1 2 Volcanic Plume Height Measured by Seismic Waves Based on a Mechanical Model 3 4 Stephanie G. Prejean1 and Emily E. Brodsky2 5 6 1. USGS Alaska Volcano Observatory 7 4210 University Ave., Anchorage AK 99508 8 9 2. University of California, Santa Cruz 10 Department of Earth and Planetary Sciences 11 Santa Cruz, CA 95064 12 13 14 15 16 17 18 19 20 21 22 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. 44 45 46 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. 79 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. 114 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 .