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Time dynamics in the point process modeling of seismicity of Aswan area (Egypt)
Chaos, Solitons & Fractals 45 (2012) 47–55
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Chaos, Solitons & Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Time dynamics in the point process modeling of seismicity of Aswan area (Egypt) Luciano Telesca a,⇑, Abuo El-Ela Amin Mohamed b, Mohamed ElGabry b, Sherif El-hady b, Kamal M. Abou Elenean b a b
Consiglio Nazionale delle Ricerche, Istituto di Metodologie per l’Analisi Ambientale, C.da S.Loja, 85050 Tito (PZ), Italy National Research Institute of Astronomy and Geophysics NRIAG, 11421 Helwan, Cairo, Egypt
a r t i c l e
i n f o
Article history: Received 15 June 2011 Accepted 23 September 2011 Available online 28 October 2011
a b s t r a c t The seismicity observed in the Aswan area (Egypt) between 1986 and 2003 was deeply investigated by means of time-fractal methods. The time dynamics of the aftershockdepleted seismicity, investigated by means of the Allan Factor, reveals that the time-clustering behavior for events occurred at shallow depths (down to 12.5 km from the ground) as well as for events occurred at larger depths (from 15 km down to 27.5 km) does not depend on the ordering of the interevent times but mainly on the shape of the probability density functions of the interevent intervals. Moreover, deep seismicity is more compatible with a Poissonian dynamics than shallow seismicity that is definitely more super-Poissonian. Additionally, the set of shallow events shows a periodicity at about 402 days, which could be consistent with the cyclic loading/unloading operations of the Lake Naser Dam. Such findings contribute to better characterize the seismicity of the Aswan area, which is one of the most interesting water reservoirs in the world, featured by reservoir-induced earthquakes. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The dynamics of a seismic process, given by a series of earthquakes, evolves through the variation of three quantities: the time of occurrence, hypocenter and energy, given by the magnitude. The characterization of all these quantities has been based on the concept of fractal, due to the presence of power-law shape in the statistics describing the temporal, the spatial and the energetic features of a seismic process; furthermore, the fractal behavior revealed in these statistics could be considered as the end-product of a self-organized critical state of the Earth’s crust, analogous to the state of a sand pile, which evolves naturally to a critical repose angle in response to the steady supply of new grains at the summit [1]. Gutenberg and Richter [2] established an empirical power-law relationship between the number of events and their energy, leading to the ⇑ Corresponding author. E-mail address: [email protected] (L. Telesca). 0960-0779/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2011.09.003
well-known Gutenberg–Richter law log(N) = a bMth, where N is the number of events with magnitude larger than the threshold Mth. Earthquakes occur in space not homogeneously but clusterized, and this indicates that a fractal spatial model is better suited than a uniform spatial model to describe the spatial distribution of seismicity. The correlation integral method was used to estimate the spatial fractal dimension of series of earthquakes in Irpinia, southern Italy [3]. The investigation and characterization of the temporal distribution of seismic sequences has been receiving much greater attention due to the implications in terms of seismic hazard analysis [4]. In fact, within the general context of the seismic hazard analysis, the reliable estimation of the probability of occurrence of a future earthquake is based on the knowledge of the statistical distribution of the time occurrence of earthquakes. For a completely random seismic process (Poissonian, memoryless, uncorrelated) the probability density function (pdf) of the interevent times is a decreasing exponential function; and such function was extensively
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used to model seismic time occurrences due to its effectiveness in fitting large events. But, some characteristics of Poissonian processes (independent and uncorrelated events) do not characterize most seismic sequences, which can be characterized by a property called time-clusterization, widely observed in several seismic catalogs [5–9]. However, the pdf of the interevent intervals is only one window into a seismic process, because it yields only firstorder information and it reveals none about the correlation properties. The spectral density S(f), which is defined in terms of the Fourier functions and describes the frequency distribution of the power of a temporal process, is the standard method able to investigate the correlation properties of a process. For purely random processes, which are realizations of white noise, the power spectrum is approximately flat for any frequency bands; the temporal fluctuations of such a process are completely uncorrelated, any sample is completely independent of the others, and no memory phenomena exist at all. On the contrary, a power-law shape of the power spectrum, which is linear if plotted on log–log scales, indicates the presence of long-range correlated structures in the process. Such behavior, called scaling, is typical of many geophysical processes and the quantification of the strength of the temporal fluctuations is just performed by estimating the value of the spectral exponent, also called scaling exponent [10]. For seismic sequences it is not possible to directly use the power spectral density, due to the point-like structure of the sequences; however, linked with it there are statistics like the Allan Factor [11], the Fano Factor [12], the Detrended Fluctuation Analysis (DFA) [13], whose power-law shape suggests, similarly to the power spectral density, the presence of long-range correlation among the earthquakes of the analyzed sequence. Discrimination between Poissonian and clusterized sequences [6], spatial variability of time-clustering behavior [14], magnitude-variability of the time-clustering [15] in seismic sequences were performed on several seismic catalogs. In the present study, we aim to analyze the time dynamics of one of the most interesting seismic areas in the world, the Aswan area (Egypt), which raised the interest of many seismologists due to the possible earthquake triggering mechanisms linked with the loading/unloading operations of the Lake Nasser, the water reservoir located in the Aswan area (Fig. 1). We will analyze the time-clustering behavior of the seismic time occurrence series.
2. Study area Aswan hosts the largest dam in Egypt ‘‘The high Dam’’ which is 111 m high, with a crest length of 3830 m and a volume of 44,300,000 cubic meters, impounds a reservoir, Lake Nasser that has a gross capacity of 169 billion cubic meters. Of the Nile’s total annual discharge, some 74 billion cubic meters of water have been allocated by treaty between Egypt and The Sudan, with about 55.5 billion cubic meters apportioned to Egypt and the remainder to The Sudan. Lake Nasser backs up the Nile about 320 km in Egypt and almost 160 km farther upstream (south) in the Sudan [16] making the high dam one of the largest dams
in the world and Nasser lake one of the largest reservoirs in the world as well. Aswan area is known to be seismically active since the occurrence of November 1981 Aswan earthquake (Mw = 5.8). Detailed geological and geophysical surveys in the area confirm the existence of few active faults to the southwest of the Aswan High Dam (e.g. Kalabsha, Khor ElRamla and Kurkur faults) [17–19]. The seismic activity in this area might be related to both tectonic activities along these active faults and/or reservoir induced seismicity due to the Nasser Lake. Regional seismological network was established since 1982 around the northern part of the Naser Lake to monitor earthquake activity. Seismological studies have shown that the majority of the local earthquakes appear to be concentrated at the intersection of the E–W and the N–S faults. This intersection is considered a convenient location for stress accumulation [20]. Generally, the overall faulting displacement in this zone is strike-slip with small normal component. The N–S faults have a low degree of seismic activity compared with the E–W faults. Woodword-Clyde Consultants [17] related the existence of the E–W faults to small differential spreading rates in the northern Red Sea to the north and south of a zone between 22° and 24° north. 3. Time dynamics of Aswan seismicity: method and data analysis We analyzed the time dynamics of the crustal seismicity recorded in the Aswan area (Egypt). The data were extracted from I. The Aswan Seismological Network (ASN) Bulletin, in the time interval 1981–1997 [21]. II. The yearly bulletins of the Egyptian National Seismological Network (ENSN), for the period from 1998 to December 2004 [22]. We analyzed the time span from January 30, 1986 to December 31, 2003. The temporal distribution of the magnitude (open triangles) is shown in Fig. 2 along with the cumulative number of events (red). At beginning of the catalog, it is visible a seismic swarm, indicated by the blue arrow, producing a step-like increase in the cumulative number. Fig. 3 shows the temporal distribution of the depth (black dots). It appears that the seismic events tend to cluster in two depth ranges. Fig. 4a shows the distributions of the depths varying the magnitude. The different curves correspond to the different magnitude classes from 0 to 4 with a bin size of 0.1. The depth distributions are bimodal. The inner plot in Fig. 4a represents the total number of events for each depth class. It is clearly visible that the separation between two groups of events can be obtained taking a threshold depth between 12.5 km and 15 km. In our study, we analyzed the two depth ranges of events: (i) for depth h 6 12.5 km and (ii) for depth h P 15 km. Instead of using only one value as a threshold depth between the two groups, we preferred to use two different threshold values, 12.5 km as the upper limit for the shallower events, and 15 km as the lower limit for
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Fig. 1. Tectonics and 1986–2003 seismicity in Aswan area.
the deeper events, in order to take into account of the depth error, which for these data is generally less than 2 km [23]. Fig. 4b shows the distributions of the magnitudes varying the depth. The different curves correspond to the different depth classes from 0 to 27.5 with a bin size of 2.5 km. The inner plot in Fig. 4b represents the total number of events for each magnitude class. It is clearly visible that the maximum of the total curve is at 2.1, which can be considered as the completeness magnitude [24]. Therefore, hereafter the analysis will be performed on the two seismic sequences: (a) magnitude m P 2.1 and depth h 6 12.5 km (defined as shallow hereafter), and (b) magnitude m P 2.1 and depth h P 15 km (defined as deep hereafter). The Allan Factor (AF) is applied to detect correlations in the sequence of the earthquake counts. Dividing the time axis into equally spaced contiguous windows of duration s, and denoting with Nk(s) the number of events falling into the kth window, the Allan Factor is defined as hðN ðsÞN ðsÞÞ2 i AFðsÞ ¼ kþ12hN ðsÞik , where hi indicates expectation vak lue. If the sequence of earthquakes is clusterized in the time domain, then AF(s) behaves as a power-law function,
AF(s) / sa [25], and the fractal exponent a can be estimated by the slope of the line that fits the curve in its linear range; for a hypothetical Poissonian earthquake sequence the AF is approximately near unity for all timescales s, with a 0. Fig. 5 shows the AF of the seismic sequences recorded in the Aswan area for timescales s from 10 s to about 2 years; the upper timescale approximately corresponds to the 1/ 10 of the entire period; higher timescales would lead to misleading results for the poorer statistics. For the shallow seismicity (Fig. 5a) the AF curve increases with a powerlaw shape s > 104.63 s up to about 107.38 s in bilogarithmic scales. The cutoff timescale 105 s is the so-called fractal onset time [25] and indicates the lower timescale from which the clustering behavior can be detected and quantified. The early flatness up to about 103 s indicates a Poissonian-like behavior of the sequence for the small timescales. The intermediate timescale region between 103 s and 104.6 s can be considered as a ‘‘transfer’’ timescale region between the two opposite behaviors, from Poissonian to clusterized dynamics. The estimate of the scaling exponent in such timescale range is s 0.15. The value of the scaling
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4.5 4.0
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days (Jan 30, 1986- Dec 31, 2003) Fig. 2. Temporal distribution of the magnitudes of Aswan earthquakes (black open triangles). The red line indicates the cumulative number of earthquakes versus time. The blue arrow A indicates the occurrence of the seismic swarm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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days (Jan 30, 1986- Dec 31, 2003) Fig. 3. Temporal distribution of the depths of Aswan earthquakes (black crosses). The red line indicates the cumulative number of earthquakes versus time. The blue arrow A indicates the occurrence of the seismic swarm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
exponent indicates a weak clustering behavior of the sequence. In order to check the significance of such behavior and verify that the obtained AF curve is significantly distinguished from that obtained by Poissonian sequences, characterized by identical mean interevent time and identical number of events, we generated 1000 Poissonian sequences. To each simulated sequence the AF was applied. For each timescale the 95th percentile among the AF values for that timescale was calculated. The final 95% confidence AF curve was, then, given by the set of the 95th
percentiles (green curve in Fig. 5a). The 95% confidence level, even if a quite subjective choice, is generally used to investigate the statistical significance of the results; in the present study we used such choice to evaluate the significant similarity or dissimilarity between the AF curves of the original and surrogate series. The AF curve is significantly different from those obtained by the Poisson surrogates within the scaling range; therefore, the scaling behavior of the seismic cluster is significantly non Poissonian (Fig. 5a). In order to check whether the scaling
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magnitude class Fig. 4. Histogram of the depths varying the magnitude (a), and the magnitude varying the depth (b). The inner plots represents the total number of events for depth (a) and magnitude (b) class.
behavior of the sequence is due to the shape of the probability density function of the interevent times or to the their orderings, we shuffled 1000 times the interevent intervals, and for each shuffle we calculated the AF curve. The 95% confidence AF curve for the shuffles was calculated as above. Such curve (red curve in Fig. 5a) is lower than the AF curve of the original sequence within the scaling range, and this indicates that the scaling behavior is due to the specific ordering of the interevent intervals. Another interesting feature visible in the AF plot for the shallow seismicity is the presence of the drop at a timescale of about 408 days. A drop in the AF indicates the presence of periodicity in the sequence [26]. In this case a periodicity of about 408 days is consistent (within the estimation error of such timescale) with the cyclic loading/unloading oper-
ations of the Lake Nasser behind the high Dam, and this corroborates the idea of predominance of reservoir-induced triggering mechanisms of the seismicity in the Aswan area, at least during the observation period. For the deep seismicity similar analysis was performed and the results are shown in Fig. 5b. Contrarily to the shallow seismicity, the deep seismicity shows a clustering behavior which seems to depend mainly on the shape of the probability density function of the interevent times, because the 95% AF confidence curve is associated with extreme values of the AF distribution of the shuffled data; in fact, the 95% confidence curve for the shuffles is similar to a sort of top envelope (extreme values) of the original data and this is an indication that clustering does not depend on the ordering. From the 95% confidence curve obtained
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original 95% shuffle 95% Poisson
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log10(τ) (s) Fig. 5. Allan Factor analysis performed on the shallow (a) and deep (b) seismicity. The red and green lines indicate the 95% confidence curves obtained with 1000 random shuffles and Poissonian surrogates respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
by applying the Poissonian surrogate method, we observe that deep events at longer timescales are non-Poissonian because the 95% confidence line does not fit the extreme values of the original data. In both cases the 95% confidence curve for the Poissonian surrogates shows an upward deviation for very long timescales, which could be probably related to the finiteness of the sample (same number of events of the real data). Therefore, from these results we can observe that also a Poisson process could looknon-Poissonian for finite samples (for very long timescales). The dataset shows a shallow aftershock-like swarm at the beginning of the catalog (see blue arrow in Fig. 2), which could influence the time-clustering of the whole shallow seismicity enhancing its short-term clustering
behavior. In order to better investigate this effect, we removed from the whole seismic sequence all the possible aftershock-like events, by means of the Reasenberg’s algorithm [27]. Fig. 6 shows the comparison between the cumulative number of events of the whole sequence and that of the aftershock-depleted sequence (in all cases we considered only the events with magnitude larger or equal to 2.1, which is the completeness magnitude). The steplike increase, given by the seismic swarm, at the beginning of the catalog is completely removed in the cumulative number curve of the aftershock-depleted sequence. We applied the AF method to the shallow aftershock-depleted sequence and the results are shown in Fig. 7, along with the 95% confidence curves obtained by the random shuffling (red) and the Poissonian surrogate method (green). The
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whole depleted
700 600
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days (Jan 30, 1986 - Dec 31, 2003) Fig. 6. Cumulative number of earthquake versus time of the whole sequence (black) and the aftershock-depleted sequence (red). The minimum magnitude of the events is in both cases given by the completeness magnitude (2.1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the AF of the original series almost overlaps with the AF 95% confidence curve of the shuffles.
AF curve of the original aftershock-depleted series is different from that of the whole sequence shown in Fig. 5a, and this indicates that the seismic swarm influences the timeclustering behavior of the whole sequence, even at long timescales. Anyway, the AF curve is well distinguished from the Poissonian 95% confidence curve, and this indicates that the aftershock-depleted sequence still shows a super-Poissonian behavior; furthermore, the time-clustering is due to the shape of the probability density function of the interevent times rather than their ordering, because
4. Discussion and conclusions The investigation of the time-clustering behavior of a seismic sequence is a fundamental step to be performed in order to assess the modeling of the seismic interevent time distribution, and, in fact, it represents one of the major goals in geophysical studies devoted to seismic analysis. In
Depleted shallow seismicity original 95% shuffle 95% Poisson
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log10(τ) (s) Fig. 7. Allan Factor analysis performed on the shallow aftershock-depleted seismicity. The red and green lines indicate the 95% confidence curves obtained with 1000 random shuffles and Poissonian surrogates, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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particular, in the recent years, the interest of researchers has been growing concerning the identification of different timescale ranges correlated with different types or phases of seismicity, like aftershocks, swarms, background seismicity, or set of mainshocks. Generally, aftershocks and swarms tend to enhance the time-clustering degree of the sequence at relatively short or intermediate timescales. For instance, it was shown by [28] that the volcanic seismicity at Etna volcano, Sicily (Italy) shows an AF curve characterized by two timescale regions, one involving the intermediate timescales up to a crossover of about 4 days and the other involving the longer timescales, describing respectively the time dynamics of seismicity associated with the two strong eruptive crisis occurred between 2000 and 2002, and that of the background [29]; the found crossover, furthermore, was shown to be consistent with the timescale of the magma penetration–induced rock fracturing processes as suggested by Vinciguerra and Barbano [30] and also with the variations of the local magnetic field observed during the main eruptive volcanic episodes [31]. The investigation of time-clustering and the identification of the main timescale ranges were also performed by means of statistical approaches different from the AF method. Mega et al. [32] used the diffusion entropy to study the interevent time distribution of the seismicity in California and found that the time intervals between two successive large earthquakes are not Poissonianly distributed, contrarily to the generalized Poisson model, in which earthquakes are grouped into temporal clusters of events, characterized by intracluster correlations (due to the aftershock activation within a cluster following the Omori’s law) and intercluster uncorrelation (due to the random distribution of the mainshocks in time). The long range (LR) model that was proposed by Mega et al. [32] and then discussed by Helmstetter and Sornette [33] and by Mega et al. [34], reproduced the power-law of the intracluster swarms and intercluster distances. The analysis performed in the present paper aimed at revealing statistical features in the time dynamics of the seismicity observed in the Aswan area (Egypt) between 1986 and 2003, one of the most interesting water reservoirs in the world, characterized by the occurrence of reservoir-induced earthquakes. The time dynamics of the aftershock-depleted seismicity, investigated by means of the Allan Factor, reveals that the time-clustering behavior for events occurred at shallow depths (down to 12.5 km from the ground) as well as for events occurred at larger depths (from 15 km down to 27.5 km) does not depend on the ordering of the interevent times but mainly on the shape of the probability density functions of the interevent intervals. However, the deep and shallow events differ in the sense that the deep events are more compatible with a Poisson process than the shallow events, which are definitely more super-Poissonian. This finding seems to reinforce the results obtained in the study performed by Mega et al. [32] that evidenced non-Poissonian features in sequences of mainshocks, that is sequences not characterized by the Omori’s effect, indicating the presence of a correlation mechanism beyond Omori’s law.
Additionally, the set of shallow events shows a periodicity at about 402 days, which could be consistent with the cyclic loading/unloading operations of the Lake Naser Dam. Acknowledgements The present study was supported by the CNR/ASRT 2011-2012 Project ‘‘Spatiotemporal seismicity patterns and earthquake precursors at Aswan, Egypt contribution to earthquake hazard assessment’’. References [1] Bak P, Tang C, Wiesenfeld K. Self-organizing criticality. Phys Rev A 1988;38:364–74. [2] Gutenberg B, Richter CF. Frequency of earthquakes in California. Bull Seism Soc Am 1944;34:185–8. [3] Telesca L, Cuomo V, Lapenna V, Macchiato M. Identifying space–time clustering properties of the 1983–1997 Irpinia–Basilicata (Southern Italy) seismicity. Tectonophysics 2001;330:93–102. [4] Main I. Statistical physics, seismogenesis, and seismic hazard. Rev Geophys 1996;34:433–62. [5] Kagan YY, Jackson DD. Long term earthquake clustering. Geophys J Int 1991;117:345–64. [6] Telesca L, Lovallo M. Non-uniform scaling features in central Italy seismicity: a non-linear approach in investigating seismic patterns and detection of possible earthquake precursors. Geophys Res Lett 2009;36:L01308. [7] Telesca L, Cuomo V, Lapenna V, Macchiato M. Intermittent-type temporal fluctuations in seismicity of the Irpinia (southern Italy) region. Geophys Res Lett 2001;28:3765–8. [8] Telesca L, Cuomo V, Lapenna V, Macchiato M. Depth-dependent time-clustering behavior in seismicity of southern California. Geophys Res Lett 2001;28:4323–6. [9] Telesca L, Lapenna V, Macchiato M. Spatial variability of timecorrelated behaviour in Italian seismicity. Earth Planet Sci Lett 2003;212:279–90. [10] Telesca L, Cuomo V, Lapenna V, Macchiato M. On the methods to identify clustering properties in sequences of seismic timeoccurrences. J Seismol 2002;6:125–34. [11] Allan DW. Statistics of atomic frequency standards. Proc IEEE 1966;54:221–30. [12] Lowen SB, Teich MC. Estimation and simulation of fractal stochastic point processes. Fractals 1995;3:183–210. [13] Peng C-K, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. CHAOS 1995;5:82–7. [14] Telesca L, Cuomo V, Lapenna V, Macchiato M. Detrended fluctuation analysis of the spatial variability of the temporal distribution of Southern California seismicity. Chaos Solitons Fract 2004;21:335–42. [15] Telesca L, Macchiato M. Time-scaling properties of the UmbriaMarche 1997–1998 seismic crisis, investigated by the detrended fluctuation analysis of interevent time series. Chaos Solitons Fract 2004;19:377–85. [16] Latif AFA. Lake Nasser the new man-made lake in Egypt (with reference to Lake Nubia). In: Taub FB, editor. Ecosystems of the world 23. Lakes and reservoirs. Amsterdam, Oxford, New York, Tokyo: Elsevier Publishing Co.; 1984. p. 385–410. [17] Woodward-Clyde Consultants. Earthquake activity and stability evaluation for the Aswan High Dam. Unpublished report, High and Aswan Dam Authority, Ministry of Irrigation, Egypt; 1985. [18] Abou Elenean, K. Seismotectonics of Egypt in relation to the Mediterranean and Red Seas tectonics. PhD thesis, Ain Shams Univ., Egypt; 1997. 191 p. [19] Abu Elenean KM. Focal mechanism and stress tensor inversion of earthquakes in and around Nasser Lake. Egypt Bull Fac Sci Zagazig Uni Egypt 2003;25:77–107. [20] Talwani P. Characteristic features of intraplate earthquakes. Seismol Res Lett 1989;59:305–10. [21] Aswan Seismological Network Bulletin, Aswan Seismological Center (1981–1997), National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt. [22] Egyptian National Seismic Network Bulletin (1997–2004), National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt.
L. Telesca et al. / Chaos, Solitons & Fractals 45 (2012) 47–55 [23] Awad M, Mizoue M. Earthquake activity in the Aswan region, Egypt. Pageoph 1995;145:69–86. [24] Mekkawi M, Grasso J-R, Schnegg P-A. A long-lasting relaxation of seismicity at Aswan reservoir, Egypt, 1982–2001. Bull Seismol Sic Am 2004;94:479–92. [25] Thurner S, Lowen SB, Feurstein MC, Heneghan C, Feichtinger HG, Teich MC. Analysis, synthesis, and estimation of fractal-rate stochastic point processes. Fractals 1997;5:565–96. [26] Turcott RG, Lowen SB, Li E, Johnson DH, Tsuchitani C, Teich MC. A nonstationary poisson point process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons. Biol Cybernet 1994;70:209–17. [27] Reasenberg P. Second-order moment of central California seismicity, 1969–1982. J Geophys Res 1985;90:5479–95. [28] Currenti G, Del Negro C, Lapenna V, Telesca L. A characteristics of local geomagnetic field and seismicity at Etna volcano and their
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dynamics in relation to the eruptive activity. Earth Planet Sci Lett 2005;235:96–106. Del Negro C, Currenti G. Volcanomagnetic signal associated with the 2001 flank eruption of Mt. Etna Geophys Res Lett 2003;30:7–10. Vinciguerra S, Barbano MS. Clustering of seismicity at Mt. Etna Phys Chem Earth 2000;25:699–703. Del Negro C, Currenti G, Napoli R, Vicari A. Volcanomagnetic changes accompanying the onset of the 2002–2003 eruption of Mt. Etna (Italy). Earth Planet Sci Lett 2004;229:1–14. Mega MS, Allegrini P, Grigolini P, Latora V, Palatella L, Rapisarda A, et al. Power-law time distribution of large earthquakes. Phys Rev Lett 2003;90:188501. Helmstetter A, Sornette D. Comment on power-law time distribution of large earthquakes. Phys Rev Lett 2004;92:129801. Mega SM, Allegrini P, grigolini P, Latora V, Palatella L, Rapisarda A, et al. Reply, to the comment. Phys Rev Lett 2004;92:129802.
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Chaos, Solitons & Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Time dynamics in the point process modeling of seismicity of Aswan area (Egypt) Luciano Telesca a,⇑, Abuo El-Ela Amin Mohamed b, Mohamed ElGabry b, Sherif El-hady b, Kamal M. Abou Elenean b a b
Consiglio Nazionale delle Ricerche, Istituto di Metodologie per l’Analisi Ambientale, C.da S.Loja, 85050 Tito (PZ), Italy National Research Institute of Astronomy and Geophysics NRIAG, 11421 Helwan, Cairo, Egypt
a r t i c l e
i n f o
Article history: Received 15 June 2011 Accepted 23 September 2011 Available online 28 October 2011
a b s t r a c t The seismicity observed in the Aswan area (Egypt) between 1986 and 2003 was deeply investigated by means of time-fractal methods. The time dynamics of the aftershockdepleted seismicity, investigated by means of the Allan Factor, reveals that the time-clustering behavior for events occurred at shallow depths (down to 12.5 km from the ground) as well as for events occurred at larger depths (from 15 km down to 27.5 km) does not depend on the ordering of the interevent times but mainly on the shape of the probability density functions of the interevent intervals. Moreover, deep seismicity is more compatible with a Poissonian dynamics than shallow seismicity that is definitely more super-Poissonian. Additionally, the set of shallow events shows a periodicity at about 402 days, which could be consistent with the cyclic loading/unloading operations of the Lake Naser Dam. Such findings contribute to better characterize the seismicity of the Aswan area, which is one of the most interesting water reservoirs in the world, featured by reservoir-induced earthquakes. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The dynamics of a seismic process, given by a series of earthquakes, evolves through the variation of three quantities: the time of occurrence, hypocenter and energy, given by the magnitude. The characterization of all these quantities has been based on the concept of fractal, due to the presence of power-law shape in the statistics describing the temporal, the spatial and the energetic features of a seismic process; furthermore, the fractal behavior revealed in these statistics could be considered as the end-product of a self-organized critical state of the Earth’s crust, analogous to the state of a sand pile, which evolves naturally to a critical repose angle in response to the steady supply of new grains at the summit [1]. Gutenberg and Richter [2] established an empirical power-law relationship between the number of events and their energy, leading to the ⇑ Corresponding author. E-mail address: [email protected] (L. Telesca). 0960-0779/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2011.09.003
well-known Gutenberg–Richter law log(N) = a bMth, where N is the number of events with magnitude larger than the threshold Mth. Earthquakes occur in space not homogeneously but clusterized, and this indicates that a fractal spatial model is better suited than a uniform spatial model to describe the spatial distribution of seismicity. The correlation integral method was used to estimate the spatial fractal dimension of series of earthquakes in Irpinia, southern Italy [3]. The investigation and characterization of the temporal distribution of seismic sequences has been receiving much greater attention due to the implications in terms of seismic hazard analysis [4]. In fact, within the general context of the seismic hazard analysis, the reliable estimation of the probability of occurrence of a future earthquake is based on the knowledge of the statistical distribution of the time occurrence of earthquakes. For a completely random seismic process (Poissonian, memoryless, uncorrelated) the probability density function (pdf) of the interevent times is a decreasing exponential function; and such function was extensively
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used to model seismic time occurrences due to its effectiveness in fitting large events. But, some characteristics of Poissonian processes (independent and uncorrelated events) do not characterize most seismic sequences, which can be characterized by a property called time-clusterization, widely observed in several seismic catalogs [5–9]. However, the pdf of the interevent intervals is only one window into a seismic process, because it yields only firstorder information and it reveals none about the correlation properties. The spectral density S(f), which is defined in terms of the Fourier functions and describes the frequency distribution of the power of a temporal process, is the standard method able to investigate the correlation properties of a process. For purely random processes, which are realizations of white noise, the power spectrum is approximately flat for any frequency bands; the temporal fluctuations of such a process are completely uncorrelated, any sample is completely independent of the others, and no memory phenomena exist at all. On the contrary, a power-law shape of the power spectrum, which is linear if plotted on log–log scales, indicates the presence of long-range correlated structures in the process. Such behavior, called scaling, is typical of many geophysical processes and the quantification of the strength of the temporal fluctuations is just performed by estimating the value of the spectral exponent, also called scaling exponent [10]. For seismic sequences it is not possible to directly use the power spectral density, due to the point-like structure of the sequences; however, linked with it there are statistics like the Allan Factor [11], the Fano Factor [12], the Detrended Fluctuation Analysis (DFA) [13], whose power-law shape suggests, similarly to the power spectral density, the presence of long-range correlation among the earthquakes of the analyzed sequence. Discrimination between Poissonian and clusterized sequences [6], spatial variability of time-clustering behavior [14], magnitude-variability of the time-clustering [15] in seismic sequences were performed on several seismic catalogs. In the present study, we aim to analyze the time dynamics of one of the most interesting seismic areas in the world, the Aswan area (Egypt), which raised the interest of many seismologists due to the possible earthquake triggering mechanisms linked with the loading/unloading operations of the Lake Nasser, the water reservoir located in the Aswan area (Fig. 1). We will analyze the time-clustering behavior of the seismic time occurrence series.
2. Study area Aswan hosts the largest dam in Egypt ‘‘The high Dam’’ which is 111 m high, with a crest length of 3830 m and a volume of 44,300,000 cubic meters, impounds a reservoir, Lake Nasser that has a gross capacity of 169 billion cubic meters. Of the Nile’s total annual discharge, some 74 billion cubic meters of water have been allocated by treaty between Egypt and The Sudan, with about 55.5 billion cubic meters apportioned to Egypt and the remainder to The Sudan. Lake Nasser backs up the Nile about 320 km in Egypt and almost 160 km farther upstream (south) in the Sudan [16] making the high dam one of the largest dams
in the world and Nasser lake one of the largest reservoirs in the world as well. Aswan area is known to be seismically active since the occurrence of November 1981 Aswan earthquake (Mw = 5.8). Detailed geological and geophysical surveys in the area confirm the existence of few active faults to the southwest of the Aswan High Dam (e.g. Kalabsha, Khor ElRamla and Kurkur faults) [17–19]. The seismic activity in this area might be related to both tectonic activities along these active faults and/or reservoir induced seismicity due to the Nasser Lake. Regional seismological network was established since 1982 around the northern part of the Naser Lake to monitor earthquake activity. Seismological studies have shown that the majority of the local earthquakes appear to be concentrated at the intersection of the E–W and the N–S faults. This intersection is considered a convenient location for stress accumulation [20]. Generally, the overall faulting displacement in this zone is strike-slip with small normal component. The N–S faults have a low degree of seismic activity compared with the E–W faults. Woodword-Clyde Consultants [17] related the existence of the E–W faults to small differential spreading rates in the northern Red Sea to the north and south of a zone between 22° and 24° north. 3. Time dynamics of Aswan seismicity: method and data analysis We analyzed the time dynamics of the crustal seismicity recorded in the Aswan area (Egypt). The data were extracted from I. The Aswan Seismological Network (ASN) Bulletin, in the time interval 1981–1997 [21]. II. The yearly bulletins of the Egyptian National Seismological Network (ENSN), for the period from 1998 to December 2004 [22]. We analyzed the time span from January 30, 1986 to December 31, 2003. The temporal distribution of the magnitude (open triangles) is shown in Fig. 2 along with the cumulative number of events (red). At beginning of the catalog, it is visible a seismic swarm, indicated by the blue arrow, producing a step-like increase in the cumulative number. Fig. 3 shows the temporal distribution of the depth (black dots). It appears that the seismic events tend to cluster in two depth ranges. Fig. 4a shows the distributions of the depths varying the magnitude. The different curves correspond to the different magnitude classes from 0 to 4 with a bin size of 0.1. The depth distributions are bimodal. The inner plot in Fig. 4a represents the total number of events for each depth class. It is clearly visible that the separation between two groups of events can be obtained taking a threshold depth between 12.5 km and 15 km. In our study, we analyzed the two depth ranges of events: (i) for depth h 6 12.5 km and (ii) for depth h P 15 km. Instead of using only one value as a threshold depth between the two groups, we preferred to use two different threshold values, 12.5 km as the upper limit for the shallower events, and 15 km as the lower limit for
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Fig. 1. Tectonics and 1986–2003 seismicity in Aswan area.
the deeper events, in order to take into account of the depth error, which for these data is generally less than 2 km [23]. Fig. 4b shows the distributions of the magnitudes varying the depth. The different curves correspond to the different depth classes from 0 to 27.5 with a bin size of 2.5 km. The inner plot in Fig. 4b represents the total number of events for each magnitude class. It is clearly visible that the maximum of the total curve is at 2.1, which can be considered as the completeness magnitude [24]. Therefore, hereafter the analysis will be performed on the two seismic sequences: (a) magnitude m P 2.1 and depth h 6 12.5 km (defined as shallow hereafter), and (b) magnitude m P 2.1 and depth h P 15 km (defined as deep hereafter). The Allan Factor (AF) is applied to detect correlations in the sequence of the earthquake counts. Dividing the time axis into equally spaced contiguous windows of duration s, and denoting with Nk(s) the number of events falling into the kth window, the Allan Factor is defined as hðN ðsÞN ðsÞÞ2 i AFðsÞ ¼ kþ12hN ðsÞik , where hi indicates expectation vak lue. If the sequence of earthquakes is clusterized in the time domain, then AF(s) behaves as a power-law function,
AF(s) / sa [25], and the fractal exponent a can be estimated by the slope of the line that fits the curve in its linear range; for a hypothetical Poissonian earthquake sequence the AF is approximately near unity for all timescales s, with a 0. Fig. 5 shows the AF of the seismic sequences recorded in the Aswan area for timescales s from 10 s to about 2 years; the upper timescale approximately corresponds to the 1/ 10 of the entire period; higher timescales would lead to misleading results for the poorer statistics. For the shallow seismicity (Fig. 5a) the AF curve increases with a powerlaw shape s > 104.63 s up to about 107.38 s in bilogarithmic scales. The cutoff timescale 105 s is the so-called fractal onset time [25] and indicates the lower timescale from which the clustering behavior can be detected and quantified. The early flatness up to about 103 s indicates a Poissonian-like behavior of the sequence for the small timescales. The intermediate timescale region between 103 s and 104.6 s can be considered as a ‘‘transfer’’ timescale region between the two opposite behaviors, from Poissonian to clusterized dynamics. The estimate of the scaling exponent in such timescale range is s 0.15. The value of the scaling
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4.5 4.0
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days (Jan 30, 1986- Dec 31, 2003) Fig. 2. Temporal distribution of the magnitudes of Aswan earthquakes (black open triangles). The red line indicates the cumulative number of earthquakes versus time. The blue arrow A indicates the occurrence of the seismic swarm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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days (Jan 30, 1986- Dec 31, 2003) Fig. 3. Temporal distribution of the depths of Aswan earthquakes (black crosses). The red line indicates the cumulative number of earthquakes versus time. The blue arrow A indicates the occurrence of the seismic swarm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
exponent indicates a weak clustering behavior of the sequence. In order to check the significance of such behavior and verify that the obtained AF curve is significantly distinguished from that obtained by Poissonian sequences, characterized by identical mean interevent time and identical number of events, we generated 1000 Poissonian sequences. To each simulated sequence the AF was applied. For each timescale the 95th percentile among the AF values for that timescale was calculated. The final 95% confidence AF curve was, then, given by the set of the 95th
percentiles (green curve in Fig. 5a). The 95% confidence level, even if a quite subjective choice, is generally used to investigate the statistical significance of the results; in the present study we used such choice to evaluate the significant similarity or dissimilarity between the AF curves of the original and surrogate series. The AF curve is significantly different from those obtained by the Poisson surrogates within the scaling range; therefore, the scaling behavior of the seismic cluster is significantly non Poissonian (Fig. 5a). In order to check whether the scaling
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magnitude class Fig. 4. Histogram of the depths varying the magnitude (a), and the magnitude varying the depth (b). The inner plots represents the total number of events for depth (a) and magnitude (b) class.
behavior of the sequence is due to the shape of the probability density function of the interevent times or to the their orderings, we shuffled 1000 times the interevent intervals, and for each shuffle we calculated the AF curve. The 95% confidence AF curve for the shuffles was calculated as above. Such curve (red curve in Fig. 5a) is lower than the AF curve of the original sequence within the scaling range, and this indicates that the scaling behavior is due to the specific ordering of the interevent intervals. Another interesting feature visible in the AF plot for the shallow seismicity is the presence of the drop at a timescale of about 408 days. A drop in the AF indicates the presence of periodicity in the sequence [26]. In this case a periodicity of about 408 days is consistent (within the estimation error of such timescale) with the cyclic loading/unloading oper-
ations of the Lake Nasser behind the high Dam, and this corroborates the idea of predominance of reservoir-induced triggering mechanisms of the seismicity in the Aswan area, at least during the observation period. For the deep seismicity similar analysis was performed and the results are shown in Fig. 5b. Contrarily to the shallow seismicity, the deep seismicity shows a clustering behavior which seems to depend mainly on the shape of the probability density function of the interevent times, because the 95% AF confidence curve is associated with extreme values of the AF distribution of the shuffled data; in fact, the 95% confidence curve for the shuffles is similar to a sort of top envelope (extreme values) of the original data and this is an indication that clustering does not depend on the ordering. From the 95% confidence curve obtained
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original 95% shuffle 95% Poisson
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log10(τ) (s) Fig. 5. Allan Factor analysis performed on the shallow (a) and deep (b) seismicity. The red and green lines indicate the 95% confidence curves obtained with 1000 random shuffles and Poissonian surrogates respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
by applying the Poissonian surrogate method, we observe that deep events at longer timescales are non-Poissonian because the 95% confidence line does not fit the extreme values of the original data. In both cases the 95% confidence curve for the Poissonian surrogates shows an upward deviation for very long timescales, which could be probably related to the finiteness of the sample (same number of events of the real data). Therefore, from these results we can observe that also a Poisson process could looknon-Poissonian for finite samples (for very long timescales). The dataset shows a shallow aftershock-like swarm at the beginning of the catalog (see blue arrow in Fig. 2), which could influence the time-clustering of the whole shallow seismicity enhancing its short-term clustering
behavior. In order to better investigate this effect, we removed from the whole seismic sequence all the possible aftershock-like events, by means of the Reasenberg’s algorithm [27]. Fig. 6 shows the comparison between the cumulative number of events of the whole sequence and that of the aftershock-depleted sequence (in all cases we considered only the events with magnitude larger or equal to 2.1, which is the completeness magnitude). The steplike increase, given by the seismic swarm, at the beginning of the catalog is completely removed in the cumulative number curve of the aftershock-depleted sequence. We applied the AF method to the shallow aftershock-depleted sequence and the results are shown in Fig. 7, along with the 95% confidence curves obtained by the random shuffling (red) and the Poissonian surrogate method (green). The
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whole depleted
700 600
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days (Jan 30, 1986 - Dec 31, 2003) Fig. 6. Cumulative number of earthquake versus time of the whole sequence (black) and the aftershock-depleted sequence (red). The minimum magnitude of the events is in both cases given by the completeness magnitude (2.1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the AF of the original series almost overlaps with the AF 95% confidence curve of the shuffles.
AF curve of the original aftershock-depleted series is different from that of the whole sequence shown in Fig. 5a, and this indicates that the seismic swarm influences the timeclustering behavior of the whole sequence, even at long timescales. Anyway, the AF curve is well distinguished from the Poissonian 95% confidence curve, and this indicates that the aftershock-depleted sequence still shows a super-Poissonian behavior; furthermore, the time-clustering is due to the shape of the probability density function of the interevent times rather than their ordering, because
4. Discussion and conclusions The investigation of the time-clustering behavior of a seismic sequence is a fundamental step to be performed in order to assess the modeling of the seismic interevent time distribution, and, in fact, it represents one of the major goals in geophysical studies devoted to seismic analysis. In
Depleted shallow seismicity original 95% shuffle 95% Poisson
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log10(τ) (s) Fig. 7. Allan Factor analysis performed on the shallow aftershock-depleted seismicity. The red and green lines indicate the 95% confidence curves obtained with 1000 random shuffles and Poissonian surrogates, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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particular, in the recent years, the interest of researchers has been growing concerning the identification of different timescale ranges correlated with different types or phases of seismicity, like aftershocks, swarms, background seismicity, or set of mainshocks. Generally, aftershocks and swarms tend to enhance the time-clustering degree of the sequence at relatively short or intermediate timescales. For instance, it was shown by [28] that the volcanic seismicity at Etna volcano, Sicily (Italy) shows an AF curve characterized by two timescale regions, one involving the intermediate timescales up to a crossover of about 4 days and the other involving the longer timescales, describing respectively the time dynamics of seismicity associated with the two strong eruptive crisis occurred between 2000 and 2002, and that of the background [29]; the found crossover, furthermore, was shown to be consistent with the timescale of the magma penetration–induced rock fracturing processes as suggested by Vinciguerra and Barbano [30] and also with the variations of the local magnetic field observed during the main eruptive volcanic episodes [31]. The investigation of time-clustering and the identification of the main timescale ranges were also performed by means of statistical approaches different from the AF method. Mega et al. [32] used the diffusion entropy to study the interevent time distribution of the seismicity in California and found that the time intervals between two successive large earthquakes are not Poissonianly distributed, contrarily to the generalized Poisson model, in which earthquakes are grouped into temporal clusters of events, characterized by intracluster correlations (due to the aftershock activation within a cluster following the Omori’s law) and intercluster uncorrelation (due to the random distribution of the mainshocks in time). The long range (LR) model that was proposed by Mega et al. [32] and then discussed by Helmstetter and Sornette [33] and by Mega et al. [34], reproduced the power-law of the intracluster swarms and intercluster distances. The analysis performed in the present paper aimed at revealing statistical features in the time dynamics of the seismicity observed in the Aswan area (Egypt) between 1986 and 2003, one of the most interesting water reservoirs in the world, characterized by the occurrence of reservoir-induced earthquakes. The time dynamics of the aftershock-depleted seismicity, investigated by means of the Allan Factor, reveals that the time-clustering behavior for events occurred at shallow depths (down to 12.5 km from the ground) as well as for events occurred at larger depths (from 15 km down to 27.5 km) does not depend on the ordering of the interevent times but mainly on the shape of the probability density functions of the interevent intervals. However, the deep and shallow events differ in the sense that the deep events are more compatible with a Poisson process than the shallow events, which are definitely more super-Poissonian. This finding seems to reinforce the results obtained in the study performed by Mega et al. [32] that evidenced non-Poissonian features in sequences of mainshocks, that is sequences not characterized by the Omori’s effect, indicating the presence of a correlation mechanism beyond Omori’s law.
Additionally, the set of shallow events shows a periodicity at about 402 days, which could be consistent with the cyclic loading/unloading operations of the Lake Naser Dam. Acknowledgements The present study was supported by the CNR/ASRT 2011-2012 Project ‘‘Spatiotemporal seismicity patterns and earthquake precursors at Aswan, Egypt contribution to earthquake hazard assessment’’. References [1] Bak P, Tang C, Wiesenfeld K. Self-organizing criticality. Phys Rev A 1988;38:364–74. [2] Gutenberg B, Richter CF. Frequency of earthquakes in California. Bull Seism Soc Am 1944;34:185–8. [3] Telesca L, Cuomo V, Lapenna V, Macchiato M. Identifying space–time clustering properties of the 1983–1997 Irpinia–Basilicata (Southern Italy) seismicity. Tectonophysics 2001;330:93–102. [4] Main I. Statistical physics, seismogenesis, and seismic hazard. Rev Geophys 1996;34:433–62. [5] Kagan YY, Jackson DD. Long term earthquake clustering. Geophys J Int 1991;117:345–64. [6] Telesca L, Lovallo M. Non-uniform scaling features in central Italy seismicity: a non-linear approach in investigating seismic patterns and detection of possible earthquake precursors. Geophys Res Lett 2009;36:L01308. [7] Telesca L, Cuomo V, Lapenna V, Macchiato M. Intermittent-type temporal fluctuations in seismicity of the Irpinia (southern Italy) region. Geophys Res Lett 2001;28:3765–8. [8] Telesca L, Cuomo V, Lapenna V, Macchiato M. Depth-dependent time-clustering behavior in seismicity of southern California. Geophys Res Lett 2001;28:4323–6. [9] Telesca L, Lapenna V, Macchiato M. Spatial variability of timecorrelated behaviour in Italian seismicity. Earth Planet Sci Lett 2003;212:279–90. [10] Telesca L, Cuomo V, Lapenna V, Macchiato M. On the methods to identify clustering properties in sequences of seismic timeoccurrences. J Seismol 2002;6:125–34. [11] Allan DW. Statistics of atomic frequency standards. Proc IEEE 1966;54:221–30. [12] Lowen SB, Teich MC. Estimation and simulation of fractal stochastic point processes. Fractals 1995;3:183–210. [13] Peng C-K, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. CHAOS 1995;5:82–7. [14] Telesca L, Cuomo V, Lapenna V, Macchiato M. Detrended fluctuation analysis of the spatial variability of the temporal distribution of Southern California seismicity. Chaos Solitons Fract 2004;21:335–42. [15] Telesca L, Macchiato M. Time-scaling properties of the UmbriaMarche 1997–1998 seismic crisis, investigated by the detrended fluctuation analysis of interevent time series. Chaos Solitons Fract 2004;19:377–85. [16] Latif AFA. Lake Nasser the new man-made lake in Egypt (with reference to Lake Nubia). In: Taub FB, editor. Ecosystems of the world 23. Lakes and reservoirs. Amsterdam, Oxford, New York, Tokyo: Elsevier Publishing Co.; 1984. p. 385–410. [17] Woodward-Clyde Consultants. Earthquake activity and stability evaluation for the Aswan High Dam. Unpublished report, High and Aswan Dam Authority, Ministry of Irrigation, Egypt; 1985. [18] Abou Elenean, K. Seismotectonics of Egypt in relation to the Mediterranean and Red Seas tectonics. PhD thesis, Ain Shams Univ., Egypt; 1997. 191 p. [19] Abu Elenean KM. Focal mechanism and stress tensor inversion of earthquakes in and around Nasser Lake. Egypt Bull Fac Sci Zagazig Uni Egypt 2003;25:77–107. [20] Talwani P. Characteristic features of intraplate earthquakes. Seismol Res Lett 1989;59:305–10. [21] Aswan Seismological Network Bulletin, Aswan Seismological Center (1981–1997), National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt. [22] Egyptian National Seismic Network Bulletin (1997–2004), National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt.
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