting phase velocity matches the observations in Figure2. 755
756
757
Figure 5 – a) Raw waveform of third large ash producing explosion of Kasatochi, as 758
recorded at short-period station TASE at Tanaga Volcano, 177 km distant from 759
Kasatochi. b) First distinct burst of energy, which we analyze by bandpass filtering raw 760
waveform between 0.5 and 1.5 Hz and measure maximum displacement. c) Spectrogram 761
of energy recorded at TASE. 762
763
Figure 6 – Ground displacement at 1 s period of co-eruptive seismicity with distance 764
from Kasatochi volcano for the large ash producing explosion at 2008. Large dots are 765
broadband stations ATKA and AMKA. Small dots are short-period stations. Preferred 766
forward model fit shown with solid line (v=80m/s). 767
768
Figure 7- Ground displacement at 0.5 - 2 s period of co-eruptive seismicity with distance 769
from Augustine volcano for the large ash producing explosions on January 14 and 17, 770
2006. Model fits for velocities of 78 m/s and 95 m/s are shown with lines. 771
35
772
Figure 8 – Expected ground displacement at 1 s period due to a plume observed at Great 773
Sitkin, 40 km distant from Kasatochi, for three vent velocities, 50 m/s (dashed), 100 m/s 774
(solid), and 200 m/s (dotted). Vertical line indicates average noise level at Great Sitkin 775
seismic stations. 776
777
Figure 9 – Minimum detectable plume heights with distance, assuming a conservative 778
detection threshold of 0.4e-6 m at 1 second period and vent velocities of 50 m/s (dashed), 779
100 m/s (solid), and 200 m/s (dotted). 780
180 -178 -176
51
52
53
KasatochiGreat Sitkin
KanagaTanagaGareloi
Amchitka Island
Atka
Figure 1
0 400 kmAlaska
BogoslofSeguam Augustine
Moveout 3.4 km/s
100 200 300 400 500 600 700 time (s)
Velo
city
(nm
/s)
Figure 2
Figure 3
40 km70 km
118 km
177 km
227 km
3.4 km/s
Figure 4
20000 40000 60000 80000
x 10
-5000
0
5000
22000 26000 30000 34000�-5000
0
5000
Time (s)
Freq
uenc
y
0 10000 20000 30000 400000
0.5
1
a
b
c
Vel
ocity
(nm
/s)
Figure 5
10 2 10 310 -2
10�-1
10 0
10�1
10�2
Dis
plac
emen
t at 1
s pe
riod
(µm
)
Distance from Kasatochi (km)
Broadband seismometer
Short period seismometer
Figure 6
0 0.5 1 1.5 2 2.5 38
9
10
11
12
13
14
15
16
Plum
e H
eigh
t (km
)
Displacement at OPT, 37 km Distance (mm)
14 Jan. 2006
17 Jan. 2006
Figure 7
v = 78 m/s
v = 95 m/s
0 0.5 1 1.5 2 2.5 38
10
12
14
16
18
20
Plum
e H
eigh
t (km
)
Displacement (µm)
Figure 8
v = 50
v = 100
v = 200
10 10 10 10
6
8
10
12
14
16
18
Distance (km)
Plum
e H
eigh
t (km
)
v = 100 m/s
v = 50 m/s
v = 200 m/s
Figure 9
1 2 3 4