Source process of very-long-period events accompanying long-period signals at Cotopaxi Volcano, Ecuador

Journal of Volcanology and Geothermal Research 176 (2008) 119–133

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Journal of Volcanology and Geothermal Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j vo l g e o r e s

Source process of very-long-period events accompanying long-period signals at Cotopaxi Volcano, Ecuador Indira Molina a, Hiroyuki Kumagai b,⁎, Alexander García-Aristizábal a, Masaru Nakano b, Patricia Mothes a a b

Instituto Geofísico, Escuela Politécnica Nacional, P.O. Box 17-01-2759, Quito, Ecuador National Research Institute for Earth Science and Disaster Prevention, 3-1 Tennodai, Tsukuba, Ibaraki 305-0006, Japan

a r t i c l e

i n f o

Article history: Received 19 January 2007 Accepted 31 July 2007 Available online 29 August 2007 Keywords: long-period event very-long-period event crack model waveform inversion dike degassing process

a b s t r a c t Renewed seismic activity of Cotopaxi, Ecuador, began in January 2001 with the increased number of longperiod (LP) events, followed by a swarm of volcano-tectonic (VT) earthquakes in November 2001. In late June 2002, the activity of very-long-period (VLP) (2 s) events accompanying LP (0.5–1 s) signals began beneath the volcano. The VLP waveform was characterized by an impulsive signature, which was accompanied by the LP signal showing non-harmonic oscillations. We observed temporal changes of both the VLP and LP signals from the beginning until September 2003: The VLP signal gradually disappeared and the LP signal characterized by decaying harmonic oscillations became dominant. Assuming possible source geometries, we applied a waveform inversion method to the observed waveforms of the largest VLP event. Our inversion and particle motion analyses point to volumetric changes of a sub-vertical crack as the VLP source, which is located at a depth of 2–3 km beneath the northeastern flank. The spectral analysis of the decaying harmonic oscillations of LP events shows frequencies between 2.0 and 3.5 Hz, with quality factors significantly above 100. The increased VT activity and deformation data suggest an intrusion of magma beneath the volcano. A release of gases with small magma particles may have repetitively occurred due to the pressurization, which was caused by sustained bubble growth at the magma ceiling. The released particle-laden gases opened a crack above the magma system and triggered the resonance of the crack. We interpret the VLP and LP events as the gas-release process and the resonance of the crack, respectively. © 2007 Elsevier B.V. All rights reserved.

1. Introduction Cotopaxi Volcano (elevation, 5876 m) located in the Eastern Cordillera of the Ecuadorian Andes is one of the highest glacier-clad active volcanoes in the world. Cotopaxi experienced bi-modal eruptive activity during late Holocene. While recent eruptive activity was characterized by andesitic eruptions, rhyolitic eruptions occurred about every 2000 years (Hall and Mothes, 1995). According to historical archives, after the Spanish arrival in Ecuador, major eruptive episodes of Cotopaxi took place in 1534, 1742–1744, 1766–1768, and 1877. These eruptions were accompanied by pyroclastic flows, ash falls, and lahars that devastated the surrounding areas (e.g., Mothes et al., 1998). Cotopaxi is located 60 km south of Ecuador's capital city of Quito (pop. 1,200,000) and 40 km north of Latacunga City (pop. 120,000) (Fig. 1a). These major cities and other towns and villages in the surrounding area could be affected by future Cotopaxi eruption. Barberi et al. (1995) estimated the average recurrence interval of eruptive episodes of Cotopaxi as 117 years based on historical and stratigraphic records over the last 2000 years.

⁎ Corresponding author. E-mail address: [email protected] (H. Kumagai). 0377-0273/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jvolgeores.2007.07.019

Cotopaxi Volcano has been monitored by the Instituto Geofísico (IG), Escuela Politécnica Nacional of Ecuador since 1977 when a 1 Hz seismometer was installed on the northwestern flank of the volcano. A telemetered network of four permanent seismic stations featuring 1 Hz seismometers was deployed on the volcano in 1989. In response to increased seismic activity of Cotopaxi in 2001, the network was strengthened by deploying three additional permanent stations featuring 1 Hz seismometers and one temporal station featuring a seismometer with bandwith of 0.2–40 Hz (Fig. 1b). Over the years Cotopaxi seismic network has recorded long-period (LP) events, tremor, and volcano-tectonic (VT) earthquakes (Ruiz et al., 1998; Troncoso, 2004) as well as icequakes in the summit glaciers (Metaxian et al., 2003). Renewed seismic activity of Cotopaxi began in January 2001 with an increased number of LP events showing non-harmonic oscillations, which was followed by a swarm of VT earthquakes in November 2001 (Fig. 2a). In late June 2002, a different type of seismic activity began beneath the volcano. The events observed in this activity have a broad spectral peak around 2 s, and accompany LP signals showing nonharmonic oscillations in the band 0.5–1 s. The period of 2 s lies at the boundary between long-period (0.2–2 s) and very-long-period (VLP) (2–100 s) ranges, according to the classification scheme used by Chouet (1996a) and many other studies (e.g., Ohminato et al., 1998;

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Fig. 1. (a) Location of Cotopaxi Volcano in Ecuador. (b) Topographic contours of Cotopaxi Volcano showing the locations of the seismic stations. Stations employed in this study are shown as big solid squares, while the stations not used are in small solid squares. The distant station (PITA) in the north of volcano is not shown here. The big and small stars, respectively, show the location of the base and prism used to obtain the Electronic Distance Measurements (EDM).

Kumagai and Chouet, 2000; Kumagai et al., 2002b; Hill et al., 2002; Arciniega-Ceballos et al., 2003). An impulsive signature is not the general oscillating character of LP events, but is common to VLP events observed at various active volcanoes. Therefore, we refer to the impulsive waveforms in these events as VLP signals. We note that both the VLP and LP signals observed at Cotopaxi displayed temporal changes from the beginning of its activity until September 2003: The VLP signal gradually disappeared and the LP signal characterized by decaying harmonic oscillations became dominant. LP and VLP events have been widely observed at active volcanoes. LP events are interpreted as acoustic vibrations of fluid-filled resonators in magmatic and hydrothermal systems (e.g., Chouet, 1996a; Neuberg, 2000). Despite that various geometries were proposed for the LP source, source mechanisms estimated by waveform inversions of LP signals are consistent with a crack geometry at the source of LP events (Kumagai et al., 2002a; Nakano et al., 2003; Kumagai et al., 2005; Nakano and Kumagai, 2005a). Waveform simulations based on the crack model (Chouet, 1986, 1988, 1992) suggest that various types of fluids are involved in a crack such as hydrothermal fluids (Kumagai et al., 2002b, 2005; Nakano and Kumagai, 2005c) and ash–gas mixtures (Gil Cruz and Chouet, 1997; Molina et al., 2004). Broadband seismic observations have revealed that VLP signals are commonly observed at active volcanoes such as Aso, Japan (Kawakatsu et al., 1994; Kaneshima et al., 1996; Yamamoto et al., 1999; Kawakatsu et al., 2000; Legrand et al., 2000), Stromboli, Italy (Neuberg et al., 1994; Chouet et al., 1999, 2003), Kilauea, Hawaii (Dawson et al., 1998; Ohminato et al., 1998; Almendros et al., 2002), and others (Kawakatsu et al., 1992; Rowe et al., 1998; ArciniegaCeballos et al., 1999; Nishimura et al., 2000; Kumagai et al., 2001; Yamamoto et al., 2002; Kumagai et al., 2003; Arciniega-Ceballos et al., 2003; Kobayashi et al., 2003; Aster et al., 2003; Chouet et al., 2005; Kumagai, 2006). These studies suggest that VLP signals are primarily

linked to mass transport processes in magmatic and/or hydrothermal systems. VLP events accompanying LP signals were observed at Kilauea, Hawaii (Dawson et al., 1998), Popocatepetl, Mexico (Arciniega-Ceballos et al., 1999, 2003), and Stromboli, Italy (Chouet et al., 2003). However, a temporal transition from VLP to LP signals as observed at Cotopaxi has not been reported in previous studies. This transition may be a key issue for our improved understanding of the generation and evolution processes of VLP and LP events. In this paper, we present a detailed description of the VLP and LP signals observed at Cotopaxi Volcano, on which spectral analyses were performed to identify the temporal evolution of these signals. Since our data for the VLP signals were limited to a single three-component station, an ordinary waveform inversion was not applicable. We therefore used the waveform inversion method proposed by Nakano and Kumagai (2005a, 2005b). This method assumes possible source geometries to reduce the number of free parameters in a waveform inversion so that we can constrain the source mechanism of the VLP event with the limited waveform data. We discuss source processes associated with the VLP and LP events and their implications. 2. VLP and LP events 2.1. Waveform features We used the waveform data recorded at station VC2 (3.5 km from the summit) featuring a Lennartz LE-3D/5s seismometer (bandwidth of 0.2–40 Hz and sensitivity of 400 V/(m/s)), which was temporarily operated in June–July 2002 (Fig. 1b). The continuous waveform data from the Lennartz seismometer were recorded by a Lennartz MARSlite 20-bit data logger with a sampling frequency of 31.25 Hz. We also used the waveform data recorded at station COV1 featuring a Mark Products L-4C-3D three-component seismometer with a natural

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Fig. 2. Seismic activity of Cotopaxi during the period from January 1989 through December 2003. (a) The monthly number of LP events and VT earthquakes. LP events include those showing both non-harmonic and decaying harmonic oscillations. (b) The daily number of LP events and VLP/LP events in the period between April 2002 and January 2003. LP events are only those showing decaying harmonic oscillations.

frequency of 1 Hz. This station is closest to the summit crater of Cotopaxi Volcano (1.68 km from the summit), and provided the best quality waveform data in the permanent seismic network (Fig. 1b). The waveform data from COV1 were transmitted by an analogue telemetry system to the central office in Quito, and digitized by an 8bit AD converter in a sampling frequency of 100 Hz. Fig. 3 displays a vertical velocity seismogram, time–frequency diagram (spectrogram), and amplitude spectrum observed at VC2 for a seismic event recorded at 0:35 on 26 June 2002 (Greenwich Meridian Time: GMT). The waveform data were corrected for instrumental response and high-pass filtered at 0.1 Hz. The seismogram shows an impulsive waveform for a brief time at the event onset, which is followed by non-harmonic oscillations. The impulsive waveform is characterized by a broad spectral peak around 0.5 Hz and the nonharmonic oscillations have spectral peaks in the band 1–2 Hz. We refer to the onset and coda portions as VLP and LP signals, respectively, as explained in the previous section. These events were frequently observed in the period between 24 June and 3 July 2002. Fig. 4

illustrates vertical velocity seismograms bandpassed between 0.2 and 1 Hz for selected VLP events observed at VC2 during this period. As seen in this figure, the VLP signals show slight temporal changes, suggesting repetitive and transient processes at the source of the VLP events. We used the waveform data from the permanent station COV1 to identify a long-term trend in the VLP/LP activity, although the VLP signals of the dominant period around 2 s were not fully recorded by the 1-s short-period seismometer at this station. We performed a time-frequency analysis using triggered LP waveforms from COV1. Fig. 5 plots normalized amplitude spectra for individual LP waveforms as a function of time between June and September 2002. We can find relatively large spectrum amplitudes at around 1 Hz during the period between late June and early July 2002. These peaks correspond to the VLP signals. Broad spectral peaks occupying the 2–3 Hz band are seen from late June to September 2002. A few spectral peaks in the 3–5 Hz band are visible during late July, and a spectral peak at 3.5 Hz is prominent in the middle of September 2002.

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Fig. 3. (a) Vertical velocity seismogram of the largest VLP event recorded at station VC2. The trace is high-pass filtered at 0.1 Hz. (b) A time-frequency diagram (spectrogram) of the waveform shown in (a), which is calculated by the discrete Fourier transform with a 5-s time window sliding in 0.2 s time steps. (c) An amplitude spectrum of the waveform shown in (a).

Fig. 6 plots observed waveforms at COV1 for selected VLP/LP signals. We note that the waveform in Fig. 3 and the first trace in Fig. 6 originated from the same event. Comparison of these two waveforms indicates that the VLP signal also appears as a low-frequency oscillation for a brief time interval at the event onset in the shortperiod waveform. Temporal changes of both the VLP and LP signals are evident in Fig. 6. At the beginning of the VLP/LP activity, the VLP signal was dominant and accompanied by the LP signal showing nonharmonic oscillations. Later a harmonic signature gradually appeared in the LP signal and became dominant over the VLP signal. After November 2002, we observed the LP events showing decaying harmonic oscillations without VLP signatures at the event onsets, which were detected until September 2003 (Fig. 2b). 2.2. Complex frequencies of LP events We used the Sompi method (Kumazawa et al., 1990) to estimate the complex frequencies (frequency and quality factor, Q) of the LP events. Sompi is a spectral analysis method based on an autoregressive (AR) model. We selected the LP signals displaying decaying harmonic oscillations observed from 22 September 2002 to 19 September 2003. The Sompi method was applied to these signals following the procedure described in Nakano et al. (1998) and Kumagai and Chouet (2000). The frequency, Q, and amplitude at the event onset determined by Sompi as well as the daily number of events are plotted as a function of time in Fig. 7. A swarm of LP events was observed during the period from 22 September to 6 October 2002, in which the daily number of LP events reached 9. The frequency and Q determined for the LP events during the LP swarm activity are also shown in Fig. 8. The frequency gradually decreased from 3.5 to 3.0 Hz, while Q showed wide scatters in the values larger than 100. Following the swarm activity until September 2003, the LP events intermittently

occurred with a decreasing trend in the number of events (Fig. 7). During this period, the frequency remained roughly constant at 2.5– 2.8 Hz except for an LP event that occurred on 7 May 2003, which had a frequency of 2.0 Hz (Fig. 7). Q remained roughly constant at around 100 after the swarm activity (Fig. 7). The amplitudes of the LP signals were relatively small during the swarm activity, and large amplitude signals were observed in November 2002 and February 2003 (Fig. 7). The complex frequency of an LP event is determined by the characteristic properties of a resonator (the sizes of the resonator, acoustic velocity and density of a fluid in the resonator, and P and S wave velocities and density of the surrounding rock matrix). The smooth trend of the observed frequency, therefore, suggests that the characteristic properties are almost identical among these LP events. This feature can be simply explained if we assume that the LP events originated from a single resonator. The scatter of Q may be attributed to errors and instabilities that stem from fitting exponentially decaying oscillations in the spectral analysis. 3. Waveform analyses of VLP events 3.1. Particle motions We performed particle motion analyses for the VLP signals to obtain constraints on the source location. We selected 19 VLP events during the period from 24 June to 30 June 2002. These signals were recorded at both VC2 and COV1 with fairly good signal-to-noise ratios. The waveform data from other stations were contaminated by noise due to the relatively large distances from the source of these events and local site conditions. Particle motions were estimated from the onset portions of the velocity seismograms at VC2 and COV1 in the 0.2–1 Hz and 0.8–1.2 Hz bands, respectively. Fig. 9a illustrates particle motion trajectories for the impulsive onset of the largest VLP event

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Fig. 4. Vertical velocity seismograms of the VLP events recorded at station VC2. These seismograms are bandpassed between 0.2 and 1 Hz. Amplitudes (m/s) are indicated by vertical bars at the left of the seismograms.

that occurred at 0:35 on 26 June 2002 (Figs. 3 and 6). The particle motions at both VC2 and COV1 indicate elliptical trajectories in both vertical and horizontal planes. The particle motions in the vertical– radial planes at both VC2 and COV1 show nearly vertical elliptical trajectories, which may be caused by the interaction between P and SV waves. The horizontal particle motions at VC2 and COV1 show narrow trajectories pointing to southwest and southeast, respectively. Similar elliptical trajectories were obtained for other VLP signals. The main axes of particle motion trajectories for individual signals and their averages are indicated by thin and thick arrows, respectively (Fig. 9b). The horizontal particle motions at VC2 and COV1 also point to southwest and southeast, respectively. These features suggest a source located beneath the north to northeastern flank of the volcano for the VLP events, although an estimation of the source depth from particle motion analyses may not be possible due to the interaction between P and SV waves.

source mechanism and location with limited waveform data. We considered horizontal and vertical cracks and a vertical pipe as possible geometries at the source of the VLP events. We use Cartesian coordinates x, y, and z corresponding to E, N, and up, respectively, throughout this study. We consider a tensile crack opening/closing in the direction Ym described by the angles θ and ϕ. θ is the angle of Ym measured from the up (z) direction, while ϕ is the angle of horizontal projection of Ym measured from the east (x) direction (Fig. 10). The moment tensor for the crack is given by (e.g., Chouet, 1996b) 0 1 λ=μ þ 2sin2 θcos2 / 2sin2 θsin/cos/ 2sinθcosθcos/ Y 2 2 2 @ M ¼ M0 2sin θsin/cos/ λ=μ þ 2sin θsin / 2sinθcosθsin/ A; ð1Þ 2sinθcosθcos/ 2sinθcosθsin/ λ=μ þ 2cos2 θ

3.2. Inversion method

where λ and μ are Lame's constants, M0 = μΔV, and ΔV represents the incremental volume change of the crack. If we assume λ = μ, the moment tensor for a vertical crack (θ = π / 2) is given by

We used the waveform inversion method proposed by Nakano and Kumagai (2005a, 2005b) to quantify the VLP source. This method assumes possible source geometries to reduce the number of free parameters in a waveform inversion, permitting us to quantify the

0 1 1 þ 2cos2 / 2sin/cos/ 0 Y M ¼ M0 @ 2sin/cos/ 1 þ 2sin2 / 0 A; 0 0 1

ð2Þ

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and the tensor for a horizontal crack (θ = 0) is given by 0 1 1 0 0 Y @ M ¼ M0 0 1 0 A: 0 0 3

ð3Þ

Assuming λ = μ, the moment tensor for a vertical pipe is defined as 0 2 0 Y M ¼ M0 @ 0 2 0 0

1 0 0 A: 1

ð4Þ

Thus, for a horizontal crack and vertical pipe, M0 is the only free parameter, while M0 and ϕ are the parameters for a vertical crack. Following the method of Ohminato et al. (1998) and Nakano et al. (2003), we estimate source-time functions of the moment tensor components for the individual geometries as a superposition of successive sub-events generated with an elementary source-time function. A grid search is conducted in space for a horizontal crack and vertical pipe. For a vertical crack, a search is conducted in both ϕ and space. We minimize the residual defined as PNt PNs−1 Δ¼

2 j¼0 ½ui ðjΔtÞ−wi ðjΔtÞ ; PNt PNs−1 2 i¼1 j¼0 ½ui ðjΔtÞ

i¼1

ð5Þ

where ui and wi are the i-th traces of the observed and synthetic seismograms, respectively, and Δt is the sampling interval. Using Gik (jΔt) to denote the spatial derivative of Green's function, the synthesized waveform wi(jΔt) is given as wi ðjΔtÞ ¼

6 X X Ns −1 k¼1

l¼0

M0 ðlΔtÞmk Gik ðjΔt−lΔtÞΔt:

ð6Þ

Here mk represents the six independent elements of the moment tensor for a crack or pipe given in Eqs. (1)–(4) and M0(jΔt) is the

source-time function, which is expressed by a superposition of Nr successive sub-events with elementary source-time function S(jΔt) and time interval Δτ as M0 ðjΔtÞ ¼

XNr −1 n¼0

CðnΔτÞSðjΔt−nΔτÞ:

ð7Þ

Here C(nΔτ) represents Nr coefficients, which are determined by the iterative method proposed by Nakano et al. (2003). Since the number of free parameters is different between the possible source geometries, Akaike's Information Criterion (AIC) (Akaike, 1974) may be used to evaluate the models. AIC is defined as AIC ¼ Nt Ns ln Δ þ 2Nf ;

ð8Þ

where Nt, Ns, and Nf are the number of waveforms, the number of samples in each waveform, and the number of free parameters, respectively. Here, Nf = Nr for a horizontal crack and vertical pipe and Nf = Nr + 1 for a vertical crack (Nakano and Kumagai, 2005a). 3.3. Waveform inversion We calculated Green's functions using the finite-difference method of Ohminato and Chouet (1997). The computational domain was defined with lateral dimensions of 10 by 10 km covering the volcanic edifice and with a vertical extent of 6 km. Our calculations were performed over a uniform grid of 40 m, yielding a 3-D mesh with 251 × 251 × 151 nodes. Our model included the topography of the volcano, and assumed a homogeneous medium with a compressional wave velocity of 3500 m/s, a shear wave velocity of 2000 m/s, and a density of 2650 kg/m3. Since the short-period seismograms at COV1 lacked full recording of the VLP signals, our inversion relied only on three-component waveform data recorded at VC2. We used the waveform data for the largest VLP event (Fig. 3) yielding the best signal-to-noise ratio. After

Fig. 5. Plots of normalized amplitude spectra estimated for 1045 triggered LP waveforms at COV1 as a function of time between June and September 2002. Colors indicate velocity spectrum amplitudes normalized in individual LP events according to the scale at the bottom right.

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Fig. 6. Vertical short-period velocity waveforms of VLP/LP events observed at station COV1. Vertical bars at the left of the seismograms indicate an amplitude of 5 × 10− 6 m/s. The event times are in Greenwich Meridian Time (GMT).

instrumental correction, displacement seismograms were obtained by integration of the velocity seismograms and then bandpassed between 0.2 and 1 Hz using a two-pole Butterworth filter. We used a one-cycle cosine function as the elementary source-time function,  SðtÞ ¼

½1−cosð2πt=tp Þ=2; 0VtVtp ; 0; tNtp ;

ð9Þ

with the characteristic period tp = 0.3 s. This function has been widely used in waveform inversions of VLP and LP events (Kumagai et al.,

2002a, 2003; Chouet et al., 2003; Kumagai et al., 2005; Nakano and Kumagai, 2005a), since a superposition of one-cycle cosine functions can flexibly represent impulsive as well as oscillatory functions. Our grid size of 40 m for the finite-difference calculations satisfied the criterion of minimum number of grids per wavelength established by Ohminato and Chouet (1997) for the one-cycle cosine function with tp = 0.3 s. We re-sampled the observed waveforms, and used Δt = 0.02 s for both Green's functions and observed waveforms. Fig. 11 illustrates contour plots of spatial distributions of the residuals in the inversion assuming a vertical crack. We plot the

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Fig. 7. Results of the Sompi analysis of the LP events showing decaying harmonic oscillations observed at station COV1: (a) The daily number of events, (b) amplitude at the event onset, (c) frequency, (d) and Q factor plotted as a function of time between September 2002 and October 2003. The frequency and Q in shaded areas are also plotted in Fig. 8.

residual distributions in four different layers from 1.0 to 4.0 km above sea level. In each layer, a solid square and triangle denote the locations of station VC2 and the summit crater, respectively. Source points for the grid search are indicated by small solid circles, which are

distributed in a region covering the summit region. We conducted a grid search with respect to ϕ in an interval of 20°. We can find a region characterized by a small residual of ∼ 0.4 beneath the northeastern flank of the volcano at a depth of 3 km above sea level (Fig. 11b). Small

Fig. 8. Temporal variations in the frequency and Q determined for the LP events during the swarm activity from 22 September 2002 through 7 October 2002 (see also Fig. 7).

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Fig. 9. Particle motions for the VLP events obtained from the onset portions of the velocity seismograms at VC2 and COV1 in the 0.2–1 Hz and 0.8–1.2 Hz bands, respectively: (a) Particle motion trajectories for the largest VLP event recorded on June 26, 2002 00:35 GMT. The trajectories are plotted at the corresponding station locations (left) and in the horizontal and radial–vertical planes (right). (b) The main axes of particle motion trajectories for 19 VLP events during the period from 24 June to 30 June 2002. Thin and thick arrows indicate the main axes for the individual events and their averages, respectively. The radial direction is positive outward from the summit.

residual regions are also seen in a similar location at a depth of 2 km (Fig. 11c) and in the eastern flank at a depth of 1 km (Fig. 11d). The contour plots of spatial distributions of the residuals in the inversion assuming a horizontal crack are shown in Fig. 12. We can observe large residual regions characterized by a residual larger than 0.7 beneath the southeastern flank in all the layers, and the residuals decrease toward the northeastern and western directions. Small residual regions, as found in the inversion assuming a vertical crack, do not exist in these residual distributions. The inversion assuming a vertical pipe yielded residuals greater than 0.6 at most of the source points. We also did not find small residual regions in the residual distributions for a vertical pipe, although these are not shown here. We obtained Δ = 0.369 and AIC = − 2489 (Nt = 3, Ns = 1000, Nf = 251, Nr = 250, and Δτ = 0.08 s) for the inversion assuming a vertical crack at the position indicated by an arrow in Fig. 11c, which lies in the small residual region at a depth of 2 km above sea level. We found that this value of AIC is smaller than those obtained at all the source points for the inversions assuming a horizontal crack and vertical pipe. Therefore, we can reasonably adopt a vertical crack, which is the most appropriate geometry for the VLP source among the possible

geometries. However, the residuals in the small residual regions decrease as the depth increases, and the regions move toward the southeast with increasing depth (see Fig. 11). These features indicate that the source location is not well constrained in our inversion based on a single three-component station. Since our particle motion analyses suggest that the source is beneath the north to northeastern flank of the volcano, it is highly possible that the source position is located in the small residual regions beneath the northeastern flank at a depth of 2–3 km above sea level (Fig. 11b and c). We conducted a detailed search in θ and ϕ at the possible source position indicated by an arrow in Fig. 11c. A search was conducted with respect to θ and ϕ in an interval of 10°. We obtained θ = 70° and ϕ = 170° with Δ = 0.2866 and AIC = − 3245 (Nt = 3, Ns = 1000, Nf = 252, Nr = 250, and Δτ = 0.08 s). These represent a sub-vertical crack extending in a north–south direction. The source-time functions of six moment tensor components for the sub-vertical crack and the corresponding waveform matches are shown in Figs. 13 and 14, respectively. Solid and dashed lines in Fig. 14 represent observed and synthetic displacement seismograms, respectively. The observed features are fairly well reproduced by the synthetic waveforms. The

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Fig. 10. Source coordinates and geometries of a crack (a) and pipe (b).

source-time functions show initial inflation, followed by deflation and subsequent re-inflation with an oscillatory signature. We note that similar solutions were stably obtained for different source locations near this position. 4. Discussion 4.1. The VLP source We used the method of Nakano and Kumagai (2005a) to estimate the source mechanism and location of the VLP event using the waveform data from station VC2. The numerical tests of Nakano and Kumagai (2005a) indicate that waveform data from at least 2 threecomponent stations surrounding the source are required to accurately estimate the source mechanism and location. This condition was not satisfied in our case, and therefore it was not possible to locate the source solely based on the inversion. On the other hand, the particle motion analyses of the VLP signals at VC2 as well as their corresponding waveforms at COV1 indicated that their trajectories point to a position beneath the north to northeastern flank of the volcano (Fig. 9a). We therefore concluded that it is highly possible that the source is located in the small residual regions beneath the northeastern flank at a depth of 2–3 km above sea level, which only appeared in the inversion assuming a vertical crack. Our detailed search in θ and ϕ at the possible source location indicated that a subvertical crack yielded the best fits to the observed seismograms. Since particle motions of other VLP events are similar to those of the largest event (Fig. 9), the estimated source may have repetitively triggered other VLP events. A sub-vertical crack at such depth is suggestive of a magmatic dike system. The VLP/LP activity was preceded by a swarm of VT earthquakes (Fig. 2a). It is well known that magma intrusion is associated with VT earthquake swarms (e.g., Einarsson and Brandsdottir, 1980; Savage and Cockerham, 1984; Okada and Yamamoto,

1991). VT earthquakes occur due to the brittle response of the volcanic rock governed by the stress transferred by magmatic fluid movements (e.g., Toda et al., 2002). Detailed hypocenter locations of VT earthquakes during swarms point to vertical dike-like structures (e.g., Rubin et al., 1998; Hayashi and Morita, 2003). Thus, it is very probable that the VT earthquake swarm in the renewed seismic activity of Cotopaxi was triggered by the intrusion of a magmatic dike. Further supporting evidence for magma intrusion is suggested from deformation data. Since 1990 the IG has made repeated geodetic baseline measurements of 5 sectors of Cotopaxi's flanks by using an electronic distance measurement (EDM, Geodimeter 114), which employs an infrared light source. The instrument is placed over a fixed point, out from volcano's base (Loma) and the target which receives the infrared beam is a reflecting prism permanently anchored, in this case, to a massive lava surface at about 4500 m elevation (Luis) (Fig. 1b). The length between the two points is a slope distance and is 6038 m. Nominal precision of the instrument allows an accuracy of ± 11 mm for each measurement taken, given optimal climatic conditions. During 1991–2004, the instrument, operator, and data-taking procedures remained unchanged. Although other EDM baselines are measured on the W, E, N and SE flanks of the cone, only the data from measurements on the NE sector have shown notable variations in slope distance of about 10 cm. However, the patterns of the other lines slightly mirror the pattern shown in Fig. 15, showing a change in line length starting around 2002. On the NE flank's line the strain is greater than 10− 5 and the slope distance between the fixed point and the prism is contracting (Fig. 15). We interpret the linelength changes as being provoked by an inflationary source beneath the NE flank, which took place in or earlier than 2002, when there was also a coincident very significant jump in the number of VT earthquakes. Although it is not possible to estimate the geometry and the precise location of the deformation source from the limited data, the contraction of the EDM lines followed by the VT swarm suggests a magma intrusion beneath this flank. 4.2. The LP source The individual VLP events were accompanied by the LP signals, which showed temporal changes from non-harmonic oscillations to a signature characterized by decaying harmonic oscillations. The waveform inversion was not applicable to the LP waveforms with the dominant frequencies at around 3 Hz, since such high-frequency seismograms could be highly affected by local paths and/or site effects associated with structural heterogeneities. However, it may be reasonable to assume the resonance of a crack as the source of the LP events at Cotopaxi in view of the results from recent waveform inversions of LP events (Kumagai et al., 2002a; Nakano et al., 2003; Kumagai et al., 2005; Nakano and Kumagai, 2005a). Our Sompi analysis of the decaying harmonic oscillations in the LP waveforms showed Q values significantly larger than 100 (Figs. 7 and 8). According to the acoustic properties of a crack containing various types of magmatic and hydrothermal fluids (Kumagai and Chouet, 2000), such high Q values may only be achieved by an ash–gas or water droplet–gas mixture in a crack. The close association of the LP signals with the VLP events suggests that the LP source was intimately linked to the VLP source. A water droplet can not exist at the possible VLP source depth at around 2–3 km above sea level (2–3 km below the flank), since the critical pressure and temperature of water are 22 MPa (roughly 1 km depth from a surface) and 646 K, respectively. Therefore, an ash–gas mixture is the most possible fluid in a crack at the source of the LP events. 4.3. Proposed model for source processes of VLP and LP events The temporal changes observed in both the VLP and LP signals suggest repetitive and transient source processes. Synthesizing our

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Fig. 11. Contour plots of spatial distributions of the residuals obtained from the waveform inversion assuming a vertical crack in four different layers. The depth of each layer above sea level is indicated at the top of each plot. In each layer, a solid square and triangle denote the locations of the station VC2 and the summit crater, respectively. Source points for the grid search are indicated by small solid circles. Small residual regions in the layers of 1000, 2000, and 3000 m are indicated by open circles with dashed lines.

results obtained above, we interpret the overall VLP/LP activity as follows. Magma intrusion began beneath Cotopaxi in November 2001, and triggered a swarm of VT earthquakes. Magma in a vertical dike intruded into the shallower edifice up to a depth of 2–3 km above sea level beneath the northeastern flank of the volcano (Fig. 16a). Supersaturated conditions were reached in the intruded magma. The pressure inside the magma increased through decompression-induced degassing and vesicle growth, while the outer part of the magma solidified due to chilling from the surrounding rock (Fig. 16b). As stress due to the pressurization reached the shear strength of the magma, a brittle fracture occurred at the top of the magma body, releasing small magma particles with gases. The released particle-laden gas opened a crack in the rock matrix just above the magma system (Fig. 16c). A volumetric expansion is expected during the fracturing in the magma and opening of a crack in the rock matrix. The pressure inside the magma decreased in response to the release of particle-laden gas. The pressure drop in the magma, however, could be recovered due to the growth of tiny bubbles contained in the magma (Nishimura, 2004). Viscous deformation of the magma led to rapid welding and healing of the fracture at the top of the magma body (Tuffen et al., 2003; Tuffen and Dingwell, 2005). We interpret that the initial inflation phase in the source-time functions estimated for the VLP event (Fig. 13) represents the volumetric expansion during the fracturing in the magma and opening of the crack. The following deflation and re-

inflation phases reflect the pressure drop due to the gas release and recovery due to the bubble growth in the magma, respectively. The LP events can be interpreted as the resonance of the crack above the magma system. This process repeated itself until saturation conditions were reached in the magma. At the beginning of the VLP/LP activity, the LP source region above the magma system consisted of a dendritic system of cracks so that the LP waveforms displayed complex non-harmonic oscillations (Fig. 16c). Repetitive injections of particle-laden gas gradually developed a single crack in the source region and generated the LP signals showing simple harmonic oscillations (Fig. 16d). The fracture served as a pathway for particle-laden gas at the top of the magma body, and was more easily opened as the fracture was repeatedly used. Consequently, less pressurization in the magma was required to release the particleladen gas and trigger the LP event. This may explain that the VLP signature gradually disappeared in the observed seismograms. According to Tuffen et al. (2003), fracture occurs in magma if ε′ η N τs, where ε′, η, and τs are the shear strain rate, magma viscosity, and shear strength of magma, respectively. Magma viscosity must be in the range 109–1014 Pa s for fracture to occur, if we assume typical magma shear strength of 106–107 Pa and a plausible range of strain rates between 10− 2 and 10− 6 s− 1 (Tuffen et al., 2003). The possible magma beneath Cotopaxi is low-SiO2 andesite (basaltic andesite to andesite), and its viscosity may be less than 104 Pa s. Magma viscosity depends on temperature, and fracture may have occurred at the top of

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Fig. 12. Contour plots of spatial distributions of the residuals obtained from waveform inversion assuming a horizontal crack in four different layers.

the magma body, where the viscosity range 109–1014 Pa s may have been reached by effective cooling. Henry's law (e.g., Sparks, 1978) indicates that bubble formation occurs in andesitic magma at the possible source depth (a depth of 2– 3 km beneath the flank), if magma contains more than 2.1–3.6 wt.% of water. Here, we assume Henry's constant between 9.0 × 10− 12 and 1.6 × 10− 11 Pa− 1 (Nishimura, 2004). Prousevitch et al. (1993) estimated the time scale of bubble growth in basaltic magma based on the dynamical model of diffusive bubble growth. Their results indicate that the time scale is mainly controlled by ambient pressure, diffusivity, and initial volatile content. Note that viscosity does not control bubble growth dynamics in low-viscosity magma (b 104 Pa s). Recently, Shimomura et al. (2006) showed that the number density of gas bubbles also controls the time scale of bubble growth. The sourcetime functions of the VLP event indicate that the time duration of the re-inflation phase is 1–2 s (Fig. 13). We assume that the bubble growth associated with the VLP signals may have occurred in central, hot, lowviscosity regions (b 104 Pa s) in the magma. Then, if the magma contains more volatile content than 4 wt.% water and/or has a smaller diffusivity coefficient than 10− 8 m2/s, the observed time duration of 1– 2 s can be consistent with the time scale of bubble growth in the magma at the possible source depth. LP events showing decaying harmonic oscillations have been widely observed at various volcanoes such as Kusatsu-Shirane, Japan (Fujita et al., 1995; Nakano et al., 1998; Kumagai et al., 2002a, 2002b; Nakano et al., 2003), Asama, Japan (Fujita and Ida, 1999; Aoyama and Takeo, 2001), Galeras, Colombia (Nárvaez et al., 1997; Gómez and

Fig. 13. Source-time functions of moment tensor components for the sub-vertical crack (θ = 70° and ϕ = 170°) obtained from the waveform inversion of the VLP event at the possible source location indicated by an arrow in Fig. 11c.

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Tuffen and Dingwell, 2005). On the other hand, hydrothermal origins are proposed for LP events at Kusatsu-Shirane, Japan (e.g., Fujita et al., 1995; Nakano et al., 1998; Kumagai et al., 2002a, 2002b; Nakano et al., 2003 Nakano and Kumagai, 2005c) and Kilauea, Hawaii (Saccorotti et al., 2001; Kumagai et al., 2005). These LP events may have different source mechanisms from the image obtained here, indicating that various processes are involved in the generation of LP events. 5. Conclusions

Fig. 14. Waveform match obtained from the waveform inversion of the VLP event. Solid and dotted lines represent observed and synthetic displacement waveforms, respectively.

Torres, 1997, Gómez et al., 1999; Seidl et al., 1999), Kilauea, Hawaii (Saccorotti et al., 2001; Kumagai et al., 2005), Kelut, Indonesia (Lesage and Surono, 1995), and Tungurahua, Ecuador (Molina et al., 2004). Although the observed data of the VLP/LP events at Cotopaxi were limited, our quantitative analyses provided a comprehensive image of the source processes, including the evolution processes of the VLP/LP events. Our image is consistent with the source process models proposed for LP events observed at Galeras, Colombia (Gil Cruz and Chouet, 1997) and Tungurahua, Ecuador (Molina et al., 2004) as well as the triggering mechanism model for LP events (Tuffen et al., 2003;

We observed VLP events accompanying LP signals associated with renewed seismic activity of Cotopaxi. We observed temporal changes of both the VLP and LP signals, in which a harmonic signature gradually appeared in the LP signal and became dominant over the VLP signal. The Sompi spectral analysis of decaying harmonic oscillations in the tails of the LP waveforms showed frequencies between 3.0 and 3.5 Hz, with Q values significantly larger than 100. We applied the inversion method of Nakano and Kumagai (2005a) to constrain the source mechanism and the location of the largest VLP event. Our inversion, together with particle motion analyses of the VLP signals, indicated that the volumetric changes of a sub-vertical crack located beneath the northeastern flank of the volcano (at a depth of 2–3 km above sea level) is the most probable source of the VLP event. The sub-vertical crack may represent an intruded magmatic dike, manifested by the increased VT activity and deformation data. A release of gases with small magma particles may have occurred due to the pressurization, which was caused by sustained bubble growth at the magma ceiling. The pressure inside the magma decreased in response to the release of particle-laden gas. The pressure drop in the magma recovered due to the growth of tiny bubbles contained in the magma. We interpret the VLP signals as the volumetric changes associated with the release of particle-laden gas and subsequent pressure drop and recovery in the magma. The LP events can be interpreted as the resonance of a crack above the magma system, which was triggered by the release of particle-laden gas. At the beginning of the VLP/LP activity, the LP source region above the magma system consisted of a dendritic system of cracks so that the LP waveforms displayed complex non-harmonic oscillations. Repetitive injections of particle-laden gas gradually formed a single crack in the

Fig. 15. Temporal change in the slope distance between Loma and Luis (Fig. 1b) measured by an electronic distance measurement instrument (EDM). The length between the two points is 6.038 km.

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Fig. 16. Conceptual model for source processes of the VLP and LP events observed at Cotopaxi Volcano. See text for details.

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