To get insights into the source mechanism behind NB and BB tremors, information about the volcanic activity is essential. For example, eruptive tremors occur during eruptive periods, and they have particular characteristics (McNutt and Nishimura 2008). Before comparing the occurrence of observed tremors with the volcanic activity, we shall evaluate whether non-volcanic sources can also generate similar seismicity.

Many studies have shown that rivers (Díaz et al. 2014) and glaciers (Roeoesli et al. 2016) are prone to generate long-duration seismicity with tremor-like spectral content. However, due to the lack of large rivers and glaciers around the seismic station, these sources are not suitable candidates to explain the NB and BB tremors at Copahue. Other possible source is induced ambient noise during strong winds. However, associated wavefield are characterized by high-entropy, unpolarized particle motions, and homogeneous spectrum (Melchor et al. 2020). Therefore, we interpret that both NB and BB episodes must be driven by volcanic or hydrothermal processes.

Copahue activity

We chronologically constructed the volcanic activity timeline from different sources and available data to compare it with tremor occurrence. The detailed activity of Copahue in the 2012–2019 period was obtained from reports of the Chilean Southern Andean Volcano Observatory (OVDAS) and the Global Volcanism Program (GVP), which periodically summarize seismic and infrasonic events, deformation, and surficial activity (Additional file 3). We also tracked the deformation of the Copahue volcano using the descending synthetic aperture radar (SAR) imagery acquired during 2011–2019 by the RADARSAT-2 satellite. The time series of cumulative displacements in the line-of-sight (LOS) direction was computed for each acquisition epoch, and the linear rate was estimated using linear regression.

The (hbox {SO}_2) emission of Copahue is continuously tracked by the Global Sulfur Dioxide Monitoring Group (https://so2.gsfc.nasa.gov), which publishes almost daily OMI and TROPOMI-based images of SO(_2) vertical column density at middle tropospheric altitudes (5–7.5 km). We reviewed all available images to classify periods of “High”, “Low”, or “No” SO(_2) emissions.

Thermal and infrared bands of LANDSAT 7 and 8 with high spatial resolution led us to estimate the Land Surface Temperature (LST) in the crater. Indeed, we tracked the maximum LST (from now on symbolized as MVT) value inside the crater over time. Finally, ash emission and the presence/absence of the crater lake were estimated by observation of LANDSAT 7, 8, and Sentinel S2 true-color images. Additional files 3 and 4 contain specific details of the methods and data, respectively.

Figures 10, 11, 12 compare the time evolution of eruptive activity with NB and BB episodes. The rows in Fig. 10, 11, 12a depict, from top to down, whether the crater lake was present or not, the intensity of the SO(_2) anomaly, the presence of ash around the crater, and the explosions reported. Figures 10, 11, 12b and  10, 11, 12c show the deformation in the LOS-direction of the satellite and the MVT, respectively.

Fig. 10
figure10

Time evolution of (a) surficial activity, b LOS-displacement, c LST temperature, d frequency and (C_P) of dominant frequencies of NB tremors, and e energy of BB tremors for the periods June 2012 to December 2014. Gray shadows in c and d depict periods without seismic data

Fig. 11
figure11

Time evolution of (a) surficial activity, b LOS-displacement, c LST temperature, d frequency and (C_P) of dominant frequencies of NB tremors, and e energy of BB tremors for the periods January 2015 to December 2016. Gray shadows in c and d depict periods without seismic data

Fig. 12
figure12

Time evolution of a surficial activity, b LOS-displacement, c LST temperature, d frequency and (C_P) of dominant frequencies of NB tremors, and e energy of BB tremors for the periods January 2018 to December 2019. Gray shadows in c and d depict periods without seismic data

The LOS-displacement time series represents the evolution of the inflationary process centered NW from the crater, coinciding with the geothermal field. A two-source system has been proposed to explain this behavior (Velez et al. 2016; Lundgren et al. 2017). Both studies coincide in the presence of a shallow, elongated (sim)2.5km conduit beneath the active crater connected with a magmatic reservoir at 7–9 km depth below the surface. Moreover, (Lundgren et al. 2017) proposes that (i) the shallow conduit is above the hydrothermal system and (ii) the magmatic reservoir has an elongated pipe-like shape plunging 25(^{circ }) to the east, reaching the center of the caldera. We observe that the inflationary process that stopped in 2016 activated in the last quarter of 2019 (Fig. 12b).

Except for the ash emissions in 2016, when high values of MVT were observed, possibly, due to the high temperatures of the gas plume, the highest values of MVT coincides with the presence of the crater lake. Moreover, we observed a correlation between these two series from mid-first to second quarters of 2014, 2018, and 2019. In these periods, the progressive decrease of MVT coincides with the crater lake’s subsequent disappearance. Similarly, the gradual increase of MVT coincides with the lake’s subsequent formation in the following periods: December 2013 to January 2014, June 2018 to January 2019, and in the last months of 2014 and 2019. The temperature and volume of the crater lake depends on the balance between inputs (volcanic fluids and gases and meteoric water from a glacier that is constantly supplying) and outputs (evaporation, seepage, and other processes (Hurst et al. 2015)). We noted a seasonality with the crater lake forming in summer, possibly, due to an increase in the volume of water caused by the thaw.

Eruptive and non-eruptive tremors

The chronological description of the Copahue’s activity led us to classify BB and NB episodes as eruptive or non-eruptive, providing insights into their origin. We classified them as eruptive (E) when they coincide with a period classified as “Ash Plume”, “Recent ash”, “High SO(_2)”, or “Explosions” (see Figs. 10, 11, 12d). Conversely, when they coincide with a period of “Low SO(_2)”, “No SO(_2)”, or “No Ash”, tremor episodes are classified as non-eruptive (NE). In case of no information during the occurrence of the tremor, this is classified as unknown (UK). The classification was done manually by comparing the accumulated duration of each tremor episode and the number of days of activity (see Additional file 5: Table S4). In total, we classified 18 E, 42 NE, and 25 UK episodes.

NB tremors

Before discussing the difference of E, NE, and UK episodes, it is worth pointing out the observed independence in the frequency peaks of the NB episodes. For example, the 1.4 and 1.0-Hz peaks, which are the most common, can appear alone (as monochromatic episodes) or within other peaks. Moreover, observed gliding only affected one peak in episodes with multiple frequencies. This suggests that the frequencies characterizing the non-monochromatic episodes should be considered independently and not as harmonics of a fundamental period. With this in mind, we can classify as eruptive or non-eruptive either NB episodes and characteristic frequencies (see Additional file 5: Table S5).

Most of the peaks showed low values of PD and, therefore, low (C_P). This can occur by an increase in isotropic noise or interference with other sources. When, for example, wind speed is high, both isotropic noise and surface waves increase in the wavefield, leading to the appearance of polarized directions modes in the complex space (Greenhalgh et al. 2018). This mechanism would affect all the frequencies alike since wind increases noise at a wide spectral band (Withers et al. 1996). However, the ambient noise could be polarized at specific frequencies by site effects, interfering with the tremor wavefield and reducing the (C_P) of some peaks. This can explain the low values of (C_P) below 1 Hz, both for E and NE peaks (Additional file 5: Tables S6, S7). On the other hand, the loss of R produces low (C_L) values. We observed that the range of R, defined as the distance between their minimum and maximum value (see Figs. 3d and 5e), is low at frequencies above 2 Hz. This suggest that both E and NE peaks are more affected by scattering effects, noise, multipathing, or seismic interference (Neuberg and Pointer 2000; Hellweg 2003; Greenhalgh et al. 2008; Almendros et al. 2012) below that frequency. Large values of the range of R may also suggest that the tremor wavefield is composed of multiple polarizations, as have been observed in other volcanoes (Goldstein and Chouet 1994; Saccorotti et al. 2004; Almendros et al. 2014).

A comparison between the number of E and NE peaks with (C_Pne 0) and (C_Lne 0) (Additional file 6: Figs. S6–S8) shows that E peaks are more linearly polarized ((sim)56%) than NE ((sim)37%), suggesting an increase of body waves in the wavefield during eruptive activity. E peaks have no particular characteristics that distinguish them from NE peaks and, therefore, a relationship between surface activity with the frequency of NB episodes cannot be stated (Fig. 13). In general, both E and NE peaks have the same number of occurrences. Thus, there is not clear evidence that a particular frequency, e.g., 1.5 Hz, is linked with ash emissions or intense degassing (see Additional fie 5: S5). For example, peaks at 0.7, 1.0, and 1.5 Hz characterize both the 22 December 2012 strombolian eruption (Fig. 10) and the continuous ash emissions in February–June 2016 (Fig. 11). However, these frequencies are also excited during quiescent periods. Moreover, (Theta _H) and (Theta _V) values for the frequencies of those E episodes are similar but also for NE episodes (see Additional file 1).

Fig. 13
figure13

Polarization attributes in frequency for all dominant peaks of NB tremors. (up) Horizontal azimuth (down) vertical incidence according to definition in Fig. 3

In general, (Theta _H) and (Theta _V) of E, NE, and UK peaks do not show clear patterns when they are compared (see Additional file 5: Tables S6–S8 and Additional file 6: Figs. S1–S4). We interpret these result as strong path or site effects controlling the wavefields. If we also define the range of (Theta _H) and (Theta _V) as the absolute difference between their minimum and maximum value in the PDF (see Fig. 3e and f), we noted these values decrease as (C_P), (C_L), and frequency increases (Fig. 13 and Additional file 6: Fig. S2, S4), being the peaks with frequencies above 2 Hz those with shortest azimuth ranges. This suggests that the peaks below the 2 Hz are more influenced by path effects.

The time evolution of the (Theta _H) reveals remarkable patterns (Figs. 13c and Additional file 6: Fig. S6). In 2012 and 2013, frequency peaks showed an azimuth direction of (sim)50(^{circ }), whereas 2013 and 2018, albeit also present azimuths around this angle, spread its direction in a wider range (see Additional file 6: Fig. S6). This last observation can, therefore, reflect changes in the source or path conditions.

BB tremors

The similarity of BB episodes suggests a common source. However, they not always coincide with eruptive activity. For this reason, we do not consider this tremor as eruptive. Nevertheless, it is worth making some observations about their relationship with ash emissions. BB tremors show seasonal behavior, with 70% of the episodes occurring in spring (see Additional file 5: Table S9). This season is also characterized by the highest number of days with ash emission and without crater lake (Additional file 6: Figs. S1 and S2).

We observed BB episodes 4 days before the 22 December 2012 eruption; 3 days before the explosive activity of 5 March 2013; 8 days before the explosions of 28 October 2013 (Fig. 10); 6 days before the explosions of 5 October 2014; during the explosions of September 2015 (Fig. 11); 3 days before the ash emissions of 22 June 2018; and during the explosions of September 2019 (Fig. 12). In these periods, they emerged in swarms with a trend to decrease their energy. Conversely, BB tremors also occurred without any sign of unrest at posterior periods. Thus, we cannot consider these tremors as a precursor of explosive activity but related to the internal dynamics of the volcano.

Implications for the source of NB tremor

The peaked spectra of NB tremors are commonly viewed as a result of a flow-induced oscillations triggered by instabilities in the magmatic or hydrothermal systems. The seismic radiation released in the interface with elastic medium propagates to the seismic receiver, leading to the duration of the tremor depending on the energy losses by elastic radiation and dissipation processes at the source (Chouet and Matoza 2013).

Eruptive episodes suggest a long-lived mechanism related to activity in the open conduit. For example, a possible explanation for the 2196-hr-long tremor related to 2016 ash emissions is the pressure turbulence in the vent (McNutt and Nishimura 2008). In non-eruptive episodes, long-duration tremors can be explained by acoustic resonance in closed pipe-like conduits filled with low-viscosity fluids (Neuberg et al. 2000). However, the presence of an extended hydrothermal system (Barcelona et al. 2019) can also suggest a different origin, such two-phase flow instabilities or hydrothermal boiling. Another mechanism able to explain the long-duration of NB episodes is the superposition of successive short-duration events too close together in time to be distinguished or a recursive feedback mechanism of long-period seismicity (Neuberg et al. 2006). However, this mechanism produces harmonics through the Dirac comb effect that are unseen in the records.

The observed seismic silences cannot be only attributed to changes in the pressure conditions during ash emissions (Morales et al. 2015) since it also was observed in NE episodes. To gain insight into the mechanism behind these silences, more seismic stations are required.

Polarization attributes provide insights into the propagation direction of the tremor wavefield. However, the use of a three-component sensor to identify that direction is insufficient unless assuming that the major semi-axis of the polarization ellipse is parallel to the direction of propagation (Anderson and Nehorai 1996). Indeed, only when the tremor wavefield is composed of P-waves and the medium is laterally homogeneous, (Theta _H) and (Theta _V) point out the source direction.

The most striking result is that NB episodes reveal neither a characteristic spectral pattern nor a clear relationship between their frequencies and surficial activity. This may suggest different but interconnected source origins, or a complex heterogeneous medium. At frequencies around 2.4 Hz, (Theta _H) centers 20(^{circ }) north (Fig. 13a and c), pointing towards the geothermal field, which has proved to be a source of long-duration seismicity (Ibañez et al. 2008). However, we also observed frequencies from eruptive and non-eruptive NB episodes with similar azimuths, which suggest strong path effects. Another possibility is that those eruptive frequencies are composed of S-waves and, thus, the propagation direction is 110(^{circ }), coinciding with the crater-receiver direction. On the other hand, the high (Theta _V) (Fig. 13b and d) means that the propagation direction of the linear polarized waves composing the NB episodes has a vertical incidence, which reinforces the idea of strong heterogeneities along the propagation paths.

The hydrothermal nature of BB tremor

The origin of BB tremor seems to be different from NB tremor. As stated above, the correlation between BB episodes and ash emissions (see Table 2) is close enough to suggest their origin involves internal volcanic processes. By analogy with banded tremors observed in other volcanoes (Cannata et al. 2010; Fujita 2008), we speculate BB tremor is triggered by instabilities of the hydrothermal system beneath the crater of Copahue, which behaves like a steam-water mixture system (Varekamp et al. 2009).

The observed seasonality is therefore easily explained by the recharge–discharge cycles of the hydrothermal system. This seasonality can affect the rate of the long-period seismicity (Nakano and Kumagai 2005; Park et al. 2019) and generate banded tremors (Gresta et al. 1996; Cannata et al. 2010). For example, in Mt. Etna, banded tremors occur mainly in springtime and this behavior was attributed to the recharge of the aquifer by snow melting at the summit of the volcano (Gresta et al. 1996). In this scenario, many factors can explain the duration and energy of BB episodes, including system geometry, the amount of water, and heating rate involved (Fujita 2008). For example, the reduction of the hydrothermal system or the input heat flux would explain the low presence of BB episodes in 2016 or the observed decreasing energy of BB episodes in the swarms (Figs. 10d and 11d).

The polarization attributes are consistent with this conceptual model (Fig. 9). The rectilinearity R shows a mixture of polarized waves in the wavefield (Fig. 9b), possibly due to a high contribution of surface waves. The low values of (Theta _V) suggest a sub-horizontal incidence, which is interpreted as a shallow source, whereas (Theta _H) points out in the SW direction (Fig. 9c), i.e., around 90(^{circ }) from the direction of the crater. Thus, we interpret this as S-waves propagating transversely from the crater. The increase of the azimuth range with frequency can be explained by scattering effects (Hellweg 2003).

The broader spectral content of BB tremor suggests a complex source mechanism, which is poorly understood. A simple attempt to explain it would be by the composition with other sources, such as assuming that the brittle failure of the rocks constraining the fluid by pressure changes causes the higher frequencies of the spectrum. On the other hand, changes in the seismic velocity of the system can also cause spectral peaks to shift, leading to a broader spectral content in the seismic record (Neuberg and O’Gorman 2002). This last mechanism has been used to explain the broad spectrum of the volcanic tremors recorded at Bromo (Gottschämmer 1999) or White Island (Sherburn et al. 1998), among others.

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