Tracking changes at volcanoes with seismic interferometry. M. M. Haney 1, A. J. Hotovec-Ellis 2, N. L. Bennington 3, S. De Angelis 4, and C.

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1 1 Tracking changes at volcanoes with seismic interferometry 2 3 M. M. Haney 1, A. J. Hotovec-Ellis 2, N. L. Bennington 3, S. De Angelis 4, and C. Thurber U.S. Geological Survey, Alaska Volcano Observatory, Anchorage, AK, USA 2 University of Washington, Seattle, WA, USA 3 University of Wisconsin-Madison, Madison, WI, USA 4 University of Liverpool, Liverpool, UK 9 1

2 Abstract Volcano monitoring hinges on the ability to detect unrest at the earliest moment possible. Relevant types of changes at volcanoes that are routinely monitored include variations in seismicity, deformation, infrasonic radiation, gas emission, and surface temperature. Changes in subsurface structure at volcanoes have only recently begun to be detected and quantified in a systematic way using techniques broadly referred to as seismic interferometry and coda wave interferometry. This article presents an overview and discussion of the application of these methods at volcanoes. Case studies from Okmok and Pavlof volcanoes in the Aleutian Arc illustrate different applications of the method. At Okmok, analysis of pairs of broadband seismometers within the 10 km wide caldera leads to the observation of seasonal changes due to snow loading from correlations of ambient noise. At Pavlof, repeating explosions during the 2007 eruption offer a different type of source for interferometry. Although co-eruptive time-lapse changes in the conduit at Pavlof have been previously documented, the precise mechanism of the change remains unresolved beyond a few hypothesized models capable of explaining the observations. Two new developments in coda wave interferometry, based on the use of stable noise sources and the detection of scattering changes in the subsurface, show promise for expanding the use of interferometry at volcanoes Introduction The detection and evaluation of time-dependent changes at volcanoes forms the foundation upon which successful volcano monitoring is built. Temporal changes at volcanoes occur over all time scales and may be obvious (e.g., earthquake swarms) or 2

3 subtle (e.g., a slow, steady increase in the level of tremor). Some of the most challenging types of time-dependent change to detect are those that occur at depth, beneath active volcanoes. Although difficult to measure, such changes carry important information about stresses and fluids present within hydrothermal and magmatic systems. These changes are imprinted on seismic waves that propagate through volcanoes In recent years, there has been a quantum leap in the ability to detect subtle structural changes systematically at volcanoes with seismic waves. The new methodology is based on the idea that useful seismic signals can be generated at will from seismic noise [Haney et al., 2009]. This means signals can be measured any time, in contrast to the often irregular and unpredictable times of earthquakes. With seismic noise in the frequency band Hz arising from the interaction of the ocean with the solid Earth known as microseisms, researchers have demonstrated that cross-correlations of passive seismic recordings between pairs of seismometers yield coherent signals [Campillo and Paul, 2003; Shapiro and Campillo, 2004]. Based on this principle, coherent signals have been reconstructed from noise recordings in such diverse fields as helioseismology [Rickett and Claerbout, 2000], ultrasound [Weaver and Lobkis, 2001], ocean acoustic waves [Roux and Kuperman, 2004], regional [Shapiro et al., 2005; Sabra et al., 2005; Bensen et al., 2007] and exploration [Draganov et al., 2007] seismology, atmospheric infrasound [Haney, 2009], and studies of the cryosphere [Marsan et al., 2012] Initial applications of ambient seismic noise were to regional surface wave tomography [Shapiro et al., 2005]. Brenguier et al. [2007] first used ambient noise tomography 3

4 (ANT) to map the 3D structure of a volcanic interior at Piton de la Fournaise. Subsequent studies have imaged volcanoes with ANT at Okmok [Masterlark et al., 2010], Toba [Stankiewicz et al., 2010], Katmai [Thurber et al., 2012], Asama [Nagaoka et al., 2012], Uturuncu [Jay et al., 2012], and Kilauea [Ballmer et al., 2013b]. In addition, Ma et al. [2013] have imaged a scatterer in the volcanic region of Southern Peru by applying array techniques to ambient noise correlations. Prior to and in tandem with the development of ANT, researchers discovered that repeating earthquakes, which often occur at volcanoes, could be used to monitor subtle time-dependent changes with a technique known as the doublet method or coda wave interferometry (CWI) [Poupinet et al., 1984; Roberts et al., 1992; Ratdomopurbo and Poupinet, 1995; Snieder et al., 2002; Pandolfi et al., 2006; Wegler et al., 2006; Martini et al., 2009; Haney et al., 2009; De Angelis, 2009; Nagaoka et al., 2010; Battaglia et al., 2012; Erdem et al., 2013; Hotovec-Ellis et al., 2014]. Chaput et al. [2012] have also used scattered waves from Strombolian eruption coda at Erebus volcano to image the reflectivity of the volcanic interior with body wave interferometry. However, CWI in its original form was limited in that repeating earthquakes, or doublets, were not always guaranteed to occur. With the widespread use of noise correlations in seismology following the groundbreaking work by Campillo and Paul [2003] and Shapiro [2005], it became evident that the nature of the ambient seismic field, due to its oceanic origin, enabled the continuous monitoring of subtle, time-dependent changes at both fault zones [Wegler and Sens-Schönfelder, 2007; Brenguier et al., 2008b; Wegler et al., 2009; Sawazaki et al., 2009; Tatagi et al., 2012] and volcanoes [Sens-Schönfelder and Wegler, 2006; Brenguier et al., 2008a] without the need for repeating earthquakes. 78 4

5 Seismic precursors to eruptions based on ambient noise were first detected at Piton de la Fournaise volcano on the island of Reunion [Brenguier et al., 2008a; Duputel et al., 2009]. The studies at Piton de la Fournaise demonstrated the possibility of resolving small (~0.1 %) decreases in seismic velocity in the weeks leading up to eruptions. Brenguier et al. [2008a] and Duputel et al. [2009] further showed how subtle spatial and temporal changes at the volcano could be mapped and used as a real-time tool for volcano monitoring and eruption forecasting. Traditionally, the forecasting ability of volcano seismology has rested on the assumption that volcanic unrest is preceded in advance by a significant increase in seismicity. However, some eruptions, such as Okmok in 2008 [Larsen et al., 2009], have begun with little or no precursory seismicity. For those eruptions, advance warnings cannot be made and the public is at risk of being exposed to the harmful effects of volcanic activity. Methods based on ambient noise have the potential to assist with forecasting of volcanic unrest in such cases Principles of Coda Wave Interferometry CWI can in principle detect several types of temporal variations, among them changes in subsurface velocity, changes in the source location, changes in bulk scattering properties, and changes in the focal mechanism of earthquakes [Snieder, 2006]. The sensitivity to subsurface velocity changes initially led to the widespread adoption of CWI for applications at volcanoes. The sensitivity to subsurface velocity can be shown in simple terms with a model of a homogeneous halfspace of velocity v with randomly distributed, small-scale scatterers. For this model, the travel time t for a particular scattering path is given simply as 5

6 t= d v (1) where d is the total distance traveled for that path. Note that this distance is not necessarily along a straight-line path. To analyze variations in traveltime, assume that the velocity changes by an amount Δv but the locations of the scatterers do not change. Since the locations do not change, the distance d traveled by each path stays the same. However, the change in velocity Δv causes there to be a resulting change in the traveltime Δt, causing the relation in equation (1) to become t+!t= d v+!v (2) Assuming the changes are small and taking a Taylor series approximation of equation (2) yields t+!t= d #!v & % 1" ( (3) v $ v ' Combining equations (1) and (3) finally gives the well-known result [Snieder, 2006] !t t = "!v v (4) 6

7 Equation (4) is widely used in CWI and it states that the fractional traveltime change is equal to the negative of the fractional velocity change. Thus, by measuring the fractional traveltime change, the change in the subsurface can be estimated. Three different methods have been proposed to measure the time shifts in CWI: time-windowed crosscorrelations [Snieder et al., 2002], the stretching method [Wegler and Sens-Schönfelder, 2007], and the phase of the cross-spectrum [Poupinet et al., 1984]. Note that equation (4) applies to direct waves as well as scattered or coda waves. However, for a given velocity change, the time shift is greater for waves with longer traveltimes, i.e. scattered or coda waves. Thus, CWI, in contrast to many other seismic techniques, benefits from higher amounts of scattering since later-arriving waves have larger and more clearly identified time shifts An alternative to the above derivation is for a changing 1D resonator of length d and with an internal propagation velocity v. Resonators have been discussed extensively in volcano seismology as models for sources acting in a crack or cavity [e.g., Fee et al., 2010]. This model is different from the model of randomly distributed scatterers but still produces a sequence of late-arriving waves. In this case, the derivation proceeds along the same lines as shown above, except that the length d is also allowed to vary, yielding the following expression for the traveltime change: !t t =!d d "!v v (5) 145 Haney et al. [2009] have interpreted CWI delay times measured from repeating 7

8 explosions at Pavlof Volcano in the context of this resonator model. As a result, the observed traveltime change could be interpreted as a change in the length of the resonator, a change in the velocity of the material inside the resonator, or a suitable combination of both types of changes (see discussion on page 173 of Garces and McNutt [1997]). The implication is that changing properties of the resonator, or conduit, control the changes observed in the coda of the repeating explosions at Pavlof. Landro and Stammiejer [2004] similarly make use of equation (5) for interpreting time-lapse changes from a subsurface layer in an exploration seismic setting Overview of Coda Wave Interferometry at Volcanoes Coda waves of repeating earthquakes, or doublets, have been used to observe temporal changes in the subsurface for several decades [Poupinet et al., 1984]. As described by Snieder et al. [2002], CWI takes advantage of subtle time shifts in the coda of repeating seismic events. In CWI, the time-lag between events as a function of recording time is determined via time-windowed cross-correlation of the traces. From the observed timelags, a corresponding change in velocity can be determined. The technique can detect small changes at volcanoes [e.g., Haney et al., 2009; Nagaoka et al., 2010, Hotovec-Ellis et al., 2014], with temporal resolution on the same order as the rate of the repeating events [e.g., hourly resolution in Hotovec-Ellis et al., 2013]. However, the requirement of repeating events precludes the use of CWI at many volcanoes where repeating events are infrequent or short-lived. In contrast, ambient noise occurs continuously and, if the signal is highly repeatable, offers the ability to observe temporal changes at volcanoes at will [Sens-Schönfelder and Wegler, 2006]. 8

9 Since the field of interferometry is in its early stages, only a handful of studies [Sens- Schönfelder and Wegler, 2006; Brenguier et al., 2008a; Duputel et al., 2009; Baptie, 2010; Mordret et al., 2010; Anggono et al., 2012; Obermann et al., 2014] have employed ambient seismic noise to study changes at volcanoes. The existing studies have typically found velocity decreases at volcanoes due to or preceding activity: -0.5% by Baptie [2010], -2.3 to 3.3% by Anggono et al. [2012], -0.8% by Mordret et al. [2010], and -0.4% by Brenguier et al. [2008a]. The changes detected with ambient noise to date include seasonal variations [Sens-Schönfelder and Wegler, 2006], eruption precursors due to magma pressurization [Brenguier et al., 2008a; Duputel et al., 2009; Anggono et al., 2012], post-eruption changes in the volcanic edifice due to dome collapse [Baptie, 2010], and changes in the hydrothermal system [Mordret et al., 2010] The determination of subtle changes in velocity using ambient noise interferometry is carried out in a similar way to the process used in CWI with repeating earthquakes. Following Duputel et al. [2009], a long time period seismic correlation between station pairs is computed, and this correlation represents the reference correlation function (CF). The reference CF must be determined over a period of quiescence at the volcano [Duputel et al., 2009]. The reference CF in Duputel et al. [2009] was generated during a two month period when Piton de la Fournaise was relatively quiet. To identify temporal variations in velocity, they determined the current CF as the seismic correlation between a station pair over a smaller period of time than the reference CF by averaging over a time period of 10 days. Duputel et al. [2009] and Hadziioannou et al. [2009] 9

10 demonstrated that the stretching technique is a stable method of determining the relative velocity change between station pairs showing significant time lags. The stretching method is an alternative to the traditional method of time-windowed correlations [Snieder et al., 2002]. In the stretching method, the reference CF is stretched or compressed to best match the current CF. This stretched/compressed CF is calculated using an assumed relative change in velocity. Over a set of possible relative velocity changes, the relative velocity change that yields the best correlation between the stretched/compressed CF and the current CF is selected. Note that the stretching method assumes a uniform velocity change in the subsurface when measuring time delays between signals. This need not be the case, as demonstrated by Pacheco and Snieder [2006] in their study of time delays from localized velocity perturbations. There remains debate over the relative performance of the stretching method and time-windowed correlations [Zhan et al., 2013]. A third method, known as the cross-spectrum method [Poupinet et al., 1984], is closely related to the time-windowed correlation method, since the two represent equivalent processes implemented in either the time or frequency domain In the following sections, case studies of CWI are given that use ambient noise and repeating earthquakes at two volcanoes in the Aleutian Islands of Alaska: Okmok and Pavlof. The locations of these volcanoes within the Aleutian Arc are given in Figure 1A. The seismic stations at Pavlof and Okmok discussed in the following sections are shown in Figure 1B and Figure 2, respectively. These two case studies illustrate the relative advantages and disadvantages of using ambient noise or repeating earthquakes to 10

11 measure changes at volcanoes. Following these two case studies, new developments in coda wave interferometry are discussed that will influence future studies at volcanoes Seasonal Changes from Ambient Noise at Okmok Volcano, Alaska Okmok Volcano is one of the most active volcanoes in the Aleutian Arc, with an average of one eruption every decade over the past 100 years. Its broad shield structure is interrupted by a roughly 10 km wide caldera, the remnant of 2 historical caldera-forming eruptions in the past 10,000 years [Larsen et al., 2009]. The most recent eruption of Okmok in 2008 occurred with almost no warning, the only precursory activity being a short-lived earthquake swarm during the 5 hours prior to the eruption [Larsen et al., 2009] At Okmok, as in most of the Aleutian Islands, the majority of the seismic stations are short-period installations. However, several high-quality broadband seismic stations have existed at different times within the Okmok network. These stations represent some of the most remote broadbands in the network operated by the Alaska Volcano Observatory (AVO), a partnership between the University of Alaska Fairbanks Geophysical Institute, the Alaska Division of Geological and Geophysical Surveys, and the U.S. Geological Survey. Three of the five broadbands at Okmok have been sited within the large caldera. The locations of these stations are shown in Figure 2. The stations have operated over different time periods: OKNC (2010-present), OKCE (2003-present), and OKCD ( ). Station OKCD was destroyed during the initial explosive phase of the 2008 eruption, which emanated from a nearby intracaldera cone. Here, ambient noise 11

12 correlations are analyzed for station pair OKCE-OKNC during late 2012 and station pair OKCE-OKCD during During both of these times, Okmok Volcano was in a period of quiescence In Table 1, several parameters related to the practical implementation of CWI are given. The values of the parameters depend on the desired time-scale of resolution, quality control of the correlations, and desired frequency band. The use of the frequency band from Hz represents a trade-off between having a high level of ocean-related noise and being sufficiently high enough in frequency to ensure the generation of scattered waves in the subsurface over the length scale of a volcano. Note that CWI is subject to statistical considerations related to random scattering paths, and therefore the moving window measurement in CWI must be sufficiently wide to average over scattering from subsurface heterogeneities [Snieder, 2006]. At Okmok, the coda has been examined using the time-windowed correlation method between time-lags of 5-60 s using a moving window of 20 s length (see Table 1). The sensitivity of late-arriving coda waves to changes is shown in Figure 3 between stations OKCE and OKNC at Okmok. As seen in Figure 3, the late-arriving coda waves are more sensitive compared to the early-arriving direct and forward-scattered waves. Furthermore, as discussed below, the changes in Figure 3 are consistently observed for both positive and negative lags, which constitutes a redundancy check for CWI based on ambient noise [Brenguier et al., 2008a] Additional CWI parameters concern the similarity between the reference and current CFs and temporal averaging. For the application at Okmok, the peak of the time-windowed 12

13 correlation is required to exceed 0.9 in order for the associated time-lag measurement within the moving time window to be considered when fitting the linear relationship in equation (4). Wegler et al. [2006] employed a similar criterion based on a minimum correlation coefficient in a CWI study at Merapi Volcano, Indonesia. In addition to those parameters, the use of ambient noise requires that the nonstationarity of the ocean noise source be taken into account. Brenguier et al. [2008a] found that temporal averaging of the cross-correlations over a time interval on the order of one week renders ocean noise a sufficiently repeatable source. In the following application at Okmok, the current correlation functions (CFs) have similarly been averaged over eight days centered on the current time (Table 1). The reference CFs are the result of averaging over the entire time period under consideration, either 365 days for the 2006 data or 135 days for the 2012 data As mentioned briefly above, CWI based on ambient noise is inherently redundant, since changes should be independently observed for both the positive and negative lags for a correlation between a single station pair [Brenguier et al., 2008a]. However, if a pair of stations is relatively close compared to the wavelength or if the changes can be assumed to be uniform in space, then 2 additional redundancies exist based on the autocorrelations of the two stations. This is because the autocorrelations can be viewed as ambient noise Green s functions for the case of a coincident source and receiver. For such a configuration, coda waves are still measured. This suggests that changes can be observed in 4 independent ways for stations that are in relatively close proximity. CWI best practices should exploit these redundancies to apply quality control to the observed 13

14 283 changes, as shown in the following examples from Okmok For CWI to be meaningful, error estimates on the relative traveltime change given in equation (4) must be provided. Following Brenguier et al. [2008a], the standard devaition of the time lag (i.e., the root-mean-square uncertainty of the linear fit) is given by: !!t = N ) i=1 #!t i "!v v t & % i ( $ ' N 2 (6) where N is the number of time-lag measurements. From equation (6), the standard deviation of the relative traveltime change follows from Brenguier et al. [2008a] as !!t/t = N ) i=1 #!t i "!v v t & % i ( $ ' N ) N t i 2 i=1 2 (7) Equation (7) provides the formal error bars on estimates of the relative traveltime and, through equation (4), velocity changes. However, in addition to formal error bars, goodness-of-fit criteria must be taken into account as well [Press et al., 1986]. In the implementation of CWI at Okmok, two goodness-of-fit criteria are required to be met in order to accept an estimate of relative traveltime, irrespective of the error estimate in equation (7). It must be that either a) the standard deviation in equation (6) is less than one time sample or b) the Pearson linear correlation coefficient given by 14

15 r xy = " " " " " N x i y i! x i y i ( ) 2 ( ) 2 N" x 2 i! x i N y 2 i! " y i (8) is greater than 0.8, where, for CWI, the (x,y) variables in equation (8) are the traveltime and the time lag: (t,δt). Values of r xy exceeding 0.8 are taken to indicate a strong linear relation. In practice, the first criterion means that measurements between similar waveforms in which the changes are not appreciable are automatically accepted. The second and possibly more important criterion requires that Δt and t have a strong linear correlation when the standard deviation is greater than one time sample, which in practice occurs when the changes are significant. Note that a linear relation between Δt and t may not resemble the measured Δt-t curve in general [Pacheco and Snieder, 2006]. However, if a linear model is being used, then it is at least consistent to require that the linear fit is good. Without considering the goodness-of-fit criterion in equation (8), it may be the case that the formal error in equation (7) is acceptable even though the linear fit is not good. This emphasizes the need for a goodness-of-fit criterion, as discussed in Press et al. [1986] Taking into account the above considerations, Figure 4 shows the relative velocity changes computed from both positive and negative lag portions of cross-correlations and autocorrelations for stations OKCE and OKNC over the final 135 days of The formal uncertainties on the measurements are also provided in Figure 4. Note that the various time series are discontinuous at certain points due to the CWI measurements 15

16 failing to satisfy the goodness-of-fit criteria. The relative velocity changes in Figure 4 are observed to vary between +/- 0.2%. Moreover, the changes are internally consistent in that they are observed independently for both positive and negative lags. Consistent changes are also observed for the autocorrelations, indicating that the spatial distribution of the change in the subsurface is generally uniform inside of the caldera. The source of the change will be discussed after examining data from 2006, but in principle it could be the result of magmatic or seasonal variations in the subsurface. Seasonal changes observed with CWI measurements have been studied previously by Sens-Schönfelder and Wegler [2006], Meier et al. [2010], Tsai [2011], and Hotovec-Ellis et al. [2014]. Sources of the seasonal changes include thermoelastic and hydrologic effects and, at high elevations or high latitudes, the annual snow cycle In Figure 5, relative velocity changes are shown between stations OKCE and OKCD for all of Positive and negative lag correlations are plotted, in addition to the autocorrelation of OKCD. The autocorrelation of OKCE is not plotted in Figure 5 since in 2006 it suffered from a type of uncorrelated electronic noise. Since the noise only affected OKCE, it does not have an impact on the cross-correlation computed between OKCE and OKCD. In spite of this noise, the three correlations plotted in Figure 5 show consistent estimates of relative velocity change during The subsurface velocity is observed to be slightly higher in winter and spring (days and ) and lower in summer and fall (days ). These annual variations are highly similar to the relative velocity changes observed by Hotovec-Ellis et al. [2014] at high elevation sites on Mt. St. Helens. Although the observations at Okmok are based on ambient noise, the 16

17 observations by Hotovec-Ellis et al. [2014] were derived from long-term (decadal) records of repeating local earthquakes. Hotovec-Ellis et al. [2014] concluded that the annual variability at high elevation sites on Mt. St. Helens was controlled by the snow cycle, and at lower elevation sites by shallow fluid saturation (Figure 6). The snow loading interpretation would apply at Okmok as well in spite of the low elevation of the caldera, since Okmok is located within the high latitude chain of the Aleutian Islands. Returning to Figure 4, the overall increase in velocity during the final 135 days of 2012 can be attributed to the onset of the snowpack as fall transitioned into winter. Taken together, the relative velocity variations observed at Okmok during times of quiescence in 2006 and 2012 are seasonal in nature and, due to the annual snow cycle, in agreement with the conclusions by Hotovec-Ellis et al. [2014] at high elevation sites on Mt. St. Helens Conduit Changes from Repeating Explosions at Pavlof Volcano, Alaska The 2007 eruption of Pavlof Volcano was Strombolian in character and generated lava flows, lahars, and small explosions [Waythomas et al., 2007]. Seismicity consisted of volcanic tremor and repeating long period signals associated with the small explosions at the summit of the volcano. Haney et al. [2009] have previously applied CWI to the repeating explosions during the 2007 Pavlof eruption and detected subtle changes. In contrast to CWI based on ambient noise, as shown in the previous section, CWI based on explosions at Pavlof takes advantage of the highly repetitive waveforms to observe small changes in the later portion of their signals. In this section, we summarize the study of Haney et al. [2009] and give some additional supporting observations. 17

18 To put the entire Pavlof eruption in context, shown in Figure 7 is the reduced displacement (D R ) computed at station PVV on the east side of the volcano (see Figure 1A). D R is a measure related to the energy radiated by volcanic tremor [Aki and Koyanagi, 1981]. As indicated in Figure 7, the 2007 Pavlof eruption began on August 14 and, over the next 10 days, the tremor level was relatively low. Short periods of elevated D R during the first 10 days of the eruption were not the result of elevated tremor but instead corresponded with lahars flowing close to PVV. On August 24, 10 days into the eruption, the tremor increased from a D R of 0.5 cm 2 to a D R of 1.5 cm 2 and stayed at that level until the end of the eruption. It was during this period of relatively higher tremor amplitude that repetitive explosions occurred at the summit of Pavlof, at the rate of approximately 1 explosion every 3 to 6 minutes. These Strombolian explosions represented a subtle increase in the overall intensity and explosivity of the eruption As described in Haney et al. [2009], the waveforms due to the repeating explosions over the entire eruption were identified using the master event matched filter technique described by Petersen [2007]. Once the catalog of repeating events had been identified, Haney et al. [2009] stacked the repeating waveforms within successive 12-hour time periods to increase the signal-to-noise ratio and applied CWI using the stack from the earliest time period as the reference. Table 2 gives additional parameters used for the application of CWI with the repeating explosions. Plotted in Figure 8 is the relative traveltime change over the final 20 days of the eruption, along with the average rate of explosions during each 12-hour time period. An overall increase in the relative traveltime 18

19 of 0.4% is observed as the eruption progressively came to an end over its final 20 days. The relative traveltime change is plotted in Figure 8 instead of relative velocity change since Haney et al. [2009] interpreted the change in terms of the resonator model of equation (5). According to this model, the increase in traveltime can be interpreted as an increase in the length of the resonator, or conduit, a decrease in the internal propagation velocity of the conduit, or a suitable combination of both types of change. Without additional information, the source of the change at Pavlof cannot be resolved further among these possible models. Although the relative travel time changes are only shown for station PV6 in Figure 8, Haney et al. [2009] also observed similar changes at station PN7A located to the west of the summit (Figure 1B) Based on the frequency content of the explosions and common spectral peaks between stations PV6 and PN7A, Haney et al. [2009] concluded the relative traveltime changes observed in Figure 8 were the result of changes within the volcanic conduit at Pavlof. The interpretation by Haney et al. [2009] is significant since the changes are therefore the result of a varying source effect instead of a varying path effect. This is in contrast to the conclusions of most CWI studies at volcanoes. A notable exception is the study by Erdem and Waite [2013] in which relative velocity changes were detected with CWI at Fuego Volcano with repeating explosions over short time scales, in as little as hours. Erdem and Waite [2013] concluded the variations were occurring within the conduit due to the differences in the apparent relative velocity changes measured on seismometers at different distances from the volcano

20 To illustrate the interpretation by Erdem and Waite [2013] based on seismometers at different distances, the resonator model shown in equation (5) needs to be reconsidered. For this, consider the travel time of the n-th reverberation within the conduit, given by t n = t E + nd v (9) in which t E is the travel time needed to propagate through the Earth from the conduit to the seismometer. Assuming small changes in the conduit length d, velocity within the conduit v, and travel time of the n-th reverberation t n, but no changes in the travel time through the Earth t E, a first-order perturbation of equation (9) yields ( )!d!t n = t n " t E # d "!v & $ % v ' ( (10) Equation (5) in a special case of equation (10) when t E = 0 and t n is identified as the travel time. In addition, equation (5) can be viewed as an approximation that applies at times much later than the time needed to propagate through the Earth from the conduit to the seismometer (t n >> t E ). When these conditions are not met, the use of equation (5) underpredicts the actual velocity change, as noted by Haney et al. [2009]. Erdem and Waite [2013] astutely noted that the amount of underprediction varies for seismometers at different distances from the volcano and used that fact to diagnose the source of timelapse changes at Fuego Volcano

21 An additional piece of evidence for conduit changes at Pavlof, not presented in Haney et al. [2009], follows from the spectral properties of the repeating explosions. For a simple 1D resonator, the change in the resonance frequency is related to changes in the propagation velocity inside the resonator and the length of the resonator as follows [e.g., Garces and McNutt, 1997] !f f =!v v "!d d (11) Note that the righthand side of this equation is the negative of the righthand side of equation (5). Thus, the relative changes in resonance frequency and traveltime for the model of a resonator have the same absolute value but are opposite in sign. Whereas the traveltime, or residence time, of a 1D resonator increases when its internal velocity is decreased, its resonance frequency decreases. In Figure 9, amplitude spectra of the repeating explosions are shown at station PV6 for time periods 1 week apart. The dominant resonant peak in both amplitude spectra exists at approximately 2.4 Hz and is seen to shift toward lower frequencies later in the eruption. Garces and McNutt [1997] reported on a larger -18% change in the spectral peaks of tremor before and after an eruption at Mount Spurr Volcano in The change at Pavlof, observed in the spectral domain, is consistent with the change derived from CWI in the time domain. This consistency in the spectral domain supports the interpretation by Haney et al. [2009] of conduit resonance and hints at deeper connections between the methods of interferometry and spectroscopy in physics [Zadler et al., 2005]. In fact, the CWI experiment described in Snieder et al. [2002], involving a sample of Elberton granite, could have been 21

22 equivalently analyzed in the frequency domain since the waves traversed the finite-sized sample many times over the time window of the experiment New Developments in Coda Wave Interferometry Two emerging areas of research concerning the use of seismic interferometry for monitoring changes at volcanoes are highlighted in this section. The first example addresses the use of new sources besides repeating earthquakes and the oceanic microseism. Potential sources include stable volcanic tremor [Ballmer et al., 2013a], which may be useful for monitoring changes during an eruption. The second example concerns the use of decorrelation between repeating signals in addition to traditional time-lag measurements. Whereas time-lag measurements are sensitive to bulk velocity changes, decorrelation is sensitive to changes in the properties, locations, or numbers of subsurface scatterers The simple relationship in equation (1) holds for the direct wave portion of the ambient noise Green s function in a homogeneous medium with d the interstation distance. However, if the distribution of noise sources is not uniform, spurious arrivals can appear in ambient noise Green s functions. This issue is a problem for ANT, since tomography requires accurate interstation traveltimes. However, as will be shown here, this isn t an issue for CWI with ambient noise. Consider an extreme case in which the noise source comes from a single azimuth, as shown in Figure 10. For this case, the interstation traveltime for the direct wave is given by

23 t= d cos! v (12) where θ is the azimuthal angle between the interstation azimuth and the backazimuth of the plane wave source. Equation (12) shows that for this case the arrival is spurious since it doesn t correspond to a physical wave in the Green s function, which would arrive at t=d/v. Proceeding as in equations (1) through (4), assume that the subsurface velocity changes by an amount Δv. The change in velocity Δv causes there to be a resulting change in the traveltime Δt. In addition, consider that the source azimuth changes by Δθ, giving the following relation d cos (! +!!) t+!t= v+!v (13) Assuming small changes and taking a first-order Taylor series approximation of equation (13) yields t+!t= d # 2!! % cos! "!! sin! " v $ 2 cos! &# ( 1"!v & % ( (14) ' $ v ' Combining equations (12) and (14) yields !t t = "!v v #!v & "!! tan! % 1" ("!! 2 $ v ' 2 (15) 23

24 An important outcome of this result is that, in the case of no change in the azimuth of the source (Δθ=0), equation (15) is the same as equation (4) in spite of the Green s function being incorrect due to the noise only coming from one direction. Equation (15) for a stable source (Δθ=0) shows the insensitivity of ambient noise based CWI to the direction of an oblique plane wave source. It is a simple demonstration that accurately detecting changes does not require the cross-correlations to be the true Green s function. Nonphysical arrivals in Green s function constructed from ambient noise, so-called spurious arrivals [Snieder et al., 2008], still obey equation (4) when the source is stable. Hadziioannou et al. [2009] first took note of this property and concluded that time-lapse changes can be reliably estimated even when the Green s function is not properly reconstructed. Hadziioannou et al. [2009] further concluded that the only condition necessary for monitoring changes is the relative stability of the noise These results bring up the possibility of using unconventional, localized sources in the future that are nonetheless continuous and stable to detect changes. An example of such a source is man-made cultural noise produced by machinery or traffic. Another example is stable volcanic tremor, which at some volcanoes can persist for weeks, months, or even years. This also motivates the study of such noise sources to establish their stability prior to using them for detecting time-lapse changes. The wave fields from these localized noise sources do not even begin to satisfy the conditions necessary for imaging with a technique such as ambient noise tomography; however, the reduced requirement of relative source stability for monitoring permits a wider set of applicable noise sources. 24

25 A recent development by Obermann et al. [2014] addresses decorrelation instead of timeshifts in coda wave measurements at Piton de la Fournaise volcano. In CWI, when two seismograms are cross-correlated over a small time window, the time delay is related to the time lag of the peak. The value of the peak itself is the correlation coefficient C; the decorrelation coefficient is simply defined as D=1-C. This approach offers a new type of measurement in addition to the widely used time delay in CWI. Obermann et al. [2014] applied a technique based on decorrelation at Piton de la Fournaise and found information about changes in the subsurface that was complementary to the information provided by conventional CWI based on time-shifts. Specifically, whereas time-shift measurements detected velocity variations in the subsurface, decorrelation measurements detected changes in scattering. Newly created cracks in the subsurface related to magma intrusions were interpreted by Obermann et al. [2014] to be the source of the decorrelation signal. In the following, the expression for decorrelation due to a single scatterer presented in Obermann et al. [2014] is specialized for the case of randomly distributed scatterers in a homogeneous background medium. This expression forms the link between the decorrelation coefficient in Obermann et al. [2014] and similar expressions first derived in Snieder et al. [2002] From Obermann et al. [2014], the decorrelation for a single scatterer with scattering cross section S in a background medium with wavespeed v is expressed as: D(s 1, s 2, x 0,t) = vs 2 K(s, s, x 1 2 0,t) (16) 25

26 where s 1 and s 2 are the locations of the two stations, x 0 is the location of the single scatterer, and K is the CWI sensitivity kernel presented in Pacheco and Snieder [2005]. The CWI sensitivity kernel expresses the spatial location of the sensitivity of a CWI measurement in a generally variable background medium. The derivation of equation (16) for the case of a single scatterer is quite complicated [Rossetto et al., 2011]; however, as shown below, its generalization to a distribution of new scatterers leads to a simple and insightful expression. The terminology of new scatterers refers to scatterers that developed in the intervening time period between measurements taken at different times. Given N identical new scatterers in a small area da, the effect of the individual new scatterers on the decorrelation can be assumed to be additive: D(s 1, s 2, x 0,t) = NvS 2 K(s 1, s 2, x 0,t) (17) Multiplying and dividing this expression by the small area da leads to D(s 1, s 2, x 0,t) = nvs 2 K(s 1, s 2, x 0,t)dA (18) where n = N/dA is the (2D) number density of the new scatterers. Integration of both sides of this equation over the whole spatial area considered gives the decorrelation due to a distribution of scatterers:

27 573 D(s 1, s 2,t) = nvs! 2 K(s, s, x,t) da (19) which similarly assumes as before that the effects of the different areas are additive, although here the different areas may have variable scattering cross sections S(x 0 ). The product of the number density and scattering cross section is related to the inverse of the mean free path within the independent scattering approximation (L=1/nS) [Obermann et al., 2014]. Note that this mean free path is for the new scatterers not present in the background medium. Assuming the background velocity is constant finally gives D(s 1, s 2,t) = v 2 K(s 1, s 2, x 0,t)! da (20) L where the mean free path L is taken to have a dependence on the spatial coordinate x To further simplify the expression, a model is adopted in which the mean free path for the new scatterers is constant everywhere (globally). This is the opposite end member of a single scatterer, equation (16), among models. It is also similar to the global change in velocity that gives rise to equation (4). Given the following expression for traveltime known as the Chapman-Kolmogorov equation [Pacheco and Snieder, 2005] t =! K(s 1, s 2, x 0,t) da (21) the decorrelation for a constant mean free path increases linearly with time according to 27

28 D(t) = v 2L! K(s, s, x,t) da = vt 2L (22) The linearly increasing decorrelation behavior with time is in fact the same type of behavior described by Snieder et al. [2002] for a model of moving scatterers, in which all scatterers are randomly perturbed by a distance Δ. This model is different from the model of Obermann et al. [2014] that consists of new scatterers appearing among otherwise stationary and unchanging background scatterers. From Snieder et al. [2002], the decorrelation for the moving scatterer model is given by D(t) = k 2! 2 vt l (23) where k is the wavenumber and l is the mean free path in the background medium. This result means that the two models - either the moving scatterers of Snieder et al. [2002] or the newly appearing scatterers of Obermann et al. [2014] - both predict a linear increase in decorrelation when the changes are global and are thus indistinguishable in that case. A possible way to discern these two models in the case of global changes would be to carefully exploit the wavenumber dependence for the moving scatterer model in different frequency bands. It is not clear whether these models are indistinguishable for changes that are local, but the fact that they are indistinguishable for global changes does hint at some amount of intrinsic nonuniqueness in resolving the different models

29 Equation (22), D(t) = vt/2l, can be rewritten as D(d) = d/2l, where d is the total distance traveled by the path. This relation clearly shows the mechanism of the decorrelation in the model of Obermann et al. [2014], which is scattering by the new scatterers. It is the fraction of the total distance divided by twice the scattering mean free path of the newly appearing scatterers. Note that this mean free path L is not necessarily close to the mean free path of the background medium. The advancements in the understanding of decorrelation reported in Obermann et al. [2014] should lead to increased use of this measurement in future studies of time-lapse changes at volcanoes Conclusion As demonstrated by the flurry of research activity in recent years, tracking changes at volcanoes with seismic interferometry has the potential to become a powerful volcano monitoring tool. The ambient seismic noise arising from the interaction of the ocean with the solid Earth yields repeatable signals that can detect subtle time-dependent changes at volcanoes. In addition to the overview of previous studies discussed in this paper, two examples of detecting time-lapse changes have been presented for Okmok and Pavlof volcanoes in Alaska. Interestingly, Newhall [2007] independently pointed out an approach similar to ambient noise CWI in a review of volcanology and volcano monitoring. Newhall [2007], when discussing the challenge of interpreting indirect geophysical measurements at volcanoes, suggested to track changes at the volcano in response to known, repeating natural signals. With the advent of ambient noise interferometry, the concept of using repeatable, natural sources of energy from the ocean to probe volcanoes has been realized and offers a new opportunity to understand the 29

30 640 fascinating and complex inner workings of magmatic systems worldwide Acknowledgements: Thanks go out to Mike West for access to the Okmok seismic data from

31 Table 1: Parameters for ambient noise based coda wave interferometry at Okmok Parameter Value Length of time window considered 5-60 s Frequency passband Hz Moving window length 20 s Min correlation to accept Δt measure 0.9 Temporal averaging window +/- 4 days Table 2: Parameters for explosion based coda wave interferometry at Pavlof Parameter Value Length of time window considered 0-20 s Frequency passband 1-4 Hz Moving window length 6 s Min correlation to accept Δt measure 0.7 Temporal averaging window +/- 6 hours 31

32 Figure 1: (A) Regional map of the Aleutian Arc showing the two volcanoes discussed in this paper, Pavlof and Okmok. (B) Local map of Pavlof Volcano and the seismic stations in the monitoring network analyzed in this paper. 32

33 Figure 2: Local map of Okmok Volcano and the seismic stations in the monitoring network analyzed in this paper. The three stations all sit within the 10 km wide caldera and are broadband installations. 33

34 Figure 3: Reference and current correlation functions (CFs) between station pair OKCE- 680 OKNC in late The reference CF is obtained by averaging over the final 135 days of The current CF is centered on September 9, 2012 with the average including +/ days around this center time. Panels (A) and (C) depict early lag times in the reference 683 (blue) and current (red) CFs for both the positive (A) and negative (C) lag. At early times, 684 between 1-10 s lag, the CFs virtually overlap. Panels (B) and (D) depict late lag times of 685 the same CFs for positive (B) and negative (D) lag. At late lag times, between s, 686 the current CF (red) shows a subtle time delay relative to the reference correlation 687 function (blue) for both positive and negative lags

35 Figure 4: Plotted in the top panel are the relative velocity changes computed from correlations of stations OKCE and OKNC in 2012 for positive lags (blue) and negative lags (black). The bottom panel shows the relative velocity changes for the OKCE (blue) and OKNC (black) autocorrelations. All four measurements are broadly in agreement, which they should be for velocity changes that are spatially extensive. This redundant property of ambient noise correlations can be used to measure the confidence of the velocity changes. 35

36 Figure 5: Plotted in the top panel are the relative velocity changes computed from correlations of stations OKCE and OKCD in 2006 for positive lags (blue) and negative lags (black). The bottom panel shows the relative velocity change for the OKCD autocorrelation. Station OKCE suffered from electronic noise that was not present on OKCD and thus its autocorrelation is not shown. Since the noise only appeared on OKCE, it did not affect the OKCE-OKCD cross-correlation. All three measurements are broadly in agreement, with subtle velocity increases in the winter/spring and velocity decreases in summer/fall. Station OKCE suffered from electronic noise that was not present on OKCD and thus its autocorrelation is not shown. 36

37 Figure 6: Velocity as a function of month of year at Mount St. Helens, with demeaned raw solutions in light gray and average in thicker black. Dashed line corresponds to average yearly snow load at a SNOTEL station in Sheep Canyon. Dotted line corresponds to average lake elevation at Spirit Lake, plotted with an inverted y axis to better illustrate the anticorrelation and interpreted to correspond to changes in shallow fluid saturation. Shaded area denotes months of the year with increased shallow seismicity. Reproduced from Hotovec-Ellis et al. [2014]. 37