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Identifying bubble collapse in a hydrothermal system using hidden Markov models



[1] Beginning in July 2003 and lasting through September 2003, the Norris Geyser Basin in Yellowstone National Park exhibited an unusual increase in ground temperature and hydrothermal activity. Using hidden Markov model theory, we identify over five million high-frequency (>15 Hz) seismic events observed at a temporary seismic station deployed in the basin in response to the increase in hydrothermal activity. The source of these seismic events is constrained to within ∼100 m of the station, and produced ∼3500–5500 events per hour with mean durations of ∼0.35–0.45 s. The seismic event rate, air temperature, hydrologic temperatures, and surficial water flow of the geyser basin exhibited a marked diurnal pattern that was closely associated with solar thermal radiance. We interpret the source of the seismicity to be due to the collapse of small steam bubbles in the hydrothermal system, with the rate of collapse being controlled by surficial temperatures and daytime evaporation rates.

1. Introduction

[2] The Norris Geyser Basin of Yellowstone National park is located outside the northwest rim of the Yellowstone Caldera (Figure 1). With more than 700 thermal features, the basin is the most diverse thermal area and exhibits the highest measured temperatures of all of the geothermal reservoirs of Yellowstone National Park [White et al., 1988]. The individual geothermal features of the basin have been observed to change rapidly with time [White et al., 1988; Friedman, 2007]. Since 1987 a stream gauge on Tantalus Creek, which measures the hydrothermal discharge from the basin, shows two general diurnal patterns in basin-wide water temperature and outflow [Friedman, 2007; Clor et al., 2007]. The first is a winter pattern with an increase in water flow and water temperature that closely tracks the daytime air temperature. The second is a summer pattern where water and air temperature are closely correlated whereas stream flow stays relatively constant except for a strong decrease during the afternoon and early evening.

Figure 1.

Map of the Norris Geyser Basin showing locations of the broadband seismic stations (red dots). Air temperature, barometric pressure, and precipitation were recorded at the Norris Museum (black star). Basin-wide water temperature and flow were measured at the Tantalus Creek weir. Water temperature was measured in the pool of Porkchop Geyser and soil temperature at Junction Trail. Horizontal particle motions for the background tremor are bounded within grey ellipses at stations N01–N04. Thermal ground and surface traces of natural fractures are fromJaworowski et al. [2006]. Map location within Yellowstone National Park is shown by the black square in the inset.

[3] Beginning in July 2003, the basin exhibited an increase in ground temperature and hydrothermal activity that prompted the closure of part of the southern basin to visitors. In response to the rapidly changing dynamics of the hydrothermal system, the Yellowstone Volcano Observatory deployed seven broadband seismographs and five global positioning receivers across the geyser basin (Figure 1). Air temperature, barometric pressure, precipitation, and temperature from individual geothermal features were monitored by the National Park Service.

[4] In this letter we describe the continuous seismic record for stations N01–N04 and focus on station N02, deployed about 100 m southwest of a geothermal pool and inactive geyser called Porkchop Geyser (effectively a bubbling pool). Of the seven deployed stations, N02 recorded the highest amplitude background tremor, interspersed with many small high-frequency (>15 Hz) seismic events. Because of their small amplitude, lack of strong waveform similarity, varying durations, and background noise the identification of these events with standard waveform correlation techniques is impractical. We demonstrate that these small events in the continuous seismic record can be identified using hidden Markov model theory [Rabiner and Juang, 1993], and compare their rate of occurrence, duration, and inter-event times with the available temperature, flow, pressure, and precipitation gauges. We demonstrate that the seismicity is synchronized with diurnal basin–wide thermal patterns, and suggest the source mechanism is due to the collapse of rising steam bubbles encountering cooler thermal water in the hydrothermal system. Similar seismic signals were observed at the Old Faithful Geyser of Yellowstone National Park [Kedar et al., 1998].

2. Data

[5] The seismic stations consisted of broadband seismometers with natural periods of 0.03 to 50 Hz recorded continuously at 100 samples s−1. The stations were deployed beginning on August 6, 2003 and were removed at the end of September 2003. Stations N02 and N06 recorded data for most of this time, while the other stations had significant (1–5 week) periods of data loss. Station N07 was found to be unusable due to electronic noise. Spectral and time-series analyses of the data from stations N05 and N06 (the northernmost stations) found no significant seismic energy that could be correlated with the rest of the network. An example of typical seismicity observed on 20 August, 2003 at stations N01-N04 is shown inFigure 2. Figure 2ashows a one-minute record of ground velocity for each station andFigure 2b shows the corresponding network normalized spectral amplitudes. Each station exhibits background tremor at ∼8 Hz (Figure 2b). The horizontal polarization of the background tremor at stations N01-N04 for a narrow frequency band (7.5 ≤f ≤ 8 Hz) is shown in Figure 1for this one-minute record. Stations N02 and N03 exhibit a NNW polarization, while stations N01 and N04 exhibit a NNE polarization. Station N02 exhibits discrete seismic events with durations less than 1 s that are apparent on all three components. Station N03 exhibits pulses of high frequency energy with durations of 2–4 s that are observed predominantly on the horizontal components.Figures 2c and 2dshow an example of one of the high-frequency events and station normalized amplitude spectra recorded at station N02. The observed high-frequency events seen at stations N02 and N03 are not correlated in time.

Figure 2.

Typical waveforms and spectral characteristics of the network data. (a) A one-minute long window showing the three components of ground velocity for stations N01–N04, (b) the corresponding network normalized amplitude spectra. (c) A two-second window of ground velocity for station N02 (shaded box in Figure 2a), and (d) the corresponding component normalized amplitude spectra.

[6] Hydrothermal fluids from the Norris Geyser Basin enter Tantalus Creek, where their discharge and temperature are measured by stream gauge (sample interval = 10 minutes in 2003). Air temperature and barometric pressure were measured at the Norris Museum with a sample interval of five minutes, and a co-located precipitation gauge reported rainfall times for increments of 0.2 cm. Water temperature in the pool at Porkchop Geyser (0.2 m depth) and soil temperature (0.2 m depth) at Junction Trail were collected with a sample interval of one minute. All times reported in this letter are referenced to local time (Mountain Daylight Time, −6 hours from UTC).

3. Identification of High-Frequency Events Using Hidden Markov Model Theory

[7] The temporal characteristics of the high–frequency events observed on the vertical component of station N02 show event durations of ∼0.2 < d < 0.5 s, with about ten noticeable events occurring per minute (one is outlined in grey in Figure 2a). Many more small events that merge into the background tremor can be seen as well. There is little marked coherence between events, while the spectral characteristics of each event are quite similar to those shown in Figure 2d. The similar spectral characteristics of these events suggests that a common source process located close to station N02 is responsible for their generation.

[8] Hidden Markov model theory (HMM) pattern recognition techniques (commonly applied in automatic speech recognition systems) have been successfully used to identify seismic events [Granat and Donnellan, 2002; Benítez et al., 2007; Dawson et al., 2010]. HMM applied to seismic signals takes advantage of the rich spectral characteristics of seismic energy, and is particularly useful for recognizing volcanic/hydrothermal seismic events that have a common source process but differ in temporal character due to the non-linear fluid dynamics involved in their generation and the presence of noise. A hidden Markov model is a finite-state machine with several possible states, transition probabilities between states, and observation probability density functions associated with each state. In this work hidden Markov models are obtained through a training process where a portion of the seismic signal from the vertical component of station N02 is segmented into event types, and the parameters describing each event type are determined through re-estimation procedures (we use the Baum-Welch algorithm [Rabiner and Juang, 1993]). After the hidden Markov models are defined, the continuous seismic signal from station N02 is analyzed using feature extraction and decoding based on the Viterbi algorithm [Rabiner and Juang, 1993]. The output is a sequence of recognized events with confidence measures and global accuracy scores. We use the Hidden Markov Model Tool Kit (HTK) to perform the training and decoding steps [Young et al., 2006].

[9] Four hidden Markov models are considered here: the first (M1) represents clearly defined small amplitude events, the second (M2) represents visually apparent high amplitude events, the third (M3) represents possible events, and the fourth (M4) represents background noise. The models were determined for the frequency band 1 ≤ f ≤ 30 Hz, while the segmentation of the continuous record into event types was conducted in the frequency band 18 ≤ f≤ 22 Hz. A 10-minute period from the vertical component of station N02 (August 9, 2003) was used to train the models and to verify the choice of parameters for each model. Figure S1 in theauxiliary materialshows an example of the segmentation and recognition process for an 11 s portion of the training record. A second 10-minute period (August 9, 2003), in which the events were visually identified, was decoded to confirm the recognition of event types M1, M2, and M4. The models labeled M3 are attributed to one of the other three models during decoding. The recognition system identifies 83% of the visually identified M1 events, 96% of the M2 events, and 97% of the M4 segments. After decoding 54 days of continuous data, ∼4.6 × 106 events of type M1 and ∼0.8 × 106 events of type M2 were identified. Additional information available from the decoding process includes event durations and event interval times (time between individual events).

4. Comparison Between Seismic, Hydrologic, and Climate Data

[10] We focus on comparing the temporal characteristics of the high–frequency seismicity seen at station N02 to the water temperature of Porkchop Geyser, air temperature, the temperature of Tantalus Creek (2 km downstream from Porkchop), and precipitation. Detailed views of additional data streams for specific time periods are shown in Figures S2–S5 in the auxiliary materials. To graphically represent the large number of identified seismic events we calculate the event rate, mean duration, and mean interval for one–hour bins. Assuming M1 and M2 represent only a difference in source energy (they both exhibit similar patterns of occurrence), we combine the two event types and show the resulting curves in Figures 3a and 3b. The general pattern in number of events and event duration is diurnal, with a rapid increase between ∼1000 and 1200 hours and a maximum plateau between ∼1200 and 1800 hours. A secondary plateau is observed between ∼1800 and 0200 hours. A minimum in event rate and duration is seen between ∼0200 and 1000 hours. The number of events ranges between ∼3500 and 5500 per hour, and mean event durations range from ∼0.35 to 0.45 s. In addition, four periods of time with significant differences in these patterns can be seen from August 8–27, August 28–September 12, September 13–22, and September 23–30, 2003.

Figure 3.

(a) Number of events occurring per hour, (b) mean event duration per hour in seconds, (c) Porkchop Geyser water temperature, (d) air temperature at the Norris Museum, (e) water temperature measured at the Tantalus Creek weir, and (f) precipitation measured at the Norris Museum. Solid vertical lines indicate midnight, and dotted vertical lines indicate noon, Mountain Daylight Time (−6 hours from UTC).

[11] The water temperature in the pool of Porkchop Geyser (Figure 3c) exhibited a diurnal pattern with a characteristic ∼2 to 5° C drop in pool temperature between ∼1200 and 2400 hours. An overall decrease in mean pool temperature of 10° C was seen between August 8–September 30, 2003. Air temperature (Figure 3d) generally increased 10 to 20° C between ∼0600 and 1200 hours, with a peak in temperature lasting until ∼1800 after which the temperature decreased until ∼0600. The minimum air temperature remained above 0°C until early September, 2003. The water temperature at the Tantalus weir (Figure 3e) exhibited a diurnal pattern that closely matched air temperature. About 25 cm of precipitation was recorded (Figure 3f) with most of this occurring between September 6–13, 2003. The following observations are depicted graphically in Figures S2–S5 in the auxiliary materials. The mean event interval was inversely proportional to the rate of occurrence (shorter intervals with increasing number of events). Basin–wide water flow measured at the Tantalus weir exhibited a weak diurnal pattern with flow decreasing by about 0.5 cubic feet per second in the afternoon. This pattern was often masked by increased flow due to precipitation. Soil temperature at Junction Trail exhibited a diurnal pattern similar to that seen in water temperature at the Tantalus weir. Barometric pressure exhibited a weak diurnal pattern of a few millibars that was lower in the afternoon than during the night. This pattern was obscured by the large variations due to weather systems that produced significant precipitation, particularly in mid-September, 2003. The theoretical Earth tide showed no obvious correlation to the observed diurnal patterns described above.

5. Discussion

[12] Because the seismic events were not seen at stations N01 or N04 (distances of ∼240 and 500 m from N02) and they were not correlated with the high–frequency energy seen at station N03 (Figure 2a), they must have occurred near station N02. We suggest that the most likely explanation for the source of the seismicity seen at N02 (Figure 2c) is the collapse (cavitation) of small rising steam bubbles at a thermal discontinuity (cooler water) in the immediate vicinity of the station. The implosion of a steam bubble produces a significant amount of mechanical energy [Leighton, 1994; Thiéry and Mercury, 2009], which may couple to the surrounding rock to produce seismic energy. Another possible source could be the interaction of the oscillation of a cloud of steam bubbles in proximity to a solid wall [Ichihara and Nishimura, 2009]. Qualitatively similar seismicity was observed at the Old Faithful Geyser in the Yellowstone Caldera [Kedar et al., 1996, 1998], where high-frequency events were interpreted to be due to the repeated collapse of steam bubbles near the top a superheated water column, and where the collapse rate is dependent upon local heat and mass flux in the geyser system.Kedar et al. [1998] also argued that the repeated collapse of steam bubbles observed at Old Faithful produced the observed background tremor there. The relative amplitudes of the 8 Hz tremor seen at stations N01–N04 (Figure 1) indicate the presence of a tremor source near station N02, suggesting a close relationship between the tremor and seismic events. The tremor source was stable over time with polarization of horizontal particle motions similar to those shown in Figure 1. The closest major thermal feature to station N02 is Porkchop Geyser, located about 100 m to the northeast. During the time of this experiment there was no observed geyser (eruption) activity at Porkchop Geyser. If the seismic events were associated with Porkchop Geyser, then a very attenuating velocity structure to the north of this geyser would have to be invoked as the events are not seen at station N01.

[13] The strong diurnal pattern seen in the hydrologic data has been occurring since monitoring began in 1987 [Friedman, 2007]. The occurrence of repeating seismicity synchronized with the basin–wide thermal pattern is a new observation. Clor et al. [2007] suggest that the very close correlation between high air and Tantalus Creek water temperatures (where water temperature responds to air temperature and solar radiation), high discharge temperatures of hot springs, and the shallowness of Tantalus Creek combine to promote evaporation in the afternoon, thus reducing stream flow. This implies that the daily change in surface temperature and amount of available surface water directly influences the pressure and temperature regime that drives the observed periodicity of bubble collapse in the hydrothermal system. Subtle changes in the pressure/temperature regime could drive the systematic increase in event rate seen between 8–28 August (Figure 3a) as well as the marked steps in activity seen on August 27, September 15, and September 21, 2003. The large influx of meteoric water (the storm system and increased precipitation in early September, 2003) may be responsible for the significant increase in seismicity seen between September 13–22, 2003, where enhanced boiling and bubble collapse would be expected as the cooler water migrates into the hydrothermal system. The daily afternoon drop in pool temperature at Porkchop Geyser is only weakly correlated with the increase in event rates, suggesting that this thermal feature itself was not the source of the seismic events. It is not clear why the water temperature in the pool at Porkchop Geyser is cooling each afternoon, but it could be due to a decrease in influx of thermal water or to an increase in surface evaporation which would allow the pool to cool.

[14] The dominant trends of natural fractures (solid black lines in Figure 1) that control the flow of hydrothermal fluids in the vicinity of station N02 are northwest, east-west, and north-south [Jaworowski et al., 2006]. The most vigorous hydrothermal activity observed in 2003 included audible sounds and felt vibrations in an area extending 10 to 15 m south-southeast of Porkchop Geyser and along an east-west trending series of new geothermal pools extending 40 m to the east of Porkchop Geyser (dotted line inFigure 1). This east–west trend in observed surface disturbance extends westward from Porkchop Geyser (solid line in Figure 1) as a mapped fracture to an intersection with a north trending fracture about 50 m north of station N02 (see Figure 1). The east-west fracture system provides a natural explanation for the pattern of particle motions seen at 8 Hz as a resonating east-west trending crack located north of station N02 could produce the observed polarization. The intersection of this fracture system with the north trending fracture may provide a natural location for steam bubble collapse, particularly if the intersecting fractures contain fluids with different temperatures. The tremor and seismic sources appear to be originating from a source close to station N02, rather than from the Porkchop Geyser, suggesting that the seismicity is related to the intermixing of hydrothermal fluids at the intersection of natural fractures. The high-frequency energy seen at station N03 implies that other sources of bubble collapse were occurring near this station as well. Deployment of dense, small–aperture seismic arrays and the application of signal processing techniques [Almendros et al., 2001; Cros et al., 2011] would be required to accurately locate the tremor and seismic source locations.

6. Concluding Remarks

[15] By applying a technique commonly used in speech recognition and modified for continuous seismic data, we have demonstrated the ability of hidden Markov model theory to identify small high–frequency (>15 Hz) seismic events embedded in continuous background tremor. The seismicity is interpreted to be caused by steam bubble collapse in the hydrothermal system. The recognition of these events is primarily due to the fortuitous deployment of a seismic station in close proximity to the source region (<∼100 m). Applied in conjunction with other geophysical, hydrologic, and climate data, the use of this technique can extend and improve our understanding of the complexity of hydrothermal systems.


[16] Robert B. Smith, Greg Waite, Dave Drobeck (University of Utah) and Chris Dietel (USGS) were instrumental in deploying the seismic instrumentation. Jamie Farrell (University of Utah) provided quality control of the seismic data. Henry Heasler (NPS) provided invaluable assistance in obtaining the appropriate permits to conduct this study. He also installed the temperature and barometric sensors and provided their data, and with Irving Friedman (USGS) provided the Tantalus weir temperature and flow data. Global positioning receivers were provided by UNAVCO, and the broadband seismic sensors were provided by the Incorporated Research Institutions for Seismology. M. C. Benítez gratefully acknowledges the support provided by the Spanish Ministry of Education. We thank R. Thiéry and J. Vandemeulebrouck for their critical reviews of this letter.

[17] The Editor thanks Regis Thiery and Jean Vandemeulebrouck for their assistance in evaluating this paper.