Interactions between earthquakes and volcano activity

GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L24303, doi:10.1029/2007gl031438, 2007 Interactions between earthquakes and volcano activity Nicolas Lemarchand 1 and Jean-Robert Grasso 1 Received 29 July 2007; revised 1 October 2007; accepted 15 October 2007; published 21 December 2007. [1] Using the 1973 2005 worldwide catalogues for M 4.8 seismicity and VEI 0 volcano eruptions, we find a significant, when tested against catalogue randomizations, increase of eruption onsets on the earthquake day. This result emerges from stacking time series of daily eruption rates relatively to earthquake time, t 0, over the whole seismicity catalogue. It is stronger for earthquake-volcano pairs for which the volcano is within ten rupture size from the epicenter. These results show that M 4.8 VEI 0 earthquake-volcano pairs are as important for interaction processes as the M 7 and VEI 2 5 pairs previously reported to interact. The clustering in time for earthquakeeruption pairs is not bounded to t 0.Itremainsabovethe background noise 6 10 days before and after t 0, and follows a power law distribution. These patterns, which are similar to the direct and inverse Omori s laws observed for tectonic earthquakes, are the first evidence for the volcano eruptions to be contemporary of a stochastic brittle damage in the earth crust. The clustering we observe in time and space (i) rejects the earthquake triggering as the single process that drive earthquake-volcano interactions; (ii) supports a regional tectonic coupling in the earth crust damage. Citation: Lemarchand, N., and J.-R. Grasso (2007), Interactions between earthquakes and volcano activity, Geophys. Res. Lett., 34, L24303, doi:10.1029/2007gl031438. 1. Introduction [2] Earthquakes and volcano eruptions have recently been shown to interact in the far field (200 800 km) when large earthquake-eruption pairs are involved, i.e., M 7, VEI 2 5 for earthquake and eruptions, respectively [e.g., Linde and Sacks, 1998; Marzocchi, 2002; Marzocchi et al., 2004; Manga and Brodsky, 2006]. Such interactions have also been observed for mud volcanoes, whose eruptions are statistically more numerous after regional M 5 earthquakes [Mellors et al., 2007]. Most of these interactions are conceptually explained by dynamic triggering of an eruption by the seismic waves. The observations and the possible mechanics of the delayed triggering of eruptions by earthquakes, for example, years, are more difficult to quantify than the immediate correlation with seismic wave arrival times [e.g., Marzocchi, 2002; Manga and Brodsky, 2006]. In this paper we revisit these interactions by using recent data for small size event pairs, M 4.8, VEI 0, during 1973 2005. By exploring space and time interrelationships between earthquakes and volcano eruptions we find that volcanoes are sensitive to moderate earthquake sizes on time scale of a few days. Because the time patterns 1 Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Grenoble, France. Copyright 2007 by the American Geophysical Union. 0094-8276/07/2007GL031438 of the observed interactions mimic those between aftershocks and foreshocks, we discuss earthquake-eruption interactions in the context of the brittle damage response of the earth crust to generic forcings. 2. Data Analysis and Methods [3] The earthquakes we used are M 4.8 from the U. S. Geological Survey catalogue (http://neic.usgs.gov/neis/epic/ epic.html). In the period 1973 2005. M = 4.8 is the completude magnitude we estimated for this catalogue by using the method described by Ogata and Katsura [1993]. Eruption data are from the Smithsonian Institution Global Volcanism Program catalogue (http://www.volcano.si.edu). We select 883 eruption onsets, corresponding to 231 volcanoes, for which the onset time is known with an accuracy of one-day. [4] In order to analyse how earthquakes and volcano eruptions interact, we use a procedure similar to that of Linde and Sacks [1998]. Conditioning the time on the earthquake occurrence time, t 0, we stack time series of eruptions relative to the earthquake date, for different distance and magnitude ranges (Figure 1). A peak in the daily eruption rate emerges on the earthquake day for volcano eruptions within 30 km from the earthquake (Figure 1b) whereas no signal is observed for earthquake-eruption pairs without distance sorting (Figure 1a). These observations suggest that when analysing M 4.8 earthquakes, we recover similar patterns closer to the volcanoes than the one observed by Linde and Sacks [1998] for larger earthquakes, i.e., a peak in eruption rate at t 0 for M 8 earthquakes in the 0 250 and 500 750 km distance ranges from the volcanoes, and within 200 km distance for M 7 7.9 earthquakes. Within 30 km of a volcano are the regular volcano tectonic (VT) earthquakes that are classically related to brittle failure induced by magma transport within the volcano edifice (for a review, see, e.g., McNutt [2002]). The VT patterns as resolved by local seismic monitoring are small M 3 4 local earthquakes within the volcano edifice, D 5 10 km [e.g., McNutt, 2002; Scott, 1989]. These events are not included in our global M 4.8 catalogue. Thus the peak value we observe for earthquake-volcano interaction for D 30 km is not due simply to regular VTevents. Additionally the highest signal to noise ratio for the peak value of eruption rate is not observed on the volcano edifice per see, including a 15 km epicenter location accuracy (Figures 1 and 2). [5] To explore further the possible coupling between earthquakes and volcano eruptions we select earthquakeeruption pairs by using the D/L ratio. This ratio normalizes the earthquake-eruption distance, D, by the earthquake rupture length, L. This technique is derived from the one used to analyse earthquake-earthquake interactions [e.g., Felzer and Brodsky, 2006]. [6] The best signal to noise ratio is obtained for D/L 10 (Figure 1d), i.e the earthquake-eruption interactions are L24303 1of5

Figure 1. Stacked time series of daily eruption rates relative to earthquake time (for M 4.8 earthquake from the USGS catalogue and eruptions onsets from Smithsonian catalogue): (a) all events, (b) earthquake-eruption pairs with distance D 30 km, (c) earthquake-eruption pairs, D 30 km and D/L 10; L is the earthquake rupture length as derived from the magnitude [Wells and Coppersmith, 1994], (d) earthquake-eruption pairs for D/L 10, and (e) Earthquake-eruption pairs for D/L [10,20]. For Figures 1b 1e, the signal to noise ratios are 40, 48, 12, and 4, respectively. We define the signal as the peak of daily eruption rate value at t 0 and the noise is the mean value of daily eruption rate on the 500, +500 day window. statistically higher when the volcanoes are at distances less than ten fault lengths from the earthquakes. For D/L 10 and all distance ranges, the signal to noise ratio is better than when selecting event pairs with distance criterion only (Figures 1b, 1c, and 2). The t 0 peak value of eruption rate is related to 29 earthquake-eruption pairs for which the magnitude ranges from a M = 4.8 earthquake on the volcano to M = 7.8 at a 160 km distance (Table S1). 1 All these observations are given with a 99% confidence interval. Significant t 0 peak values of eruption rate are not observed when randomizing the initial catalogue either on eruption dates or volcano coordinates. By randomizing the volcano locations and the eruption times we always accept the peak value in the observed eruption rates at t 0 above the 99.7% confidence level. 3. Patterns of Earthquake-Eruption Interactions 3.1. Earthquake-Eruption Pairs at Intermediate Distance: Extending the VT Event Definition [7] The 29 earthquakes, that interact with eruptions at t 0, D/L 10, range in magnitudes and distances from a M = 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2007GL031438. 4.8 earthquake on the volcano to M = 7.8 at a 160 km distance (Table S1). These patterns does not fit the long recognized volcanic earthquake definition [e.g., M 3 4, 5 10 km McNutt, 2002; Scott, 1989].There is no quantitative definition of a VT event in the volcanology community, and also there is a lack of quantitative definition of earthquake foreshocks and aftershocks. Bak et al. [2002] successfully collapse all the California seismicity onto the same curve, demonstrating that there is neither a maximum distance nor a maximum time to define an earthquake as an aftershock, both limits being bounded by the catalog length. The same way, our results suggest that VT events, when defined as earthquakes which interact with a volcano eruption, can be as large as 4.8 7 in magnitude and up to D/L 10. 3.2. Sizes of Events for Interacting Earthquake-Eruption Pairs [8] The distribution in sizes of the 29 earthquake-eruption pairs that cluster at t 0, with D/L 10, significantly differ from the size distributions for both the earthquake catalogue and the eruption catalogue (Figure 3). The probability for a given VEI on the earthquake day is larger 2of5

[12] To compare the after- and fore-shock rates triggered by earthquake-earthquake and earthquake-eruption interactions, respectively, we use the same criteria for both data sets. Accordingly, using the USGS catalogue for stacked Figure 2. Signal to noise ratio for peak amplitude of the eruption rate at t 0 as a function of earthquake-eruption distances. For D 15 km, the signal to noise ratio for event selected by using D/L 10 (black line) is larger than the one of pairs selected using D only (grey line). D, L and signal to noise ratio, same as on Figure 1. than the one expected from the Smithsonian catalogue (Figure 3a). [9] To compare the magnitude distribution of earthquakes which interact with a volcano eruption at t 0 with those of the USGS catalogue, we remove the effects on the probability distribution of sizes that are induced by conditioning the earthquake catalogue with D/L 10. Accordingly, we built synthetic earthquake catalogues by randomly picking one master point in seismic areas, and by selecting, in the USGS earthquake catalogue, 30 events which follow D/L 10 relatively to this master point. The synthetic distributions significantly differ from the initial Gutenberg-Richter distribution (Figure 3b). The distribution of sizes for the 29 earthquakes involved in the D/L 10 earthquakeeruption clustering at t 0, is significantly below the synthetic distributions we constructed using D/L 10 (Figure 3b). Selecting earthquake by (i) a t 0 coupling with eruption onsets and (ii) D/L 10, increases the relative contribution of the smaller earthquake size to earthquake-eruption interactions. 3.3. Time Clustering of Earthquake-Volcano Interactions: Inverse and Direct Omori-Like Patterns [10] Our analysis shows that the clustering of earthquakeeruption pairs exists a few days before and after t 0. Although the associate rate values are smaller than the t 0 peak value, they remain above the noise level and fit an increase of rate toward t 0 whether before or after the t 0 reference event (Figure 4). These power law increases of event rates toward t 0 are reminiscent of the direct and inverse Omori s laws found before and after tectonic earthquakes, respectively. These two Omori s laws are observed when stacking time series of seismicity before and after earthquakes in the same way we stacked eruption rates before and after earthquakes [Omori, 1896; Jones and Molnar, 1979; Helmstetter and Sornette, 2003]. [11] The small number of events above the noise level imposes rough estimates of the exponent values for the Omori s law in the 0.8 0.5 range. Figure 3. Comparison between the cumulative probality size distribution of earthquakes and eruptions paired at t 0, D/L 10 and the original catalogues (see auxiliary material for details). (a) Volcano Explosivity Index (V.E.I.) distribution, black dotted line (Smithsonian catalogue). Eruptions paired with earthquakes at t 0, D/L 10, black line. The 100 realizations of 29 eruptions randomly picked in the Smithsonian catalogue, light grey curves. (b) Earthquake magnitude distribution. For reference, the black dotted line (USGS catalogue). The analytic derivation of black dotted line, when imposing D/L 10, black dashed line. The 100 magnitude distributions of 29 events picked in the USGS catalogue with D/L 10 from an other earthquake, i.e., in a seismic area, light grey lines. The 29 earthquakes that are paired with eruption at t 0, the red line. The distribution of earthquakes that occur a few days after and before eruptions, light and dark orange lines close to the red line, respectively (see Figure 4). 3of5

after and before tectonic earthquakes, respectively. We also notice that the magnitude distribution, for earthquakes that are paired with volcano eruptions within a few days apart, are similar to that for earthquake-eruption pairs at t 0 (Figure 3b). Furthermore the event rate at t 0 is not larger than the one predicted by the power law increase days before and after the eruption day. This lack of specific pattern for the event rate and event size at t = 0, (Figures 3 4) within the one day accuracy we are bound to use for eruption onset timing, are negative evidences for any specific so-called dynamic triggering process at t 0. Figure 4. (a) Number of earthquake-eruption pairs which occur 20 days after t 0,forD/L 10. Because of symmetry in time between earthquakes and volcano eruptions, it can be read either as the number of earthquakes before eruptions or as the number of eruptions after earthquakes. (b) Same as Figure 4a for pairs which occur 20 days before t 0. Power law fits to the event rate and event rate with error bars, black and black-dotted lines, respectively. Noise level as estimated by the average rate on 500/+500 days window, light grey line is. Noise level plus once and twice the noise standard deviation, grey dashed lines. Inserts are the same data in log/log plots. Note that in Figure 4b, the data, especially the bump in the 4 8 day window, can be better fitted using models with a higher degree of freedom (A. Hakimhashemi, personal communication, 2007). However this bump is driven by event pairs relative to one single eruption. It is not a general trend from the stack that deserves to use a more complex data fitting process. earthquake time series where earthquake-earthquake pairs are selected by D/L 10 we find exponent values of seismicity rates after and before earthquakes close to unity. At any rate, the changes in seismicity rates toward and from the eruption onsets are significantly slower than the ones 4. Discussion and Conclusion [13] When applying the same techniques and using the same robustness criteria that demonstrate that M 7 earthquakes are efficient in triggering both volcano eruptions and each other [e.g., Linde and Sacks, 1998; Manga and Brodsky, 2006], we show that using M 4.8, VEI 0 and D/L 10, 1973 2005, 0.3% of eruptions interact with earthquakes. This rate is the same than the 0.4% value found for M 8, VEI 2 and D 800 km, i.e., D/L 5, 1500 2005 by Manga and Brodsky [2006]. The pioneering work of Linde and Sacks [1998], which focussed on large M 7 earthquake-large VEI 2 eruption interactions is only one aspect of the possible earthquake-volcano interactions, with the Linde and Sacks results corresponding to D/L 5 interactions. By normalizing the earthquakevolcano distances by the earthquake size, we highlight the importance of smaller earthquakes in volcano-earthquake interactions, as proposed for earthquake-earthquake interactions by Helmstetter [2003]. The D/L 10 threshold for which the interactions are strongest selects distances within the distance range observed for earthquake interactions [Felzer and Brodsky, 2006], i.e., the so-called aftershocks patterns. Such normalisation by earthquake sizes supports a frequency independent process for earthquake-eruption interactions as suggested for earthquakeearthquake interactions [e.g., Manga and Brodsky, 2006]. [14] Manga and Brodsky [2006] estimated that a 0.4% fraction of triggered eruptions is too large to be expected from the interplay between seismic loading rate and rate of increase of magma overpressure rate with time. This argues for the peak activity of eruptions we observe on the earthquake day not to be driven solely by earthquake triggering. Furthermore, any eruption rate triggered by earthquakes through either static stress changes or dynamic wave skaking is expected to spread a few days-months after the seismic loading, not before it; that is, we expect a non symmetrical eruption rate around t = 0. This is not in agreement with our observation (Figure 4). The time clustering of earthquake-eruption pairs is spread significantly 6 10 days around t 0. [15] On the other hand, these results can be read as purely volcano driven seismicity that extends beyond the regular definition of VT events, these later being bounded to be relatively small M 3 4 events, in the immediate D 5 10 km vicinity of a volcano. Because the best signal to noise ratio is roughly constant up to D/L = 10, our results are not driven solely by earthquakes very close, i.e., D/L 1 3, to the volcanoes. Thus the minimum interaction distance we 4of5

have to consider is in the 20 50 km range (see Table S1), i.e., the order of magnitude of crustal thickenesses. [16] For seismicity rate after and before eruptions, we resolved a power law increase in event rates toward t 0. Although the limited number of earthquake-volcano pairs does not permit determination of accurate values for each of the power law exponents, the 0.5 0.8 values we observed after-before eruptions are significantly smaller than the 0.9 1 values before and after tectonic earthquake-earthquake pairs in the same catalogue. These changes in seismicity rate after and before eruptions are positive evidence for (i) the coupling between earthquakes and volcano eruptions to induce similar seismicity patterns to those observed for earthquake-earthquake interactions; (ii) the slower the loading rate change, i.e., the day-month scale of the volcano processes relative to the second-minute earthquake dynamics, the slower the induced seismicity rate changes. While most of these deterministic properties can be reproduced by many physical processes, including but not restricted to the rate and state friction law models [e.g., Dieterich, 1994], the statistical properties we observe for stacked time series of earthquake-eruption pairs remain unexplained. [17] Because of the reciprocity in time between eruption onsets and earthquake occurrences, the clustering patterns we resolve in Figure 4 question the causality that drives the earthquake-eruption interactions. First we can reject earthquake triggering as the single process involved in increasing the eruption rate. Earthquake triggering cannot induce eruption before the earthquake, as tested by randomizing eruption time. Second, the observed coupling between earthquakes and eruption onsets can possibly be driven by volcano dynamics alone with power law seismicity rates after and before eruptions. This interpretation requires extending the regular VT earthquake definition to larger magnitude and larger distance, i.e., M 4.8 and D/L 10. The last possible process is a common external driving that correlates the regional eruptions and seismicity. As resolved by the signal to noise ratio from the catalogues, the scale of such a crustal-mantle coupling has a minimum size of a few hundred km and a minimum time scale of a few tens of days. One possible candidate for such a regional stress field increase can be a deep magma storage area at the base of the lithosphere. [18] Acknowledgments. We thank A. Linde, A. Helmstetter, G. Daniel, and D. Marsan for helpful discussions and suggestions. We thank A. Linde and an anonymous reviewer for constructive comments. NL and JRG are supported by VOLUME and TRIGGS EC-FP6 projects, contract 08471 and 043386, respectively. References Bak, P., K. Christensen, L. Danon, and T. Scalon (2002), Unified scaling law for earthquakes, Phys. Rev. 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Katsura (1993), Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophys. J. Int., 113, 727 738. Omori, F. (1896), On the aftershocks of earthquakes, J. Colloid. Sci., 7, 111 200. Scott, W. E. (1989), Volcanic and related hazards, in Volcanic Hazards, Short Course Geol. Ser., vol. 1, edited by R. I. Tilling, pp. 9 23, AGU, Washington, D. C. Wells, D. L., and K. J. Coppersmith (1994), New empirical relationship among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am., 84, 974 1002. J.-R. Grasso and N. Lemarchand, Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Université Joseph Fourier, BP 53, F-38041 Grenoble CEDEX, France. (grasso@obs.ujf-grenoble.fr; nicolas.lemarchand@obs.ujf-grenoble.fr) 5of5