Remote seismic influence on large explosive eruptions

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 17, NO. B1, 218, 1.129/21JB37, 22 Remote seismic influence on large explosive eruptions Warner Marzocchi Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Naples, Italy Received 26 September 2; revised 31 January 21; accepted 2 August 21; published 26 January 22. [1] The physical process governing the occurrence of the greatest explosive eruptions is characterized by a very high number of degrees of freedom. In this case, as well as for any stochastic and/or complex system, the knowledge of the process can be significantly improved by identifying any kind of nonrandom pattern. For example, a correlation with other processes would imply that some degrees of freedom are more important than the others. In this view, the main goal of this paper is to test if the perturbation induced on a volcanic area by great tectonic earthquakes can modify the probability of a volcanic event. The results obtained show that the occurrence of the largest explosive eruptions of the last century is significantly correlated to the earthquakes that occurred 5 and 3 35 years before, at distances up to 1 km. Such a coupling might be attributed to the coseismic and postseismic stress diffusion. This result provides new insights that may be used in volcanic risk mitigation. INDEX TERMS: 8414 Volcanology: Eruption mechanisms, 732 Seismology: Seismicity and seismotectonics; KEYWORDS: Explosive eruptions, Triggering, Stress interaction, Post-seismic stress variations 1. Introduction [2] Until few years ago, the volcanoes were usually considered isolated systems, that is, systems without significant interactions with the surrounding regions. Indeed, in spite of some reported cases in which eruptions were apparently linked to regional earthquakes [Yokoyama, 1971; Nakamura, 1975], the lack of convincing statistical arguments fed a general skepticism about this coupling. Recently, the first quantitative and statistically significant evidence for such interactions were found [Marzocchi et al., 1993; Linde and Sacks, 1998]. Nevertheless, these studies differ in terms of the time lag identified (from few seconds to one decade), and they do not consider the largest eruptions. Since both issues are of primary concern for their scientific and social implications [e.g., Heiken, 1999], they deserve a further detailed analysis. [3] The physical process behind the occurrence of a volcanic eruption, as well as any natural process, is a stochastic process governedby a very high number of degrees of freedom [e.g., Feynman, 1967; Ventsel, 1983]. The study of these systems should focus first on the relative weights of these degrees of freedom. In the case when most have the same relative importance, the resulting stochastic process tends to have a Poissonian distribution [Feller, 1968], and the future evolution of the system can be forecast by simply estimating the single parameter of the distribution. The data obtained from such a system do not show any significant correlation with other processes and, in general, no departure from complete randomness. Hence the knowledge of the processes occurring outside the system itself does not add any significant information to improve the forecasting. [4] In contrast, if a few degrees of freedom are more important than others, their empirical or theoretical modeling enhances the physical knowledge of the system, and as a direct consequence, it improves the forecasting capability. In this case, the data set obtained from such a system shows nonrandom patterns, such as memory, regularities, and/or correlations with other processes occurring inside and/or outside the system. [5] Here, I assess the correlation between regional earthquakes (occurring outside the volcanic areas) andthe largest explosive eruptions of the last century. Particular attention is devoted to the Copyright 22 by the American Geophysical Union /2/21JB37$9. estimation of the time lag between the events because it may provide useful indications on the physics of the underlying processes. 2. Data Set [6] The eruption data are taken from the catalogs reported by the Smithsonian Institution [Simkin and Siebert, 1994]; they consist of eight volcanic events with VEI 5 in the last century (see Table 1). The choice of this threshold is based on three considerations, two technical and one practical. The first is that for such a threshold the volcanic catalog of the last century is certainly complete. The second one is that magmas erupted in large Plinian events are probably gas charged and in some (or perhaps all) cases water saturated. So they are easily disturbed by transient or static stress changes. Compressible volatile phases will respond much more to stress changes than will an incompressible silicate melt. The third consideration is that the volcanic eruptions of such a magnitude are by far the most important from a social point of view. [7] The seismic data are relative to two different data sets. One is composed by the Pacheco and Skyes [1992] catalog that contains the worldwide shallow (depth 7 km) seismic events with M s 7. in the period For the remaining decade ( ) this catalog has been integrated with M s 7. seismic events reported by the Harvard centroid moment tensor (CMT) catalog [Dziewonski et al., 1981; Dziewonski and Woodhouse, 1983]. The total number of events of this data set (hereinafter referred to as PSCMT-M7) is 792 (see Figure 1). The other data set (hereinafter referred to as P-M6) is formed by the Perez s [1999] catalog, which consists of 3186 seismic events with M s 6. in the period (see Figure 2). 3. Strategy of Analysis [8] The first step for each kind of statistical analysis is to provide a clear definition of the null hypothesis H to be tested. This choice strictly depends on the a priori knowledge of the process itself and on the philosophy of work adopted. Here, under the assumption of an almost complete ignorance on the physics of the process, the minimalist philosophy of Occam s razor is followed. The simplest model is certainly a completely random EPM 6-1

2 EPM 6-2 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS Table 1. List of Eruptions With VEI 5 in the 2th Century Date VEI Index Name 24 Oct Santa Maria 28 March Ksudach 6 June Novarupta 1 April Cerro Azul (Quizapu) 3 March Bezymianny 18 May Mount St. Helens 15 June Pinatubo 8 Aug Hudson spatiotemporal process in which the volcanic eruptions occur independently from regional seismic activity. This model would be rejected if the data show significant departures from this model. The test of the null hypothesis involves the following two steps Defining the Perturbation Function [9] In the first step, I define a perturbation function f (k) i (t). Mo j, x j, and t j are the seismic moment, the epicentral coordinates, and the time of occurrence of the jth seismic event of the data set, respectively; X k, and T k the coordinates and the time of onset of the kth volcanic eruption. Under the assumption that the perturbation that might be induced by an earthquake on a volcano is directly proportional to the seismic moment released and decays with the distance [King et al., 1994; Pollitz, 1992; Piersanti et al., 1995, 1997] the perturbation function can be written as f ðkþ i ðtþ ¼ XN j¼1 Mo j w d jk Hi t; T k t j : ð1þ In (1), i is a positive integer, t is a time window fixed a priori, N is the number of earthquakes of the data set, w(d jk ) is a weight function depending on the distance d jk = X k x j, and H i (t; z) is the step function: H i ðt; zþ ¼ 1 ði 1Þt < z it otherwise: ð2þ In other words, f (k) i (t) mimics the perturbation that might be induced on the kth erupting volcano by earthquakes that occurred at a time t for which (i 1)t < T k t it. The plot of f (k) i (t) versus i describes the time trend of the perturbation function. For example, f (2) 3 (t = 5 years) represents the perturbation that might be induced by earthquakes that occurred 1 15 years before the second eruption of the catalog. The weight function w kj (see Figure 3) has been computed through a polynomial fit of the averaged spatial evolution of the postseismic stress due to a point source in a spherical self-gravitating model [Piersanti et al., 1995, 1997]. [1] It might be argued that the perturbation function f (k) i (t) resembles the stress perturbation induced on a volcano by tectonic earthquakes. Despite the undoubted similarity, it is worth noting that two important differences exist. The first one is that f (k) i (t) is radially symmetrical around the epicenter, while the stress induced by earthquakes is not. The latter can be evaluated only by knowing the details of the source mechanism of the earthquakes. The second difference is that the weight function w probably underestimates the effect of very strong earthquakes (such as Chile 196, Alaska 1964) because in that case, the assumption of point source does not hold. In practice, the function w decreases of some order of magnitude in the first hundreds of kilometers (see Figure 3), a dimension comparable to the length of the rupture of the largest earthquakes. [11] In any case, the perturbation function f (k) i (t) can be considered a reliable estimator of a possible coupling between tectonic earthquakes and volcanic eruptions. This coupling, indeed, would be the most likely physical mechanism to explain eventual statistically significant peaks in the f (k) i (t) function Statistical Significance of the Test [12] The second step consists of estimating the significance level a at which the null hypothesis is rejected. In order to accomplish this, I define a function i (t): i ðtþ ¼ XM k¼1 f ðkþ i ðtþ; where M is the number of eruptions in the catalog. The summation over M leads to a stacking of the effects. This procedure has the ð3þ Figure 1. Plot of the PSCMT-M7 seismic data set.

3 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS EPM Figure 2. Plot of the P-M6 seismic data set. advantage of enhancing the signal-to-noise ratio, since the signal tends to be in phase while the noise does not. This procedure is useful in the present case where there is scarce knowledge of the process, and the perturbations produced by the earthquakes are probably comparable to the noise [e.g., Kelly and Sears, 1984]. [13] The test consists of verifying if the largest peaks of the function i (t) can be attributed to random fluctuations by keeping the seismic data set fixed and using 1 synthetic volcanic data sets. In order to do this, 1 synthetic functions (s) i (t) are generated through equations (1) and (3). The index s stands for the sth synthetic volcanic data set used. Each synthetic eruption data set is generated by assuming that the interevent times are exponentially distributed, that is, the occurrence of volcanic eruptions follows a Poisson process. This hypothesis is not rejected for the real data set by using the one-sample Kolmogorov-Smirnov test [Hollander and Wolfe, 1973]. Each erupting volcano in the synthetic data set is selected randomly from the volcanoes that experienced at least one eruption in the last four centuries having the same volcanic explosivity index (VEI) value of the real data set (VEI 5[Simkin and Siebert, 1994]). In order to avoid bias in the results it is set that each synthetic eruption cover the same length of the past seismic catalog as the corresponding real volcanic eruption. [14] Therefore the significance level a of a generic kth peak of the function i (t) is estimated through 4. Discussion and Final Remarks [16] Figures 4 and 5 report f i (k) (t) for each eruption in the catalog by using t = 3 and 5 years and the two seismic data sets. As can be seen from Figures 4 and 5, only two volcanic events, the Novarupta and Mount St. Helens eruptions, do not show any peak in the f i (k) (t) function. Five out of eight events have a peak at 5 years before, and two out of four events, the Bezymianny and the Hudson eruptions, have a large peak 3 years before (see Figure 4). For the latter peak, I consider only four events in total, because the first four eruptions occurred too early in the century to be counted in the results. For each kth eruption, Table 2 reports the earthquakes of the catalog that produce the peaks in the f i (k) (t) function. [17] Figure 6 reports the stacked function i (t) and the significance level of the largest peaks for t = 3 and 5 years and for the different data set used. Two different significant peaks, relative to anomalous high values of the function i at 5 years and 3 35 years, are found. Both patterns are stable, independent from the a ¼ 1 P s¼1 h i Z s k ðtþ; k ðtþ 1 ; ð4þ where Z i ða; bþ ¼ 1 a b otherwise: ð5þ [15] In order to check the dependence of the results on the choice of t, two different values, 3 and 5 years, are used in the analysis. Figure 3. Common logarithm of the weight function w(d) (see equation (1)), where d is the distance between an earthquake and an erupting volcano.

4 EPM 6-4 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS Figure 4. Plot of the perturbation function f (k) i (t) for each eruption of the catalog (see Table 1). The PSCMT-M7 seismic data set is used. The function f (k) i (t) (in arbitrary units) and the time lag (in years) are reported in the y axis and x axis, respectively. value of t and the seismic data set used. The significance level of these two peaks (i.e., the probability to observe them by chance) ranges from.2 to.12. A further check of the stability of the results has been performed by excluding the Chile earthquake from the real seismic data set; indeed, this event is by far the largest of all the other earthquakes, and therefore it could potentially bias the results of the analysis. The results obtained in this case are the same reported in Figure 6. The goodness of the method has been also verified by applying the same procedure to the eruptions and the following earthquakes. In this case, as expected, I do not find any significant and stable peak. [18] To summarize, the obtained results suggest a statistically significant coupling between the largest eruptions and the earthquakes that occurred 5 and 3 35 years before. It is still remarked that in spite of the low number of volcanic eruptions considered (eight), the significance level found indicates that the coupling observed has a low probability to be due to a chance. I interpret this link in terms of the coseismic ( 5 years) and postseismic (3 35 years) stress changes in the volcanic areas induced by the regional earthquakes. [19] The coseismic stress is a well-established feature responsible for the distribution of the aftershocks [King et al., 1994;

5 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS EPM 6-5 Figure 5. As for Figure 4 but for the P-M6 seismic data set. Stein et al., 1992], and sometimes, it is also invoked to forecast possible epicenters of great earthquakes after a main shock [Parson et al., 2]. The results obtained here might represent the first statistically significant evidence of the coseismic effects on the explosive volcanic activity at a global scale. Recently, a coseismic stress model has been successfully applied to the volcanic eruptions of the Pinatubo and Vesuvius [Bautista et al., 1996; Nostro et al., 1998]. Actually, these models assume a complete elastic medium and therefore without any time lag between the events. The time lag found here ( 5 years) can be attributed to the inertia of the volcanic system in reacting to the static stress changes, to a delay due to a nonperfect elasticity of the crust, and/or to the stress corrosion effect [e.g., Main and Meredith, 1991]. [2] The other time lag, 3 35 years, is a novelty. The values obtained are compatible to the relaxation time of a viscous asthenosphere [Piersanti et al., 1995, 1997; Pollitz et al., 1998]. In this regard, it is interesting to note that the largest part of the volcanic and seismic events considered in the analysis occurred in the proximity of the Pacific ring where a well-formed viscous asthenosphere is present. This time lag is compatible with the Kenner and Segall s [2] empirical findings; through recent geodetic data, they calculated that the effective relaxation time for long-term postseismic deformation following the 196 San Francisco earthquake is 36 ± 16 years. In few words, at that time lag the postseismic stress diffusion almost reaches its maximum effect. [21] The postseismic effects were extensively studied in the last years [Pollitz, 1992; Piersanti et al., 1995, 1997; Pollitz et Table 2. Earthquakes of the PSCMT-M7 Catalog Coupled to the Explosive Eruptions With VEI 5 Volcano a Date Latitude, N Longitude, E Time Lag, years Distance, km f b Santa Maria 23 Sept April Ksudach 25 June June Novarupta Cerro Azul 1 Dec Bezymianny 4 Nov April Feb Feb Mount St. Helens Pinatubo 16 July Hudson 6 June May a See Table 1. b Perturbation function in arbitrary units (see text).

6 EPM 6-6 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS Figure 6. Stacked results (all eruptions in the data set). The functions (t) relative to the two different seismic data sets (PSCMT-M7, and P-M6), and for t = 3 and 5 years, are reported; a is the significance level of the test, i.e., the probability to observe a peak by chance. al., 1998]; however, their significant effects on the Earth s crust were only hypothesized [Romanowicz, 1993; Pollitz et al., 1998] but not statistically proved [Johnson and Sheridan, 1997]. This lack of convincing empirical evidence in favor of a significant contribution of the postseismic effects on the state of stress raised a scientific debate [Kerr, 1998] and, at the same time, led to a large amount of skepticism regarding this issue. The results found here might be considered the first statistically significant evidence supporting postseismic effects at a global scale. [22] The adopted procedure investigates only the temporal aspect of the coupling. The spatial aspect can be checked by plotting, for each one of the two significant peaks, a histogram reporting the fractions of the value of i (t) as a function of the distance of the earthquakes. Such histograms are given in Figure 7 for t = 5 years and the PSCMT-M7 catalog. As it can be seen from Figure 7 (and Table 2), for the shorter time lag ( 5 years), most of the earthquakes that produce a significant perturbation in the volcanic area occurred 1 3 km from the volcanoes. This value is comparable to the mean distance between the subduction zones where most of the earthquakes occur and the location of the volcanoes related to the subduction. [23] Most interesting is the plot of the longer time lag (3 35 years); in this case, a significant percentage of the stacked perturbation function i (t) is linked to the Chile earthquake (see Table 2) which occurs 8 km from the Hudson volcano. This is further confirmation of a postseismic effect, since the models show that the relative importance of the postseismic compared to the coseismic effects grows with distance [Piersanti et al., 1995, 1997]. [24] The significant correlation that was found suggests that some large explosive eruptions might be promoted by earthquakes at distances of hundreds of kilometers. These distances are much larger than what suspected until a few years ago, and they would indicate that the volcanic areas cannot be considered as isolated systems. The use of the term promote rather than the term trigger throughout this paper is worth being remarked. Indeed, the word trigger appears to imply a more deterministic link between earthquakes and eruptions, such as a one-to-one correlation. Actually, the found coupling represents only one prominent degree of freedom out of the high number that characterize the erupting process. Therefore the coupling acts on a probabilistic (rather than deterministic) level by significantly altering the probability of occurrence of the volcanic event. [25] In principle, this finding can be profitably used to reduce the volcanic risk. However, to be effective, this issue needs a lot of further work. In this respect, the most impelling questions concern three different aspects. The first one consists of improving the study of the coseismic and postseismic effects by taking into account the focal mechanism of the earthquakes and the geometry of the tectonic structure of the volcanic areas [e.g., Nostro et al., 1998]. [26] The second one concerns the physical mechanism of the largest eruptions. As a matter of fact, no one knows what the most effective physical mechanism is by which a stress perturbation can promote a volcanic event. In general, an earthquake can promote an eruption by increasing the pressure on the magma chamber and/ or facilitating the opening of the conduits toward the surface. However, other more complex mechanisms that amplify the stress perturbations are possible (see, for example, the rectified diffusion proposed by Brodsky et al. [1998]). [27] The third aspect is converting the coupling found into a well-defined increase in probability of an eruption. As mentioned before, the found coupling represents one important degree of freedom (though certainly not the only one) in promoting a large explosive volcanic eruption. Through its modeling, we can reduce the range of unpredictability for the forecasting of the volcanic eruption. These aims are certainly the most important challenges for future research in this field.

7 MARZOCCHI: REMOTE SEISMIC INFLUENCE ON LARGE EXPLOSIVE ERUPTIONS EPM 6-7 Figure 7. Histograms reporting the fraction of the function (t = 5y) versus the distance of the earthquakes for the two peaks at 5 years and at 3 35 years (PSCMT-M7 catalog). [28] Note added in proof. Recently, L. Siebert of the Smithsonian Institution told me that the El Chichon (Mexico) eruption in 1982 also had a VEI index of 5. The inclusion of this eruption in the calculation does not modify the results reported in this paper. [29] Acknowledgments. I would like to thank Dave Hill, the Associate Editor, and an anonymous referee for their helpful comments. The paper has greatly benefit from their reviews. The paper was supported by the Gruppo Nazionale di Vulcanologia. References Bautista, B. C., L. P. Bautista, E. S. Barcelona, R. S. Punongbayan, E. P. Laguerta, A. R. Rasdas, G. Ambubuyog, E. Q. Amin, and R. S. 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