Three years of seismic record.
The first step is to evaluate the robustness of the temporal evolution of the SE. We selected the eruptive stage occurring on Volcán de Colima between January 2015 and May 2017, analysing more than two years of data recorded at 4 different seismic stations. In Figure 2 we show the envelope of the SE evolution, calculated with the signal recorded at stations SOMA (blue) and INCA (green), selected for being near the crater (less than 2 km far) and for their complementary records throughout time. It is a normal and usual fact in volcanic seismic networks, the operability interruptions of seismic stations due to numerous causes: e.g. ash falls that make it impossible for solar panels to function and feed electronic equipment, impossibility of maintenance by volcanic risks or by bad climatology, or even damage caused by eruptions.
Noteworthy, SE evolves in a similar way in the two seismic stations, implying SE is directly associated with volcanic dynamics. It is well known that volcanic structures are very heterogeneous (Sychev et al., 2019; Castro-Melgar et al., 2021; D’Auria et al., 2022). Therefore, although the two stations are at the same distance, but at different azimuths, they may be influenced by strong scattering and attenuation effects. However, it is observed that the SE is very similar between them, representing a robust and reliable value.
Notice, the temporal evolution of the SE plotted in Figure 2 starts from low values. As reported by Carrara et al. (2019), the 28 of December 2014 Volcán de Colima had an intense eruptive episode dominated by lava flows. This eruptive episode was not included in our analysis since we focused our study in explosive episodes. It is noteworthy the SE is also sensible to any type of eruptive mechanism, as demonstrated by Rey-Devesa et al., (2023). It is also interesting to observe how after the last volcanic explosion and the beginning of a rest period of Volcán de Colima, the SE has higher and more stable values. Finally, we highlight that the two main volcanic processes selected (11 July 2015 and 1 October 2016) show how SE reaches values very close to zero evidencing their high energy and the coherence of the seismic process prior to the eruptions.
The 11th of July 2015 volcanic explosion.
Prior to the high energy volcanic explosion of July 11th, SE trend was abruptly changed, dropping to minimum values close to zero (Figure 3). According to Figure 3a and 3b the pre-eruptive short term interval of this explosion was of 5 days (green area of figure 3a and red line of figure 3b). This interval corresponds to the stable decay of the SE below the 70% of threshold. Notice that when the two associated pyroclastic flows happened the SE has a decay value of 100%. Fitting the decay of the SE we could be able to determine in advance the timing of the first pyroclastic flow, demonstrating this parameter could be a powerful tool to determine the beginning of a volcanic eruption.
According to Reyes-Dávila et al., 2016 and Arámbula-Mendoza et al, 2019, this explosion presented a low VT or LP level of seismicity on the base of the use of ML techniques as Hidden Markov Models (Benítez et al., 2009) lacking classical pre-eruptive precursors. This observation gives an added value to the use of the SE as short term volcanic precursor.
The 1st of October 2016 volcanic eruption.
The selected eruptive interval started with an effusive style finalizing with a Vulcanian explosion. As evidenced in Figure 2, the decay of the SE to values close to zero occurred just before the vulcanian explosion. Again, non-intense pre-eruptive VT or LP seismicity was reported (Dávila et al., 2019). However, the SE shows a pre-eruptive decay two days in advance. Notice as the pre-eruptive time is shorter than in the previous explosion that was more energetic than the present one (Figure 2). We realized the pre-eruptive interval determined by the decay of SE seems to be associated to the magnitude of the eruptive episode.
The intense explosive period of June 2015.
As reported by Arámbula-Mendoza et al, (2019), the most leading precursory activity of 11 of July 2015 pyroclastic flows was the high number of small volcanic explosions occurred in June. In figure 4 we zoomed in detail this period in order to observe the temporal evolution of SE according to the less energetic explosions. This study corresponds to a re-analysis of this period using windows 1 minute long overlapped the 50%. We identified the excursions of SE towards lower values (local minima) and associated them with the corresponding images recorded by the visual monitoring system. As observed in figure 4, all local minima of the SE were associated to small volcanic explosions, whenever the weather conditions allowed getting these images. These variations towards the local minima take place in a short time and it is not possible to assign a potential forecasting interval, as observed in the two largest eruptive episodes analysed before.
The local minima associated to small volcanic explosions do not always are below the defined decay STA/LTA threshold. Since we have values of the SE after the volcano began the present quiescence period, we redone a re-estimation of the STA/LTA ratio changing the dynamical model for a static procedure. In the dynamic model, the LTA term was calculated within two months interval prior to the estimation of the STA. In the static approximation we estimated a fixed average value of the LTA for a period between March and May 2017, when the volcano was in quiescence. In this case, results of the decay indicate that all the local minima of the SE of the analysed period are below 70% of the threshold. This result can be interpreted as these periods of intense explosive activity of lower energy also present an ordering of the seismic energy to generate the explosions. We can affirm that the entire period can be considered a single eruptive state from the point of view of the SE.
Note we can use these local minima of SE as a tool to developing a more efficient and robust recognition system using ML of small explosions. It is well known that a seismic signal recognition training process using ML requires a high number of previously labelled events, but also with the certainty that these labels undoubtedly correspond to that type of seismic event. Moderate and small volcanic explosions have a signature that is not easy to generalize (Palo et al., 2009). Thus, it is very common to confirm the existence of this type of event visually. But not all volcanoes have visual monitoring systems, nor is it always possible to observe these explosions due mainly to climatic conditions. Therefore, making a double check between the local minima of the SE in active volcanoes and the seismograms would permit: a) to confirm the existence of these explosions, and b) to improve seismic and eruptive catalogues. Thus, an added value to the use of the SE in seismic monitoring is that it can be used to improve the training processes of ML algorithms to be able to recognize volcanic explosions on seismograms.
The explosive sequence prior the quiescence volcanic stage.
After February 2017, the eruptive activity of Volcán de Colima ceased (Arámbula-Mendoza et al., 2020). This is reflected in figure 2, where we can appreciate how SE started to grow reaching the maximum values of all the period studied between March and May 2017. We finalized our study analysing how SE evolves during the end of an eruptive period. Arámbula-Mendoza et al. (2020) identifies 10 volcanic explosions between January 7th and February 3rd, 2017, prior to the quiescence phase started after them (end of February 2017).
As observed in Figure 2, even if there are several volcanic explosions in the period selected in this study, the SE was in a trend to have higher values than in previous months. We can interpret this increase of the SE values due to the approaching of the end of the eruptive episode. However, we could identify relative minima of the SE and associated them with images of the visual monitoring network. In Figure 5 we associated the pictures of 8 of the 10 explosions reported by Arámbula-Mendoza et al. (2020) with the minima of the SE. The other 2 explosions (January 7th and 27th) were not recorded on camera due to high fog, but we can observe minima values for SE (Figure 5). Notice in the pictures that even the ash column is big, the white colour of the clouds leads us to think about a big phreatic component taking part of these explosions, identifying them as low energetic explosions (Palo et al., 2009). As in the previous analysis, these minima presented STA/LTA values close above the 70% of threshold in a dynamic case but below the 70% in case of static analysis.
Remarks.
We remark the systematic analysis of the SE can be a very useful tool in the processes of monitoring and seismic surveillance of volcanoes. Analysing three years of seismic signals at Volcán de Colima SE presents high and stable values when the volcanic activity is low or the volcano is quiescent, while whenever the SE has local minima, or tends towards values close to zero, it is marking eruptive processes.
SE measures the uncertainty in probability distributions (Malfante et al., 2018b), associating maximum SE with maximum uncertainty (all possible outcomes have equal probabilities), and vice-versa coherent outcomes show high probabilities (minimum SE). On the other hand, the Entropy defined by the Statistical Physics establishes that the macroscopic state of a physical system is characterized by a distribution of microstates (Posadas et al., 2021 and cites). A volcanic system is a set of different inner processes defined by a set of microstates defining the exchange of energy with the medium. The configuration of equilibrium of a volcanic system, for example a quiescence period, is associated with minimum exchange of energy and low values of Entropy. Seismic record associated to this state is characterized by a random low energetic composition of signals providing high SE values. In opposition, seismic signals with similar temporal and frequency patterns (same source) provide low SE values. In tectonic seismology high Entropy and low SE are associated to the arrival of large earthquakes with impulsive and energetic phases generated in the same source (van Ruitenbeek et al., 2020). In volcanic systems the increase of the Entropy is related to several microstates associated to the inner dynamic of the volcano. Particles of gas, magma, bubbles, solid material and other components existing in the interior of the volcano interact between them and with the limits of the volcanic structure, exchanging energy. When these microstates are coherently organized to generate a “volcanic macrostate”, i.e. oriented to produce a volcanic eruption, then the values of the SE is moved toward zero and the Entropy is maximum.