Temporal evolution of a hydrothermal system in Kusatsu-Shirane Volcano, Japan, inferred from the complex frequencies of long-period events

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B10, 2236, doi: /2001jb000653, 2002 Temporal evolution of a hydrothermal system in Kusatsu-Shirane Volcano, Japan, inferred from the complex frequencies of long-period events Hiroyuki Kumagai National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan Bernard A. Chouet U.S. Geological Survey, Menlo Park, California, USA Masaru Nakano Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan Received 1 June 2001; revised 4 April 2002; accepted 9 April 2002; published 18 October [1] We present a detailed description of temporal variations in the complex frequencies of long-period (LP) events observed at Kusatsu-Shirane Volcano. Using the Sompi method, we analyze 35 LP events that occurred during the period from August 1992 through January The observed temporal variations in the complex frequencies can be divided into three periods. During the first period the dominant frequency rapidly decreases from 5 to 1 Hz, and Q of the dominant spectral peak remains roughly constant with an average value near 100. During the second period the dominant frequency gradually increases up to 3 Hz, and Q gradually decreases from 160 to 30. During the third period the dominant frequency increases more rapidly from 3 to 5 Hz, and Q shows an abrupt increase at the beginning of this period and then remains roughly constant with an average value near 100. Such temporal variations can be consistently explained by the dynamic response of a hydrothermal crack to a magmatic heat pulse. During the first period, crack growth occurs in response to the overall pressure increase in the hydrothermal system caused by the heat pulse. Once crack formation is complete, heat gradually changes the fluid in the crack from a wet misty gas to a dry gas during the second period. As heating of the hydrothermal system gradually subsides, the overall pressure in this system starts to decrease, causing the collapse of the crack during the third period. INDEX TERMS: 7280 Seismology: Volcano seismology (8419); 7260 Seismology: Theory and modeling; 8419 Volcanology: Eruption monitoring (7280); 8424 Volcanology: Hydrothermal systems (8135); KEYWORDS: long-period event, crack model, hydrothermal fluid, magmatic heat, Q, Sompi method Citation: Kumagai, H., B. A. Chouet, and M. Nakano, Temporal evolution of a hydrothermal system in Kusatsu-Shirane Volcano, Japan, inferred from the complex frequencies of long-period events, J. Geophys. Res., 107(B10), 2236, doi: /2001jb000653, Introduction [2] A fundamental goal of volcano studies is to gain a better understanding of the state of fluids and physical processes beneath volcanoes. Volcano-tectonic (VT) earthquakes, long-period (LP) events, tremor, and very long period (VLP) signals all provide glimpses of the internal processes occurring beneath volcanoes. VT earthquakes are indistinguishable from ordinary double-couple tectonic earthquakes. LP events and tremor are both characterized by oscillating signatures with typical periods in the range Copyright 2002 by the American Geophysical Union /02/2001JB000653$ s [Chouet, 1996]. VLP signals show oscillating or impulsive signatures with periods longer than a few seconds [e.g., Kawakatsu et al., 1992, 1994, 2000; Neuberg et al., 1994; Uhira and Takeo, 1994; Kaneshima et al., 1996; Ohminato and Ereditato, 1997; Ohminato et al., 1998; Dawson et al., 1998; Rowe et al., 1998; Chouet et al., 1999; Arciniega-Ceballos et al., 1999; Yamamoto et al., 1999; Legrand et al., 2000; Nishimura et al., 2000; Kumagai et al., 2001]. [3] VT earthquakes are associated with the brittle response of the volcanic rock to fluid movements. These events essentially act as gauges which map stress concentrations within a wide region surrounding magma conduits and reservoirs. As such VT activity provides information about ESE 9-1

2 ESE 9-2 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM the state of the solid but is of little use for defining the dynamic state and properties of volcanic fluids. In contrast, LP events and tremor have their origins in acoustic oscillations of fluid-filled conduits driven by pressure disturbances accompanying mass transport in magmatic or hydrothermal systems [Chouet, 1996]. Therefore these signals provide direct windows into the state of volcanic fluids. VLP signals are also intimately linked to fluid activity and reflect inertial forces associated with mass transport in magmatic [e.g., Ohminato et al., 1998] or hydrothermal systems [e.g., Kawakatsu et al., 2000]. Appropriate analyses and a correct physical interpretation of LP, tremor, and VLP signals thus constitute critically important steps toward a better understanding of the state of fluids and physical processes beneath volcanoes. [4] Among these signals, we focus our attention here on the LP event, whose waveform is characterized by a harmonic decaying signature except for a brief time interval at the event onset. The LP event may be viewed as the oscillatory acoustic response of a fluid-filled resonator triggered by a time-localized excitation. This type of event is of particular significance in volcanic studies because the characteristic properties of the resonator system at the source of the event can be directly determined from the complex frequencies of the decaying harmonic oscillations in the tail of the LP waveform. We define the complex frequency as f p ig, where f is the frequency, g is the growth rate, and i ¼ ffiffiffiffiffiffi 1. We use the quality factor, Q, defined in terms of the complex frequency as Q = f/(2g). The complex frequencies depend on the acoustic properties of the fluid and solid, and geometry of the resonator. We can estimate the state of the fluids in the resonator through an interpretation of the acoustic properties of the fluid, provided the effects of resonator geometry and acoustic properties of the solid are properly removed from the observed complex frequencies. [5] It is now recognized that the complex frequencies of LP events may show spatial as well as temporal variations [Lesage and Surono, 1995; Gil Cruz and Chouet, 1997; Nakano et al., 1998; Kumagai and Chouet, 1999], in which Q can have values ranging from tens to several hundred. Kumagai and Chouet [2000, 2001] presented a comprehensive description of the acoustic properties of a crack containing various types of fluids whose compositions are compatible with those expected for magmatic and hydrothermal fluids. Their results show that Q predicted from the crack model ranges from almost unity to several hundred, consistent with the wide variety of quality factors observed in LP events. These features strongly support the idea that the observed complex frequencies of LP events can provide important information about the compositions of fluids beneath volcanoes. [6] Kusatsu-Shirane is a composite andesitic volcano located in central Japan (Figure 1). Summit eruptions have been recorded at Kusatsu-Shirane since Frequent phreatic eruptions were observed in , and the most recent eruption occurred in Three crater lakes (Yugama, Mizugama, and Karagama) occupy the summit of the volcano and numerous hot springs are found in the area, marking Kusatsu-Shirane as one of the major hot spring regions in Japan. These features point to an active magmatic system and enhanced circulation of hydrothermal fluids beneath the volcano. Geochemical studies provide further Figure 1. Location of seismic stations (solid circles and triangles) operated by the Earthquake Research Institute of the University of Tokyo at Kusatsu-Shirane Volcano. Solid circles indicate three-component seismometers, and solid triangles indicate vertical-component seismometers. A solid star marks the epicenter of LP events determined by Nakano et al. (submitted manuscript, 2002). The inset shows the location of Kusatsu-Shirane in central Japan. support for the presence of a hydrothermal reservoir beneath the summit, with hydrothermal activity resulting from the interaction of hot volcanic gases with groundwater [Hirabayashi, 1999; Ohba et al., 2000]. LP events characterized by nearly monochromatic oscillatory signatures have been frequently observed at this volcano [Hamada et al., 1976; Oikawa et al., 1993; Fujita et al., 1995], and temporal variations in the complex frequencies of these LP events have also been documented [Nakano et al., 1998]. The observed temporal variations in complex frequencies may be directly related to the evolution of the hydrothermal system in response to magmatic activity. [7] In this paper, we present a detailed description of the temporal variations in the complex frequencies of LP events observed at Kusatsu-Shirane Volcano during the period from August 1992 through January We follow Kumagai and Chouet [2000, 2001] in our interpretation of the complex frequencies of the LP events and in our estimation of the acoustic properties of a crack containing hydrothermal fluids. We show that the observed temporal variations are consistent with the dynamic response of a hydrothermal crack to a magmatic heat pulse beneath Kusatsu-Shirane Volcano. 2. Complex Frequencies of LP Events [8] Kusatsu-Shirane Volcano is monitored by a network of seven seismic stations belonging to the Earthquake Research Institute of the University of Tokyo (Figure 1). Four stations (JIE, YNE, YGW, and AIM) feature threecomponent seismometers, and another three (JIW, MZW, and YNW) feature vertical-component seismometers. The seismometers have a natural frequency of 1 Hz and are critically damped, and all the records are sampled at 120

3 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM ESE 9-3 Figure 2. Waveforms of LP events observed at YNE. The amplitude scales are indicated by vertical bars at the left of the seismograms, where the length of each bar indicates an amplitude of 1 mm/s. samples per second per channel [Ida et al., 1989]. We use the waveform data of LP events observed by the Kusatsu seismic network during the period August 1992 to January 1993, which represents the late stage of renewed volcanic activity in While a few tens of VT earthquakes per month are typically recorded during inactive periods, a maximum daily number of 40 VT earthquakes was observed during this interval of renewed activity [Hirabayashi, 1999]. Eruptive activity in was limited to a small eruption that occurred at the bottom of the Yugama crater lake immediately before the start of this period. M. Nakano et al. (Source mechanism of long-period events at Kusatsu-Shirane Volcano, Japan, inferred from waveform inversion of the effective excitation functions, submitted to Journal of Volcanology and Geothermal Research, 2002, hereafter referred to as Nakano et al., submitted manuscript, 2002), performed waveform inversions of a subset of seven LP events recorded during this period and estimated source mechanisms by conducting a grid search to find the source locations providing best fits between data and synthetics. Their best fit locations obtained for individual events are nearly colocated at a depth of about 300 m between the Yugama and Mizugama crater lakes (Figure 1), suggesting that these LP events originated in the same resonator. [9] Figure 2 shows four examples of LP waveforms observed at YNE. The waveforms all share the same dilatational first motion and they all consist of a superposition of simple decaying sinusoids except for a brief time interval at the event onset. The wide variety of decaying characteristics apparent in Figure 2 are indicative of temporal variations in the complex frequencies of these LP events. We analyze these waveforms using the Sompi method [Kumazawa et al., 1990; Hori et al., 1989] based on an autoregressive (AR) model and allowing high-resolution spectral analyses. We delete the inhomogeneous onset portion of the LP waveform, and apply the Sompi method to the remainder of the signal. We use trial AR orders between 4 and 60, in which the complex frequency in each waveform is determined by taking the mean value of the estimates of five successive AR orders that contain the least variance. The errors in the complex frequency are estimated from the variance of the estimates of the five successive AR orders. The results of Sompi analyses of the waveforms in Figure 2 are shown in Figure 3 in the form of frequencygrowth rate ( f-g) diagrams of the complex frequencies of wave elements for all the trial AR orders. Densely populated regions in the f-g diagrams represent signals for which the complex frequencies are stably determined for different AR orders, while scattered points represent incoherent noise. Figure 4 shows the amplitude spectra calculated by the fast Fourier transform [Cooley and Tukey, 1965] for the same waveforms. [10] As seen in Figure 3, the LP waveforms are characterized by a wide variety of Q. The averaged complex frequencies of the events on 22 October and 18 November are representative of values of Q between 20 and 50, and the events on 13 and 14 September are characterized by values of Q around 100. Although several oscillation modes are apparent in the f-g diagrams (Figure 3) and spectra (Figure 4), we use the complex frequencies of the dominant peaks in Figure 4 corresponding to the clusters of points shown within ellipses in Figure 3, to quantify the temporal variations of complex frequencies. The selected mode corresponds to the mode analyzed in a previous study by Nakano et al. [1998]. We use available waveforms from the seven stations for each event and determine the complex frequency of the dominant mode from each individual waveform. The estimated complex frequencies are then averaged for each event. [11] Our analysis focuses on LP events recorded between 8 August 1992 and 27 January The temporal variations in complex frequencies determined for the dominant spectral peaks are shown in Figure 5. Both the frequency and Q show significant variations during this time interval. The peak frequency ranges from 1.3 to 5.4 Hz, and Q ranges between 10 and 160. The observed temporal variations in complex frequencies can be divided into three periods. During the first period, before 5 September the frequency rapidly decreases from around 5 to 1.3 Hz, and Q remains roughly constant with an average value near 100, although the values of Q are highly scattered. During the second period, between 5 September and 6 December, the frequency gradually increases up to 2.5 Hz, and Q gradually decreases from 160 to 30, with both f and Q showing some scatter in their values along these trends. During the third period, after 6 December, the frequency increases more rapidly from 3 to 5 Hz, and Q shows an abrupt increase at the beginning of this period and then remains roughly constant with an average value near Acoustic Properties of a Crack Containing Hydrothermal Fluids [12] To interpret the observed temporal variations in the complex frequencies of LP events, we estimate the acoustic properties of a crack containing various types of fluids whose compositions and temperature and pressure conditions are compatible with those expected for LP events beneath Kusatsu-Shirane. Our justification for our assump-

4 ESE 9-4 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM Figure 3. Plots of the complex frequencies of individual wave elements for all the trial AR orders (4 60) estimated for the waveforms shown in Figure 2. The clusters of points represent clear signal, and the scattered points represent incoherent noise. The solid lines represent lines along which Q is constant. We use the signals shown within ellipses to quantify the temporal variations of the complex frequencies. tion of crack geometry is based on analyses of the source mechanism of LP events observed at Kusatsu-Shirane by Nakano et al. (submitted manuscript, 2002), which indicate a subhorizontal crack-like geometry for the source of these events. A crack geometry is not surprising as it represents the most natural geometry satisfying mass transport conditions at depths beneath a volcano. [13] We follow Kumagai and Chouet [2000, 2001] and use the rectangular crack model of Chouet [1986, 1988, 1992]. The parameters of the model are a/a, b/m, W/L, and crack stiffness C =(b/m)(l/d), in which a is the compressional wave velocity of the rock matrix, a is the sound speed of the fluid, b is the bulk modulus of the fluid, m is the rigidity of the solid, and W, L, and d are the crack width, length, and aperture, respectively. The ratios a/a and b/m are related to r f (density of the fluid) and r s (density of the solid) through the relation r f ¼ 1 a 2 b ð1þ r s 3 a m for Lame s coefficients l = m. We define the dimensionless complex frequency as n ix. Accordingly, Q r is defined as Q r ¼ n=ð2xþ; ð2þ which represents the quality factor due to the radiation loss. It should be noted that the observed quality factor Q of the LP event may be expressed as Q 1 ¼ Q 1 r þ Q 1 i ; ð3þ where Q i represents the quality factor due to intrinsic losses in the fluid [Aki, 1984]. [14] In light of the shallowness of the source, it seems reasonable to assume that the fluids in the resonator at the source of LP events observed at Kusatsu-Shirane are hydrothermal fluids. Water, H 2 O gas (steam), and CO 2 gas are possible major constituents of the fluids beneath Kusatsu- Shirane. Therefore we consider fluids made of water and mixtures of H 2 O and CO 2 gases. Fluids consisting of water and steam may be in the form of either bubbly water, or water foam, or misty gas. Bubbly water is a water-steam mixture with a gas-volume fraction less than 10%, water foam is a water-steam mixture with gas-volume fraction between 10 and 90%, and a misty gas is a water dropletsteam mixture with gas-volume fraction larger than 90%. As the hypocenters of the LP events are located at a depth near 300 m, we assume an ambient pressure of 5 MPa at the source. We consider a temperature of 537 K for fluids consisting of water and steam to satisfy the saturation

5 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM ESE 9-5 Figure 4. Amplitude spectra estimated for the waveforms shown in Figure 2. We use the dominant peaks, which correspond to the signals shown within ellipses in Figure 3, to quantify the temporal variations of the complex frequencies. condition of the water-steam mixture at this pressure, and further assume 800 K for the temperature of the H 2 O CO 2 gas mixture. We use values of 2500 m/s [Ida et al., 1989] and 2300 kg/m 3 for the compressional wave velocity and density of the rock matrix, respectively. [15] We attribute the dominant peak in the observed spectra to the transverse mode with wavelength 2W/3 and use the acoustic properties determined for this mode in a rectangular crack with a width to length ratio W/L = 0.5 and aspect ratio L/d =10 4 [Kumagai and Chouet, 2001]. The effects of our choice of mode are discussed in a later section. Figures 6a and 6b, respectively, show contour plots of Q r and n for the mode 2W/3, together with plots of the acoustic properties of the fluids in the a/a r f /r s domain. The contour plots of Q r and n are derived from estimates of these parameters obtained from Sompi analyses of synthetic far-field displacement seismograms generated with the crack model, shown as solid dots in Figure 6. The acoustic properties of the fluids are calculated from the equations of Commander and Prosperetti [1989] (bubbly water), Kieffer [1977] (water foam), Morrissey and Chouet [2001] (water foam and gas-gas mixture), and Temkin and Dobbins [1966] (misty gas). Details of the procedure are given by Kumagai and Chouet [2000]. [16] We sample the Q r and n contour surfaces along the curves of a/a versus r f /r s representative of the different fluids shown in Figure 6. The resultant Q r and n for a crack containing the different types of the fluids are shown in Figure 7. For a crack containing a gas mixture of H 2 O CO 2, Q r ranges from 26 to 37, and n ranges from 0.25 to 0.28 (Figures 7a and 7d). For a crack containing a bubbly water, Q r may range from almost 1 for pure liquid water to 60 at a gas-volume fraction of 10%, and n is nearly constant at 0.06 (Figures 7b and 7e). For a crack containing a water foam, Q r is larger than Q r in the bubbly water and ranges up to 95, and n is also nearly constant at up to a gas-volume fraction of 50% (Figures 7b and 7e). For a crack containing a misty gas, Q r ranges up to 180 at a few weight percent of steam, and n decreases with decreasing weight fraction of steam, reaching a value of 0.05 or smaller. [17] According to Kumagai and Chouet [2000], Q i in a gas-gas mixture is significantly large compared to Q r. While there are no reliable estimates of Q i in a water foam, Q i in a bubbly water becomes comparable to or smaller than Q r in the presence of bubbles whose radii are larger than 1 mm. Q i in a misty gas is significantly large compared to Q r for small-size droplets whose radii are less than 10 mm. 4. Interpretation of the Complex Frequencies [18] Q measured in LP events observed at Kusatsu- Shirane shows values significantly larger than 100 during

6 ESE 9-6 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM Figure 5. Temporal variations in (a) Q and (b) frequency, determined for the dominant spectral peaks of LP events. The solid lines spanning the second period in Figures 5a and 5b show best fits of Q r and n calculated for a crack containing a misty gas, respectively, with crack parameters L = 290 m, W = 145 m, and d = 29 mm (see text for details). The dotted lines in the first and third periods in Figure 5a represent averaged values of Q in each period. The dotted lines in the first and third periods in Figure 5b connect the observed data points. the early stage of the second period (Figure 5a). Among the possible fluids examined above, a misty gas is the only fluid that can explain values of Q larger than 100 (Figure 7c). Furthermore, we find that the systematic trends observed in the temporal variations of Q and frequency in LP events during the second period are consistent with an increase in gas-weight fraction in the misty gas from a few percent to almost 100%. Figures 5a and 5b, respectively, show the observed temporal variations in Q and f during the second period, together with fits of Q r and n calculated for a crack containing a misty gas. The fits are obtained by trial and error assuming a proportionality between the gas-weight fraction and time. To fit the observed temporal variation in frequency, we used the geometrical parameters for the crack, L = 290 m, W = 145 m, and d = 29 mm, which may represent realistic sizes for the resonator. [19] Although some discrepancies are apparent, the overall fits to the observed temporal variations in the second period are fairly good, indicating that the decreasing trend of Q and increasing trend of f are both reasonably well reproduced by the fits. These results suggest that the source region of the LP events during the second period starts off fairly wet (with only a few gas-weight percent), then gradually dries out, and ends up completely dry (100% gas-weight percent). The simplest interpretation for such drying out process is a gradual heating of the hydrothermal system in response to a magmatic heat pulse beneath the volcano. The heat may be transferred by a flux of volcanic gases from the magma as suggested by geochemical studies [Hirabayashi, 1999; Ohba et al., 2000]. [20] During the first and third periods the temporal variations in the frequency of LP events show opposite trends. While the frequency decreases from around 5 to 1.3 Hz during the first period, the frequency increases from 3 to around 5 Hz during the third period. In contrast to these systematic variations in frequency, Q remains roughly

7 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM ESE 9-7 Figure 6. Contour diagrams of (a) Q r and (b) n and plots of a/a versus r f /r s curves for different hydrothermal fluids at a pressure of 5 MPa. Solid dots mark points where synthetic waveforms are calculated. constant with an average value near 100 during both periods. As shown in Figure 7, a value of Q around 100 may be explained by either a water foam with gas-volume fraction near 50%, or a misty gas with gas-weight fraction near 10%. However, it is not possible to produce large variations of n in either water foam or misty gas without also producing a change in Q r (see Figure 7). [21] We therefore examine the effects of crack geometry to explain the temporal variations observed during the first and third periods. A decrease (or increase) in frequency can generally be interpreted by an increase (or decrease) in crack size under fixed acoustic properties of the fluid in the crack. While f is related to the crack length L through the relation f = na/l, Q r is given by Q r = n/(2x). A change in L with fixed L/d and W/L therefore varies f without affecting Q r. As discussed by Kumagai and Chouet [2001], a change in the ratio W/L with fixed aspect ratio L/d also varies n and therefore f without significantly

8 ESE 9-8 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM Figure 7. Q r and n for a crack containing different types of hydrothermal fluids: (a,d) a gas mixture of H 2 O CO 2, (b,e) a water-steam mixture, and (c,f) a misty gas. changing Q r for the transverse mode. Therefore a change in crack size under an assumed constant L/d can reasonably explain the temporal variations observed during the first and third periods. [22] During the first period, f rapidly decreases from near 5 to almost 1 Hz, which may be attributed to a crack that grows almost five times in either length or width. The measured Q during the first period is around 100 so that either a water foam with gas-volume fraction near 50%, or misty gas with gas-weight fraction near 10%, may satisfy the required acoustic properties of the fluid in the crack. It should be noted that while the estimates of Q show considerable scatter, f seems to be independent of the scatter in Q values during the first period (see Figure 5). This feature can also be explained by either a water foam or misty gas. For example, n in water foam and bubbly water remains almost constant up to a gas-volume fraction of 50%, while Q r for water foam and bubbly water varies strongly over the same range of gas-volume fractions (see Figures 7b and 7e). Alternatively, Q i in a misty gas containing droplets whose radii are larger than 10 mm may become smaller than Q r so that Q may show considerable variations with changes in droplet sizes without significant attendant variations in n [Kumagai and Chouet, 2000]. [23] During the third period, Q increases abruptly at the beginning of the period and then remains roughly constant with an average value near 100. There seems to be no significant gap in the values of frequency measured at the end of the second period and beginning of the third period, and the frequency increases rapidly from 3 up to 5 Hz over the course of the third period. To explain the value of Q around 100, a water foam with gas-volume fraction around 50%, or misty gas with gas-weight fraction around 10%, is also required. This feature suggests that the crack may have been replenished by a new batch of wet steam at the beginning of the third period. This process, however, should be accompanied by a decrease in frequency since n for a crack containing a water foam or misty gas is lower than n for a crack containing pure steam (see Figure 7). If the crack size remains unchanged, the frequency should decrease to around 1 Hz in association with the replenishment of the crack with either water foam or misty gas. A simple explanation for the apparent lack of decrease in frequency at the beginning of the third period is that a simultaneous decrease occurred in the crack size. This explanation also seems consistent with the increasing trend of the frequency and constant Q factor observed during the third period, both of which are consistent with a decrease in crack size. Including a possible abrupt decrease in crack size at the beginning of the third period, the crack may have decreased by a factor of five in either length or width by the end of the third period. These changes are comparable in size to those estimated during the first period. [24] We therefore interpret the overall temporal variations observed in the complex frequencies of LP events as follows. During the first period a growth of the crack at the source of the LP events occurs in response to an overall pressure increase in the hydrothermal system caused by a heat pulse transferred by the flux of volcanic gases from the magma beneath the volcano. During this time of crack formation the crack may be filled with either a wet misty gas or a water foam. Once crack formation is complete, heat gradually changes the fluid in the crack from a wet misty gas to a dry gas during the second period. As heating of the hydrothermal system gradually subsides, the overall pressure in this system starts to decrease, causing a collapse of the crack and allowing cooler water to seep in from the surrounding region during the third period. This influx of

9 KUMAGAI ET AL.: EVOLUTION OF A HYDROTHERMAL SYSTEM ESE 9-9 colder water changes the fluid in the crack from a dry gas to a wet misty gas or a water foam. 5. Discussion [25] We have presented a detailed description of the temporal variations in the complex frequencies of LP events observed at Kusatsu-Shirane Volcano during the period August 1992 to January The observed complex frequencies are consistent with the acoustic properties of a crack containing hydrothermal fluids. The temporal variations in complex frequencies point to the existence of three major phases, which can be reasonably interpreted in terms of the dynamic response of a hydrothermal crack to a magmatic heat pulse. [26] We have used the transverse mode with wavelength 2W/3 for our interpretation of the observed complex frequencies. We have no clear justification for the use the mode 2W/3 other than that this mode is the lowest dominant mode for a crack excitation triggered by a step increase in pressure applied at the center of the crack [Kumagai and Chouet, 2000, 2001]. As demonstrated by Kumagai and Chouet [2001], however, our interpretation of acoustic properties in a crack containing various types of fluids is not strongly affected by the choice of mode, except for what concerns the actual ranges of Q r and n. Therefore our interpretation of the temporal variations in fluid properties are not changed, although our estimates of the crack dimensions are strongly affected by the choice of mode. Specifically, if we interpret the dominant spectral peak of LP events as the mode 2W/5, we also find fairly good fits to the observed temporal variations in complex frequencies during the second period, but our estimates of crack dimensions are twice as large as those obtained for the mode 2W/3. [27] We have interpreted the first and third periods as crack growth and collapse phases, respectively. In this interpretation we have assumed a fixed L/d. It may also be possible to assume that d does not vary significantly during crack growth and collapse, resulting in an increase in L/d as the crack grows, or a decrease of this ratio as the crack collapses. Kumagai and Chouet [2001] showed that both n and Q r decrease as L/d increases. Therefore, by assuming a fixed d we can also explain the observed decreasing and increasing trends of f with less variations in L compared to those required by a fixed L/d. Since f changes between 1 and 5 Hz in our data, fivefold changes in L/d are therefore possible (e.g. between 10 4 and ). The corresponding variation of Q r may reach up to 20 [Kumagai and Chouet, 2001], which is within the observational errors during the first and third periods. It thus appears that the effects of L/d do not strongly affect our interpretation. [28] Nakano et al. [1998] interpreted temporal variations in the complex frequencies of three LP events observed at Kusatsu-Shirane on 5 and 20 October and 11 November 1992, based on intrinsic losses (Q 1 i ) in a bubbly water, in which they neglected the effect of the radiation loss (Q 1 r ) according to a formula for Q r for the fundamental radial mode of a sphere [Aki et al., 1977]. As discussed by Kumagai and Chouet [2000], there are significant differences between the values of Q r calculated for a sphere and values of Q r estimated for the crack model. While it is also possible to explain the data of Nakano et al. [1998] by intrinsic losses in a bubbly water, the high-q values observed in early September (see Figure 5a) are incompatible with the acoustic properties of a crack containing a bubbly water. Our interpretation, which relies on the acoustic properties of a crack containing hydrothermal fluids and is based on comprehensive estimates of the complex frequencies of LP events observed over the course of six months, may provide a better view of the temporal evolution of the coupled hydrothermal and magmatic systems beneath Kusatsu-Shirane. [29] Further evidence for the presence of a magmatic heat source beneath the volcano is provided by geomagnetic data. Measurements of the geomagnetic field at the volcano were performed by the Japan Meteorological Agency (JMA) [e.g., JMA, 1991]. A significant decrease in the total intensity of the geomagnetic field was observed between 1989 and 1991 in association with the observed renewal of volcanic activity. To explain the decrease in the total intensity, Yamazaki et al. [1992] proposed two alternative thermal demagnetization models, whose sources were positioned at depths near 550 m and 900 m beneath the crater lakes. In either model the depth of the demagnetized region is deeper than the estimated depth of the LP source. Temporal variations in the total intensity measured at a point close to the epicenter of LP events show a decreasing trend lasting through the early months of 1993 [e.g. JMA, 1995]. These features strongly suggest the existence of a sustained magmatic heat source located immediately below the source of LP events during the period from 1989 until early This view is consistent with our interpretation of the observed complex frequencies of LP events. Although the LP data are suggestive of short-term fluctuations in magmatic heat, it may be difficult to interpret such fluctuations in the geomagnetic data due to the effects of unidentified seasonal variations. Therefore further discussion of these effects is premature until future detailed analyses of the geomagnetic data have been completed. 6. Concluding Remarks [30] We have used the acoustic properties of a fluid-filled crack to obtain a coherent interpretation of the complex frequencies of LP events observed at Kusatsu-Shirane. Observed temporal variations in the complex frequencies can be consistently explained by the dynamic response of a hydrothermal crack to a magmatic heat pulse. Our study demonstrates the usefulness of the complex frequencies of LP events to diagnose the state of fluids and to investigate physical processes in magmatic and hydrothermal systems. LP events have been widely observed at various volcanoes, and our approach is generally applicable to quantitative interpretations of this activity. The real-time observation and routine analyses of LP waveforms may hold great potential to image and monitor hydrothermal and magmatic systems beneath a volcano, thus helping the effort to predict eruptive behavior and mitigate volcanic hazards. [31] Acknowledgments. We thank Yoshiaki Ida, Jun Oikawa, and members of Earthquake Research Institute, University of Tokyo, for sharing the waveform data from Kusatsu-Shirane Volcano. We also thank Kenji

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