This paper presents a simple method to distinguish infrasonic signals from wind noise using a cross-correlation function of signals from a microphone and a collocated seismometer. The method makes use of a particular feature of the cross-correlation function of vertical ground motion generated by infrasound, and the infrasound itself. Contribution of wind noise to the correlation function is effectively suppressed by separating the microphone and the seismometer by several meters because the correlation length of wind noise is much shorter than wavelengths of infrasound. The method is applied to data from two recent eruptions of Asama and Shinmoe-dake volcanoes, Japan, and demonstrates that the method effectively detects not only the main eruptions, but also minor activity generating weak infrasound hardly visible in the wave traces. In addition, the correlation function gives more information about volcanic activity than infrasound alone, because it reflects both features of incident infrasonic and seismic waves. Therefore, a graphical presentation of temporal variation in the cross-correlation function enables one to see qualitative changes of eruptive activity at a glance. This method is particularly useful when available sensors are limited, and will extend the utility of a single microphone and seismometer in monitoring volcanic activity.
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 Infrasonic monitoring methods have been used at various volcanoes and have provided useful information about eruptive activity of the volcanoes. The biggest problem in infrasonic monitoring is wind noise, and great efforts have been made to reduce the noise. Several effective methods have been presented, that include recording with multiple sensors in an array [Ripepe and Marchetti, 2002; Matoza et al., 2007], adequately designed spatial filters consisting of a network of pipes [Alcoverro and Le Pichon, 2005; Hedlin et al., 2003], and selecting an observation site that blocks winds such as a densely forested area [Garcés et al., 2003]. Advances in measurement and data analysis have made it possible to detect volcanic infrasound at up to thousands of kilometers from the source [Evers and Haak, 2005; Matoza et al., 2011]. Nevertheless, observations close to the crater are still important to get high-frequency signals and detailed information about the activity. However, to construct and maintain an array of microphones and a noise-reducing system are not easy. Moreover, for monitoring purposes, real-time data transmission is essential. Only a limited number of volcanoes in the world are equipped with infrasonic monitoring systems close to the crater.
 It is often the case that during an eruption only one or a few microphones are available, typically along with some seismic data. This was the case for the 2009 Asama eruption, as well as the 2011 Shinmoe-dake eruption, when only one of the online stations near the active crater had been equipped with a microphone, which lacked a high-quality noise reduction system. Although a single microphone is useful in observing strong infrasonic signals associated with major explosions, it is generally unable to distinguish the infrasonic pressure signal of interest from noise due to wind and ground shaking. This paper presents a simple method for making use of a collocated seismometer in identifying infrasound using data from a single microphone. The method enables detection of not only the main eruptions, but also the associated activity that generates weak infrasound.
2. Methods and Theoretical Basis
 The pressure change P on the ground surface mainly consists of three components:
where pin is an incident pressure wave, Hwp is the transfer coefficient from the vertical ground velocity due to an incident seismic wave, win, to the pressure change, Np is local pressure change due to wind, and (t, xp) are the time and the observation point, respectively. Similarly, the vertical velocity W observed at xs is:
where Hpw and Hpwnare the coefficient for the pressure wave and the wind pressure to generate vertical ground velocity, respectively. It is shown in the following paragraphs that the cross-correlation function between aboveP(t, xp) and W(t, xs) is dominated by the cross-correlation between the termspin(t, xp) and Hpwpin(t, xs).
 The incident waves at (t, x) are represented by:
where ω is the angular frequency, x is the horizontal axis in the direction of the wave propagation, and ca and csare apparent phase velocities of the pressure and seismic waves, respectively. For simplicity in (3), the seismic wave is represented by surface Rayleigh wave that generates infrasound most effectively, and the only acoustic waves are considered as the pressure wave (i.e., acoustic-gravity and gravity waves are not considered).
 Assuming that the pressure wave from the crater propagates to the observation site along the surface, Hpw in (2) is given by equation 9.186 of Ben-Menahem and Singh  as
where λ and μ are Lame's constants of the ground. These constants of the ground surface can be as small as 109 Pa, and ca = 340 m/s, so that Hpw is on the order of 10−7 m/s/Pa. It is noted that e−iπ/2 in (4) indicates that the vertical ground velocity generated by the pressure wave is delayed by a quarter of a cycle relative to the pressure wave itself.
where ρa is the density of the air. Equation (5) indicates Hwp is larger for the smaller cs as long as cs > ca, which is generally true. The Rayleigh wave speed at volcanoes is about 1000–1500 m/s [Nagaoka et al., 2012], so that ca/cs < 0.3. Then with ρa ∼ 1.2 kg/m3, one may limit Hwp < 450 Pa ⋅ s/m.
 The cross-correlation function ofW(t, xs) to P(t, xp) is denoted by R[τ; W(t, xs), P(t, xp)], where τ is defined as the delay of W to P.It consists of cross-correlation functions of the individual terms in(2) and (1). The pairs of the local noise and the incident waves, which are HpwnNp − pin, Hpwpin − Np, win − Np, and HpwnNp − Hwpwin have no correlation and thus all vanish. The pair of HpwnNp(t, xs) and Np(t, xp) is effectively reduced when the distance between xs and xp is larger than the correlation length of the wind noise. It has been shown that the correlation length of wind noise of a given frequency fis about one-third the eddy size (v/f), where v is the wind speed [Wilson et al., 2007; Shields, 2005], and is much shorter than the infrasonic wavelength of the same frequency (ca/f). The pair of Hpwpin and Hwpwin can be neglected compared with the pair of win and pin, because |HpwHwp| ≪ 1 as estimated above. Then only three terms are left:
Because |xs − xp| is small compared with the seismic and infrasonic wavelengths, the distance and orientation are not considered for these terms and arguments like (t, xs) are omitted in (6). The first term is significant only when the incident seismic and infrasonic waves have a common source. In this case, it has the maximum value at τ < 0 corresponding to the travel time difference between the seismic and infrasonic waves. The second and the third terms are essentially autocorrelation functions and always have a certain value around τ = 0 when the corresponding incident waves exist. The second is an autocorrelation function of win multiplied by a real constant Hwp so that it has the maximum value at τ = 0. In the third term, on the other hand, Hpwpin is behind pin itself due to the coefficient e−iπ/2 in (4). Therefore, it has the maximum value in τ > 0 and a node at τ = 0 as shown in the next paragraph. Making use of the different dependence on τ, one may distinguish which term is dominant in the total cross-correlation function. Moreover, the seismic autocorrelation term is usually dominated by the infrasonic one, according to the above estimates forHpw and Hwp. For example, when the seismic and infrasonic wave amplitudes are on the order of 10−6 m/s and 1 Pa, respectively, |R(τ; win, Hwpwin)| ∼ Hwp|win|2 ∼ 5 × 10−10 and |R(τ; Hpwpin, pin)| ∼ |Hpw||pin|2 ∼ 10−7. Indeed, the seismic autocorrelation term is not recognized in the real volcanic data, as shown in the next section.
 The feature of the infrasonic term R[τ; Hpwpin, pin] is demonstrated in Figure 1, which is calculated as follows. The autocorrelation function of a given function p is:
where S(ω) is the power spectrum of p. Due to the phase delay of π/2 generated by Hpw,
Results of (7) and (8) are shown in Figures 1b and 1c, respectively, for two cases of p having power spectra as in Figure 1a. The correlation functions are normalized by the square of the powers of the input signals. The infrasonic term (Figure 1c) has the highest peak around τ = 1/(4fo), where fo is the characteristic frequency of p (in case 1 of Figure 1a, fo = 1 Hz), the negative peak around τ = − 1/(4fo), and a node at τ= 0. It is oscillatory when the input signal is narrow-banded (case 1), while a pair of positive and negative peaks adjacent toτ = 0 become dominant when the signal is broader (case 2).
 Below, the cross-correlation function of seismic and infrasonic records,W and P, respectively, are investigated in the following way. (1) A 1–7 Hz band-pass filter is applied to both records. This frequency range is chosen to guarantee that the microphone-seismometer distance is larger than the correlation length of wind noise for realistic wind speed and is much shorter than infrasonic wavelength, that isv/3/|xs − xp| < f ≪ ca/|xs − xp|. (2) A normalized cross-correlation function of the filteredW and Pis calculated using a 5-s sliding time window. (3) The cross-correlation function is graphically displayed in thet − τ axis in order to find the pattern associated with incident infrasound.
3. Applications to Volcanic Eruptions
3.1. Asama Volcano, 2009 Eruption
 Asama volcano, central Japan, had an eruption on 2 February 2009 with ejection of ash and ballistics and the formation of a new vent in the main crater. A number of small eruptions and gas emission events followed over a year. A microphone (Bruel and Kajer, 4193-L-004, 0.07–20000 Hz) was installed on 10 August 2008 to a telemetered station at the east edge of the crater, along with a broadband seismometer (CMG-3T, 360 s), and signals were sampled at 100 Hz. All the instruments were installed in the shelter, and the microphone was connected to the atmosphere by a 4-m-long tube.
 The records of infrasonic and seismic signals during the main event are presented in Figures 2a and 2b, and the envelopes of the band-passed signals used for the correlation analysis and the normalized cross-correlation function are shown inFigures 2c and 2d, respectively. The Japan Meteorology Agency (JMA) reported that the eruption began at 1:51, but gas thrust is recognized in video records from 2:01 to 2:13, peaked at 2:08 [Kaneko et al., 2010]. These times are marked by dash lines in Figure 2. The infrasonic amplitude increases at 2:01, and the cross-correlation function clearly shows a pattern similar toFigure 1c, which means the term R(τ; Hpwpin, pin) in (6) is dominant. Increase of the seismic amplitude observed before this moment generates no characteristic pattern (see around 1:51), which means the term R(τ; win, Hwpwin) is not detectable. It also indicates response of the microphone to shaking is negligible. The strong pressure perturbation generating a different cross-correlation pattern (see 1:15–1:30) is wind noise. Because wind direction is not stable, the delay time of the peaks and nodes of the correlation function fluctuate, contrasting the fixed node close toτ = 0 when contribution of infrasound is dominant. The slight shift of the node from the theoretical position (τ = 0) is probably because the station is at the edge of the crater rim.
 The same analysis is performed for data on 12 February 2009, when the activity had decreased (Figure 3). JMA reported emissions of small ash clouds as high as a few hundreds of meters at 16:51, 18:07, and 21:02–22:12, which are marked by dashed lines. The microphone signal is very weak for the entire record, and the eruption signals are not obvious in the waveform (Figure 3a). In contrast, the correlation function clearly highlights these events (Figure 3d). Although the infrasound correlation pattern is accompanied by an increase of the seismic amplitude, the seismic wave alone cannot generate the pattern, as is shown theoretically in the previous section, and is also observed in Figure 2d. The result in Figure 3 demonstrates that the present method can effectively identify very weak infrasound signals. It is noted that the method can distinguish infrasound from wind noise, but cannot distinguish whether the infrasound is volcanic or not. In order to relate an infrasonic correlation pattern to volcanic activity, further information like video images are required. The method can pick candidates of volcanic activity and reduce effort to analyze video records. Moreover, the method is useful in detecting not only occurrences of volcanic activity but also its changes, as demonstrated in the next.
3.2. Shinmoe-dake Volcano, 2011 Eruption
 Shinmoe-dake volcano, southwestern Japan, was very active in late January 2011, starting with 3 subplinian eruptions on the 26th and 27th of January, and followed lava effusion from the 28th to the 31st. Harmonic tremor was observed in the seismic signals during the final stage of the lava effusion, as well as in the infrasonic signals after the 31st of January. An infrasonic microphone (Hakusan, SI102, 0.1–1000 Hz) was installed on 6 December 2010 with an existing telemetered broadband seismic station (Trillium 120P), about 700 m from the active crater. The distance between the microphone and the seismometer is about 5 m. The signals are recorded at 100 Hz.
Figure 4compares the correlation pattern with the heights of the incandescent magma fountain and the ash plume for the second subplinian event. The heights are measured in the video images taken from the south by JMA. Increase in the seismic and infrasonic wave amplitudes, and heights of the fountain and the plume correspond to gradual changes in the infrasonic correlation pattern starting around 1:50. At 3:08, the infrasonic amplitude decreases while the seismic amplitude increases, which eliminates the infrasonic correlation pattern. At the same time, the plume height also increases, and the fountain is not visible behind the ash plume. A monitoring camera located west of the crater showed that the fountain column widened and its main part shifted from the south edge of the crater to the center at this time. When the fountain is visible again at 3:17, the correlation pattern is also recovered. A clear change of pattern is observed again at 4:40, when the fountain and plume heights rapidly decline. This example demonstrates that the correlation pattern highlights qualitative changes in the eruptive activity. It is noted that disappearance and re-appearance of the correlation pattern do not necessarily indicate cessation and restart of volcanic infrasound, but they do indicate change in the relative strength of the incident seismic and infrasonic waves, which is another important metric of changing volcanic activity [Ripepe et al., 2005; Johnson and Aster, 2005].
 Although an incident seismic wave alone does not generally show noticeable correlation patterns, it may eliminate the infrasonic pattern (as in the previous example), or contaminate the pattern. When the seismic wave is dominated by a single frequency component as , for example, the correlation function (6) is approximated by:
The first term of the right-hand-side of(9) is a sinusoidal function of τ, and can be significant in the entire range of τ if pin has enough power at the frequency ωo. One example is shown in Figure 5a. The banded correlation pattern having a node at τ= 0 seems to indicate a narrow-banded infrasonic signal, as the case 1 inFigure 1. In fact, the infrasound itself has a broad spectrum. The wavy structure of the correlation function is a result of the dominant component of the seismic wave at 4.3 Hz exaggerating the same frequency component of the infrasound. It is emphasized that such a correlation pattern is not generated by a monotonic seismic wave alone without a significant accompanying power in infrasound. Figure 5c is a contrasting example. Harmonic seismic tremor was intermittently observed during this period. Every time the tremor occurs, the increased amplitude of the ground oscillation erases the correlation pattern generated by weak persistent infrasound, even though the tremor has a few dominant peaks (Figure 5d). This is because the infrasound does not have enough power in the frequencies that match any of the modes of the tremor to be exaggerated. In the case of Figure 5e, harmonic tremors were observed both in the seismic and infrasonic signals. They have common peaks in the spectrum (Figure 5f), which makes the banded correlation pattern. The pattern does not have a stable node at τ = 0, which is the essential feature of the infrasonic correlation pattern. The strange pattern in Figure 5e is considered to be generated by R[τ; win, pin], indicating the incident seismic and infrasonic waves have a common source.
 Although this method does not directly represent the spectral features or cessation of infrasound in this way, the graphical representation of the correlation function enables detection of qualitative changes in the activity at a glance. What causes appearance, disappearance, and change of the correlation pattern may be identified by comparing the pattern with the amplitudes and the spectra of the seismic and infrasonic waves.
 Existence of infrasonic signals are effectively detected by investigating the correlation function of signals from a microphone and a collocated seismometer. Infrasound and vertical ground motion generated by the infrasound generates a particular pattern in the correlation function, which is distinguishable from contributions of wind noise and incident seismic waves. The correlation pattern changes when the spectral feature of the infrasound and/or the seismic wave changes and the relative strength of infrasound and seismic wave changes, both of which are expected to be accompanied by change in eruptive activity. This method is particularly useful when there is only one station available close to the active crater. Certainly, an array of microphones is ideal to investigate the infrasound itself, and multiple microphones are necessary to determine its source location. However, at active volcanoes, observations are rarely done with ideal monitoring networks. The correlation method provides a way to get information about eruptive activity using a single microphone and seismometer located relatively close to the crater.
 This study has been supported by the MEXT Grant-in-Aid for Scientific Research (20740251, 22540431). We are grateful to the Japan Meteorology Agency and Aira-Isa Regional Development Bureau of Kagoshima prefecture for providing video images, and J. Lyons, R. S. Matoza, and D. Fee for improving the paper.
 The Editor thanks Robin Matoza and David Fee for their assistance in evaluating this paper.