Egypt

Elsevier Editorial System(tm) for Tectonophysics Manuscript Draft Manuscript Number: TECTO11694R2 Title: Dynamical characterization of the 1982-2015 seismicity of Aswan Region (Egypt) Article Type: Research Paper Keywords: Aswan, induced seismicity, b-value, coefficient of variation, clustering Corresponding Author: Dr. Luciano Telesca, Corresponding Author's Institution: IMAA First Author: Luciano Telesca Order of Authors: Luciano Telesca; Raafat Fat Elbary; Tony A. Stabile; Mohamed Haggag; Mohamed Elgabry Abstract: In this study, the seismicity occurred in Aswan region from 1982 to 2015 is deeply investigated using robust statistical methodologies. The completeness magnitude, estimated by using two different methods (MAXC and GFT) is 2.5 for the whole catalogue with classes of events were identified with a threshold at about 12 km. The events deeper and shallower than the threshold could be likely generated by different mechanisms; the deep events are mainly due to tectonic processes of stress accumulation and release, while the loading/unloading operation of the Lake Nasser reservoir could significantly influence the time dynamics of the shallow ones. In fact, the analysis of the timeclustering properties of the shallow earthquakes reveals the presence of annual modulation that is absent in the time dynamics of the deep earthquakes. Furthermore, the shallow events are featured by the Allan Factor scaling exponent (measuring the strength of the time-clustering in an earthquake sequence) lower than that of the deep events, indicating a tendency of the time dynamics of the shallow earthquakes to behave more regularly than the deep ones. The detrended fluctuation analysis of the magnitude series suggests that the earthquake series are weakly persistent, characterized by the tendency of events of similar value of magnitude to follow each other. Suggested Reviewers: P. Varotsos [email protected] Qinghua Huang [email protected] Leticia Flores-Marquez [email protected] Ashutosh Chamoli [email protected]

Cover Letter

Dear Editor We have re-revised our paper addressing all the issues of referee and Editor. We are confident that our paper, now, thanks to the remarks and suggestions, could meet your approval. Regards The authors

*Abstract Click here to download Abstract: abstract_re_rev.doc

Dynamical characterization of the 1982-2015 seismicity of Aswan Region (Egypt)

Luciano Telesca1*, Raafat Fat Elbary2, Tony A. Stabile1, Mohamed Haggag2, Mohamed Elgabry3 1

National Research Council, Institute of Methodologies for Environmental Analysis, C.da S. Loja,

85050 Tito (PZ) Italy 2

Aswan Regional Earthquake Center, Aswan, Egypt

3

National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt

*Corresponding author: tel. +39-0971-427277, fax +39-0971-427277, email: [email protected]

Abstract In this study, the seismicit y that occurred in Aswan region from 1982 to 2015 is investigated using robust statistical methodologies. The completeness magnitude, estimated by using two different methods (MAXC and GFT) is 2.5 for the whole catalogue with b 1.07. By using the expectation maximization algorithm, two depth classes of events were identified with a threshold at about 12 km. The events deeper and shallower than the thresho ld could be likel y generated by the same mechanism:

the loading/unloading operation of the Lake Nasser reservoir. We

suggest that the shallow seismicit y occurs on shallow small fractures in correspondence of the intersection of N -S faults with E -W faults, which may form a minor pull -apart basin. The deep events mainl y occur along the right -lateral, strike-slip, E–W Kalabsha fault and the seismicit y is characterized by mainshock -

aftershocks sequences that mask the annual periodicit y if not properl y aftersho ckdepleted. Indeed, before appl ying the declustering on the seismic catalogue, the anal ysis of the time-clustering properties of the shallow earthquakes reveals already the presence of annual modulation that is not evident in the time dynamics of the deep earthquakes. Furthermore, the shallow events are featured by the Allan Factor scaling exponent (measuring the strength of the time -clustering in an earthquake sequence) lower than that of the deep events, indicating a tendency of the time dynamics of the shallow earthquakes to behave more regularl y than the deep ones. The detrended fluctuation analysis of the magnitude series suggests that the earthquake series are weakl y persistent, characterized by the tendency of events of similar value of magnitude to follow each other.

Keywords: Aswan, induced seismicity, b-value, coefficient of variation, clustering

*Revision Notes Click here to download Revision Notes: reply.doc

Editor I asked the more critical one of the two original reviewers to read your revised manuscript. The reviewer is quite happy with the revision but has suggested some further minor changes. However, I am rather disappointed with your effort to improve the English writing. For example, the error in the use of the word "occur" was corrected in parts of the abstract but still keeps occurring in the rest of the paper. I request that you ask a native English speaker to proofread and correct the English before submitting the next version. To avoid yet another round of minor revision just for language correction, please take this request seriously. We have revised the English and correct properly. Reviewer #2 1. Fig. 5: In order to keep consistency with other figures (e.g., Figs.7, 10, 11), it would be better to exchange the order of Fig. 5a and Fig. 5b (i.e., show the result of shallow earthquakes in Fig. 5a). Done 2. The format of references is inconsistent with the journal format, e.g., the references in Lines 697, 779, 781, 784 and 822 do not follow the required order; the correct complete information in Line 739 should be "111(B4), B04301, doi:10.1029/2005JB003982". The references in lines 697, 779, 781, 784 do not present page numbers but article number; this is the format used by the journals where these papers were published. We corrected the reference at line 822 and at line 739.

*Highlights

1. Aswan 1982-2015 seismicit y is complete for M 2.5 with b1.07 2. A depth threshold is identified at a bout 12 km 3. Lake Nasser level variations seem to influence shallow as well as deep seismicit y 4. Time-clustering of shallow seismicit y is lower than that of the d eep one 5. The magnitudes are weakl y persistent

*Revised manuscript with changes marked Click here to view linked References

1 2


3 4

5

Luciano Telesca1*, Raafat Fat Elbary2, Tony A. Stabile1, Mohamed Haggag2, Mohamed Elgabry3

6

1

7

85050 Tito (PZ) Italy

8

2


9

3



10 11

*Corresponding author: tel. +39-0971-427277, fax +39-0971-427277, email:

12

[email protected]

13 14

Abstract

15

In this study, the seismicit y that occurred in Aswan region from 198 2 to 2015 is

16

investigated using robust statistical methodologies. The completeness magnitude,

17

estimated by using two different methods (MAXC and GFT) is 2.5 for the whole

18

catalogue with b 1.07. By using the expectation maximization algorithm, two depth

19

classes of events were identified with a threshold at about 12 km. The events deeper

20

and shallower than the thresho ld could be likel y generated by the same mechanism:

21

the loading/unloading operation of the Lake Nasser reservoir. We suggest that the

22

shallow seismicit y occurs on shallow small fractures in correspondence of the

23

intersection of N-S faults with E-W faults, which may form a minor pull -apart basin.

2

24

The deep events mainl y occur along the right -lateral, strike-slip, E–W Kalabsha fault

25

and the seismicit y is characterized by mainshock -aftershocks sequences that mask the

26

annual periodicit y if not properl y aftersho ck-depleted. Indeed, before appl ying the

27

declustering on the seismic catalogue, the anal ysis of the time -clustering properties

28

of the shallow earthquakes reveals already the presence of annual modulation that is

29

not evident in the time dynamics of the deep earthquakes. Furthermore, the shallow

30

events are featured by the Allan Factor scaling exponent (measuring the strength of

31

the time-clustering in an earthquake sequence) lower than that of the deep events,

32

indicating a tendency of the time dynamics of the shallow earthquakes to behave

33

more regularl y than the deep ones. The detrended fluctuation anal ysis of the

34

magnitude

35

characterized by the tendency of events of similar value of magnitude to follow each

36

other.

37


series

suggests

that

the

earthquake

series

are

weakl y

persistent,

38 39

1. Introduction

40

River Nile, the longest river in the world, is a common basin between 11 countries ,

41

traveling over 2700 km through Sahara Desert withou t any significant perennial

42

tributary inputs (Woodward et. al, 2007). Throughout time the river has gone through

43

natural and anthropological changes , being a structurall y controlled stream since its

44

earl y stages. Several studies (i.e. Adamson and Williams, 1980; Said, 1981, 1993)

45

have proposed that the river Nile is in continuous evolving process by major tectonic

2

3

46

phenomena and climatic changes including the Rifting of East African that could be

47

the shaping factor for the location of sedimentary basin and t he drainage pattern.

48

The river has gone through many water resources management mega projects ; the

49

largest till now is the Aswan High Dam constructed between 1960 -1971, which is 111

50

m high, a crest length of 3830 m , and impounds the second largest reservoir in the

51

world, the Lake Nasser, that has a gross capacit y of 169 billio n cubic meters . On

52

November 14, 1981, an Ms 5.3 earthquake took place south of the dam. This

53

earthquake has raised the concerns about the dam stabilit y from one side and its

54

relation to seismicity from the other side. A network of 13 station s was established

55

(Simpson et al., 1987) to monitor seismicit y aro und the lake since 1982 , and intense

56

seismic activit y has been recorded since then (Simpson et al., 1 990; Gahalaut et al.,

57

2016, and references therein ).

58

Several researchers explored the relationship between the Aswan reservoir water

59

level and the obser ved seismicit y in the region ( e.g., Kebeasy et al., 1981; Simpson et

60

al., 1990; Hassoup 1994; Selim et al., 2002; Mekkawi et al., 2004; Haggag et al.,

61

2008; Telesca et al., 2012 ; Gahalaut et al., 2016 ) and, even if in some periods there

62

were found no or we aker reservoir influence ( Hassoup 1994; Selim et al., 2002;

63

Mekkawi et al., 2004 ; Telesca et al., 2012 ), it has been commonl y accepted t hat the

64

Aswan seismicit y is a case of continuous reservoir triggered seismicit y (RTS).

65

Therefore, Aswan area belongs to the reservoir sites that exhibit triggered seismicit y

66

every year or after a gap of a few years , such as Lake Mead in the USA (Carder,

67

1945), Koyna-Warna reservoir

68

2010), Nurek Dam in Tajikistan (Simpson and Negmatullaev, 1981),

69

Brazil (El Hariri et al., 2010), and Pertusillo reservoir in Italy (Stabile et al., 2014 ;

-

,

3

4

70

Telesca et al., 2015). In all the cases mentioned above delayed seismic response to

71

water

72

mechanism of the observed continued RTS is the diffusion of pore fluid pressures .

73

Particularl y for the As wan area, Gahalaut and Hassoup (2012) demonstrated from an

74

anal ytical simulation that although the stress due to the reservoir load stabilizes

75

seimogenic faults of the area, the effect of pore fluid pressure leads the faults to go

76

beyond the critical stres s for failure.

77

Due to the presence of the High Dam and the seismic risk that it could raise, a deep

78

dynamical

79

challenging and, at same time, crucial to best understand the mechanisms related t o

80

the generation of local earthquakes.

81

In fact, it is widely recognized that investigating with detail the structure of

82

magnitude, space and time distribution of earthquakes is fundamental for earthquake

83

hazard assessment as well as for the comprehension o f properties of seismic

84

processes (see e.g. Goltz, 1997; Kagan, 1997; Matcharashvili et al., 2009). In

85

particular, the investigation of the characteristics of time distribution of earthquake

86

occurrences on various temporal scales has been the focus of very intense research.

87

Several studies based on different conceptual frameworks approached the anal ysis of

88

earthquake time patterns by means of both field and laboratory data as well as

89

numerical

90

Matcharashvili et al., 2000; Telesca et al., 2004). Most of such studies highlight that

91

seismic processes are characterized by intermittent time behavior with phases of

92

intense seismic activit y interspersed with those of low seismicit y (Ben -Zion and

93

Lyakhovsky, 2002; Ki yashchenko et al., 2004; Pliakis et al., 2012; Vallianatos et al.,

fluctuations

of

reservoirs

characterization

simulations

of

( e.g.

was

the

Issac

observed

seismic

et

al.,

suggesting

process

2004;

that

governin g

Lyakhovsky

the

dominant

Aswan

et

al.,

area

is

2001;

4

5

94

2012); thus, evidencing the presence of nonrandom components in earthquake

95

generation in energy, space and time domains ( Lliopoulos and Pavlos, 2010).

96

Within this context, i n this study, we aim at investigating the dynamical properties of

97

the most updated seismic catalogue of Aswan appl ying several robust statistical

98

methodologies to the magnitude and time distribution of seismicit y that occurred

99

nearby Lake Nasser from 1982 to 2015 in order to better characterize its time

100

dynamics.

101 102 103

2. Seismo-tectonic settings and data description

104

Aswan (or S yene as its Greek name, which is named after the t ype localit y for the

105

igneous rock syenite) is located in the southern part of Egypt at the interface between

106

the stable Archean craton of the Nubian Shield and the less stable Pan -African

107

orogeny of the southern most of the Egyptian Eastern Desert. Aswan exhibits a

108

complex geological situation with a number of different rock t ypes , ranging from

109

quaternary deposits to cretaceous sedimentary rocks of Nubian sandstone , to igneous

110

and metamorphic rocks of the deep -lying basement complex, which have been

111

uplifted and exposed to surface. In many areas in and around Aswan the river has

112

eroded the ov erl ying Nubian sandstone and carved deep channels into the igneous

113

rocks (Greiling, et, al. 1994).

114

From earl y satellite imagery, El Shazl y et al. (1973) has described the structural

115

trends in Aswan area to be mainl y NNW -SSE fractures making notable horizon tal

116

separation and NW -SE fractures showing horizontal and vertical separation along

117

geological and relief boundaries. Furthermore, the NNE -SSW fault west to Kurkur 5

6

118

shows horizontal left -lateral trend. In addition, two major fracture trends are present

119

in NE-SW and the ENE -WSW. According to El Shazl y et al. (1973) the NE -SW

120

fractures do not show separation, and they may be major tension fractures

121

perpendicular to the principal force creating the previousl y mentioned two major

122

fault trends. Fractures seem to represent tension zones along the hinges of major

123

folds, which may have been faulted along the same zones.

124

These trends been reactivated as both strike -slip E-W dextral and N-S sinistral faults

125

(WCC, 1985; Abdeen et al., 2000) , and dip-slip faults (Issawi, 1978) and propagated

126

up through the sedimentary cover. The seismic activit y is concentrated along N -S and

127

E-W fault intersections. The N -S faults have less activit y than that of E -W faults.

128

Recent stress regime deduced from Earthquak e focal mechanism (Hus sein et al.,

129

2013) is in good agreement with that of geological studies and borehole breako ut data

130

(Bosworth and Strecker, 1997) with Shmax E-W and Shmin NNE-SSW. Under this

131

stress regime, the province is found to be consistent with both right lateral faul ts (E–

132

W striking) and left lateral faults (N –S striking).

133

The largest of the Aswan earthquakes was of magnitude Ms 5.3, and occurred on 14

134

November 1981. From the intensit y data, the well-determined locations of numerous

135

aftershocks recorded using portable stations and a telemetered network, the event

136

appears located on the Kalabsha fault beneath Gebel Marawa (Kebeasy et al. 1987).

137

The depths of the aftershocks and the special study of teleseismic records of the

138

mainshock (WCC 1985) indicate that the mainshock was at a depth from 18 to 20 km.

139

Prior November 14, 1981, no earthquakes had been reported in the Aswan area in the

140

c

141

1920. Because of the lack of continuous and reliab le data during the earl y stages of

g

f h

S

g c

C

SC)

c

h

SC’

c

6

7

142

the filling of the Aswan reservoir, it is not possible to determine exactl y when low -

143

magnitude activit y may have started. The first seismographs installed in the Aswan

144

area that were capable of recording small local earth quakes were Soviet short -period

145

(SMK) instruments installed at Aswan and Abu Simble in 1975. Although the

146

operation of the stations was irregular prior to 1981, 20 events of magnitude greater

147

than 2.5 have been identified by Helwan Institute located in the Wadi Kalabsha area.

148

Thirteen of these took place during approximatel y 200 days of station operation

149

between August 1980 and August 1981. A long sequence of aftershocks followed the

150

14 November 1981 earthquake , including the immediate aftershocks and the

151

continuation of Aswan activit y until the present both in the area of the mainshock and

152

around the northern part of the Aswan reservoir.

153

Following the mainshock, portable microearthquake recorders were installed in the

154

northern part of reservoir area by Eg yptian Geological survey from December to June

155

1982. In late June 1982 , the portable seismic field stations were replaced by a

156

telemetry network erected by Helwan Observatory and Lamont -Dohert y Geological

157

Observatory (USA). The purpose of the telemetry net work is to monitor the

158

induced/triggered seismicit y along the Kalabsha fault (Fig. 1), which continues to

159

occur in the area of the November 14, 1981 earthquake (Kebeasy et al 1987 ; Fat-

160

Helbary et al., 2002 ). Data were transmitted to a data center to record the output

161

signals coming from the field stations. Five monitors with pen recorder were used for

162

the visual record and all the data were recorded in the F M magnetic tape as analog

163

data and in the 9 -track tape as digital data. A playback unit and computer facilities

164

had been installed at the center to allow earthquakes to be quickl y anal yzed and

165

located. Since 2009, the Aswan Seismic Network has been updated and replaced by 7

8

166

new digital broad band network. The transmission system is changed from telemetry

167

to satellite and in addition some stations in field were moved to near better sites. As

168

well as the data from field stations is sent to the main center for the necessar y

169

anal ysis using the recent software programs such as Atlas and Earl ybird.

170

171 172

Fig. 1. Aswan Seismic Network .

173 174

The output data include latitude, longitude, focal depth, origin time, epicenter

175

distance and azimuth for each station. Various measures of location accuracy are also

8

9

176

given. The output data are used for constructing the seismici ty map of the Kalabsha

177

area (Fig. 2).

178 179

a)

9

10

6

5

Mi

4

3

2

1

0 0

2000

4000

6000

8000

i

180 181

b)

182

Fig. 2. (a) Seismicity map of Aswan region ( a: Gebel Marawa zone, b: East-1 of

183

Gebel Marawa zone, c: East -2 of Gebel Marawa zone, d: khore El -Ramla zone, e:

184

Abu Derwa zone, and f: Old stream zone). (b) Magnitude plot of the earthquakes in

185

the investigated region during 1982 –2015. Horizontal axis indicates the ith event and

186

vertical axis indicates its magnitude.

187 188

3. Methods and results

189

In this study we investigate the seismicit y that occurred from January, 1, 1982 to

190

December 31, 2015 in the area of Aswan (Fig. 2). We employed several independent

191

statistical methods to obtain the most complete picture of the dynamical properties of

192

the seismic process in the area.

193 10

11

194

3.1. The frequency -magnitude distribution

195

The Gutenberg-Richter (GR) law (Gutenberg and Richter, 1944) relates the threshold

196

magnitude M t h and the number of earthquakes with magnitude M> M t h in a power-law

197

manner usuall y represented in semi -log scales as log 1 0 (N)=a-bM t h , where N is the

198

number of earthquakes with magnitude M> M t h , a is the earthquake productivit y, and

199

b is a value that indicates the proportion of small events respect to the large ones.

200

The GR law is generall y used to fit t he frequency magnitude distribution (FMD). The

201

b-value is a critical parameter that can inform on the stress crustal conditions ;

202

therefore, estimating with a good accuracy and reliabilit y the b-value is important to

203

characteriz e different stages of the evolution of seismicit y, linked with dynamical

204

changes of the seismic process, and, as a consequence, is crucial for reliable s eismic

205

hazard assessments (Scholz, 1968; W yss, 1973) .

206

In our study, the estimation of the b-value was performed by using the maximum

207

likelihood method (MLE) (Aki, 1965),

208 209

b

log10 (e) , (1) M bin    M    Mc  2  

210 211

where is the average magnitude of the sub-set of earthquakes whose magnitude

212

is larger or equal to the completeness magnitude M c and  M b i n represents the binning

213

width of the catalogue (Utsu, 1999).

214

The standard deviation of the estimate of b

215

(1982) formula,

c c

by

g h

Sh

B

’

216 11

12

N

217

 b  2.3b 2

 M i 1

i

  M 

N  N  1

2

. (2)

218 219

As it is deduced from formula (1), the b-value depends on the estimat ion of the

220

completeness magnitude M c that is the lower magnitude above which the seismic

221

catalogue can be considered complete.

222

It is obvious that to get reliable results of any anal ysis performed on the seismic

223

catalogue, onl y the events with magnitude MM c have to be selected . The maximum

224

curvature method (MAXC) (Wiemer and W yss, 2000) allows a fas t estimation of M c

225

that corresponds to the largest bin in the noncumulative FMD. Another method is the

226

goodness-of-fit (GFT) (Wiemer and W yss, 2000) between the observed and synthetic

227

cumulative FMDs, the last calculated employing the a- and b-values of th e GR-law of

228

the observed seismic set for magnitude larger or equal to a n increasing threshold

229

magnitude that estimates M c when the 90% of the observed data are well modeled by

230

a straight line.

231

As already shown above, s ince 1980 the Aswan seismic network un derwent several

232

upgrades that have certainl y influenced the earthquake detection sensitivit y and, thus,

233

the completeness magnitude through time. Therefore, it is necessary to investigate

234

preliminaril y the time variation of the completeness magnitude. A visual impression

235

about how the magnitude of completeness varies with time and about possible artifact

236

in the catalog can be got by using the M i -i plot with horizontal axis indicating the ith

237

earthquake and vertical axis indicating its magnitude M i (Huang, 2006). Fig. 2b

238

shows a slight decrease of the magnitude with time and this indicates that the 12

13

239

completeness magnitude changes with time. Fig. 3 shows the time variation of M c for

240

the seismicit y at Aswan calculated by means of the MAXC method (red) and the GFT

241

method (blue).

242

entire catalog with a shift of 1 0 events. In each window, the completeness magnitude

243

M c (associated with the time of the last event in the window) was computed onl y in

244

case the nu mber of events wa s larger or equal to 50 (Woessner and Wiemer, 2005).

245

We can see that MAXC and GFT methods give very similar results in all the three

246

examined cases ( W N =200, 500 and 1000 events), although the MAXC method

247

estimates a slightl y lower value o f the completeness magnitude. The range of

248

variation of the completeness magnitude depends on the length of the moving

249

window, being larger for W N =200 and smaller for W N =1000.

We considered a fixed event number window (W N ) sweeping the

250 251 MAXC GFT WN=200

3.5

MAXC GFT WN=500

3.0

3.0 2.5

2.5 2.0

MC

MC

2.0

1.5

1.0

1.0

0.5

0.5

0

2000

4000

6000

8000

10000

12000

14000

0

time (days since January 1, 1982)

252

1.5

2000

4000

6000

8000

10000

12000

14000


a)

b)

13

14

MAXC GFT WN=1000

3.0

2.5

MC

2.0

1.5

1.0

0.5 0

2000

4000

6000

8000

10000

12000

14000


253

c)

254

Fig. 3. Time variation of the completeness magnitude in the Aswan area (red: MAXC method; blue:

255

GFT method, see text for details): (a) WN=200 events; (b) WN=500 events; (c) WN=1000 events.

256 257

A conservative choice of the completeness magnitude would require taking it as the

258

largest value of the time evolution of M c . But, this choice would strongl y decrease

259

the amount of available data, and consequentl y would inc rease the uncertaint y of the

260

statistical estimates due to smaller sample sizes. For instance, considering the time

261

variation of M c for W N =1000 events, the highest completeness magnitude on the base

262

of the GFT method is 3.0 that would reduce the amount of availa ble data to 375 over

263

9592 that is the size of the whole catalog . So, it is impo rtant to find a sort of

264

compromise between the size of the dataset, large enough to perform the statistical

265

anal ysis with good accuracy, and the value of M c that should guarantee a good

266

completeness of the catalog. On the base of the results shown in Fig. 3, by visual

267

inspection we believe that a reasonable choice of M c is 2.5; in fact, it is larger than

268

any completeness magnitude calculated by the MAXC method and lower than the

269

completeness magnitude calculated in just few windows by using the GFT method; 14

15

270

furthermore, 2.5 is quite robust with respect the size of the moving window . In this

271

case the number of earthquakes with magnitude larger or equal to 2.5 is 1327 over

272

9592; and t his size is large enough to perform significantl y the statistical anal ysis on

273

the catalog. Therefore, with M c =2.5 the b=1.070.02.

274 275

3.2. The depth distribution

276

Considering the catalog of seismic events with magnitude larger or equal to 2.5, two

277

distinct depth classes characterize t he earthquakes that occurred in the Aswan area.

278

Fig. 4 shows the depth histogram (black line) of the seismic events. It is clear that

279

the distribution is bimodal, characterized by two depth ranges, one involving the

280

shallow events and the other the deep events. Furthermore, the depth distribution

281

seems to be a mixture of two Gaussian distributions.

282

a)

15

16

283 284

b)

16

17

285

c) 17

18

286 287

Fig. 4. a) Depth distribution of the seismicity at Aswan. The red and blue curves represent the best

288

Gaussian fit of the deep and shallow events. D0 represents the estimated depth threshold separating the

289

two classes of depths; b) Depth-longitude diagram of seismicity; c) Seismicity of Aswan area for

290

magnitude larger or equal to 2.5.

291 292

In order to better discriminate the two depth ranges, we applied the expectation

293

maximization (EM) algorithm (Borman, 2004) that is a statistical method to calculate

294

the maximum likelihood estimates of the parameters of two Gaussian distributions,

295

whose mixture seems to model the bimodal depth distribution of Fig. 4. We found

296

that one Gaussian distribution (blue curve) with  G =4.8 and  G 2 =8.0 models the

297

distribution of shallow events and the other (red curve) with  G =19.0 and  G 2 =9.7

298

models that of the deep ones. The intersection between the two curves D 0 12 km can

299

be considered as the threshold depth discriminating betwe en shallow and deep events.

300

In the forthcoming anal yses we will investigate the two earthquake sub-catalogues:

301

shallow (depth < 12 km) and deep (depth  12 km). The number of the shallow events

302

is 744 and that of the deep ones is 583. For the deep sub -catalog b=0.990.03, while

303

for the shallow one b=1.140.04.

304

Fig. 4b shows the vertical cross/section depth -longitude diagram of seismicit y. The

305

events appearing at shallower depths (less than 12 km) in this cross -section are from

306

East Gebel Marawa (the composite fault plane solution indicates strike -slip faulting

307

with a normal fault component) , Khore El-Ramla (the composite fault plane solution

308

indicates a strike -slip fault and the fault plane strikes 155° and dips 65°) , Abu Dirwa 18

19

309

(the focal mechanism of this zone includes strike-slip and normal components, and

310

the fault plane strikes 177° from the north and is dipping 61°) and old stream zones

311

(the fault plane solution indicates strike slip faulting and the fault plane strikes 161°

312

and dips 77°).

313

On the other hand, the seismicit y at Gebel Marawa zone is almost all between depth

314

of 12 and 26 km and the events align along the Kalabsha fault where the mainshock

315

of November 14, 1981 occurred deeper than 12 km (Fat -Helbary et al., 2002). The

316

composite fault plane so lution of the earthquakes indicates strike -slip faulting with a

317

normal-fault component. The fault plane strikes 78° and dips 70° (Fat -Helbary,

318

1989).

319 320

3.3. The coefficients of variation

321

The coefficient of variation C v is a simple measure employed to study the time-

322

clustering properties of an earthquake process . It is defined as

323 324

Cv 

 , (3) 

325 326

where  and  are the standard deviation and the average of the interevent times ,

327

respectivel y. Fig. 5 shows the series of the interevent times of th e deep (Fig. 5a) and

328

shallow (Fig. 5b) sub -catalogues.

19

20

interevent time (day)

300

Shallow

200

100

0


-100 600

0

100

200

300

400

500

600

700

800

Deep

400 200 0 0

100

200

300

400

500

600

n

329 330

Fig. 5. Interevent time series of the shallow (a) and deep (b) sub-catalogues.

331 332

Depending on the numerical value of C v , the earthquake sequence is regular (or

333

periodic) if it is lower than 1 , purel y random (or Poissonian) if it is 1 or clustered if

334

it is larger than 1 (Kagan and Jackson, 1991). Recentl y, Telesca et al. (2016)

335

introduced the local coefficient of variation L v , defined by Shinomoto et al. (2005),

336

to investigate the local time-clustering properties of the volcano -related seismicity at

337

El Hierro, Canary Islands (Spain):

338

1 N 1 Ti  Ti 1  Lv  3 N  1 i 1 Ti  Ti 1 2 (4) 2

339

340

20

21

341

For Poissonian seismic processes, C v and L v are both 1, and for periodic processes

342

they are both 0. However, if C v can measure global variabilit y of a whole interevent

343

sequence and could be affected by event rate fluctuation s, L v measures local stepwise

344

variabilit y of interevent times , because it is rather independent of slow variation in

345

average rate. Just as an example, if one joins two peri odic point processes like those

346

in Fig. 6, C v >>1 because globall y the process appears highl y clustered, but L v 0,

347

because at local scales the process is periodic.

0

10

20

30

40

time

348 349

Fig. 6. Superposition of two periodic point processes.

350 351

We calculated both the coefficient s of variation for the deep and shallow seismicity

352

in Aswan for events with m agnitude M2.5, and obtained C v  3.37 and L v 1.16 for

353

deep seismicit y and C v  1.78 and L v 1.35 for the shallow one. To calculate the

354

significance of these results, we calculated bot h the quantities for 1,000 Poisson

355

processes randoml y generated with the same size and mean interevent time as the

356

original (deep and shallow) seismic interevent time series. The 95% confidence 21

22

357

interval, which is delimited by the 2.5 t h and 97.5 t h percentil es of the distribution of

358

C v and L v of the Poissonian surrogates , are [0.94, 1.07] for C v and [0.92, 1.08] for L v

359

in case of deep seismicit y, and are [0.93, 1.0 8] for C v and [0.92, 1.07] for L v in case

360

of shallow seismicity. The obtained values of the coef ficients of variation indicate

361

that both globall y and locall y the distribution s of the shallow and deep seismicity at

362

Aswan are clusterized at 95% confidence.

363 364

3.4. The Allan Factor

365

The coefficients of variation described in section 3.2 furnish information about the

366

time-clustering of a point process, but reveal none about the timescales where the

367

process is clusterized. To this aim, the Allan Factor (AF) is a suited method for

368

discriminating between the timescales where the process is clusterized from thos e

369

where it is not. Dividing the time axis into equall y spaced contiguous counting

370

windows of duration  , that is timescale, a sequence of earthquake counts { N k (  )} is

371

obtained, with N k (  ) being the number of earthquakes falling in the k-th window

372

(Thurner et al., 1997). The AF, then, is defined as

373

374

 ( N k 1 ( )  N k ( )) 2  AF ( )  2  N k ( )  , (5)

375 376 377

and it is related to the variabilit y of successive counts (Thurner et al., 1997); the y b

c

h

g

.

h

F h

b

g y

g

378

the time dynamics of point processes of different t ypes ( Telesca et al., 2001; Telesca

379

et al., 2005 ). 22

23

380

If the earthquake process is Poissonian that means memoryless and formed by

381

independent events, then the AF is rather flat at all timescales and assumes value

382

around 1 (except for very large timescales due to finite -size effects (Telesca et al.,

383

2012); but if the earthquake process is clusterized the AF changes with the timescale

384

 . In particular, if the earthquake process is fractal (self-similar) in time, the AF

385

behaves as a power-law (scaling behavior) :

386 

387

  AF( )  1      1  , (6)

388 389

where the exponent  quantifies the strength of clusterization;  1 is the so-called

390

fractal onset time and marks the lower limit for significant scaling behavio r in the AF

391

(Thurner et al., 1997). Therefore, if  0 the earthquake process is Poissonian , while

392

if  >0 it is clusterized.

393 394

23

24

Shallow seismicity 1.2

2

log10(AF())

1.0

=0.40+0.02

0.8

0.6

1y

1

0.4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10() (day)

395

a)

2.5

Deep seismicity

2

log10(AF())

2.0

1.5

=1.85+0.06 1.0

0.5

1

0.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10() (day)

396 397

b) Fig. 7. AF for the shallow (a) and deep (b) Aswan sub -catalogues.

398 399

Fig. 7 shows the AF (open circles) for the shallow (Fig. 7a) and deep (Fig. 7b)

400

seismicit y at Aswan, for events with magnitude M 2.5. Smoothing with adjacent 5 -

401

sample averaging (red curve) evidences more clearl y the scaling behavior in both

402

shallow and deep seismicit y between  1 and  2 that are between about 12 days and 24

25

403

about 5 months for shallow seism icit y, and between about 40 days and 9 months for

404

deep seismicit y. The scaling exponents are very different, being 0.40 for the shallow

405

and 1.85 for the deep seismicit y, indicating a higher clustering degree for deep

406

seismicit y than shallow . In order to verify the significance of the exponents, we

407

calculated the distribution of the exponents computed between  1 and  2 of 1,000

408

Poissonian seismic sequences generated with the same number of events and rate as

409

the shallow and deep original ones (Fig. 8). We can see that the obtained value of 

410

for the shallow and the deep seismicity are well above the largest value of the

411

distribution of  obtained for Poissonian surrogates; therefore, the exponents

412

calculated for the real seismicit y are signifi cant.

413

Another interesting feature is the drop at around 1 year in the smoothed curve (red)

414

obtained for the shallow seismicit y. The drop at a certain timescale in the AF curve

415

indicates the presence of periodicit y at that timescale ( Gebber et al., 2006 ); thus, the

416

drop found in the AF of the shallow seismicit y corresponds to the annual periodicit y

417

that is consistent with the loading/unloading operations of the Aswan Dam and

418

strengthens the existence of annual water modulation (Gahalaut et al., 2016) of the

419

shallow seismicit y.

420

25

26

Deep Shallow 80

N

60

40

20

0

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5



421 422

Fig. 8. Distribution of  for 1,000 Poissonian sequences with same rate and same

423

number of events as the original deep (blue) and shallow (red) sequences.

424 425

3.5. The detrended fluctuation analysis of the magnitude time series

426

The Detrended Fluctuation Anal ysis (DFA) (Peng et al., 199 5) was used to stud y

427

long-range correlations of non-stationary series of different t ypes (Telesca and

428

Lovallo, 2009; Telesca and Lovallo, 2010; Telesca and Lovallo, 2011; Telesca et al.,

429

2012; Telesca et al., 2016 ; Rong et al., 2012; Varotsos et al., 2008; Varotsos et al.,

430

2011). In the context of studies devoted to seismicit y, several authors focused on the

431

long-range correlations in the magnitude time series, since magnitude rep resent one

432

of the crucial parameter in the framework of seismic hazard assessment. Telesca et al.

433

(2016) observed that the scaling exponent of the magnitude time series calculated by

434

the DFA (see later in the text) had an increasing behavior when the volcanic activit y

435

at El Hierro, Canary Islands (Spain) reactivated in the 2011-2014. Varotsos et al. 26

27

436

(2014), performing the DFA on the magnitude series of several seismic areas,

437

evidenced a certain variabilit y of the scaling exponent with relationship with

438

earthquake prediction. Lennartz et al. (2008) us ed the DFA to investigate the long-

439

range correlations of the magnitude se ries of Northern and Southern California

440

seismicit y revealing the presence of long-term memory. Varotsos et al. (2012)

441

observed a rather sh arp variation from uncorrelated to correlated behavior in the

442

magnitudes of California seismic it y before the occurrence of large shocks .

443

Within this scientific context , we can understand how crucial is the anal ysis of the

444

temporal properties of magnitude time series to better understand the dynamics of a

445

seismic process.

446

The DFA method works as follows:

447

i) the magnitude series M i , where i=1,…,N, and N is the total number of e vents is

448

integrated:

449 450 451

yk  i 1 M i   M  , (4) k

452 453

where indicates the mean magnitude;

454

ii) the integrated series y k is divided into non-overlapping boxes of same length n;

455

iii) in each n-size box, y k is fit by the least squares by the line y n , k and detrended;

456

iv) the fluctuation, F n , is obtained by

457 458

Fn 

2 1 N  yk  yn,k  ; (5)  N k 1

27

28

459 460

v) the steps i)-iv) are repeated for all the available box sizes n; if the relationship

461

between F n n is a power-law, the magnitudes are long-range correlated:

462 463

F n n  ; (6)

464 465

vi) from the numerical value of the so-called scaling exponent  we can derive

466

information about the t ype of correlations: if the magnitude are uncorrelated, then

467

 =0.5; if the magnitudes are persistently correlated (meaning that a large (small)

468

magnitude (compared to the mean) has larger probabilit y to be followed by a large

469

(small) magnitude), then  >0.5; if the magnitudes

470

(meaning that a large (small) magnitude (compared to the mean) has larger

471

probabilit y to be followed by a small (large) magnitude), then  2.5


200

150

100

50

0

0

100

200

300

400

500

n

527

a)

31

32

800

Aftershock-depleted deep sub-catalog M>2.5

700


600 500 400 300 200 100 0

0

100

200

n

528

b)

529

Fig. 10. Interevent time series of the aftershock -depleted shallow (a) and deep (b)

530

sub-catalogues.

531 532

For the aftershock -depleted deep sub -catalog b=0.940.05, while for the shallow one

533

b=1.110.05 We also calculated for both the aftershock -depleted sub -catalogs the

534

global and local coeff icient of variations and obtained the following results (the 95%

535

confidence interval in parentheses): C v =1.31 [0.92,1.10] and L v =1.08 [0.88, 1.10] for

536

the shallow set and C v =1.93 [0.88, 1.14] and L v =1.01 [0.85, 1.16] for the deep set.

537

The onl y difference with un-declustered sub -catalogs is that after removing the

538

aftershocks both the sub -catalogs become locall y Poissonian; and this is reasonable,

539

because the aftershocks introduce a high level of clustering even for short time

540

scales.

32

33

1.0


log10(AF(t))

0.6

0.4

a=0.38+0.02 0.2

1y 0.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10(t) (day)

541

a)

1.0

Deep seismicity

0.8

log10(AF(t))

0.6

a=1.02+0.05

0.4

0.2

410 d

0.0

-0.2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10(t) (day)

542 543

b) Fig. 11. Allan Factor of the declustered shallow (a) and deep (b) sub -catalogs.

544 545

We applied the AF method to both the declustered sub -catalogs and the results are

546

shown in Fig. 11. We can observe that the scaling expo nent  decreases, but more

547

slightl y for the shallow seismicit y; this is consistent with the removal of aftershocks

548

that generall y weakens the time -clustering of the seismicit y; however, the deep sub 33

34

549

catalog is still more clusterized than the shallow one. The adjacent -5-sample-

550

averaging smoothed curve (red) on the AF for the shallow seismicit y still shows the

551

periodicit y at about 1 year, as in the original sub -catalog. However, a very interesting

552

feature is now revealed in the AF of the deep sub -catalog: the presence of a

553

periodicit y at about 410 days, which seems compatible with the annual periodicit y

554

found in the AF of the shallow sub -catalog and also consistent with the annual cycle

555

of loading/unloading of the water reservoir. Such periodicit y was not reve aled in the

556

original deep sub -catalog because it was very likel y masked by the high number of

557

aftershocks following the November 14, 1981 event.

558 559

4. Discussion and conclusions

560

A detailed anal ysis of the seismicit y that occurred in Aswan region from 1980 to

561

2015 has been performed by utilizing the most robust statistical methodologies to

562

deepl y investigate its properties in time, magnitude and depth domains.

563

The anal ysis of the completeness of the catalogue was carried out by using two well

564

assessed methodologies (MAXC and GFT). The MAXC method generall y furnishes

565

values of the completeness magnitude slightl y lower than those obtained by the GFT

566

method, by using a sliding window with different sizes sweeping the entire catalog.

567

The completeness magnitude is not constant through time but varies, decreasing

568

around the end of the investigation period; this indicates that the catalog is not

569

homogeneous in time, and this is consistent with successive upgrades of the seismic

570

network that were performed through time . The non-homogeneit y on time of the

571

completeness magnitude and the comparison between the results obtained by the

572

MAXC and GFT methods with different sliding window sizes has led us to choose the 34

35

573

value of 2.5 for the completeness magnitude; this value not onl y is reasonabl y

574

consistent with the results shown in Fig. 3, but is also low enough to guarantee a

575

sufficientl y large size of events (with magnitude larger or equal to 2.5) to appl y the

576

statistical methodologies. The obtained value of the Gutenberg -Richter b is 1.07;

577

this value lies within the range of the b-values calculated for the global seismicit y

578

(Mogi, 1962). The obtained values of b and M c differ largely from the estimates for

579

approximatel y the same area calculated by Ali (2016), who found a b-value of the

580

0.554 and a completeness magnitude of 0.9. Ali (2016) applied onl y the MAXC

581

method and obtained the estimate of b from the whole catalog, which, however,

582

begins in 1997; in our case we considered a longer dataset, beginning in 1980,

583

compared th e results obtained by the MAXC and GFT methods and calculated the

584

value of b after computing the time variation of the completeness magnitude with

585

different size of sliding window.

586

The anal ysis of the distribution of hypocentral depths has revealed a very clear

587

discrimination of two depth classes, separated by the threshold of 12 km, which

588

separates earthquakes as shallower from deeper than the threshold.

589

Table 1 summarizes the results obtained from the different robust statistical

590

methodologies used in thi s study for the dynamical characterization of the 1982 -2015

591

seismicit y in the area of Aswan.

592 593 Parameter

Shallow seismicity

Deep seismicity

Result

b-value

1.14 (1.11)

0.99 (0.94)

b-value of shallow seismicit y

35

36

higher than b -value of deep seismicit y Cv

1.78 (1.31)

3.37 (1.93)

Globall y clusterized

Lv

1.35 (1.08)

1.16 (1.01)

Locall y

clusterized ;

aftershock-depleted

the sub-

catalogs are locall y Poissonian AF

0.40 (0.38)

1.85 (1.02)

Deep

seismicity

high

clusterized DFA

0.555

0.553

Magnitudes

persistentl y

correlated 594

Table 1: Statistical parameters obtained for shallow and deep seismicit y (in

595

parentheses those for the aftershock -depleted catalog) in the area of Aswan from

596

January, 1, 1982 to December 31, 2015.

597 598

The anal ysis of depth distribution was necess ary to discriminate between possibl y

599

different earthquake generation mechanisms and/or different types of time -dependent

600

earthquake occurrence.

601

The results of our anal ysis show that the loading/unloading operation of the Lake

602

Nasser reservoir could signifi cantl y influence the time dynamics of both the shallow

603

and deep events. Indeed, the AF curve of both the shallow and deep declustered sub-

604

catalogs evidences the existence of annual periodicit y ; such periodicit y could very

605

probabl y be linked to the annual p eriodicit y of the water level fluctuations and could

606

strengthen the reservoir -triggered nature of the seismicit y down to 30 km depth. It is

607

worth noting that the annual periodicit y is not present in the AF curve of the deep un36

37

608

declustered sub-catalogue, therefore it is mostl y characterized by mainshocks -

609

aftershocks sequences whereas this time -dependent earthquake occurrence character

610

is not evident in the shallow seismicit y (AF curve shows the annual periodicit y also

611

for the un -declustered shallow sub -catalog).

612

The deep and shallow declustered seismicit y are characterized by very close values of

613

the local coefficient of variation L v and similar values of the global coefficient of

614

variation C v , although the C v for the deep seismicit y is slightl y larger than t hat of

615

shallow seismicit y. This is also revealed by the scaling exponent  obtained from the

616

AF that measure quantitativel y the strength of the time -clustering in an earthquake

617

sequence; the deep declustered sub-catalogue is characterized by  1.02, whereas the

618

shallow one by  0.38.

619

The DFA performed on the magnitude series of the shallow and deep events reveals

620

that both series are weakl y persistentl y correlated, indicating that there is a tendency

621

of similar magnitudes to follow each other. This finding support the consideration

622

that the physical driving mechanism is the diffusion of pore fluid pressure because

623

the events are responding to the same underl ying physical process that periodicall y

624

increases the seismicit y rate (Shearer, 2012) with many events of about the same

625

magnitude.

626

The higher b-value (1.11) of shallow seismicit y with respect to the b-value (0.94) of

627

the deep seismicit y indicates that the increase of pore pressure can enable shallow

628

small fractures to overcome the critical stress point fo r failure even with a low level

629

of accumulated stress. Indeed, it is well known (Scholz, 1968; W yss, 1973) that low

630

stresses cause earthquake series with high b-values.

37

38

631

The shallow seismicit y is mostl y located in the East of Gebel Marawa zone, Khore

632

El-Ramla zone, Abu Derwa zone, and Old stream zone (Fig. 4b and 4c) in

633

correspondence of the intersection of the left -lateral, strike-slip, N–S faults (El-

634

Barqa fault, Kurkur fault, and Abu -Dirwa fault) and the right -lateral, strike -slip, E–W

635

faults (Kalabsha fault and Seyal fault); therefore, w e suggest that the zones where the

636

shallow seismicit y occurs constitute a minor pull-apart basin where the seismic

637

deformation is accommodated on shallow small fractures . This hypothesis is also

638

supported by the observed oblique strike-slip motions of shallow earthquakes (focal

639

mechanisms indicate strike -slip faulting with a normal -fault component). Another

640

similar case of reservoir -triggered seismicit y in pull-apart basins generated by the

641

relative motion of strike -slip faults is the Koyna-Warna area in India (Catchings et

642

al., 2015).

643

The deep seismicit y is mostl y located in the Gebel Marawa zone along the Kalabsha

644

fault which is favorabl y oriented with the maximum principal stress direction of the

645

present tectonic stress regime and where the 14 November 1981, Ms 5.3 earthquake

646

occurred. The intersection of the eastern tip of the Kalabsha fault with the N–S faults

647

may promote fluid flow across the fault system and then along the Kalabsha fault

648

down to 30 km depth. Anyway, i t is not surprising that seismicit y can be induced by

649

the diffusion of pore fluid pressures at distance and at significant depths since it has

650

been largel y demonstrated in the literature (e.g., Rubinstein and Mehani, 2015 , and

651

references therein ).

652

Concludi ng, in the present study we have performed a detailed statistical anal ysis of

653

the

654

methodologies able to reveal dynamical properties of earthquakes in time, depth and

seismicit y

occurred

at

Aswan

from

1980

to

2015

by

utilizing

robust

38

39

655

magnitude domains. The obtained results depict the dynamics of the Aswan seismicit y

656

more deepl y evidencing the influence of the water level change in the lake on the

657

dynamics of both the shallow and the deep seismicit y which show a clear annual

658

periodicit y well correlated with t he annual loading of the lake. Moreover, the deep

659

seismicit y is mainly characterized by mainshock -aftershocks sequences mostl y

660

triggered by the water level fluctuations of the Nasser lake, and they mask the annual

661

periodicit y of the deep seismicit y if not properl y aftershock -depleted. However, this

662

study is restrained to the investigation of the seismicit y of the whole Aswan area,

663

while a more detailed statistical anal ysis of the spatial seismicit y separating different

664

source zones would lead to a better un derstanding of the seismic process.

665 666 667

References

668

Abdeen, M.M., Abdelsalam, M.G., Nielsen, K.C., Yehia, M.A., Cherif, O.H. , 2000.

669

Active dextral wrenching in southern Egypt. In: 38th Annunal Meeting of the

670

Geological Societ y of Egypt, Cairo.

671

Adamson, D.A. , Williams, F., 1980. Structural geology, tectonics and the control

672

of drainage in the Nile basin. In: The Sahara and The Nile: Quaternary

673

Environments and Prehistoric Occupation in Northern Africa (M.A.J. Williams and

674

H.Faure, Eds.).

675

Aki, K., 1965. Maximum likelihood estimate of b in the formula log(N) = a -bM

676

and its confidence limits. Bull. Earthq. Res. Inst., Univ. Tokyo 43, 237 –239.

677

Ali, S. M., 2016. Statistical anal ysis of seismicit y in Egypt and its surroundings .

678

Arabian J. Geosciences, 9, 52 . doi:10.1007/s12517 -015-2079-x. 39

40

679

Ben-Zion, Y., Lyakhovsky, V., 2002. Accelerated seismic release and related

680

aspects of seismicit y patterns on earthquake faults. Pure and Applied Geophysics

681

159, 2385–2412.

682

Borman, S., 2004. The Expectation Maximization Algorithm A s hort tutorial.

683

http://www.seanborman.com/publications/

684

Bosworth, W., Strecker, M.R., 1997. Stress field changes in the Afro -Arabian rift

685

s ystem during the Miocene to Recent period. Tectonophysics 278, 47 -62.

686

Carder, D. S., 1945. Seismic investigations in t he Boulder Dam area, 1940 –1944,

687

and the influence of reservoir loading on earthquake activity . Bull. Seismol. Soc.

688

Am. 35, 175–192.

689

Catchings, R.D., Dixit, M.M., Goldman, M.R., Kumar, S., 2015. Structure of the

690

Koyna-Warna Seismic Zone, Maharashtra, India: A possible model for large

691

induced earthquakes elsewhere. J. Geophys. Res. Solid Earth 120, 3479 –3506.

692

doi:10.1002/2014JB011695.

693

-

, I., and P. Talwani , P., 2010. Hydromechanics of the Koyna -Warna

694

region, India. Pure Appl. Geophys. 167, 183 –213. doi:10.1007/s00024 -009-0012-5.

695

Lippiello, E., de Arcangelis, L., Godano, C., 2008. Influence of Time and Space

696

Correlations on Ea rthquake Magnitude . Phys. Rev. Lett. 100, 038501

697

El Hariri, M., Abercrombie, R.A., Rowe, C.A., do Nascimento, A.F., 2010. The

698

role of fluids in triggering earthquakes: Observations from reservoir induced

699

seismicit y in Brazil . Geophys. J. Int. 181 (3), 1566–1574. doi:10.1111/j.1365 -

700

246X.2010.04554.x.

701

El Shazl y, E.M., Abdel-Hady, M.A., El Ghawaby, M.A., El Kassas, A., 1973.

702

Geologic interpretation of ERTS -1 satellite images for west Aswan area, Egypt. 40

41

703

Egyptian Academ y of Scientific Research and Technology, Re mote sensing

704

research project.

705

Fat-Helbary,

706

Determination Recorded by Aswan Seismic Network . Master Thesis, Sohag

707

Facult y, Assiute Universit y, Egypt

708

Fat-Helbary, R.E., Tealb A.A. , 2002. A study of seism icit y and earthquake hazard

709

at the proposed Kalabsha Dam Site, Aswan, Egypt . Natural Hazards 25, 117 -133.

710

Gahalaut, K., Hassoup, A. , 2012. Role of fluids in the earthquake occurrence

711

around Aswan reservoir, Egypt. J . Geophys. Res. 117, B02303. doi:10.1029/

712

2011J B008796.

713

Gahalaut, K., Hassoup, A., Hamed, H., Kundu, B., Gahalaut , V., 2016. Pure Appl.

714

Geophys., 174(1), 133–150. doi:10.1007/s00024-016-1397-6

715

Gebber, G.L., Orer, H.S., Barman, S.M., 2006. Fractal Noises and Motions in

716

Time

717

Neurophysiol. 95, 1176 –1184

718

Goltz, C., 1997. Fractal and Chaotic Properties of Earthquakes. Lecture Notes in

719

Earth Sciences, Berlin Springer.

720

Greiling, R.O., Abdeen, M.M., Dardir, A.A., El -Akhal, H., El-Raml y, M.F., Kamal

721

El-Din, G.M., Osman, A.F., Rashwan, A.A., Rice, A.H.N., Sadek, M.F. , 1994. A

722

structural

723

Geologische Rundshau 83, 484 –501.

724

Gupta, H.K., 2002. A review of recent studies of triggered earthqua kes by

725

artificial water reservoirs with special emphasis on earthquakes in Koyna, India .

726

Earth Sci. Rev. 58 (3/4), 279–310. doi:10.1016/S0012-8252(02)00063 -6.

Series

R.E.,

of

synthesis

1989.

A

Study

Presympatheti c

of

the

of

and

Proterozoic

the

Local

Sympathetic

Earthquake

Neural

Arabian –Nubian

Magnitude

Activities .

Shield

in

J.

Egypt.

41

42

727

Gutenberg, R., Richter, C.F., 1944. Frequency of earthquakes in California. Bull.

728

Seismol. Soc. Am. 34, 185–188.

729

Haggag, H.M., Gaber, H.H., Sayed, A.D., Ezzat, M.E. , 2008. A review of the

730

recent seismic activit y in the southern part of Egypt (upper Egypt). Acta

731

Geodynamica et Geomaterialia 5, 19 –29.

732

Hassoup, A., 1994. Investigation of the tectonic sett ing, seismic activit y and

733

crustal deformation in Aswan seismic region, Egypt . D.Sc. Thesis. Tokyo: Tokyo

734

Universit y.

735

Huang, Q., 2006. Search for reliable precursors: A case study of the seismic

736

quiescence of the 2000 western Tottori prefecture earthquake . J. Geophys. Res.

737

111(B4), B04301, doi:10.1029/2005JB003982 .

738

Hussein, H.M., Abou Elenean , K.M., Marzouk, I.A., Korrat, I.M., Abu El -Nader,

739

I.F., Ghazala, H.H., ElGabry, M.N., 2013. Present-day tectonic stress regime in

740

Egypt and surrounding area based on in version of earthquake focal mechanisms.

741

Journal of African Earth Sciences 81, 1 -15.

742

Iliopoulos, A.C., Pavlos G.P. , 2010. Global low dimensional seismic chaos in the

743

Hellenic region. International Journal of Bifurcation and Chaos 20(7), 2071 –2095.

744

Issac, M., Renuka, G., Venugopal, C., 2004. Wavelet analysis of long period

745

oscillations

746

Atmospheric and Solar -Terrestrial Physics 66, 919 –925.

747

Issawi, B., 1978. Geology of Nubia West area, Western Desert, Egypt. Annals of

748

the Geological Survey of Egypt 8, 237 -253.

749

Kagan, Y.Y., 1997. Are earthquakes predictable? . Geophys. J. Int. 131(3), 505–

750

525.

in

geomagnetic

field

over

the

magnetic

equator.

Journal

of

42

43

751

Kebeas y,

R.M.,

Maamoun,

M.,

Ibrahim,

E.,

1981.

Aswan

lake

induced

752

earthquakes. Bull. Int. Inst. Seismol. Earthq. Eng. 19, 155 –160.

753

Kebeas y, R.M., Maamoun, M., Ibrahim, E., Megahed, A., Simpson, D.W., Leith,

754

W.S., 1987. Earthquake studies at Aswan Reservoir, J. Geodynamics 7, 173 -193.

755

Ki yashchenko, D., Smirnova , N., Troyan, V., Saenger, E., Vallianatos, F., 2004.

756

Seismic hazard precursory evolution: fractal and multifractal aspects. Physics and

757

Chemistry of the Earth 29, 367 –378

758

Lennartz, S., Livina, V.N., Bunde, A., Havlin, S., 2008. Long -term memory in

759

earthquakes and the distribution of interoccurrence times. Europ hys. Lett. 81,

760

69001.

761

Lyakhovsky, V., Ben -zion, Y., Agnon, A., 2001. Earthquake cycle, fault zones,

762

and seismicit y patterns in a rheologically layered lithosphere. J . Geophys. Res.

763

106, 4103–4120.

764

Matcharashvili, T., Chelidze, T., Javakhishvili, Z., 2000. Nonlinear anal ysis of

765

magnitude and interevent time interval sequences for earthquakes of Caucasian

766

region. Nonlinear Processes in Geophysics 7, 9 –19.

767

Matcharashvili, T., Chelidze, T., Javakhishvili, Z., 2009. Dynamics, predictability

768

and risk assessment o f natural hazards. In: Fra Paleo, Urbano (Ed.), Building Safer

769

Communities. Risk Governance, Spatial Planning and Responses to Natural

770

Hazards. IOS Press, Amsterdam, pp. 148 –161.

771

Mekkawi, M., Grasso, J.R., Schneggm, P.A. , 2004. A long-lasting relaxation of

772

seismicit y at Aswan reservoir, Egypt, 1982 –2001. Bull. Seismol. Soc. Am. 94,

773

479–492.

43

44

774

Mogi,

K.,

1962.

Magnitude -frequency

relationship

for

elastic

shocks

775

accompanying fractures of various materials and some related problems in

776

earthquakes. Bull. Earthquak e Res. Inst. Univ. Tokyo 40 , 831-883.

777

Sarlis, N.V., Skordas, E.S., Varotsos, P.A., 2009. Multiplicative cascades and

778

seismicit y in natural time . Physical Review E 80, 022102.

779

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Lazaridou, M.S., 2008. Fluctuations,

780

under time reversal, of the natural time and the entropy distinguish similar looking

781

electric signals of different dynamics . J. Appl. Phys. 103, 014906.

782

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Uyeda, S., Kamogawa, M., 2011.

783

Natural time anal ysis of c ritical phenomena. Proc. Natl. Acad. Sci. USA 108,

784

11361-11364.

785

Peng, C.-K., Havlin, S., Stanley, H.E., Goldberger, A.L., 1995, Quantification of

786

scaling exponents and crossover phenomena in nonstationary heartbeat time series .

787

CHAOS 5, 82–87.

788

Pliakis, D., Papakostas, T., Vallianatos, F., 2012. A first principles approach to

789

understand the physics of precursory accelerating seismicit y. Ann . Geophys .

790

55(1). doi:10.4401/ag-5363.

791

Reasenberg, P.A., 1985. Second-order moment of central California seismicity,

792

1969-82. J. Geophys. Res. 90, 5479 –5495.

793

Rong, Y.M., Wang, Q., Ding, X., Huang, Q.H. , 2012. Non-uniform scaling

794

behaviour in Ultra-Low-Frequency (ULF) geomagnetic signals possibl y associated

795

with the 2011 M9.0 Tohoku earthquake . Chinese Journal Geophysics 55, 3709–

796

3717.

44

45

797

Rubinstein, J.L., Mehani, A.B., 2015. Myths and Facts on Wastewater Injection,

798

Hydraulic Fracturing, Enhanced Oil Recovery, and Induced Seismicit y. Seismol.

799

Res. Lett. 86(4), 1060 –1067. doi: 10.1785/0220150067.

800

Said, R., 1993. The River Nile: Geology, Hydrology and Utilization. Pergamon

801

Press, Oxford., 320 pp.

802

Said, R., 1981. The Geological Evolution of the River Nile. Springer -Verlag, New

803

York, 151 pp.

804

Scholz, C.H., 1968. The frequency-magnitude relation of microfracturing in rock

805

and its relation to earthquakes. Bull. Seismol. Soc. Am. 58 , 399-415

806

Selim, M.M., Imoto, M, Hurukawa, N. , 2002. Statistical investigation of reservoir -

807

induced seismicit y in Aswan area, Egypt. Earth Planets Space 54, 349 –356.

808

Shi, Y., Bolt, B., 1982. The standard error of the magnitude -frequency b

809

value. Bull. Seismol. Soc. Am. 72(5), 1677–1687

810

Shinomoto, S., Miura, K., Koyama, S., 2005. A measure of local variation of inter -

811

spike intervals. Biosystems 79, 67 –72.

812

Simpson, D.W., Negmatullaev , S.K., 1981. Induced seismicit y at Nurek Reservoir,

813

Tadjikistan, USSR. Bull. Seismol. Soc. Am. 71 (5), 1561–1586.

814

Simpson, D.W., Kebeasy, R.M., Nicholson, C., Maamoun, M., Albert, R.N.,

815

Ibrahim, E.M., Megahed, A., Gharib, A., Hussain, A., 1987. Aswan Telemetered

816

seismograph Network. J. Geophys. 7, 195 –203.

817

Simpson, D.W., Gharib, A.A., Kebeasy, R.M., 1990. Induced seismicit y and

818

changes in water level at Aswan reservoir, Egypt . Gerlands. Beitr. Geophys .

819

Leipzig 99, 191 –204.

45

46

820

Shearer, P. M. (2012), Space -time clustering of seismicit y in Cal ifornia and the

821

distance dependence of earthquake triggering, J. Geophys. Res. 117, B10306, doi:

822

10.1029/2012JB009471.

823

Stabile, T.A., Giocoli, A., Lapenna, V., Perrone, A., Piscitelli, S., Telesca, L.,

824

2014.

825

associated with the Pertusillo artificial lake (southern Ital y) . Bull. Seismol. Soc.

826

Am. 104(4). doi:10.1785/0120130333.

827

Telesca, L., Amatulli, G., Lasaponara, R., Lovallo, M., Santulli, A. , 2005. Time-

828

scaling properties in forest -fire sequences observed in Gargano area (southern

829

Ital y). Ecol. Model. 185, 531 -544.

830

Telesca, L., Cuomo, V., Lapenna, V., Macchiato, M., 2001. Statistical anal ysis of

831

fractal properties of point processes modelling seismic sequences, Phys. Earth

832

Planet. Int. 125, 65-83.

833

Telesca, L., ElShafey Fat ElBary, R., Amin Mohamed, A. E. -E., ElGabry, M. ,

834

2012. Anal ysis of the cross -correlation between seismicit y and water level in the

835

Aswan area (Egypt) from 1982 to 2010. Natural Hazards and Earth S ystem

836

Sciences 12, 2203–2207.

837

Telesca, L., Giocoli, A., Lapenna, V., Stabile, T.A., 2015. Robust identification of

838

periodic behavior in the time dynamics of short seismic series: the case of

839

seismicit y induced by Pertusillo Lake, southern Ital y. Stochastic Environmental

840

Research and Risk Assessment 29, 1437 –1446. doi:10.1007/s00477 -014-0980-6.

841

Telesca,

842

investigation of scaling properties in temporal patterns of seismic sequences.

843

Chaos, Solitons & Fractals 19(1), 1 –5.

Evidences

L.,

of

Lapenna,

low -magnitude

V.,

continued

Macchiato,

M.,

reservoir -induced

2004.

Mono -

and

seismicit y

multi-fractal

46

47

844

Telesca, L., Lovallo, Lopez, M.C., Molist, J.M. , 2016. Multiparametric statistical

845

investigation of seismicit y occurred at El Hierro (Canary Islands) from 2011 to

846

2014. Tectonophysics 672 -673, 121-128. doi: 10.1016/j.tecto.2016.01.045.

847

Telesca, L., Lovallo, M ., 2009. Non-uniform scaling features in Central Italy

848

seismicit y: a non -linear approach in investigating seismic patterns and detection

849

of possible earthquake precursors. Geophys. Res. Lett. 36, L01308.

850

Telesca, L., Lovallo, M., 2010. Long -range dependenc e in tree-ring width time

851

series of Austrocedrus chilensis revealed by means of the detrended fluctuation

852

anal ysis. Physica A 389, 4096 –4104.

853

Telesca, L., Lovallo, M., 2011. Anal ysis of time dynamics in wind records by

854

means

855

information plane . J. Stat. Mech. P07001.

856

Telesca, L., Mohamed, A. E. -E. A., ElGabry, M., El -hady, S., Abou Elenean, K.

857

M., 2012. Time dynamics in the point process modelling of seismicit y of Aswan

858

area (Egypt), Chaos Sol itons & Fractals 45, 47 -55.

859

Telesca, L., Pierini, J.O., Scian, B., 2012. Investigating the temporal variation of

860

the scaling behavior in rainfall data measured in central Argentina by means of the

861

detrended fluctuation anal ysis. Physica A 391, 1553 –1562.

862

Thurner, S., Lowen, S.B., Feurstein, M.C., Heneghan, C., Feichtinger, H.G.,

863

Teich, M.C., 1997 . Anal ysis, synthesis, and estimation of fractal -rate stochastic

864

point processes: Fractals 5, 565 -596.

865

Utsu, T., 1999. Representation and anal ysis of the earthquake size distribution: a

866

historical review and some new approaches. Pageoph 155, 509 –535.

of

multifractal

detrended

fluct uation

anal ysis

and

Fisher -Shannon

47

48

867

Vallianatos, F., Benson, P., Meredith, P., Sammonds, P., 2012. Experimental

868

evidence of a non -extensive statistical physics behavior of fracture in triaxially

869

deformed Etna basalt using acoustic emissions. Europhys . Lett. 97, 58002.

870

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., 2012. Scale-specific order parameter

871

fluctuations

872

fluctuation anal ysis . Europhys. Lett. 99, 59001.

873

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., 2014. Study of the temporal

874

correlations in the magnitude time series before major earthquakes in Japan. J.

875

Geophys. Res. Space Phys. 119, 9192 –9206.

876

WCC (Woodward-Clyde Consultants) , 1985.

877

and estimation of magnitudes and recurrence intervals . Internal Report, High and

878

Aswan Dams Authority, Egypt.

879

Wiemer, S., W yss, M., 2000. Minimum magnitude of completeness in earthquake

880

catalogs: examples from Alaska, t he Western United States, and Japan. Bull.

881

Seismol. Soc. Am. 90, 859 –869.

882

Woessner, J., Wiemer S., 2005. Assessing the qualit y of earthquake catalogues:

883

Estimating the magnitude of completeness and its uncertaint y . Bull. Seismol. Soc.

884

Am. 95(2), 684–698. doi: 10.1785/ 0120040007.

885

Woodward, J.C., Macklin, M.G., Krom , M.D., Williams, M.A.J., 2007. The Nile:

886

Evolution, Quaternary River Environments and Material Fluxes. In: Large Rivers:

887

Geomorphology and Management (Gupta, Eds).

888

Wyss, M., 1973. Towards a physi cal understanding of the earthquake frequency

889

distribution. Geophys. J. R. Astron. Soc. 31, 341 –359.

of

seismicit y before

mainshocks:

Natural

ﬁc

time

f

and

hq

detrended

k

c

890 48

49

891

49

*Revised manuscript with no changes marked Click here to view linked References

1 2


3 4

5

Luciano Telesca1*, Raafat Fat Elbary2, Tony A. Stabile1, Mohamed Haggag2, Mohamed Elgabry3

6

1

7

85050 Tito (PZ) Italy

8

2


9

3



10 11

*Corresponding author: tel. +39-0971-427277, fax +39-0971-427277, email:

12

[email protected]

13 14

Abstract

15

In this study, the seismicity that occurred in Aswan region from 198 2 to 2015 is

16

investigated using robust statistical methodologies. The completeness magnitude,

17

estimated by using two different methods (MAXC and GFT) is 2.5 for the whole

18

catalogue with b 1.07. By using the expectation maximization algorithm, two depth

19

classes of events were identified with a threshold at about 12 km. The events deeper

20

and shallower than the thresho ld could be likely generated by the same mechanism:

21

the loading/unloading operation of the Lake Nasser reservoir. We suggest that the

22

shallow seismicity occurs on shallow small fractures in correspondence of the

23

intersection of N-S faults with E-W faults, which may form a minor pull -apart basin.

2

24

The deep events mainly occur along the right -lateral, strike-slip, E–W Kalabsha fault

25

and the seismicity is characterized by mainshock -aftershocks sequences that mask the

26

annual periodicity if not properly aftersho ck-depleted. Indeed, before applying the

27

declustering on the seismic catalogue, the analysis of the time -clustering properties

28

of the shallow earthquakes reveals already the presence of annual modulation that is

29

not evident in the time dynamics of the deep earthquakes. Furthermore, the shallow

30

events are featured by the Allan Factor scaling exponent (measuring the strength of

31

the time-clustering in an earthquake sequence) lower than that of the deep events,

32

indicating a tendency of the time dynamics of the shallow earthquakes to behave

33

more regularly than the deep ones. The detrended fluctuation analysis of the

34

magnitude

35

characterized by the tendency of events of similar value of magnitude to follow each

36

other.

37


series

suggests

that

the

earthquake

series

are

weakly

persistent,

38 39

1. Introduction

40

River Nile, the longest river in the world, is a common basin between 11 countries ,

41

traveling over 2700 km through Sahara Desert withou t any significant perennial

42

tributary inputs (Woodward et. al, 2007). Throughout time the river has gone through

43

natural and anthropological changes , being a structurally controlled stream since its

44

early stages. Several studies (i.e. Adamson and Williams, 1980; Said, 1981, 1993)

45

have proposed that the river Nile is in continuous evolving process by major tectonic

2

3

46

phenomena and climatic changes including the Rifting of East African that could be

47

the shaping factor for the location of sedimentary basin and t he drainage pattern.

48

The river has gone through many water resources management mega projects ; the

49

largest till now is the Aswan High Dam constructed between 1960 -1971, which is 111

50

m high, a crest length of 3830 m , and impounds the second largest reservoir in the

51

world, the Lake Nasser, that has a gross capacity of 169 billio n cubic meters . On

52

November 14, 1981, an Ms 5.3 earthquake took place south of the dam. This

53

earthquake has raised the concerns about the dam stability from one side and its

54

relation to seismicity from the other side . A network of 13 station s was established

55

(Simpson et al., 1987) to monitor seismicity aro und the lake since 1982 , and intense

56

seismic activity has been recorded since then (Simpson et al., 1 990; Gahalaut et al.,

57

2016, and references therein ).

58

Several researchers explored the relationship between the Aswan reservoir water

59

level and the obser ved seismicity in the region ( e.g., Kebeasy et al., 1981; Simpson et

60

al., 1990; Hassoup 1994; Selim et al., 2002; Mekkawi et al., 2004; Haggag et al.,

61

2008; Telesca et al., 2012 ; Gahalaut et al., 2016 ) and, even if in some periods there

62

were found no or we aker reservoir influence ( Hassoup 1994; Selim et al., 2002;

63

Mekkawi et al., 2004 ; Telesca et al., 2012), it has been commonly accepted t hat the

64

Aswan seismicity is a case of continuous reservoir triggered seismicity (RTS).

65

Therefore, Aswan area belongs to the reservoir sites that exhibit triggered seismicity

66

every year or after a gap of a few years , such as Lake Mead in the USA (Carder,

67

1945), Koyna-Warna reservoir

68

2010), Nurek Dam in Tajikistan (Simpson and Negmatullaev, 1981),

69

Brazil (El Hariri et al., 2010), and Pertusillo reservoir in Italy (Stabile et al., 2014 ;

-

,

3

Formatted: Not Highlight

4

70

Telesca et al., 2015). In all the cases mentioned above delayed seismic response to

71

water

72

mechanism of the observed continued RTS is the diffusion of pore fluid pressures .

73

Particularly for the As wan area, Gahalaut and Hassoup (2012) demonstrated from an

74

analytical simulation that although the stress due to the reservoir load stabilizes

75

seimogenic faults of the area, the effect of pore fluid pressure leads the faults to go

76

beyond the critical stres s for failure.

77

Due to the presence of the High Dam and the seismic risk that it could raise, a deep

78

dynamical

79

challenging and, at same time, crucial to best understand the mechanisms related t o

80

the generation of local earthquakes.

81

In fact, it is widely recognized that investigating with detail the structure of

82

magnitude, space and time distribution of earthquakes is fundamental for earthquake

83

hazard assessment as well as for the comprehension o f properties of seismic

84

processes (see e.g. Goltz, 1997; Kagan, 1997; Matcharashvili et al., 2009). In

85

particular, the investigation of the characteristics of time distribution of earthquake

86

occurrences on various temporal scales has been the focus of very intense research.

87

Several studies based on different conceptual frameworks approached the analysis of

88

earthquake time patterns by means of both field and laboratory data as well as

89

numerical

90

Matcharashvili et al., 2000; Telesca et al., 2004). Most of such studies highlight that

91

seismic processes are characterized by intermittent time behavior with phases of

92

intense seismic activity interspersed with those of low seismicity (Ben-Zion and

93

Lyakhovsky, 2002; Kiyashchenko et al., 2004; Pliakis et al., 2012; Vallianatos et al.,

fluctuations

of

reservoirs

characterization

simulations

of

(e.g.

was

the

Issac

observed

seismic

et

al.,

suggesting

process

2004;

that

governin g

Lyakhovsky

the

dominant

Aswan

et

al.,

area

is

2001;

4

5

94

2012); thus, evidencing the presence o f nonrandom components in earthquake

95

generation in energy, space and time domains ( Lliopoulos and Pavlos, 2010).

96

Within this context, i n this study, we aim at investigating the dynamical properties of

97

the most updated seismic catalogue of Aswan applying several robust statistical

98

methodologies to the magnitude and time distribution of seismicity that occurred

99

nearby Lake Nasser from 1982 to 2015 in order to better characterize its time

100


dynamics.

101 102 103

2. Seismo-tectonic settings and data description

104

Aswan (or Syene as its Greek name, which is named after the type locality for the

105

igneous rock syenite) is located in the southern part of Egypt at the interface between

106

the stable Archean craton of the Nubian Shield and the less stable Pan -African

107

orogeny of the southern most of the Egyptian Eastern Desert. Aswan exhibits a

108

complex geological situation with a number of different rock types , ranging from

109

quaternary deposits to cretaceous sedimentary rocks of Nubian sandstone , to igneous

110

and metamorphic rocks of the deep -lying basement complex, which have been

111

uplifted and exposed to surface. In many areas in and around Aswan the river has

112

eroded the overlying Nubian sandstone and carved deep channels into the igneous

113

rocks (Greiling, et, al. 1994).

114

From early satellite imagery, El Shazly et al. (1973) has described the structural

115

trends in Aswan area to be mainly NNW -SSE fractures making notable horizon tal

116

separation and NW -SE fractures showing horizontal and vertical separation along

117

geological and relief boundaries. Furthermore, the NNE -SSW fault west to Kurkur 5


6

118

shows horizontal left -lateral trend. In addition, two major fracture trends are present


119

in NE-SW and the ENE -WSW. According to El Shazly et al. (1973) the NE -SW


120

fractures do not show separation, and they may be major tension fractures

121

perpendicular to the principal force creating the previously mentioned two major

122

fault trends. Fractures seem to represent tension zones along the hinges of major

123

folds, which may have been faulted along the same zones.

124

These trends been reactivated as both strike -slip E-W dextral and N-S sinistral faults

125

(WCC, 1985; Abdeen et al., 2000) , and dip-slip faults (Issawi, 1978) and propagated

126

up through the sedimentary cover. The seismic activity is concentrated along N -S and

127

E-W fault intersections. The N -S faults have less activity than that of E -W faults.

128

Recent stress regime deduced from Earthquak e focal mechanism (Hus sein et al.,

129

2013) is in good agreement with that of geological studies and borehole breako ut data

130

(Bosworth and Strecker, 1997) with Shmax E-W and Shmin NNE-SSW. Under this

131

stress regime, the province is found to be consistent with both right lateral faul ts (E–

132

W striking) and left lateral faults (N –S striking).

133

The largest of the Aswan earthquakes was of magnitude Ms 5.3, and occurred on 14

134

November 1981. From the intensity data, the well-determined locations of numerous

135

aftershocks recorded using portable stations and a telemetered network, the event

136

appears located on the Kalabsha fault beneath Gebel Marawa (Kebeasy et al. 1987).

137

The depths of the aftershocks and the special study of teleseismic records of the

138

mainshock (WCC 1985) indicate that the mainshock was at a depth from 18 to 20 km.

139

Prior November 14, 1981, no earthquakes had been reported in the Aswan area in the

140

c

141

1920. Because of the lack of continuous and reliab le data during the early stages of



Formatted: Not Highlight Formatted: Not Highlight

g

f h

S

g c

C

SC)

c

h

SC’

c

6

7

142

the filling of the Aswan reservoir, it is not possible to determine exactly when low -

143

magnitude activity may have started. The first seismographs installed in the Aswan

144

area that were capable of recording small local earth quakes were Soviet short -period

145

(SMK) instruments installed at Aswan and Abu Simble in 1975. Although the

146

operation of the stations was irregular prior to 1981, 20 events of magnitude greater

147

than 2.5 have been identified by Helwan Institute located in the Wadi Kalabsha area.

148

Thirteen of these took place during approximately 200 days of station operation

149

between August 1980 and August 1981. A long sequence of aftershocks followed the

150

14 November 1981 earthquake , including the immediate aftershocks and the

151

continuation of Aswan activity until the present both in the area of the mainshock and

152

around the northern part of the Aswan reservoir.

153

Following the mainshock, portable microearthquake recorders were installed in the

154

northern part of reservoir area by Eg yptian Geological survey from December to June

155

1982. In late June 1982 , the portable seismic field stations were replaced by a

156

telemetry network erected by Helwan Observatory and Lamont -Doherty Geological

157

Observatory (USA). The purpose of the telemetry net work is to monitor the

158

induced/triggered seismicity along the Kalabsha fault (Fig. 1), which continues to

159

occur in the area of the November 14, 1981 earthquake (Kebeasy et al 1987 ; Fat-

160

Helbary et al., 2002 ). Data were transmitted to a data center to record the output

161

signals coming from the field stations. Five monitors with pen recorder were used for

162

the visual record and all the data were recorded in the FM magnetic tape as analog

163

data and in the 9 -track tape as digital data. A playback unit and computer facilities

164

had been installed at the center to allow earthquakes to be quickly analyzed and

165

located. Since 2009, the Aswan Seismic Network has been updated and replaced by 7




8

166

new digital broad band network. The transmission system is changed from telemetry

167

to satellite and in addition some stations in field were moved to near better sites. As

168

well as the data from field stations is sent to the main center for the necessary

169

analysis using the recent software programs such as Atlas and Earlybird.

170

171 172

Fig. 1. Aswan Seismic Network.

173 174

The output data include latitude, longitude, focal depth, origin time, epicenter

175

distance and azimuth for each station. Various measures of location accuracy are also

8


9

176

given. The output data are used for constructing the seismici ty map of the Kalabsha

177

area (Fig. 2).

178 179

a)

9

10

6

5

Mi

4

3

2

1

0 0

2000

4000

6000

8000

i

180 181

b) Formatted: Not Highlight

182

Fig. 2. (a) Seismicity map of Aswan region ( a: Gebel Marawa zone, b: East-1 of

183

Gebel Marawa zone, c: East -2 of Gebel Marawa zone, d: khore El -Ramla zone, e:

184

Abu Derwa zone, and f: Old stream zone). (b) Magnitude plot of the earthquakes in

185

the investigated region during 1982 –2015. Horizontal axis indicates the ith event and

186

vertical axis indicates its magnitude.



187 188

3. M ethods and results

189

In this study we investigate the seismicity that occurred from January, 1, 1982 to

190

December 31, 2015 in the area of Aswan (Fig. 2). We employed several independent

191

statistical methods to obtain the most complete picture of the dynamical properties of

192

the seismic process in the area.

193 10


11

194

3.1. The frequency -magnitude distribution

195

The Gutenberg-Richter (GR) law (Gutenberg and Richter, 1944) relates the threshold

196

magnitude M t h and the number of earthquakes with magnitude M> M t h in a power-law

197

manner usually represented in semi -log scales as log 1 0 (N)=a-bM t h , where N is the

198

number of ea rthquakes with magnitude M> M t h , a is the earthquake productivity, and

199

b is a value that indicates the proportion of small events respect to the large ones.

200

The GR law is generally used to fit t he frequency magnitude distribution (FMD). The

201

b-value is a critical parameter that can inform on the stress crustal conditions ;

202

therefore, estimating with a good accuracy and reliability the b-value is important to

203

characterize different stages of the evolution of seismicity, linked with dynamical

204

changes of the seismic process, and, as a consequence, is crucial for reliable s eismic

205

hazard assessments (Scholz, 1968; Wyss, 1973) .

206

In our study, the estimation of the b-value was performed by using the maximum

207

likelihood method (MLE) (Aki, 1965),

208 209

b

Field Code Changed

log10 (e) , (1) M bin   M    M c  2  

210 211

where is the average magnitude of the sub-set of earthquakes whose magnitude

212

is larger or equal to the completeness magnitude M c and  M b i n represents the binning

213

width of the catalogue (Utsu, 1999).

214

The standard deviation of the estimate of b

215

(1982) formula,

c c

by

g h

Sh

B

’

216 11

12

N

217

 b  2.3b 2

 M i 1

i

  M 

N  N  1

Field Code Changed

2

. (2)

218 219

As it is deduced from formula (1), the b-value depends on the estimat ion of the

220

completeness magnitude M c that is the lower magnitude above which the seismi c

221

catalogue can be considered complete.

222

It is obvious that to get reliable results of any analysis performed on the seismi c

223

catalogue, only the events with magnitude MM c have to be selected . The maximum

224

curvature method (MAXC) (Wiemer and Wyss, 2000) allows a fas t estimation of M c

225

that corresponds to the largest bin in the noncumulative FMD. Another method is the

226

goodness -of-fit (GFT) (Wiemer and Wyss, 2000) between the observed and synthetic

227

cumulative FMDs, the last calculated employing the a- and b-values of th e GR-law of

228

the observed seismic set for magnitude larger or equal to a n increasing threshold

229

magnitude that estimates M c when the 90% of the observed data are well modeled by

230

a straight line.

231

As already shown above, s ince 1980 the Aswan seismic network un derwent several

232

upgrades that have certainly influenced the earthquake detection sensitivity and, thus,

233

the completeness magnitude through time. Therefore, it is necessary to investigate

234

preliminarily the time variation of the completeness magnitude. A visual impression

235

about how the magnitude of completeness varies with time and about possible artifact

236

in the catalog can be got by using the M i -i plot with horizontal axis indicating the ith

237

earthquake and vertical axis indicating its magnitude M i (Huang, 2006). Fig. 2b

238

shows a slight decrease of the magnitude with time and this indicates that the 12

13

239

completeness magnitude changes with time. Fig. 3 shows the time variation of M c for

240

the seismicity at Aswan calculated by means of the MAXC method (red) and the GFT

241

method (blue ).

242

entire catalog with a shift of 1 0 events. In each window, the completeness magnitude

243

M c (associated with the time of the last event in the window) was computed only in

244

case the number of events wa s larger or equal to 50 (Woessner and Wiemer, 2005).

245

We can see that MAXC and GFT methods give very similar results in all the three

246

examined cases ( W N =200, 500 and 1000 events), although the MAXC method

247

estimates a slightly lower value o f the completeness magnitude. The range of

248

variation of the completeness magnitude depends on the length of the moving

249

window, being larger for W N =200 and smaller for W N =1000.

We considered a fixed event number window (W N ) sweeping the

250 251 Field Code Changed MAXC GFT WN=200

3.5

MAXC GFT WN=500

3.0

Field Code Changed

3.0 2.5

2.5 2.0

MC

MC

2.0

1.5

1.0

1.0

0.5

0.5

0

2000

4000

6000

8000

10000

12000

14000

0


252

1.5

2000

4000

6000

8000

10000

12000

14000


a)

b)

13

14

Field Code Changed MAXC GFT WN=1000

3.0

2.5

MC

2.0

1.5

1.0

0.5 0

2000

4000

6000

8000

10000

12000

14000


253

c)

254

Fig. 3. Time variation of the completeness magnitude in the Aswan area (red: MAXC method; blue:

255

GFT method, see text for details): (a) WN=200 events; (b) WN=500 events; (c) WN=1000 events.

256 257

A conservative choice of the completeness magnitude would require taking it as the

258

largest value of the time evolution of M c . But, this choice would strongly decrease

259

the amount of available data, and consequently would inc rease the uncertaint y of the

260

statistical estimates due to smaller sample sizes. For instance, considering the time

261

variation of M c for W N =1000 events, the highest completeness magnitude on the base

262

of the GFT method is 3.0 that would reduce the amount of availa ble data to 375 over

263

9592 that is the size of the whole catalog . So, it is impo rtant to find a sort of

264

compromise between the size of the dataset, large enough to perform the statistical

265

analysis with good accuracy, and the value of M c that should guarantee a good

266

completeness of the catalog. On the base of the results shown in Fig. 3, by visual

267

inspection we believe that a reasonable choice of M c is 2.5; in fact, it is larger than

268

any completeness magnitude calculated by the MAXC method and lower than the

269

completeness magnitude calculated in just few windows by using the GFT method; 14


15

270

furthermore, 2.5 is quite robust with respect the size of the moving window . In this

271

case the number of earthquakes with magnitude larger or equal to 2.5 is 1327 over

272

9592; and t his size is large enough to perform significantly the statistical analysis on

273

the catalog. Therefore, with M c =2.5 the b=1.070.02.

274 275

3.2. The depth distribution

276

Considering the catalog of seismic events with magnitude larger or equal to 2.5, two

277

distinct depth classes characterize t he earthquakes that occurred in the Aswan area.

278

Fig. 4 shows the depth histogram (black line) of the seismic events. It is clear that

279

the distribution is bimodal, characterized by two depth ranges, one involving the

280

shallow events and the other the deep events. Furthermore, the depth distribution

281

seems to be a mixture of two Gaussian distributions.

282

a)

15


16

283 284

b)

16

17

285

c) 17

18

286 287

Fig. 4. a) Depth distribution of the seismicity at Aswan. The red and blue curves represent the best

288

Gaussian fit of the deep and shallow events. D0 represents the estimated depth threshold separating the

289

two classes of depths; b) Depth-longitude diagram of seismicity; c) Seismicity of Aswan area for

290

magnitude larger or equal to 2.5.

291 292

In order to better discriminate the two depth ranges, we applied the expectation

293

maximization (EM) algorithm (Borman, 2004) that is a statistical method to calculate

294

the maximum likelihood estimates of the parameters of two Gaussian distributions,

295

whose mixture seems to model the bimodal depth distribution of Fig. 4. We found

296

that one Gaussian distribution (blue curve) with  G =4.8 and  G 2 =8.0 models the

297

distribution of shallow events and the other (red curve) with  G =19.0 and  G 2 =9.7

298

models that of the deep ones. The intersection between the two curves D 0 12 km can

299

be considered as the threshold depth discriminating betwe en shallow and deep events.

300

In the forthcoming analyses we will investigate the two earthquake sub-catalogues:

301

shallow (depth < 12 km) and deep (depth  12 km). The number of the shallow events

302

is 744 and that of the deep ones is 583. For the deep sub -catalog b=0.990.03, while

303

for the shallow one b=1.140.04.

304

Fig. 4b shows the vertical cross/section depth -longitude diagram of seismicity . The

305

events appearing at shallower depths (less than 12 km) in this cross -section are from

306

East Gebel Marawa (the composite fault plane solution indicates strike -slip faulting

307

with a normal fault component) , Khore El-Ramla (the composite fault plane solution

308

indicates a strike-slip fault and the fault plane strikes 155° and dips 65°) , Abu Dirwa 18

19

309

(the focal mechanism of this zone includes strike-slip and normal components, and

310

the fault plane strikes 177° from the north and is dipping 61°) and old stream zones

311

(the fault plane solution indicates strike slip faulting and the fault plane strikes 161°

312

and dips 77°).

313

On the other hand, the seismicity at Gebel Marawa zone is almost all between depth

314

of 12 and 26 km and the events align along the Kalabsha fault where the mainshock

315

of November 14, 1981 occurred deeper than 12 km (Fat -Helbary et al., 2002). The

316

composite fault plane so lution of the earthquakes indicates strike -slip faulting with a

317

normal-fault component. The fault plane strikes 78° and dips 70° (Fat -Helbary,

318

1989).

319 320

3.3. The coefficients of variation

321

The coefficient of variation C v is a simple measure employed to study the time-

322

clustering properties of an earthquake process . It is defined as

323 324

Cv 

 , (3) 

Field Code Changed

325 326

where  and  are the standard deviation and the average of the interevent times ,

327

respectively. Fig. 5 shows the series of the interevent times of th e deep (Fig. 5a) and

328

shallow (Fig. 5b) sub-catalogues.

19

20


300

Shallow

200

100

0


-100 600

0

100

200

300

400

500

600

700

800

Deep

400 200 0 0

100

200

300

400

500

600

n

329 330


Fig. 5. Interevent time series of the shallow (a) and deep (b) sub-catalogues.


331 332

Depending on the numerical value of C v , the earthquake sequence is regular (or

333

periodic) if it is lower than 1, purely random (or Poissonian) if it is 1 or clustered if

334

it is larger than 1 (Kagan and Jackson, 1991). Recently, Telesca et al. (2016)

335

introduced the local coefficient of variation L v , defined by Shinomoto et al. (2005),

336

to investigate the local time-clustering properties of the volcano -related seismicity at

337

El Hierro, Canary Islands (Spain):

338

1 N 1 Ti  Ti 1  3 N  1 i 1 Ti  Ti 1 2 (4)

Field Code Changed

2

339

Lv 

340

20

21

341

For Poissonian seismic processes, C v and L v are both 1, and for periodic processes

342

they are both 0. However, if C v can measure global variability of a whole interevent

343

sequence and could be affected by event rate fluctuation s, L v measures local stepwise

344

variability of interevent times , because it is rather independent of slow variation in

345

average rate. Just as an example, if one joins two peri odic point processes like those

346

in Fig. 6, C v >>1 because globally the process appears highly clustered, but L v 0,

347

because at local scales the process is periodic.

0

10

20

30

40

time

348 349

Fig. 6. Superposition of two periodic point processes.

350 351

We calculated both the coefficient s of variation for the deep and shallow seismicity

352

in Aswan for events with m agnitude M2.5, and obtained C v  3.37 and L v 1.16 for

353

deep seismicity and C v  1.78 and L v 1.35 for the shallow one. To calculate the

354

significance of these results, we calculated bot h the quantities for 1,000 Poisson

355

processes randomly generated with the same size and mean interevent time as the

356

original (deep and shallow) seismic interevent time series. The 95% confidence 21

22

357

interval, which is delimited by the 2.5 t h and 97.5 t h percentil es of the distribution of

358

C v and L v of the Poissonian surrogates , are [0.94, 1.07] for C v and [0.92, 1.08] for L v

359

in case of deep seismicity, and are [0.93, 1.0 8] for C v and [0.92, 1.07] for L v in case

360

of shallow seismicity. The obtained values of the coef ficients of variation indicate

361

that both global ly and locally the distribution s of the shallow and deep seismicity at

362

Aswan are clusterized at 95% confidence.

363 364

3.4. The Allan Factor

365

The coefficients of variation described in section 3.2 furnish information about the

366

time-clustering of a point process, but reveal none about the timescales where the

367

process is clusterized. To this aim, the Allan Factor (AF) is a suited method for

368

discriminating between the timescales where the process is clusterized from thos e

369

where it is not. Dividing the time axis into equally spaced contiguous counting

370

windows of duration  , that is timescale, a sequence of earthquake counts { N k (  )} is

371

obtained, with N k (  ) being the number of earthquakes falling in the k-th window

372

(Thurner et al., 1997). The AF, then, is defined as

373

AF ( )  374

 ( N k 1 ( )  N k ( )) 2  2  N k ( )  , (5)

Field Code Changed

375 376 377

and it is related to the variability of successive counts (Thurner et al., 1997); the y b

c

h

g

.

h

F h

b

g y

g

378

the time dynamics of point processes of different types ( Telesca et al., 2001; Telesca

379

et al., 2005). 22

23

380

If the earthquake process is Poissonian that means memoryless and formed by

381

independent events, then the AF is rather flat at all timescales and assumes value

382

around 1 (except for very large timescales due to finite -size effects (Telesca et al.,

383

2012); but if the earthquake process is clusterized the AF changes with the timescale

384

 . In particular, if the earthquake process is fractal (self-similar) in time, the AF

385

behaves as a power-law (scaling behavior) :

386 

387

  AF( )  1      1  , (6)

Field Code Changed

388 389

where the exponent  quantifies the strength of clusterization;  1 is the so-called

390

fractal onset time and marks the lower limit for significant scaling behavio r in the AF

391

(Thurner et al., 1997). Therefore, if  0 the earthquake process is Poissonian, while

392

if  >0 it is clusterized.

393 394

23

24


2

log10(AF())

1.0

=0.40+0.02

0.8

0.6

1y

1

0.4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10() (day)

395

a)

2.5

Deep seismicity

2

log10(AF())

2.0

1.5

=1.85+0.06 1.0

0.5

1

0.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10() (day)

396 397

b) Fig. 7. AF for the shallow (a) and deep (b) Aswan sub -catalogues.

398 399

Fig. 7 shows the AF (open circles) for the shallow (Fig. 7a) and deep (Fig. 7b)

400

seismicity at Aswan, for events with magnitude M 2.5. Smoothing with adjacent 5 -

401

sample averaging (red curve) evidences more clearly the scaling behavior in both

402

shallow and deep seismicity between  1 and  2 that are between about 12 days and 24

25

403

about 5 months for shallow seismicity, and between about 40 days and 9 months for

404

deep seismicity. The scaling exponents are very different, being 0.40 for the shallow

405

and 1.85 for the deep seismicity, indicating a higher clustering degree for deep

406

seismicity than shallow. In order to verify the significance of the exponents, we

407

calculated the distribution of the exponents computed between  1 and  2 of 1, 000

408

Poissonian seismic sequences generated with the same number of events and rate as

409

the shallow and deep original ones (Fig. 8). We can see that the obtained value of 

410

for the shallow and the deep seismicity are well above the largest value of the

411

distribution of  obtained for Poissonian surrogates; therefore, the exponents

412

calculated for the real seismicit y are signifi cant.

413

Another interesting feature is the drop at around 1 year in the smoothed curve (red)

414

obtained for the shallow seismicity. The drop at a certain timescale in the AF curve

415

indicates the presence of periodicity at that timescale ( Gebber et al., 2006 ); thus, the

416

drop found in the AF of the shallow seismicity corresponds to the annual periodicity

417

that is consistent with the loading/unloading operations of the Aswan Dam and

418

strengthens the existence of annual water modulation (Gahalaut et al., 2016) of the

419

shallow seismicity.

420

25

26

Field Code Changed Deep Shallow 80

N

60

40

20

0

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5



421 422

Fig. 8. Distribution of  for 1,000 Poissonian sequences with same rate and same

423

number of events as the original deep (blue) and shallow (red) sequences.

424 425

3.5. The detrended fluctuation analysis of the magnitude time series

426

The Detrended Fluctuation Analysis (DFA) (Peng et al., 199 5) was used to study

427

long-range correlations of non-stationary series of different types (Telesca and

428

Lovallo, 2009; Telesca and Lovallo, 2010; Telesca and Lovallo, 2011; Telesca et al.,

429

2012; Telesca et al., 2016 ; Rong et al., 2012; Varotsos et al., 2008; Varotsos et al.,

430

2011). In the context of studies devoted to seismicity, several authors focused on the

431

long-range correlations in the magnitude time series, since magnitude rep resent one

432

of the crucial parameter in the framework of seismic hazard assessment. Telesca et al.

433

(2016) observed that the scaling exponent of the magnitude time series calculated by

434

the DFA (see later in the text) had an increasing behavior when the volcanic activity

435

at El Hierro, Canary Islands (Spain) reactivated in the 2011-2014. Varotsos et al. 26

27

436

(2014), performing the DFA on the magnitude series of several seismic areas,

437

evidenced a certain variability of the scaling exponent with relationship with

438

earthquake prediction . Lennartz et al. (2008) us ed the DFA to investigate the long-

439

range correlations of the magnitude se ries of Northern and Southern California

440

seismicity revealing the presence of long-term memory. Varotsos et al. (2012)

441

observed a rather sh arp variation from uncorrelated to correlated behavior in the

442

magnitudes of California seismicity before the occurrence of large shocks .

443

Within this scientific context , we can understand how crucial is the analysis of the

444

temporal properties of magnitude time series to better understand the dynamics of a

445

seismic process.

446

The DFA method works as follows:

447

i) the magnitude series M i , where i=1,…,N, and N is the total number of e vents is

448

integrated:

449 450 451

yk  i 1 M i   M  , (4)

Field Code Changed

k

452 453

where indicates the mean magnitude;

454

ii) the integrated series y k is divided into non-overlapping boxes of same length n;

455

iii) in each n-size box, y k is fit by the least squares by the line y n , k and detrended;

456

iv) the fluctuation, F n , is obtained by

457 458

Fn 

Field Code Changed

2 1 N   yk  yn,k  ; (5) N k 1 

27

28

459 460

v) the steps i)-iv) are repeated for all the available box sizes n; if the relationship

461

between F n n is a power-law, the magnitudes are long-range correlated:

462 463

F n n  ; (6)

464 465

vi) from the numerical value of the so-called scaling exponent  we can derive

466

information about the type of correlations: if the magnitude are uncorrelated, then

467

 =0.5; if the magnitudes are persistently correlated (meaning that a large (small)

468

magnitude (compared to the mean) has larger probability to be followed by a large

469

(small) magnitude), then  >0.5; if the magnitudes

470

(meaning that a large (small) magnitude (compared to the mean) has larger

471

probability to be followed by a small (large) magnitude), then  2.5


200

150

100

50

0

0

100

200

300

400

500

n

527

a)

31

32

Field Code Changed 800

Aftershock-depleted deep sub-catalog M>2.5

700


600 500 400 300 200 100 0

0

100

200

n

528

b)

529

Fig. 10. Interevent time series of the aftershock-depleted shallow (a) and deep (b)

530

sub-catalogues.

531 532

For the aftershock -depleted deep sub -catalog b=0.940.05, while for the shallow one

533

b=1.110.05 We also calculated for both the aftershock -depleted sub -catalogs the

534

global and local coeff icient of variations and obtained the following results (the 95%

535

confidence interval in parentheses): C v =1.31 [0.92,1.10] and L v =1.08 [0.88, 1.10] for

536

the shallow set and C v =1.93 [0.88, 1.14] and L v =1.01 [0.85, 1.16] for the deep set.

537

The only difference with un-declustered sub -catalogs is that after removing the

538

aftershocks both the sub -catalogs become locally Poissonian; and this is reasonable,

539

because the aftershocks introduce a high level of clustering even for short time

540

scales.

32

33

Field Code Changed 1.0


log10(AF(t))

0.6

0.4

a=0.38+0.02 0.2

1y 0.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10(t) (day)

541

a) Field Code Changed 1.0

Deep seismicity

0.8

log10(AF(t))

0.6

a=1.02+0.05

0.4

0.2

410 d

0.0

-0.2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

log10(t) (day)

542 543

b) Fig. 11. Allan Factor of the declustered shallow (a) and deep (b) sub -catalogs.

544 545

We applied the AF method to both the declustered sub -catalogs and the results are

546

shown in Fig. 11. We can observe that the scaling expo nent  decreases, but more

547

slightly for the shallow seismicity; this is consistent with the removal of aftershocks

548

that generally weakens the time -clustering of the seismicity; however, the deep sub 33

34

549

catalog is still more clusterized than the shallow one. The adjacent -5-sample-

550

averaging smoothed curve (red) on the AF for the shallow seismicity still shows the

551

periodicity at about 1 year, as in the original sub -catalog. However, a very interesting

552

feature is now revealed in the AF of the deep sub -catalog: the presence of a

553

periodicity at about 410 days, which seems compatible with the annual periodicit y

554

found in the AF of the shallow sub -catalog and also consistent with the annual cycle

555

of loading/unloading of the water reservoir. Such periodicity was not reve aled in the

556

original deep sub -catalog because it was very likely masked by the high number of

557

aftershocks following the November 14, 1981 event.

558 559

4. Discussion and conclusions

560

A detailed analysis of the seismicity that occurred in Aswan region from 1980 to

561

2015 has been performed by utilizing the most robust statistical methodologies to

562

deeply investigate its properties in time, magnitude and depth domains.

563

The analysis of the completeness of the catalogue was carried out by using two well

564

assessed methodologies (MAXC and GFT). The MAXC method generally furnishes

565

values of the completeness magnitude slightly lower than those obtained by the GFT

566

method, by using a sliding window with different sizes sweeping the entire catalog.

567

The completeness magnitude is not constant through time but varies, decreasing

568

around the end of the investigation period; this indicates that the catalog is not

569

homogeneous in time, and this is consistent with successive upgrades of the seismic

570

network that were performed through time . The non-homogeneity on time of the

571

completeness magnitude and the comparison between the results obtained by the

572

MAXC and GFT methods with different sliding window sizes has led us to choose the 34


35

573

value of 2.5 for the completeness magnitude; this value not only is reasonably

574

consistent with the results shown in Fig. 3, but is also low enough to guarantee a

575

sufficiently large size of events (with magnitude larger or equal to 2.5) to apply the

576

statistical methodologies. The obtained value of the Gutenberg -Richter b is 1.07;

577

this value lies within the range of the b-values calculated for the global seismicity

578

(Mogi, 1962). The obtained values of b and M c differ largely from the estimates for

579

approximately the same area calculated by Ali (2016), who found a b-value of the

580

0.554 and a completeness magnitude of 0.9. Ali (2016) applied only the MAXC

581

method and obtained the estimate of b from the whole catalog, which, however,

582

begins in 1997; in our case we considered a longer dataset, beginning in 1980,

583

compared th e results obtained by the MAXC and GFT methods and calculated the

584

value of b after computing the time variation of the completeness magnitude with

585

different size of sliding window.

586

The analysis of the distribution of hypocentral depths has revealed a very clear

587

discrimination of two depth classes, separated by the threshold of 12 km, which

588

separates earthquakes as shallower from deeper than the threshold.

589

Table 1 summarizes the results obtained from the different robust statistical

590

methodologies used in thi s study for the dynamical characterization of the 1982 -2015

591

seismicity in the area of Aswan.

592 593 Parameter

Shallow seismicity

Deep seismicity

Result

b-value

1.14 (1.11)

0.99 (0.94)

b-value of shallow seismicity

35

36

higher than b -value of deep seismicity Cv

1.78 (1.31)

3.37 (1.93)

Globally clusterized

Lv

1.35 (1.08)

1.16 (1.01)

Locally

clusterized;

aftershock-depleted

the sub-

catalogs are locally Poissonian AF

0.40 (0.38)

1.85 (1.02)

Deep

seismicity

high

clusterized DFA

0.555

0.553

Magnitudes

persistently

correlated 594

Table 1: Statistical parameters obtained for shallow and deep seismicity (in

595

parentheses those for the aftershock -depleted catalog) in the area of Aswan from

596

January, 1, 1982 to December 31, 2015.

597 598

The analysis of depth distribution was necess ary to discriminate between possibly

599

different earthquake generation mechanisms and/or different types of time -dependent

600

earthquake occurrence.

601

The results of our analysis show that the loading/unloading operation of the Lake

602

Nasser reservoir could signifi cantly influence the time dynamics of both the shallow

603

and deep events. Indeed, the AF curve of both the shallow and deep declustered sub-

604

catalogs evidences the existence of annual periodicity ; such periodicity could very

605

probably be linked to the annual p eriodicity of the water level fluctuations and could

606

strengthen the reservoir -triggered nature of the seismicity down to 30 km depth. It is

607

worth noting that the annual periodicity is not present in the AF curve of the deep un36

37

608

declustered sub-catalogue, therefore it is mostly characterized by mainshocks -

609

aftershocks sequences whereas this time-dependent earthquake occurrence character

610

is not evident in the shallow seismicity (AF curve shows the annual periodicity also

611

for the un -declustered shallow sub -catalog).

612

The deep and shallow declustered seismicity are characterized by very close values of

613

the local coefficient of variation L v and similar values of the global coefficient of

614

variation C v , although the C v for the deep seismicity is slightly larger than t hat of

615

shallow seismicity. This is also revealed by the scaling exponent  obtained from the

616

AF that measure quantitatively the strength of the time -clustering in an earthquake

617

sequence; the deep declustered sub-catalogue is characterized by  1.02, whereas the

618

shallow one by  0.38.

619

The DFA performed on the magnitude series of the shallow and deep events reveals

620

that both series are weakly persistently correlated, indicating that there is a tendency

621

of similar magnitudes to follow each other. This finding support the consideration

622

that the physical driving mechanism is the diffusion of pore fluid pressure because

623

the events are responding to the same underlying physical process that periodically

624

increases the seismicity rate (Shearer, 2012) with many events of about the same

625

magnitude.

626

The higher b-value (1.11) of shallow seismicity with respect to the b-value (0.94) of

627

the deep seismicity indicates that the increase of pore pressure can enable shallow

628

small fractures to overcome the critical stress point fo r failure even with a low level

629

of accumulated stress. Indeed, it is well known (Scholz, 1968; Wyss, 1973) that low

630

stresses cause earthquake series with high b-values.

37

38

631

The shallow seismicity is mostly located in the East of Gebel Marawa zone, Khore

632

El-Ramla zone, Abu Derwa zone, and Old stream zone (Fig. 4b and 4c) in

633

correspondence of the intersection of the left -lateral, strike-slip, N–S faults (El-

634

Barqa fault, Kurkur fault, and Abu -Dirwa fault) and the right -lateral, strike-slip, E–W

635

faults (Kalabsha fault and Seyal fault); therefore, w e suggest that the zones where the

636

shallow seismicity occurs constitute a minor pull-apart basin where the seismi c

637

deformation is accommodated on shallow small fractures . This hypothesis is also

638

supported by the observed oblique strike-slip motions of shallow earthquakes (focal

639

mechanisms indicate strike -slip faulting with a normal -fault component). Another

640

similar case of reservoir -triggered seismicity in pull-apart basins generated by the

641

relative motion of strike -slip faults is the Koyna-Warna area in India (Catchings et

642

al., 2015).

643

The deep seismicity is mostly located in the Gebel Marawa zone along the Kalabsha

644

fault which is favorably oriented with the maximum principal stress direction of the

645

present tectonic stress regime and where the 14 November 1981, Ms 5.3 earthquake

646

occurred. The intersection of the eastern tip of the Kalabsha fault with the N–S faults

647

may promote fluid flow across the fault system and then along the Kalabsha fault

648

down to 30 km depth. Anyway, i t is not surprising that seismicity can be induced by

649

the diffusion of pore fluid pressures at distance and at significant depths since it has

650

been largely demonstrated in the literature (e.g., Rubinstein and Mehani, 2015 , and

651

references therein ).

652

Concludi ng, in the present study we have performed a detailed statistical analysis of

653

the

654

methodologies able to reveal dynamical properties of earthquakes in time, depth and

seismicity

occurred

at

Aswan

from

1980

to

2015

by

utilizing

robust

38

39

655

magnitude domains. The obtained results depict the dynamics of the Aswan seismicity

656

more deeply evidencing the influence of the water level change in the lake on the

657

dynamics of both the shallow and the deep seismicity which show a clear annual

658

periodicity well correlated with t he annual loading of the lake. Moreover, the deep

659

seismicity is mainly characterized by mainshock -aftershocks sequences mostly

660

triggered by the water level fluctuations of the Nasser lake, and they mask the annual

661

periodicity of the deep seismicity if not properly aftershock -depleted. However, this

662

study is restrained to the investigation of the seismicity of the whole Aswan area,

663

while a more detailed statistical analysis of the spatial seismicity separating different

664

source zones would lead to a better un derstanding of the seismic process.

665 666 667

References

668

Abdeen, M.M., Abdelsalam, M.G., Nielsen, K.C., Yehia, M.A., Cherif, O.H. , 2000.

669

Active dextral wrenching in southern Egypt. In: 38th Annunal Meeting of the

670

Geological Society of Egypt, Cairo.

671

Adamson, D.A. , Williams, F., 1980. Structural geology, tectonics and the control

672

of drainage in the Nile basin. In: The Sahara and The Nile: Quaternary

673

Environments and Prehistoric Occupation in Northern Africa (M.A.J. Williams and

674

H.Faure, Eds.).

675

Aki, K., 1965. Maximum likelihood estimate of b in the formula log(N) = a -bM

676

and its confidence limits. Bull. Earthq. Res. Inst., Univ. Tokyo 43, 237 –239.

677

Ali, S. M., 2016. Statistical analysis of seismicity in Egypt and its surroundings .

678

Arabian J. Geosciences, 9, 52. doi:10.1007/s12517 -015-2079-x. 39

40

679

Ben-Zion, Y., Lyakhovsky, V., 2002. Accelerated seismic release and related

680

aspects of seismicity patterns on earthquake faults. Pure and Applied Geophysics

681

159, 2385–2412.

682

Borman, S., 2004. The Expectation Maximization Algorithm A s hort tutorial.

683

http://www.seanborman.com/publications/

684

Bosworth, W., Strecker, M.R., 1997. Stress field changes in the Afro -Arabian rift

685

system during the Miocene to Recent period. Tectonophysics 278, 47 -62.

686

Carder, D. S., 1945. Seismic investigations in t he Boulder Dam area, 1940 –1944,

687

and the influence of reservoir loading on earthquake activity . Bull. Seismol. Soc.

688

Am. 35, 175–192.

689

Catchings, R.D., Dixit, M.M., Goldman, M.R., Kumar, S., 2015. Structure of the

690

Koyna-Warna Seismic Zone, Maharashtra, India: A possible model for large

691

induced earthquakes elsewhere. J. Geophys. Res. Solid Earth 120, 3479 –3506.

692

doi:10.1002/2014JB011695.

693

-

, I., and P. Talwani, P., 2010. Hydromechanics of the Koyna -Warna

694

region, India. Pure Appl. Geophys. 167, 183 –213. doi:10.1007/s00024 -009-0012-5.

695

Lippiello, E., de Arcangelis, L., Godano, C., 2008. Influence of Time and Space

696

Correlations on Ea rthquake Magnitude . Phys. Rev. Lett. 100, 038501

697

El Hariri, M., Abercrombie, R.A., Rowe, C.A., do Nascimento, A.F., 2010. The

698

role of fluids in triggering earthquakes: Observations from reservoir induced

699

seismicity in Brazil . Geophys. J. Int. 181 (3), 1566–1574. doi:10.1111/j.1365 -

700

246X.2010.04554.x.

701

El Shazly, E.M., Abdel-Hady, M.A., El Ghawaby, M.A., El Kassas, A., 1973.

702

Geologic interpretation of ERTS -1 satellite images for west Aswan area, Egypt. 40

41

703

Egyptian Academy of Scientific Research and Technology, Re mote sensing

704

research project.

705

Fat-Helbary,

706

Determination Recorded by Aswan Seismic Network . Master Thesis, Sohag

707

Faculty, Assiute University, Egypt

708

Fat-Helbary, R.E., Tealb A.A. , 2002. A study of seismicity and earthquake hazard

709

at the proposed Kalabsha Dam Site, Aswan, Egypt . Natural Hazards 25, 117 -133.

710

Gahalaut, K., Hassoup, A. , 2012. Role of fluids in the earthquake occurrence

711

around Aswan reservoir, Egypt. J . Geophys. Res. 117, B02303. doi:10.1029/

712

2011JB008796.

713

Gahalaut, K., Hassoup, A., Hamed, H., Kundu, B., Gahalaut , V., 2016. Pure Appl.

714

Geophys. , 174(1), 133–150. doi:10.1007/s00024 -016-1397-6

715

Gebber, G.L., Orer, H.S., Barman, S.M., 2006. Fractal Noises and Motions in

716

Time

717

Neurophysiol. 95, 1176 –1184

718

Goltz, C., 1997. Fractal and Chaotic Properties of Earthquakes. Lecture Notes in

719

Earth Sciences, Berlin Springer.

720

Greiling, R.O., Abdeen, M.M., Dardir, A.A., El -Akhal, H., El-Ramly, M.F., Kamal

721

El-Din, G.M., Osman, A.F., Rashwan, A.A., Rice, A.H.N., Sadek, M.F. , 1994. A

722

structural

723

Geologische Rundshau 83, 484 –501.

724

Gupta, H.K., 2002. A review of recent studies of triggered earthqua kes by

725

artificial water reservoirs with special emphasis on earthquakes in Koyna, India .

726

Earth Sci. Rev. 58(3/4), 279–310. doi:10.1016/S0012 -8252(02)00063 -6.

Series

R.E.,

of

synthesis

1989.

A

Study

Presympatheti c

of

the

of

and

Proterozoic

the

Local

Sympathetic

Earthquake

Neural

Arabian –Nubian

Magnitude

Activities .

Shield

in

J.

Egypt.

41

42

727

Gutenberg, R., Richter, C.F., 1944. Frequency of earthquakes in California. Bull.

728


729

Haggag, H.M., Gaber, H.H., Sayed, A.D., Ezzat, M.E. , 2008. A review of the

730

recent seismic activity in the southern part of Egypt (upper Egypt). Acta

731

Geodynamica et Geomaterialia 5, 19 –29.

732

Hassoup, A. , 1994. Investigation of the tectonic sett ing, seismic activity and

733

crustal deformation in Aswan seismic region, Egypt . D.Sc. Thesis. Tokyo: Tokyo

734

University.

735

Huang, Q., 2006. Search for reliable precursors: A case study of the seismic

736

quiescence of the 2000 western Tottori prefecture earthquake . J. Geophys. Res.

737

111(B4), B04301, doi:10.1029/2005JB003982 .

738

Hussein, H.M., Abou Elenean , K.M., Marzouk, I.A., Korrat, I.M., Abu El-Nader,

739

I.F., Ghazala, H.H., ElGabry, M.N., 2013. Present-day tectonic stress regime in

740

Egypt and surrounding area based on in version of earthquake focal mechanisms.

741

Journal of African Earth Sciences 81, 1 -15.

742

Iliopoulos, A.C., Pavlos G.P. , 2010. Global low dimensional seismic chaos in the

743

Hellenic region. International Journal of Bifurcation and Chaos 20(7), 2071 –2095.

744

Issac, M., Renuka, G., Venugopal, C., 2004. Wavelet analysis of long period

745

oscillations

746

Atmospheric and Solar -Terrestrial Physics 66, 919 –925.

747

Issawi, B., 1978. Geology of Nubia West area, Western Desert, Egypt. Annals of

748

the Geological Survey of Egypt 8, 237 -253.

749

Kagan, Y.Y., 1997. Are earthquakes predictable? . Geophys. J. Int. 131(3), 505–

750

525.

in

geomagnetic

field

over

the


magnetic

equator.

Journal

of

42

43

751

Kebeasy,

R.M.,

Maamoun,

M.,

Ibrahim,

E.,

1981.

Aswan

lake

induced

752

earthquakes. Bull. Int. Inst. Seismol. Earthq. Eng. 19, 155–160.

753

Kebeasy, R.M., Maamoun, M., Ibrahim, E., Megahed, A., Simpson, D.W., Leith,

754

W.S., 1987. Earthquake studies at Aswan Reservoir, J. Geodynamics 7, 173 -193.

755

Kiyashchenko, D., Smirnova , N., Troyan, V., Saenger, E., Vallianatos, F., 2004.

756

Seismic hazard precursory evolution: fractal and multifractal aspects. Physics and

757

Chemistry of the Earth 29, 367 –378

758

Lennartz, S., Livina, V.N., Bunde, A., Havlin, S., 2008. Long -term memory in

759

earthquakes and the distribution of interoccurrence times. Europ hys. Lett. 81,

760

69001.

761

Lyakhovsky, V., Ben -zion, Y., Agnon, A., 2001. Earthquake cycle, fault zones,

762

and seismicity patterns in a rheologically layered lithosphere. J . Geophys. Res.

763

106, 4103–4120.

764

Matcharashvili, T., Chelidze, T., Javakhishvili, Z., 2000. Nonlinear analysis of

765

magnitude and interevent time interval sequences for earthquakes of Caucasian

766

region. Nonlinear Processes in Geophysics 7, 9 –19.

767

Matcharashvili, T., Chelidze, T., Javakhishvili, Z., 2009. Dynamics, predictability

768

and risk assessment of natural hazards. In: Fra Paleo, Urbano (Ed.), Building Safer

769

Communities. Risk Governance, Spatial Planning and Responses to Natural

770

Hazards. IOS Press, Amsterdam, pp. 148 –161.

771

Mekkawi, M., Grasso, J.R., Schneggm, P.A. , 2004. A long-lasting relaxation of

772

seismicity at Aswan reservoir, Egypt, 1982 –2001. Bull. Seismol. Soc. Am. 94,

773

479–492.

43

44

774

Mogi,

K.,

1962.

Magnitude -frequency

relationship

for

elastic

shocks

775

accompanying fractures of various materials and some related problems in

776

earthquakes. Bull. Earthquak e Res. Inst. Univ. Tokyo 40 , 831-883.

777

Sarlis, N.V., Skordas, E.S., Varotsos, P.A., 2009. Multiplicative cascades and

778

seismicity in natural time. Physical Review E 80, 022102.

779

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Lazaridou, M.S., 2008. Fluctuations,

780

under time reversal, of the natural time and the entropy distinguish similar looking

781

electric signals of different dynamics . J. Appl. Phys. 103, 014906.

782

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Uyeda, S., Kamogawa, M., 2011.

783

Natural time analysis of c ritical phenomena. Proc. Natl. Acad. Sci. USA 108,

784

11361-11364.

785

Peng, C.-K., Havlin, S., Stanley, H.E., Goldberger, A.L., 1995, Quantification of

786

scaling exponents and crossover phenomena in nonstationary heartbeat time series .

787

CHAOS 5, 82–87.

788

Pliakis, D., Papakostas, T., Vallianatos, F., 2012. A first principles approach to

789

understand the physics of precursory accelerating seismicity. Ann . Geophys .

790

55(1). doi:10.4401/ag-5363.

791

Reasenberg, P.A. , 1985. Second-order moment of central California seismicity,

792

1969-82. J. Geophys. Res. 90, 5479–5495.

793

Rong, Y.M., Wang, Q., Ding, X., Huang, Q.H. , 2012. Non-uniform scaling

794

behaviour in Ultra -Low-Frequency (ULF) geomagnetic signals possibly associated

795

with the 2011 M9.0 Tohoku earthquake . Chinese Journal Geophysics 55, 3709–

796

3717.

44

45

797

Rubinstein, J.L., Mehani, A.B., 2015. Myths and Facts on Wastewater Injection,

798

Hydraulic Fracturing, Enhanced Oil Recovery, and Induced Seismicity. Seismol.

799

Res. Lett. 86(4), 1060–1067. doi: 10.1785/0220150067.

800

Said, R., 1993. The River Nile: Geology, Hydrology and Utilization. Pergamon

801

Press, Oxford. , 320 pp.

802

Said, R., 1981. The Geological Evolution of the River Nile. Springer -Verlag, New

803

York, 151 pp.

804

Scholz, C.H., 1968. The frequency -magnitude relation of microfracturing in rock

805

and its relation to earthquakes. Bull. Seismol. Soc. Am. 58 , 399-415

806

Selim, M.M., Imoto, M, Hurukawa, N. , 2002. Statistical investigation of reservoir -

807

induced seismicity in Aswan area, Egypt. Earth Planets Space 54, 349 –356.

808

Shi, Y., Bolt, B., 1982. The standard error of the magnitude -frequency b

809

value. Bull. Seismol. Soc. Am. 72(5), 1677–1687

810

Shinomoto, S., Miura, K., Koyama, S., 2005. A measure of local variation of inter -

811

spike intervals. Biosystems 79, 67 –72.

812

Simpson, D.W., Negmatullaev, S.K., 1981. Induced seismicit y at Nurek Reservoir,

813

Tadjikistan, USSR. Bull. Seismol. Soc. Am. 71(5), 1561–1586.

814

Simpson, D.W., Kebeasy, R.M., Nicholson, C., Maamoun, M., Albert, R.N.,

815

Ibrahim, E.M., Megahed, A., Gharib, A., Hussain, A., 1987. Aswan Telemetered

816

seismograph Network. J. Geophys. 7, 195 –203.

817

Simpson, D.W., Gharib, A.A., Kebeasy, R.M., 1990. Induced seismicity and

818

changes in water level at Aswan reservoir, Egypt . Gerlands. Beitr. Geophys.

819

Leipzig 99, 191–204.

45

46

820

Shearer, P. M. (2012), Space -time clustering of seismicity in Cal ifornia and the

821

distance dependence of earthquake triggering, J. Geophys. Res. 117, B10306, doi:

822

10.1029/2012JB009471.

823

Stabile, T.A., Giocoli, A., Lapenna, V., Perrone, A., Piscitelli, S., Telesca, L.,

824

2014.

825

associated with the Pertusillo artificial lake (southern Italy) . Bull. Seismol. Soc.

826

Am. 104(4). doi:10.1785/0120130333.

827

Telesca, L., Amatulli, G., Lasaponara, R., Lovallo, M., Santulli, A. , 2005. Time-

828

scaling properties in forest -fire sequences observed in Gargano area (southern

829

Italy). Ecol. Model. 185, 531 -544.

830

Telesca, L., Cuomo, V., Lapenna, V., Macchiato, M., 2001. Statistical analysis of

831

fractal properties of point processes modelling seismic sequences, Phys. Earth

832

Planet. Int. 125, 65-83.

833

Telesca, L., ElShafey Fat ElBary, R., Amin Mohamed, A. E. -E., ElGabry, M. ,

834

2012. Analysis of the cross -correlation between seismicity and water level in the

835

Aswan area (Egypt) from 1982 to 2010. Natural Hazards and Earth System

836

Sciences 12, 2203–2207.

837

Telesca, L., Giocoli, A., Lapenna, V., Stabile, T.A., 2015. Robust identification of

838

periodic behavior in the time dynamics of short seismic series: the case of

839

seismicity induced by Pertusillo Lake, southern Italy. Stochastic Environmental

840

Research and Risk Assessment 29, 1437–1446. doi:10.1007/s00477 -014-0980-6.

841

Telesca,

842

investigation of scaling properties in temporal patterns of seismic sequences.

843

Chaos, Solitons & Fractals 19(1), 1 –5.

Evidences

L.,

of

Lapenna,

low-magnitude

V.,

continued

Macchiato,

M.,

reservoir -induced

2004.

Mono -

and

seismicit y

multi -fractal

46


47

844

Telesca, L., Lovallo, Lopez, M.C., Molist, J.M. , 2016. Multiparametric statistical

845

investigation of seismicity occurred at El Hierro (Canary Islands) from 2011 to

846

2014. Tectonophysics 672 -673, 121 -128. doi: 10.1016/j.tecto.2016.01.045.

847

Telesca, L., Lovallo, M ., 2009. Non-uniform scaling features in Central Italy

848

seismicity: a non -linear approach in investigating seismic patterns and detection

849

of possible earthquake precursors. Geophys. Res. Lett. 36, L01308.

850

Telesca, L., Lovallo, M., 2010. Long -range dependenc e in tree-ring width time

851

series of Austrocedrus chilensis revealed by means of the detrended fluctuation

852

analysis. Physica A 389, 4096 –4104.

853

Telesca, L., Lovallo, M., 2011. Analysis of time dynamics in wind records by

854

means

855

information plane. J. Stat. Mech. P07001.

856

Telesca, L., Mohamed, A. E. -E. A., ElGabry, M., El -hady, S., Abou Elenean, K.

857

M., 2012. Time dynamics in the point process modelling of seismicity of Aswan

858

area (Egypt), Chaos Sol itons & Fractals 45, 47-55.

859

Telesca, L., Pierini, J.O., Scian, B., 2012. Investigating the temporal variation of

860

the scaling behavior in rainfall data measured in central Argentina by means of the

861

detrended fluctuation analysis. Physica A 391, 1553 –1562.

862

Thurner, S., Lowen, S.B., Feurstein, M.C., Heneghan, C., Feichtinger, H.G.,

863

Teich, M.C., 1997. Analysis, synthesis, and estimation of fractal -rate stochastic

864

point processes: Fractals 5, 565 -596.

865

Utsu, T., 1999. Representation and analysis of the earthquake size distribution: a

866

historical review and some new approaches. Pageoph 155, 509 –535.

of

multifractal

detrended

fluct uation

analysis

and

Fisher -Shannon

47

48

867

Vallianatos, F., Benson, P., Meredith, P., Sammonds, P., 2012. Experimental

868

evidence of a non -extensive statistical physics behavior of fracture in triaxially

869

deformed Etna basalt using acoustic emissions. Europhys . Lett. 97, 58002.

870

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., 2012. Scale-specific order parameter

871

fluctuations

872

fluctuation analysis . Europhys. Lett. 99, 59001.

873

Varotsos, P.A., Sarlis, N.V., Skordas, E.S., 2014. Study of the temporal

874

correlations in the magnitude time series before major earthquakes in Japan. J.

875

Geophys. Res. Space Phys. 119, 9192 –9206.

876

WCC (Woodward-Clyde Consultants), 1985.

877

and estimation of magnitudes and recurrence intervals . Internal Report, High and

878

Aswan Dams Authority, Egypt.

879

Wiemer, S., Wyss, M., 2000. Minimum magnitude of completeness in earthquake

880

catalogs: examples from Alaska, t he Western United States, and Japan. Bull.

881


882

Woessner, J., Wiemer S., 2005. Assessing the quality of earthquake catalogues:

883

Estimating the magnitude of completeness and its uncertainty . Bull. Seismol. Soc.

884

Am. 95(2), 684–698. doi: 10.1785/ 0120040007.

885

Woodward, J.C., Macklin, M.G., Krom, M.D., Williams, M.A.J., 2007. The Nile:

886

Evolution, Quaternary River Environments and Material Fluxes. In: Large Rivers:

887

Geomorphology and Management (Gupta, Eds).

888

Wyss, M., 1973. Towards a physi cal understanding of the earthquake frequency

889

distribution. Geophys. J. R. Astron. Soc. 31, 341 –359.

of

seismicity

before

mainshocks:

Natural

ﬁc

time

f

and

hq

detrended

k

c

890 48

49

891

49