John Douglas

Consistency of ground-motion predictions from the past four decades: Peak ground velocity and displacement, Arias intensity and relative significant duration

Keywords: Strong-motion data, Ground-motion prediction equations (GMPEs), Epistemic uncertainty, Peak ground velocity, Peak ground displacement, Arias intensity, Relative significant duration

Consistency of ground-motion predictions from the past

four decades: Peak ground velocity and displacement, Arias intensity and relative significant duration

Introduction

The consistency in predicted peak ground acceleration (PGA) and elastic response spectral acceleration (SA) for 5% damping and a natural period of 1 s was discussed in [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF]. In that article, predicted PGAs and SAs from hundreds of published ground-motion prediction equations (GMPEs) for various earthquake scenarios (M w 6 at 20 km, roughly the best-represented scenario in global strong-motion datasets, and M w 7.5 at 10 km and M w 5 at 10 km, at the edges of most databases used to derive GMPEs) were plotted against their publication dates. The purpose of these plots was to investigate the epistemic uncertainty associated with GMPEs and to test whether this uncertainty is decreasing, which would be expected given the accumulation of new data and knowledge and improvements in regression techniques, for example. The scatter in predictions shown on such plots is a rough measure of epistemic uncertainty because, in the absence of such uncertainty, predictions of the median ground motion for a certain scenario should tend to a single value. The plots of [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] showed that even though epistemic uncertainty seems to be reducing slightly (predictions from different models are slowly converging), there is still considerable uncertainty in estimated PGAs and SAs even for scenarios that are well represented in strong-motion databanks, and much higher uncertainties for poorly-sampled scenarios (specifically large earthquakes at short distances).

The purpose of this short article is to extend the analysis of [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] to strongmotion parameters other than PGA and SA, which are useful for some aspects of engineering seismology and earthquake engineering. The four non-PGA/SA strong-motion parameters with most associated GMPEs are considered here, namely: peak ground velocity (PGV), peak ground displacement (PGD), Arias intensity (AI) [START_REF] Arias | A measure of earthquake intensity[END_REF] and relative significant duration (RSD) (Trifunac and Brady, 1975b). In contrast to PGA and SA, there are far fewer GMPEs published for these parameters but there are still sufficient to enable some conclusions on their predictability to be drawn. Unlike for PGA and SA, my search for GMPEs for the prediction of these other parameters only started recently and hence it is more likely that the collection of non-PGA/SA models considered here are less complete than given in [START_REF] Douglas | Ground-motion prediction equations 1964-2010[END_REF] for PGA and SA. However, a thorough literature search was conducted and various reviews were studied (e.g. Bommer and Martínez-Pereira, 1999;Bommer and Alarcón, 2006;Travasarou et al, 2003;[START_REF] Tromans | Behaviour of buried water supply pipelines in earthquake zones[END_REF]. Therefore, it is unlikely that many models are missing. Table 1 lists the considered GMPEs and gives, when possible (some of the original references could not be consulted and some authors do not provide the necessary information), their main characteristics.

In the next section, graphs are presented for the four considered strong-motion parameters and the same three earthquake scenarios as in [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF]. To facilitate comparisons with the results of [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] the same scenarios are considered here except that separate plots are not made for broad geographical or tectonic regions [western North America; Europe, the Mediterranean and the Middle East; stable continental regions; and Japan (subduction zones)]. The dependence of PGV, PGD, AI and RSD on tectonic regime is less well studied than for PGA and SA because the vast majority of GMPEs for these parameters are derived for shallow crustal earthquakes in active regions (see Table 1). It is likely that this lack of consideration of tectonic regime will slightly increase the scatter in the following plots. The same graph format is used to facilitate comparisons with the previous graphs for PGA and SA. For example, the ratio of the upper and lower limits of the abscissa, displaying the strong-motion parameter, is 25 and a logarithmic axis is used. As before those studies that were published in peer-reviewed international journals and give basic details of the datasets used for their derivation [criteria 2 and 3 of [START_REF] Cotton | Criteria for selecting and adjusting ground-motion models for specific target regions: Application to central Europe and rock sites[END_REF]] and which are not being extrapolated far outside their magnitude-distance range of applicability are indicated.

Because this study makes the same choices and considers the same scenarios as [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF], only brief details are given here. The interested reader is referred to the previous article for more information.

The differences between the aleatory variabilities (sigma) associated with GMPEs for the different parameters are not discussed here. Table IV of Travasarou et al (2003) presents such a comparison for PGA, SA(0.5 s), AI and RSD predicted by a family of GMPEs derived using a similar database, functional form and regression technique. This table shows that the aleatory variabilities for each of these parameters are similar, except for the GMPE for AI, which has a much higher sigma suggesting that AI is more intrinsically variable.

Comparing ground-motion predictions

Models have been adjusted to, where possible: moment magnitude (M w ), distance to the surface projection of the rupture (Joyner-Boore distance) (r jb ), vertical-dipping strike-slip faulting and the geometric mean of the two horizontal components. These adjustments were made using the approaches of [START_REF] Bommer | On the use of logic trees for ground-motion prediction equations in seismic-hazard analysis[END_REF] using: for PGV and PGD, style-offaulting and component definition factors of Campbell and Bozorgnia (2007) and for AI, style-of-faulting and component definition factors of [START_REF] Bommer | Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion[END_REF] 1 . For the conversion to M w from surface-wave magnitude (M s ) the equation of Ambraseys and Free (1997) was used. Local magnitude (M L ), and other magnitude scales, were assumed equal to M w .

Harmonization of models is not always possible due to a lack of information in many of the original references on, for example, definition of horizontal component and magnitude scale. This means that the predictions could be in error by roughly 20% but this will not alter the overall trends, which are the focus of this article (the reader should not seek to over-interpret details in the graphs). The size of the rupture plane and other additional parameters needed to evaluate some of the models have been computed using the methods given in Chapter 7 of Campbell and Bozorgnia (2007). To compute the epicentral and hypocentral distances the hypocentre is assumed to be at one end of the fault at a depth of 10 km and the site half way along the fault. Some authors seek to model epistemic uncertainty in ground-motion prediction by proposing more than one set of GMPEs, e.g. by providing coefficients for different functional forms (e.g. [START_REF] Bommer | Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion[END_REF]. Predictions from each of these variant GMPEs are included here.

Because it is roughly the best-represented scenario in global strong-motion datasets the first scenario considered is a M w 6 strike-slip earthquake at r jb = 20 km on a site classified as NEHRP class C (Eurocode 8 class B) (V s,30 = 490 m/s). If epistemic uncertainty in the prediction of ground motion is decreasing then it should be visible for this scenario since it is where available observations are most abundant and hence GMPEs should be the best constrained. The other two scenarios considered are: M w 7.5 strike-slip earthquake at r jb = 10 km, for which there are still few available data, and M w 5 strike-slip earthquake at r jb = 10 km, which is at the lower edge of most datasets used for the derivation of GMPEs, for 1 [START_REF] Kempton | Prediction equations for significant duration of earthquake ground motions considering site and near-source effects[END_REF] and [START_REF] Bommer | Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion[END_REF] find that style-of-faulting does not have a statistically significant effect on RSD. Factors to convert between different component definitions of RSD are not available so no adjustment was attempted.

the same site conditions. It is expected that epistemic uncertainty (and hence scatter in the predictions) will be higher for these two scenarios compared to M w 6 at r jb = 20 km due to the lack of observations and uncertainty over near-source magnitude-scaling, for example.

The following sections present the results for the four parameters in turn. As a measure of the dispersion in the median predictions the standard deviation of the common (base 10) logarithm of median estimates for each five-year interval are computed, although because of the limited number of GMPEs this statistic is quite unstable.

As for the analysis shown in [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] the median ground motion for the considered scenario obtained from a large (over 13,000 records from over 2,500 events) strongmotion database [the data from the Internet Site for European Strong-motion Data (ISESD) [START_REF] Ambraseys | Internet site for European strong-motion data[END_REF]) with the addition of many accelerograms from western North America and elsewhere] is plotted at all dates. The median should track the predictions, since similar databases were used to derive the GMPEs published up to that date, and the variability in the median should also show a reduction, since more data are being used to compute the averages. The variabilities of the medians are computed here by dividing the standard deviation by √ n, where n is the number of records used to compute the standard deviation. The medians and their variabilities were computed by considering the available records within 0.5 -M w units and 10 km of the scenario of interest and excluding a consideration of local site conditions and style of faulting. It could be argued that these bins are too broad and that a consideration of local site effects should have been made. However, given the limited data available, particularly for M w > 7, narrow bins would lead to statistics based on few records from only a handful of earthquakes. The median ground motions computed from averaging data within broad bins should not be strongly affected by the width of the bins but the variabilities of these medians may be slightly overestimated. The uniform filtering applied to the strong-motion databank used here (bandpass filtering with cut-offs of 0.25 and 25 Hz) means that the PGV and, especially, PGD observations obtained from this databank are likely to be incorrect. The averages of these PGV and PGD observations, however, are added for completeness. AI and RSD from these records, however, are likely to be little affected by the uniform filtering.

Peak ground velocity

Because of its various uses in earthquake engineering (Bommer and Alarcón, 2006) and its simplicity, following PGA and SA, PGV is the best served by GMPEs and 96 models were identified and programmed, many of which also provide coefficients for the prediction of PGA and SA. The predicted PGVs and median PGVs from the strong-motion databank for the three considered scenarios are shown in Figure 1 (some predicted PGVs are off the top or bottom of these figures, often because the GMPEs are being extrapolated far outside their range of applicability). These figures show that the dispersion in predicted PGVs from different GMPEs is large (the ratio between the smallest and largest predictions is greater than ten) and that this scatter is not obviously reducing with time (even when considering only models passing basic quality-control criteria), particularly near to large earthquakes. The standard deviation of the common logarithm of median estimates for each five-year interval are around 0.2 for M w 6 at r jb = 20 km and M w 5 at r jb = 10 km and around 0.3 for M w 7.5 at r jb = 10 km. Also roughly constant are the average PGV predicted by the models over time. The median observed PGVs are similar to those predicted by the GMPEs although lower for the M w 7.5 scenario. A similar conclusion was also noted by [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] for PGA and SA(1 s) for large earthquakes, which was related to a number of recent large earthquakes (e.g. Chi-Chi 1999;Kocaeli 1999;Denali 2002) showing lower than expected ground motions (e.g. [START_REF] Ellsworth | Near-field ground motion of the 2002 Denali Fault, Alaska, earthquake recorded at Pump Station 10[END_REF]).

[Fig. 1 about here.]

Peak ground displacement

Because of the difficulty in obtaining reliable PGDs from analogue (and even digital) accelerograms and the limited use of PGD in earthquake engineering, there are only 19 published GMPEs for PGD, which are typically associated with GMPEs for PGV. Although of limited use in most fields of earthquake engineering, the robust prediction of PGD would help constrain the long-period (> 2 s) response spectral displacements because these must converge to PGD at very long periods (Faccioli et al, 2004). The predictions from the GM-PEs for the three considered scenarios are shown in Figure 2. These graphs show the large dispersion in predictions of PGD, especially near to large earthquakes. This dispersion is probably due in large part to the difficulty in recovering reliable displacement traces from strong-motion records because of their high sensitivity to processing (e.g. low-cut filtering) (e.g. [START_REF] Paolucci | On the reliability of long period spectral ordinates from digital accelerograms[END_REF]. The observed PGDs match the predictions reasonably well for the smaller magnitudes but they are considerably lower for the M w 7.5 earthquake, which is probably since the application of a low-cut filter with a corner frequency of 0.25 Hz is likely to lead to significant loss of the true long-period energy from such large events.

[Fig. 2 about here.]

Arias intensity

As noted by, for example, Travasarou et al (2003), AI has a number of uses in earthquake engineering, particularly for slope stability analysis and liquefaction assessment. These uses have motived the development of, at least, 33 GMPEs, including variants, for AI. Some of these GMPEs only give the value of the integral and not the complete expression for AI; for these the constant π/2g was included when plotted. The predictions from these 33 models and the median observed AI for the three scenarios are plotted in Figure 3. The standard deviations of the median predicted AIs are around 0.4 for M w 5 at r jb = 10 km, around 0.3 for M w 6 at r jb = 20 km and around 0.2 for M w 7.5 at r jb = 10 km. This implies that the epistemic uncertainty in the prediction of median AI for larger earthquakes is lower than that for smaller events, which is counterintuitive since there are far fewer available records for this scenario. Two possible reasons for this observation are that regional differences in AI, modelled within local GMPEs, are stronger for smaller events, and that current GMPE developers for AI have concentrated their efforts on the prediction of AI from large earthquakes. AI was not considered by the NGA developers [START_REF] Power | An overview of the NGA project[END_REF] and, therefore, there is perhaps a requirement to develop a new generation of models for the prediction of this parameter; there have been some recent attempts in this direction (e.g. Foulser-Piggott and Stafford, 2012).

[Fig. 3 about here.]

Relative significant duration

As noted by Bommer and Martínez-Pereira (1999), many dozens of definitions of strongmotion duration have been proposed, which give widely ranging values. The definition of duration that is most commonly used in earthquake engineering (and consequently for which there are most GMPEs available) is the relative significant duration originally defined by Trifunac and Brady (1975b) as the interval between 5 and 95% of the total Arias intensity.

Despite its various uses (e.g. [START_REF] Kempton | Prediction equations for significant duration of earthquake ground motions considering site and near-source effects[END_REF], e.g. in liquefaction evaluation, only 15 GMPEs have been identified in the literature for the prediction of this parameter.

Figure 4 present the history of the predictions from these 15 models and the median observed RSDs for the three scenarios. The epistemic uncertainty in the prediction of median RSD is much lower than for the other ground-motion parameters considered here (the standard deviation of the median predicted RSDs in the past five year is less than 0.1 even for large earthquakes). This suggests that, either: a) epistemic uncertainty in the prediction of this parameter is being under represented by the different models (because they often use similar databases and functional forms) or b) this parameter is easier to predict than the other intensity measures. The widths of the confidence limits for the median observed RSD are narrower than the confidence limits for PGV, PGD and AI [and those for PGA and SA(1 s)

shown in [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF]], which hints that the epistemic uncertainty in the prediction of RSD is truly lower than for these other parameters. This could be because the physics underlying the relative duration characteristics of earthquake shaking (e.g. rupture time and wave dispersion and scattering) are perhaps easier to capture in a simple functional form compared with the physics explaining strong-motion amplitudes, measured by the other parameters.

[Fig. 4

about here.] 3 Conclusions

There have been recent studies (e.g. Baker, 2007) applying vector-valued probabilistic seismic hazard assessment (VPSHA) (Bazzurro and Cornell, 2002) for the joint prediction of pairs of parameters other than PGA and SA. Recently, Gehl et al ( 2011) present a method for the derivation of structural fragility functions of more than one intensity measure, which could be coupled with VPSHA for vector-valued risk evaluation. For this type of study the relative uncertainties in the prediction of each parameter are important. This article suggests that the epistemic uncertainties in the prediction of PGV, PGD and AI are higher even than those evidenced by [START_REF] Douglas | Consistency of ground-motion predictions from the past four decades[END_REF] for PGA and SA. For PGV and AI, this larger uncertainty is probably principally due to lesser research effort having been made in the development of GMPEs for such parameters compared to PGA and SA. Although both parameters have recently been the subject of various articles, e.g. the NGA developers also developed models for the prediction of PGV. The instability in PGD predictions is due to both lack of research interest in the development of GMPEs for this parameter, because of limited engineering applications, but also because PGD is inherently difficult to recover from strong-motion records due to its sensitivity to low-cut filtering (e.g. [START_REF] Boore | Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s[END_REF]. The epistemic uncertainty in the prediction of RSD, on the other hand, seems to be lower than that associated with the prediction of any of the other parameters, which could encourage more consideration of this parameter within earthquake hazard and risk assessments for which it has various engineering applications.

Baker JW ( 2007 5 Reported in [START_REF] Joyner | Measurement, characterization, and prediction of strong ground motion[END_REF].

6 Distance to centre of array 9 Equations stated to be for distances up to 100 km 10 Total number of components do not need to be multiplied by two.

11 Total number of components do not need to be multiplied by two.

12 Total number of components do not need to be multiplied by two. 13 Total number of components do not need to be multiplied by two. 14 Three other equations for site classes B, D and E. 15 Authors state in text that 'more than 14 000' values were used but their Table 1 gives 2 × 6899. 16 State equations valid to 4.5.

17 State equations valid up to 200 km.

18 Call it 'quadratic mean', which is assumed to be geometric mean. 19 Does not need to be multiplied by two.

20 Also develop models for the Zagros region of Iran using about 100 records.

21 Also derive model using M w .

22 Also derive model using r epi . 23 Recommend that model is not extrapolated below 5 due to lack of data.

24 Believe that model can be reliably extrapolated to 8.5.

25 Recommend that model is not extrapolated below 5 due to lack of data. 26 Believe that model can be used to 8.0.

27 Recommend that model is not used for distances ≥ 200 km.

28 Believe that model can be extrapolated down to 4.0.

29 Believe that model can be extrapolated up to 8.5 for strike-slip faulting and 8.0 for reverse faulting. 30 Believe that model can be extrapolated down to 4.0.

31 Believe that model can be extrapolated up to 8.5 for strike-slip faulting and 8.0 for reverse faulting.

32 Believe that model valid to 0 km. 33 Believe that model valid to 200 km.

34 Also model for Central USA using 14 records and 296 scaled records Filled red circles indicate models published in peer-reviewed journals, for which basic information on the used dataset is available and which are not being extrapolated far outside their range of applicability. Numbers correspond to those given in Table 1. Also shown is the median PGV within five-year intervals (black line) and the median ±1 standard deviation (dashed black lines) based on averaging predictions. Finally indicated is the median PGV (solid blue line) and its 16th and 84th confidence limits (dashed blue line) based on averaging records up until that date (see text for details). Note that the selection criteria and the fact that the database used to compute these averages has not been recently updated mean that the blue lines end before 2012.

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Soil Dynamics and Earthquake Engineering 11:387-402 Toro GR, Silva WJ (2001) Scenario earthquakes for Saint Louis, MO, and Memphis, TN, and seismic hazard maps for the central United States region including the effect of site conditions. Tech. rep., research supported by the U.S. Geological Survey (USGS), under award number 1434-HQ-97-GR-02981 Travasarou T, Bray JD, Abrahamson NA (2003) Empirical attenuation relationship for Arias intensity. Earthquake Engineering and Structural Dynamics 32:1133-1155, DOI 10.1002/eqe.270 Trifunac MD (1976) Preliminary analysis of the peaks of strong earthquake ground motion -dependence of peaks on earthquake magnitude, epicentral distance, and recording site conditions. Bulletin of the Seismological Society of America 66(1):189-219 A GMPEs considered here H Number of horizontal records (if both horizontal components are used then multiply by two to get total number) V Number of vertical components E Number of earthquakes M min Magnitude of smallest earthquake M max Magnitude of largest earthquake M scale Magnitude scale (scales in brackets refer to those scales which the main M values were sometimes converted from, or used without conversion, when no data existed), where: m b Body-wave magnitude M CL Coda length magnitude M D Duration magnitude M JMA Japanese Meteorological Agency magnitude M L Local magnitude M bLg Magnitude calculated using Lg amplitudes on short-period vertical seismographs M s Surface-wave magnitude M w Moment magnitude r min Shortest source-to-site distance r max Longest source-to-site distance r scale Distance metric, where (when available the de facto standard abbreviations of Abrahamson and Shedlock (1997) are used): r epi Epicentral distance r jb Distance to projection of rupture plane on surface[START_REF] Joyner | Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 Imperial Valley, California, earthquake[END_REF] r hypo Hypocentral (or focal) distance r q Equivalent hypocentral distance (EHD)[START_REF] Ohno | Revision of attenuation formula considering the effect of fault size to evaluate strong motion spectra in near field[END_REF] r rup Distance to rupture plane r seis Distance to seismogenic rupture plane (assumes near-surface rupture in sediments is non-seismogenic)[START_REF] Campbell | Empirical near-source attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudo-absolute acceleration response spectra[END_REF] r slip Distance to point of highest slip S Number of different site conditions modelled, where: C Continuous classification I Individual classification for each site C Use of the two horizontal components of each accelerogram [see Beyer and[START_REF] Cotton | Criteria for selecting and adjusting ground-motion models for specific target regions: Application to central Europe and rock sites[END_REF]], where: two-stage and[START_REF] Joyner | Methods for regression analysis of strong-motion data[END_REF] 2W Two-stage with second staged weighted as described in[START_REF] Joyner | Measurement, characterization, and prediction of strong ground motion[END_REF] O Other (see section referring to study) U Unknown (often probably ordinary one-stage regression) M Source mechanisms (and tectonic type) of earthquakes (letters in brackets refer to those mechanism that are separately modelled), where:A All (this is assumed if no information is given in the reference) refers to extra records from outside region used to supplement data. (. . . ) refer either to magnitudes of supplementing records or to those used for part of analysis. * means information is approximate because either read from graph or found in another way.

  For a M w 6 strike-slip earthquake at r jb = 20 km. Up until the end of 2005, 253 records from 56 earthquakes were used to compute the average observed PGV. For a M w 7.5 strike-slip earthquake at r jb = 10 km. Up until the end of 2003, 129 records from 15 earthquakes were used to compute the average observed PGV. The vertical blue line in 1985 is caused by many number of records from the same date (the Chile earthquake of 3rd March 1985) that significantly change the average computed up to that time. For a M w 5 strike-slip earthquake at r jb = 10 km. Up until the end of 1998, 51 records from 30 earthquakes were used to compute the average observed PGV.

Fig. 1

 1 Fig.1Predicted PGV at a NEHRP C site against publication date for 96 models published in the literature. Filled red circles indicate models published in peer-reviewed journals, for which basic information on the used dataset is available and which are not being extrapolated far outside their range of applicability. Numbers correspond to those given in Table1. Also shown is the median PGV within five-year intervals (black line) and the median ±1 standard deviation (dashed black lines) based on averaging predictions. Finally indicated is the median PGV (solid blue line) and its 16th and 84th confidence limits (dashed blue line) based on averaging records up until that date (see text for details). Note that the selection criteria and the fact that the database used to compute these averages has not been recently updated mean that the blue lines end before 2012.

  For a M w 6 strike-slip earthquake at r jb = 20 km. For a M w 7.5 strike-slip earthquake at r jb = 10 km. For a M w 5 strike-slip earthquake at r jb = 10 km.

Fig. 4

 4 Fig. 4 Like Figure 1 but for RSD (14 models).

Table 1 :

 1 Characteristics of GMPEs considered here

	No.	Reference			Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
											scale
	1	Esteva and Rosenblueth (1964)	W. USA	46*	-	U	U	U	U	15*	450*	r hypo	1	U	U	A	PGV
	2	Campbell and Duke (1974a,b)	W. USA		Hybrid approach	Ms	4.5	U	10	47	r hypo	5	A	O	A	AI
	3	Trifunac	and	Brady	W. USA	181	181	57	3.8	7.7	Mostly	6 2 *	400 3 *	r epi	3	B	O	A	PGV,
		(1975a),Trifunac (1976) & Tri-							M L								PGD
		funac and Brady (1976)
	4	Trifunac and Brady (1975b)		W. USA	188	188	48	3.8	7.7	Mostly	6*	400*	r epi	3	B	O	A	AI,
											M L								RSD
	5	McGuire (1977)			W. USA	34	-	22	5.3	7.6	M L	14	125	r hypo	1	B	U	A	PGV,
																			PGD
	6	Dobry et al (1978)		W. USA	84	-	14	4.7	7.6	M L	0.1	130	rrup	2	B	1	A	RSD
	7	McGuire (1978)			W. USA	70	-	17+*	4.5*	7.7	U 4	11*	210*	r hypo	2	B	U	A	PGV,
																			PGD
	8	McGuire and Barnhard (1979)	W. USA	50	-	U	U	U	U	U	U	rrup	2	B	1	A	RSD
														(r epi
														for
														some)
	9	Cornell et al (1979)		W. USA	70	-	U	U	U	M L	U	U	r hypo	1	C	U	A	PGV,
																			PGD
	10	Hasegawa et al (1981)		E. & W. Canada		Hybrid approach	4*	7.6*	U	5*	400*	r hypo	1	U	O	A	PGV×2
	11	Joyner and Boore (1981)		W. N. America	182	-	23	5.0	7.7	Mw	0.5	370	r jb	2	L	2	A	PGV
											(M L )
	12	Faccioli (1983)			Worldwide		Hybrid approach	4.7	7.7	Mw	4*	95*	r hypo	C	R	O	A	AI
	13	Joyner and Fumal (1984) and	W. N. America	182	-	23	5.0	7.7	Mw	0.5	370	r jb	C	L	2	A	PGV
		Joyner and Fumal (1985)								(M L )
	14	Kamiyama (1984)		Japan	192	-	U	4.1	7.9	M JMA	10	310	r epi	I	B	1	A	RSD
	15	Kawashima et al (1984) &	Japan	197	-	90	5.0	7.9	M JMA	5*	550*	r epi	3	R	1	A	PGV,
		Kawashima et al (1986)																PGD
	16	Wilson and Keefer (1985)		W. USA	30	-	20	5.0	7.4	Mw	6	130	r jb	1	A	1	A	AI
									continued on next page

2 Note only valid for R ≥ 20 km 3 Note only valid for R ≤ 200 km 4 Idriss (1978) finds magnitudes to be mixture of M L , m b and M s .

Table 1 :

 1 continued

	No.	Reference	Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
									scale
	26	Theodulidis and Papazachos (1992)	Greece+16 foreign	105+16 7	-	36+4	4.5	7.0	Ms,	1 (48)	128	r epi	2	B	O	A	PGV,
							(7.2)	(7.5)	Mw,		(236)						PGD
									M JMA
	27	Midorikawa (1993)	Japan	U	-	U	6.5	7.8	Mw	U	U	rrup	1	U	1	A	PGV
	28	Wilson (1993)	W. USA		Hybrid approach	5.3	7.5	Mw	3*	100*	r jb	1	G	O	A	AI
	29	Lee et al (1995)	W. N. America	1926	1926	297	1.7	7.7	Usually	2	200+	r hypo	9, 3 ×	U	1	A	PGV,
									M L				C				PGD
									for
									M ≤
									6.5
									and
									Ms for
									M >
									6.5
	30	Molas and Yamazaki (1995)	Japan	2166	-	387	4.1*	7.8*	M JMA	8*	1000*	rrup	I	L	O	A	PGV
												for 2
												earth-
												quakes,
												r hypo
												other-
												wise
	31	Abrahamson and Silva (1996)	California with some others	U	U	U	4.7	7.4	Mw	0.1	220*	rrup	2	G	1M	A	RSD
	32	Sabetta and Pugliese (1996)	Italy	95	95	17	4.6	6.8	Ms if	1.5,	179,	Both	3	L	1	A	PGV,
									M L &	1.5	180 8	r jb &					AI
									Ms ≥			r epi
									5.5
									else
									M L
	33	Singh et al (1996)	Himalayas	86	-	5	5.7	7.2	m b	33.15	340.97	r hypo	1	U	1	A	PGV
	34	Atkinson and Boore (1997a)	E. N. America	Simulation approach	4.0	7.0	Mw	10	500	r hypo	2	G	O	A	PGV
							continued on next page
	7 Total number of components does not need to be multiplied by two
	8 State equations should not be used for distances > 100 km

Table 1 :

 1 continued

	No.	Reference	Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
									scale
	48	Hernandez and Cotton (2000)	Italy & California	272 13	-	40*	3.2	7.4	M L	1	109	rrup	2	B	1	A	RSD
									for
									M < 6,
									Ms
									other-
									wise
	49	Paciello et al (2000)	Greece & Italy	115	-	18	4.5	U	Mw or	U	U	r epi	2	B	1	A (N)	PGV,
									Ms								PGD,
																	AI
	50	Si and Midorikawa (1999, 2000)	Japan	856	-	21	5.8	8.3	Mw	0*	280*	Both	2	L	O	A	PGV
												rq &
												rrup
	51	Toro and Silva (2001)	Central USA		Simulation approach	5.5	7.5	Mw	1	400	r jb	1	G	1	A	PGV
																	×2
	52	Wu et al (2001)	Taiwan	1941	-	60	4.8	7.6	Mw	0.05*	400*	rrup	1 & I	U	U	A	PGV
									(M L )			(r epi
												for
												some)
	53	Gregor et al (2002)	Shallow crustal worldwide	993	993	68	4.4	7.4	Mw	0.1	267.3	rrup	2	U	1M	A (S,	PGV,
			(mainly California)													R/O,	PGD
																T)
	54	Margaris et al (2002a) & Margaris	Greece	744	-	142	4.5	7.0	Mw	1	150	r epi	3	B	O	A	PGV,
		et al (2002b)															PGD
	55	Silva et al (2002)	Cen. and E. N. America		Simulation approach	4.5	8.5	Mw	1	400	r jb	1	G	1	A	PGV
																	×5
	56	Tromans and Bommer (2002)	Europe	249	-	51	5.5	7.9	Ms	1	359	r jb	3	L	2	A	PGV,
																	PGD
	57	Zonno and Montaldo (2002)	Umbria-Marche	161	-	15	4.5	5.9	M L	2*	100*	r epi	2	L	2	N, O	PGV,
																	AI
	58	Megawati et al (2003)	Sumatran interface		Simulation approach	4.0	8.0	Mw	174	1379	rrup	1	G	1	F	PGV
							continued on next page

Table 1 :

 1 continued

	No.	Reference	Area		H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
										scale
	59	Boatwright et al (2003)	N. California		4028	-	104	3.3	7.1	Mainly	1*	370*	r hypo	4	U	O	A	PGV
										Mw,
										M L
										for
										some
	60	Travasarou et al (2003)	Mainly W. USA		1208	-	75	4.7	7.6	Mw	0.1*	200*	rrup	3	A	1M	A (N,	AI
																	R)
	61	Bray and Rodriguez-Marek (2004)	Worldwide		54	-	13	6.1	7.6	Mw	0.1	17.6	Mrup	2	N	1M	A	PGV
	62	Hwang et al (2004)	Chi-Chi (Taiwan)	221 14	-	4	6.2	7.7	Mw	U	U	r jb	1	A	2M	A	AI
	63	Lin and Lee (2004)	Taiwan		U	-	41	U	U	U	U	U	rrup	1	U	1	A	AI
	64	Midorikawa and Ohtake (2004)	Japan		3335	-	33	5.5	8.3	Mw	0*	300*	rrup	2	L	1	A (C,	PGV
																	B, F)
	65	Pankow and Pechmann (2004) and	Worldwide	extensional	142	-	39	5.1	7.2	Mw	0	99.4	r jb	2	G, O	1M	NS	PGV
		Pankow and Pechmann (2006)	regimes
	66	Bragato and Slejko (2005)	E Alps (45.6-46.8 • N & 12-	1402	3168	240	2.5	6.3	M L	0	130	r jb &	1	R	O	A	PGV,
			14 • E)										r epi					AI
	67	Frisenda et al (2005)	NW Italy		6899 15	-	>1152	0.0*	5.1 16	M L	0	300 17	r hypo	2	B	1	A	PGV
	68	García et al (2005)	Central Mexico		277	277	16	5.2	7.4	Mw	4*	400*	rrup	1	G 18	1M	B	PGV
													for
													Mw >
													6.5,
													r hypo
													other-
													wise
								continued on next page

Table 1 :

 1 continued

	No.	Reference	Area	H	V	E	M min	Mmax	M		r min	rmax	r scale	S	C	R	M	IM
									scale
	69	Liu and Tsai (2005)	Taiwan	7907	7907	51	4.05	7.10	Mw	5*	300*	r hypo		1	M	2M	A	PGV
									(M L )
	70	McGarr and Fletcher (2005)	Central Utah coal-mining ar-	72	-	12	0.98	4.2	Mw	0.5*	10*	r hypo		2	L	2M	M	PGV
			eas						(M CL )
	71	Megawati et al (2005)	Sumatran interface	Simulation approach	4.5	8.0	Mw	150	1500	rrup		1	G	1	F	PGV
	72	Wald et al (2005)	California	U	-	U	U	5.3*	Mw	U	U	r jb		1	L	U	A	PGV
	73	Atkinson and Boore (2006)	E. N. America	Simulation approach	3.5	8.0	Mw	1	1000	rrup		1	G	1	A	PGV
	74	Bindi et al (2006)	Umbria-Marche	239	-	45	4.0	5.9	M L		1*	100*	r epi &	4	L	1M	NS	PGV
													r hypo
	75	Kanno et al (2006)	Japan+some foreign	3392+377	-	73+10	5.0*	8.2*	Mw	1*	450*	rrup		C	R	2M	A	PGV
				(shal-		& 111	(6.1)	(7.4)	(M JMA )	(1.5*)	(350*)	(r hypo
				low) &			& 5.5*	& 8.0*			& 30*	&	for
				8150								450*	some)
				(deep)
	76	Kempton and Stewart (2006)	Worldwide shallow crustal	1559	-	73	5.0*	7.6*	Mw	0*	200*	rrup		C	G	1M	A	RSD
	77	Pousse et al (2006)	Japan	9390 19	-	U	4.1	7.3	(Mw)	5*	250*	r hypo		5	B	2M	A	AI,
													(rrup						RSD
													for
													some)
	78	Akkar and Bommer (2007)	Europe & Middle East	532	-	131	5.0	7.6	Mw	0	99	r jb		3	G	1WM	A (N,	PGV
																		S, R)
	79	Ghodrati Amiri et al (2007a) &	Alborz and central Iran 20	200*	200*	50*	4.5*	7.3*	Ms		5*	400*	r hypo		2	L	1	A	PGV
		Ghodrati Amiri et al (2007b)							(m b )
	80	Bindi et al (2007)	NW Turkey	4047	4047	528	0.5	5.9	M L	21	5*	200*	r hypo	22	2	L	1M	A	PGV
	81	Convertito et al (2007)	Campania, Italy	Mainly simulated with some natural	5	7	Mw	5	150	r epi		1	G	1	A	PGV
						continued on next page

Table 1 :

 1 continued

	No.	Reference	Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
									scale
	82	Danciu and Tselentis (2007a) &	Greece	335	-	151	4.5	6.9	Mw	0*	136	r epi	3	A	1M	A (ST,	PGV,
		Danciu and Tselentis (2007b)														N)	PGD,
																	AI
	83	Fukushima et al (2007)	Japan	8615	-	158	5.0	6.8	M JMA	18.1	448.4	rrup	1	R	1	A	PGV
	84	Megawati (2007)	Hong Kong		Simulation approach	5.3	6.8	Mw	20*	60*	rrup	1	G	1	A	PGV
	85	Atkinson (2008)	E. N. America	Referenced-empirical approach	4.3	7.6	Mw	10*	1000*	r jb	C	I50	O	A (N,	PGV
																R, S,
																U)
	86	Al-Qaryouti (2008)	Dead Sea area	26	-	19	4.0	6.2	M L	5.8	330.6	r epi	1	U	2	A	PGV
	87	Abrahamson and Silva (2008) &	Worldwide shallow crustal	2754	-	135	4.27 23	7.9 24	Mw	0.06*	200*	rrup	C	I50	1M	A (N,	PGV
		Abrahamson and Silva (2009)														R, S,
																HW)
	88	Boore and Atkinson (2007) &	Worldwide shallow crustal	1574	-	58	4.27 25	7.90 26	Mw	0	280 27	r jb	C	I50	2M	A (N,	PGV
		Boore and Atkinson (2008)														R, S,
																U)
	89	Campbell and Bozorgnia (2007),	Worldwide shallow crustal	1561	-	64	4.27 28	7.90 29	Mw	0.07	199.27	rrup	C	I50	1M	A (N,	PGV,
		Campbell and Bozorgnia (2008b) &														R, S,	PGD
		Campbell and Bozorgnia (2008a)														HW)
							continued on next page

Table 1 :

 1 continued

	No.	Reference	Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
									scale
	90	Chiou and Youngs (2008)	Worldwide shallow crustal	1950	-	125	4.265 30	7.90 31	Mw	0.2* 32	70* 33	rrup	C	I50	1M	A (N,	PGV
																R, S,
																HW,
																AS)
	91	Jin et al (2008)	Fujian (China)	1974	1974	94	2.8	4.9	M L	13	462	r epi	1	U	O	A	PGV
	92	Liang et al (2008)	SW W. Australia	Simulation approach	4.0	7.0	M L	10	200	r epi	1	G	1	A	PGV
	93	Massa et al (2008)	Northern Italy	306	306	82	3.5 &	6.3 &	Mw	1*	100*	r epi	3	L	1M	A	PGV
								6.5	(M L )
									& M L
	94	Mezcua et al (2008)	Spain	250	-	149	3.1	5.3	Mw	5*	100*	r hypo	1	U	1	A	PGV
									(m b (Lg ))
	95	Snaebjörnsson and Sigbjörnsson	Europe & Middle East	71	-	13	5.0*	7.6*	Mw	0*	100*	r jb	1	U	1	SS	RSD
		(2008)
	96	Bindi et al (2009a)	Italy	241	241	27	4.8	6.9	Mw	0	190	r jb	3	L, G	1M	A (N,	PGV
												(r epi				S, R)
												for
												small)
	97	Bindi et al (2009b)	Italy	235	-	27	4.6	6.9	Mw	0	183	r jb ,	3	L	1M	A	PGV
									(M L )			r epi
	98	Bommer et al (2009)	Worldwide shallow crustal	2406	-	114	4.8	7.9	Mw	1.5*	100*	rrup	C	B	O	A	RSD
	99	Lee (2009)	W. USA 34	324	324	49	5.0	7.6	Mw	0.1	199.1	rrup	2	A	1M	A	AI×2,
																	RSD×2
	100	Stafford et al (2009)	New Zealand + foreign	144+241	-	23+41	5.08	7.51	Mw	0.07	300	r jb &	3	L, O,	1M	A	AI×4
				&								rrup		G, A		(S/N,
				144+200												R)
							continued on next page

Table 1 :

 1 continued State that only use data with M s ≥ 4 but one earthquake in their Appendix A has M s 3.2.

	No.	Reference	Area	H	V	E	M min	Mmax	M	r min	rmax	r scale	S	C	R	M	IM
									scale
	101	Akkar and Bommer (2010)	Europe & Middle East	532	-	131	5.0	7.6	Mw	0	99	r jb	3	G	1M	A (N,	PGV
																S, R)
	102	Akkar and C ¸agnan (2010)	Turkey	433	-	137	5.0	7.6	Mw	0*	200*	r jb	C	G	1M	A (N,	PGV
																S, R)
	103	Ghodrati Amiri et al (2010)	Alborz and central Iran 35	416	-	189	3.2 36	7.7	Ms	5*	400*	r hypo	2	L	1M	A	AI
									(m b )
	104	Bindi et al (2010)	Italy	561	561	107	4.0	6.9	Mw		100*	r jb ,	3	L	1M	A	PGV
												r epi
	105	Chiou et al (2010) 37	S & N California	15684	-	U	3*	6*	Mw	5*	200*	rrup	C	I50	1M	A (N,	PGV
																R, S,	×2
																HW,
																AS)
	106	Iervolino et al (2010)	Italy	95	-	17	4.6	6.8	Ms if	1.5,	179,	r jb &	3	L	1	A	PGV,
									M L &	1.5	180	r epi					AI
									Ms ≥
									5.5
									else
									M L
	107	Megawati and Pan (2010)	Sumatran interface		Simulation approach	5	9	Mw	300*	1200*	r E	1	G	1	F	PGV
	108	Rajabi et al (2010)	Zagros, Iran	37	-	35	4.1	7.0	Mw	5	150	r epi	1, 3 &	L	1	A	AI×5
													4
	109	Atkinson (2008) modified by	E. N. America	Referenced-empirical approach	4.3	7.6	Mw	10*	1000*	r jb	C	I50	O	A (N,	PGV
		Atkinson and Boore (2011)														R, S,
																U)
	110	Atkinson and Boore (2006) modi-	E. N. America		Simulation approach	3.5	8.0	Mw	1	1000	rrup	1	G	1	A	PGV
		fied by Atkinson and Boore (2011)
							continued on next page

35

Also develop models for the Zagros region of Iran using 309 records from 190 earthquakes. 36 37 Adjustment of GMPE of

[START_REF] Chiou | An NGA model for the average horizontal component of peak ground motion and response spectra[END_REF]

for M w < 6 39 Recommend that model is not used for distances ≥ 200 km.

Acknowledgements

The work presented in this article has been mainly undertaken within the PERPETU-ATE (Performance-based approach to earthquake protection of cultural heritage in European and Mediterranean countries) project of the EC-Research Framework Programme FP7 and the internal BRGM research project SEISMORISK. I thank two anonymous reviewers for their constructive comments on a previous version of this article.

List of Figures

1

Predicted PGV at a NEHRP C site against publication date for 96 models published in the literature. Filled red circles indicate models published in peer-reviewed journals, for which basic information on the used dataset is available and which are not being extrapolated far outside their range of applicability. Numbers correspond to those given in Table 1. Also shown is the median PGV within five-year intervals (black line) and the median ±1 standard deviation (dashed black lines) based on averaging predictions.

Finally indicated is the median PGV (solid blue line) and its 16th and 84th confidence limits (dashed blue line) based on averaging records up until that date (see text for details). Note that the selection criteria and the fact that


Keywords: Network coding, wireless sensor networks, event-centric dissemination

We propose Wireless Sensor Coding (WSC) an eventcentric data-dissemination scheme for Wireless Sensor Networks (WSN). WSC is based on a distributed network coding scheme. In this solution, nodes do not only forward packets, but also perform linear random information coding in order to increase the throughput of the network, to reduce the number of transmissions and the end-to-end delay. These improvements involve a reduction of the energy consumption, which is one of the key-issues in WSN architecture design.

I. INTRODUCTION

One of the most promising examples of pervasive computing are wireless sensor networks (WSNs). Their ability to automatically produce localized and relevant knowledge in a particular area, makes them a major step-forward in the way we will behave with technology. Indeed, distributed sensing and computing will increasingly expand people's ability to remotely interact with the physical world, whether in outdoor or indoor environments (farms, oil extraction stations, streets, houses, factories, etc.). Several research entities and engineering corporations see in the WSNs a new class of computer systems and a real breakthrough, just like the internet was at the end-seventies.

We will focus in this work on Event-centric wireless sensor networks (EC-WSN). An event-centric WSN can be seen as an applicative view of wireless sensor networks; it is characterized by its real-time nature and the fact that the communication phase is triggered only when a node perceives a notable change in its immediate sensing-range. As well as in classic WSN, the main issues of EC-WSNs remain: the energy consumption cutback, the information delivery efficiency, the robustness, the reliability and the computation constraint.

The application considered in this paper is the following dynamic event-subscription service. Clients use the WSN to get updates from sensors about a specific event interest. For example, mobile clients interested in parking spots availability in a specific area may subscribe to this service and get updates each time the sensor network detects that off-street parking is available. To this end, a complete "fresh" view of the sensed area has to be replicated across the entire network since clients maybe connected anywhere and also be mobile. Such vision of a sensor network reveals some questions, What is the scalability of the system when the frequency of events grows? What is the most appropriate dissemination scheme? What is the convergence time of the system?

We describe in this paper, a data-dissemination system based on network coding for the distribution of critical pieces of information across the sensor network. This cooperative solution has the advantage of being completely decentralized and self-organized. It delivers the data from the source-sensors (nodes that detect the event) to the whole network by performing random linear coding dissemination. The aim is to increase the throughput of the network, to reduce the number of transmissions and the end-to-end delay, and thus to increase the WSN lifetime. Through our study, we try to give inclusive answers to the questions exposed above and to illustrate the benefits of using network coding techniques in EC-WSNs. Furthermore, our use of the sensor network is original, since data sinks can move inside the network and subscribe to one or more event-interests.

To quantitatively assess our approach, we perform a detailed performance analysis of WSC (Wireless Sensors Coding), our novel data-dissemination protocol for eventcentric WSNs. We compare three different dissemination schemes with WSC in various scenarios (high or low event occurrence frequency and different network density) and shows an important transmission cutback in the network and an enhancement of the convergence time.

The reminder of the paper is organized as follows: in Section II we give definitions of EC-WSNs and of network coding; followed in section III by a state of the art about the data dissemination in WSNs. Then, we proceed by describing characteristics of our system in Section IV. We introduce WSC, our distributed propagation scheme, in Section V. WSC is compared with three different protocols in Section VI. The paper concludes with a brief discussion in Section VII.

A. Event-Centric Wireless Sensor Networks

Event-centric wireless sensor networks differ from common WSNs, where the communications are triggered either by an on-demand or a sink-based process. The purpose of an EC-WSN is to provide a "real-time" view of all the occurring events in a specific area at all the edges of the network (see

Network Coding for Event-Centric Wireless Sensor Networks

Ismail Salhi 1 , Yacine Ghamri-Doudane 1,2 , Stéphane Lohier 1 and Gilles Roussel 1 1 Université Paris-Est ; LIGM ; 77420 Marne-la-Vallée Cedex 2, France 2 ENSIIE ; 1 Square de la Résistance, 91025 Evry Cedex, France isalhi@etudiant.univ-mlv.fr, ghamri@ensiie.fr, {lohier, gilles.roussel}@univ-paris-est.fr Figure 1). EC-WSNs have been well investigated in prior academic works because of their inherent energy consumption efficiency due to the fact that they perform necessarily less radio-transmissions compared to the more traditional periodic or on-demand approach. Authors of [START_REF] Naik | Sprinkler: A Reliable and Scalable Data Dissemination Service for Wireless Embedded Devices[END_REF] for example, use a very large platform of wireless sensors to test their event triggered dissemination scheme for intrusion detection scenarios. In [START_REF] Dutta | Arora Wireless Sensor Network Platform for Detecting Rare, Random, and Ephemeral Events[END_REF], authors propose a new architecture to detect and classify rare, random and ephemeral events for different event-detection applications. While [START_REF] Mazo | On Event Controlover Sensor/Actuator 2008[END_REF] and [15] deal with the network throughput optimization for EC-WSNs. In such architectures, clients (or sinks) are not necessarily static and the communication are no longer on-demand neither sinkbased. It is the occurrence of an event that triggers a data transmission.

In this work, we propose to use the EC-WSN as an information provider to mobile clients. In fact, each user can subscribe to one or more event-interest and gets information about it wherever he is, given the assumption that he is connected to the network. We can envision several applications for this type of architecture, particularly in an urban environment. Clients may connect to a large scale event-centric sensor network using their cell-phones or other devices and subscribe to various event-interests like: parking lots or public bikes availability, queues and lines status in different offices (postal office, supermarkets, fuel stations, etc.), or even pollution levels in parks and public places.

B. Network Coding

The network coding theory introduced by Ahlswede et al. [START_REF] Ahlswede | Flow[END_REF] had a significant impact on the way researchers consider an information network, whether at the practical level (protocol engineering) or the theoretical level (graph and information theories). Indeed, the well established forwarding schemes based on the store-and-forward transportation scheme are more to be insufficient in many kinds of communication networks, such as multicast networks [START_REF] Ahlswede | Flow[END_REF], or as in wireless ad hoc networks: where [START_REF] Deb | Network coding for wireless applications: A brief tutorial[END_REF] for example, shows that the inherent shared and broadcast nature of the radio channel is not well used to increase wireless networks performances. Katti et al. provided with their two major contributions: [START_REF] Deb | Network coding for wireless applications: A brief tutorial[END_REF] and [START_REF] Katti | in the air: practical wireless network coding Transactions on Networking[END_REF] very interesting ways of using the network coding in wireless ad hoc networks. They have identified important wireless networks properties that the network coding can use to increase the performance of such networks.

The basis of a network coding based communication system is to employ coding mechanisms at intermediate nodes in order to achieve bandwidth optimality [START_REF] Ahlswede | Flow[END_REF]. These mechanisms consist essentially of a linear combination of two or more messages in one output message using random coding vectors built from a finite field. The well-known "butterfly example" introduced in [START_REF] Ahlswede | Flow[END_REF] explains more in details how network coding helps to reach this optimality.

III. RELATED WORKS

A. Information dissemination in EC-WSN

Previous work has been done in data dissemination within event-centric wireless sensor networks. [1] for example treats the case of single static data-sink, while [2] deals with N non mobile data-sinks. However, and to the best of our knowledge, the case of data dissemination toward multiple mobile sinks is not treated yet in the literature. Nevertheless, we have chosen three efficient dissemination mechanisms for WSNs to compare with the performance of our solution. It is important to notice that none of these data propagation protocols was designed for our dynamic subscription-based approach of event-centric WSNs, especially for gossiping which is not designed for fast data dissemination but rather for minimal energy consumption. Nevertheless, these dissemination algorithms are the most adequate solutions in the literature to be used as an event-centric propagation model.

1) Backoff-based Flooding

In backoff-based flooding, nodes disseminate data to all their neighbors by broadcasting the information. When a node receives a message, it makes a copy of it and waits a random limited duration, and sends it to all its neighbors. The convergence time (i.e. the propagation duration to all the nodes of the network) of this algorithm is relatively short comparing to other approach like Gossiping (c.f. bellow) but several problems emerge from this approach, like data implosion [START_REF] Heinzelman | Balakrishnan for information dissemination in wireless sensor networks MobiCom'99[END_REF] and convergence duration which is a linear function of the network degree.

2) Gossiping

Gossiping [START_REF] Hedetniemi | A survey of Gossiping and Broadcasting in Communication networks[END_REF] is a classical dissemination protocol for WSNs based on randomization. Instead of forwarding data to all the sender's neighbors, it transmits its flow to one randomly selected neighbor. Gossiping reduces data implosion by sending only one copy of each message at any node. However, in order to lower the energy consumption, its data dissemination becomes slow, which is not suitable for eventcentric WSNs where fast data propagation is required.

3) SPIN SPIN [START_REF] Heinzelman | Balakrishnan for information dissemination in wireless sensor networks MobiCom'99[END_REF] is a family of adaptive dissemination protocols based on negotiation and resource-adaptation. It is one of the most efficient propagation schemes for WSNs. However, it requires the utilization of meta-data (descriptors about the sensed data) and the presence of a resource-manager that keeps track of resource consumption in every sensor, which is not always feasible in "real-world" situations -in most manufactured sensors, energy consumption status is not available. Moreover, SPIN uses a three phase process for its data propagation with a sequence of three distinct types of messages each time an event occurs, which can lead to a serious overhead in the number of transmissions, even if the meta-data size is less important than the size of the data itself.

B. Network Coding based dissemination

In a network-coding-based dissemination protocol, a linear combination of all available messages is generated by the source using randomly picked coding coefficients, and then sent to the destination. When a node receives enough linearly independent combinations of messages, it can reconstruct the entire original message using a decoding matrix.

In this paper, we propose to use network coding techniques to improve the data dissemination in event-centric wireless sensor networks. Gkantsidis et al. have already proposed in [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF] a content distribution scheme of large files that is based on network coding but for Internet peer-tocomparable approach, we propose to use the randomization and cooperative information propagation network coding to rapidly disseminate collected across an event-centric WSN avoiding the implosion problem and reducing the energy consumption.

Our dissemination scheme (detailed however different from the solution proposed in [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF] where the messages are blocks of one file from one original node. I case, the messages may be generated by different nodes detecting the event. Another significant approach is the fact that there is no need knowledge about the number of messages (b of [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF]) that were generated at the source level

IV. SYSTEM DESCRIPTION

A. Event Occurrence Distribution

Consider a system of n sensors scattered uniformly through a square area. We denote by ܵ ൌ ሼ1, 2 … sensors. ܧ is the number of simultaneous new events that may occur and thus are detected by sensors within this area same time. We define the event occurrence frequency number of occurring events every unit of time. different random process depending on application. Each occurring event can be detected by sensors chosen from S with a certain probability, with 1 ݉ ݊. These ݉ nodes compose ܦ set of all sensors that detect an event ݅. As detects event according to a process of rate such that ∑ ݔ ൌ ߤ. In the rest of the paper we refer to the detector nodes by source nodes.

Any occurring event in an EC-WSN several sensors. This redundancy is essential to guarantee lossless data propagation and a better availability of the information. In some cases, this surplus of information can also be used to increase the confidence incidence. For example, in critical applicat flood detection, false positives have to be discarded by validating the event from different sources.

B. Message Propagation

We assume that every source node ݆ single message ܯ ሺ݆ሻ, i.e. every event-detection message transmission from all nodes of includes information about the event i (timestamp, id data…). The goal of the network after the message generation, is to disseminate the messages ܯ ሺ݆ሻ describing the eve across the entire network. We denote by messages already received by a node convergence time of an event i, i.e. the duration all the messages to be received by nodes of verified).

∀ ݆ ∈ ܦ , ∀ ݇ ∈ ܵ, ܯ ሺ݆ሻ ∈

C. Event-Interest Subscription

In our approach, final users (subscribers) may be different types: information display units mobile users (cell phone, laptops, PDA), or internet gat -peer networks. In a , we propose to use the randomization propagation induced by the network coding to rapidly disseminate collected information avoiding the implosion problem (detailed in section V) is however different from the solution proposed in [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF] where the file from one original node. In our generated by different nodes particularity of our re is no need for previous knowledge about the number of messages (blocks in the case generated at the source level.

ESCRIPTION s scattered uniformly through … , ݊ሽ the set of all the the number of simultaneous new events that may occur and thus are detected by sensors within this area at the . We define the event occurrence frequency ߤ by the unit of time. ߤ may follow ss depending on the EC-WSN event can be detected by m with a certain probability, with ܦ ൌ ሼ1, 2 … , ݉ሽ the As a result, a node ݆ detects event according to a process of rate ݔ 0, ݆ ∈ ܦ

In the rest of the paper we refer to the WSN can be detected by ncy is essential to guarantee lossless data propagation and a better availability of the information. In some cases, this surplus of information can confidence about the event incidence. For example, in critical application such as fire or flood detection, false positives have to be discarded by validating the event from different sources.

݆ ∈ ܦ generates one detection triggers one from all nodes of ܦ . Where ܯ ሺ݆ሻ timestamp, id, metaof the network after the message generation, ሻ describing the event i

We denote by ݊ܫሺ݇ሻ the set of by a node ݇. ܶ ሺ݅ሻ is the , i.e. the duration necessary for nodes of S (equation 1 is

ሻ ݊ܫሺ݇ሻ ሺ1ሻ

In our approach, final users (subscribers) may be from information display units (digital billboards), , or internet gateways for instance. The only condition is that subscribers have to use the same communication protocol as the one used Since the network is event replicated in every node, it becomes simple to any data about its interest anywhere in the V. WIRELESS Source nodes ܦ share data backoff message broadcast ( random backoff time before sending its message to avoid collisions). Every message is time information about the event order to provide to subscribers across the network, information replicated from ݅ܦ to every node of avoiding the implosion and the famine problem Fig. 2

-WSC queuing system overview

In order to reach this goal, t 2 is used after the reception of a message by any node.

A. Message Queuing

Whenever a node ܽ ∈ ܵ receives a a source node j with ሺ݆ ് ܽ source message (it has not been encoded) message in what we call its coding in Figure 2. If ܽ has already received ݊ܫሺܽሻሻ it simply drops it. However, if the message is already coded, a proceeds to what we call a detailed in section V.D.

B. Message Encoding

We assume that messages are transmitted as vectors of bits which are of equal length ݈ሺܯ in the finite field ॲ ଶ ಿ . The length of transmissions and for all events buffering period), all the messages in the node a are encoded following message ܯܥ is sent with a back

∀ ܯ ∈ ܳ ௨௧ ሺܽሻ, ܯܥ ൌ
We denote ݃ Ԧ ൌ ሺ݃ ሺ݅ሻሻ, the ܯܥ . In a similar approach as the one proposed case of P2P, we make use of method where each node selects autonomously and randomly the coding vector's coefficients The only condition is that subscribers have to use the same communication protocol as the one used in the WSN. Since the network is event-centric and all the data are , it becomes simple to any user to get anywhere in the network.

IRELESS SENSOR CODING data of detected event ݅ with a classic broadcast (i.e., each node waits a specific random backoff time before sending its message to avoid collisions). Every message is time-stamped, contains information about the event and has a unique identifier. In to subscribers a fresh view of the sensed data , information about event i has to be every node of ܵ as fast as possible, implosion and the famine problems.

WSC queuing system overview this goal, the scheme described by Figure eption We assume that messages are transmitted as vectors of bits ሺܯሻ ൌ ܰ, represented as elements . The length of a vector is equal in all and for all events. After ܶ ௨ units of time (the , all the messages in the coding queue of the following equation 2; the encoded sent with a backoff broadcast to its neighbors.

ൌ ݃ ሺ݅ሻ. ܯ |ொ ೠ ሺሻ| ୀ ሺ2ሻ
, the coding vector of the message In a similar approach as the one proposed in [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF] for the , we make use of a randomized propagation method where each node selects autonomously and randomly the coding vector's coefficients ݃ ሺ݅ሻ from a finite field ॲ ଶ ಿ .

Each encoded message contains in addition to the coded data ܯܥ : the message Id, a combination of the coded messages Ids (CODED_IDS)-this value is used by the receiver to know which messages are encoded within Cܯ , the coding vector, the source address, the message lifetime, and the number of all encoded messages (see Figure 3).

Fig. 3 -WSC message header format

In case where the coding queue is empty, the node reinitiates its buffering timer and waits for the next round. While if ܳ ௨௧ ሺܽሻ contains only one message, node a sends it only once with a backoff broadcast. Note that the number of messages available in ܳ ௨௧ ሺܽሻ is highly correlated with the buffering duration ܶ ௨ : If the value of ܶ ௨ is too small, then the node will not have enough time to receive additional messages in its coding queue; in this special case WSC works exactly like Backoff-based Flooding. Obviously, when the value of ܶ ௨ is too large, the coding queue may also runoff space, the coding operations will take more time and messages may be lost. But depending on the expected event occurrence frequency ߤ, it is simple to choose an appropriate value for ܶ ௨ that avoids those problems.

C. Message Decoding

The decoding process in WSC consists in solving a linear equation system of ݑ unknowns. We define the decoding queue ܳ ሺܽሻ for each node ܽ ∈ ܵ where all the coded messages that ܽ received are enqueued (see Figure 2). ݑ is the number of distinct ids present in the CODED_IDS field of every message within ܳ (ܽ). In order to solve the system of equations, each node receives messages which are linear combinations of source messages and stores them into a matrix with their respective coding vectors as shown in equation 3. Where ܩ ௧ symbolizes the matrix of all the received coding vectors, and ℎ the number of coded messages received and to decode. As shown in [START_REF] Ho | The benefits of coding over routing in a randomized setting[END_REF], it is possible to recover all the source messages ܯ , … , ܯ as long as the matrix ܩ ௧ has full rank ℎ (see equation 4).

ܯ

⋮ ܯ ൩ = ܩ ௧ ିଵ ܯܥ ⋮ ܯܥ ൩ ( 4
)
According also to [START_REF] Ho | The benefits of coding over routing in a randomized setting[END_REF], ܩ ௧ will be invertible with high probability if the coefficients ܿ of the coding vectors are random and picked from a finite field ॲ ଶ ಿ that is large enough. Authors of [START_REF] Koetter | An algebraic approach to network coding[END_REF] set that a size of 2 ଵ gives a probability higher than 0.996 for ܩ ௧ to be invertible.

D. Super-Coding

In many situations, nodes may receive two or more already coded messages. If a node chooses -like nodes l and k in Figure 4 -to forward only one of them ܯܥ( in this case) and not to proceed to a re-coding operation, neighbors like m might get the same coded message from two different sources (l and k in this case), which can reduce the randomization within the network and thus decrease the decoding speed.

Fig. 4 -Linear dependency problem

To cope with this problem, we propose to adapt the operation of re-coding previously encoded messages employed by Gkantsidis et al in [START_REF] Gkantsidis | Rodriguez, content distribution[END_REF], to augment the randomization and to create more innovative messages that increase the number of linearly independent equations at the receiver's level.

Fig. 5 -Super-coding illustration

Figure 5 shows a case where WSC makes use of super coding. First, the event is detected by nodes 1,2, … , ݉, each one generates and broadcasts a message ܯ ଵ , … , ܯ . When i and j receives ܯ ଵ , ܯ ଶ and ܯ ସ , they respectively choose

ܿ ప ሬሬሬԦ = (ܿ ଵ , ܿ ଶ , ܿ ସ ) and ܿ ఫ ሬሬሬԦ = (ܿ ଵ , ܿ ଶ , ܿ ସ
) as their coding vectors then, they code the source messages into ܯܥ and ܯܥ before broadcasting them. When ݇ receives ܯܥ and ܯܥ , instead of sending only one of them to avoid redundant message transmission (since both include the same source messages), ݇ chooses two random coefficients ܿ ଵ , ܿ ଶ and generates a linear combination of ܯܥ and ܯܥ into one "super-coded" message ܯܥ (see equation 5) Before ݇ sends ܯܥ it also builds a new coding vector as depicted in equation 6:

ܯܥ = ܿ ଵ . ܯܥ + ܿ ଶ . ܯܥ (5)
ܿ ሬሬሬሬԦ = ܿ ଵ . ܿ ప ሬሬሬሬԦ + ܿ ଶ . ܿ ఫ ሬሬሬԦ (6)
Note that the decoding process remains the same in this case, since the coding vectors are modified each time a super coding operation is used.

VI. PERFORMANCE EVALUATION

A. Preliminaries

We have considered the performance of WSC and compared the results with other dissemination schemes (namely: SPIN, Gossiping and backoff-based flooding) using the Qualnet 4.5 simulation framework (see [11]). We focused in this study on the most important characteristics that may alter the behavior of the information dissemination. Specifically: 1) The event occurrence frequency ߤ, 2) The number of sensors |ܵ|, and 3)

The average number of source nodes ܦ ௩ , with:

ܦ ௩ = ∑ ܦ| | ୀଵ ܸ
Where ܸ is the number of events that occurred during the simulation.

In order to evaluate the performance of WSC and to compare it to each of the three chosen protocols, we have considered two important event-centric WSNs metrics: 1) The average convergence time: the convergence time ܶ is a key parameter in EC-WSNs, it indicates the duration in which event data is distributed to all the nodes of the network. We suggest to study the impact of ߤ, |ܵ| and ܦ ௩ on ܶ for WSC, SPIN, Gossiping and backoff-based flooding. Indeed, these three parameters are those that influence the most the performance of these protocols while used in EC-wireless sensor networks.

2) The number of transmissions: in order to determine which scheme implies less overhead, we computed the number of transmissions ܰ ௦ for all the sensors, compared the results and thus deduced the bandwidth efficiency of each scheme.

B. Simulation environment

To implement the selected algorithms, we designed for each one a specific routing module directly linked with the MAC layer of the simulation platform. We also modified the design of the 802.11b physical layer so that the transmission radius and the bit rate correspond more properly to a realistic WSN experience. Moreover, we developed an extension feature for Qualnet that allows to randomly trigger events through the network with a given occurrence frequency.

For our simulation, we used a fully connected wireless sensor network of 150 nodes uniformly spread through a squared plan area of 1500 × 1500 squared meters. The power of the radio transmitters is set so that the communication radius is about 50 meters. The rest of the simulation attributes are summarized in table 1.

C. Simulation results

Firstly, we calculated for each scheme the value of the convergence time ܶ considering different values of ߤ (see table 1), so we can see which algorithm is faster for the data propagation. In the case of WSC we configured the value of the buffering time ܶ ௨ relatively to the event frequency. Note that the combination of ߤ and the average number of source nodes ܦ ௩ determines the traffic density of the network (as ߤ and ܦ ௩ grow the traffic density increases). Thus, we can also infer the scalability of each protocol.

Figure 6 shows the results of this first analysis, and confirms the benefit of using WSC. Indeed, the convergence time of SPIN is higher than WSC, which is due to the fact that SPIN uses a three-step communication system with a sequence of ADV→REQ→DATA messages for its event information propagation. Backoff-based flooding has also a longer convergence time mostly because of its redundant message transmissions. Gossiping has meanwhile the longest convergence duration since its data propagation is very slow (each transmission is addressed to only one destination). The only case where the convergence time of WSC is longer than SPIN is when ߤ = 0.1; this is due to the fact that the buffering period ܶ ௨ is longer than the SPIN sequence duration. But in a realistic scenario we can imagine that an EC-WSN has a higher event occurrence frequency than 0.1 event/second.

As depicted in Figure 7, the convergence of WSC remains low as the number of nodes increases comparing to the other protocols. This is due to the fact that WSC is broadcast-based and uses the cooperative data propagation induced by network coding. We can conclude from these results and from Figure 6 that WSC stays efficient even when the traffic load and the number of nodes are important in the network.

We can see from Figure 8 that the number of transmitted messages ܰ ௦ with WSC is very low compared to SPIN which was predictable because there are no additional messages (ADV and REQ). Since in Gossiping, every node sends only one unicast message to one of its neighbors, the number of messages becomes also very high. ܰ ௦ in backoffbased flooding is higher than in WSC: the additional messages in backoff-based flooding are due to the fact that each node sends a message to all its neighbors even if they already got it from another path. Note that the energy consumption in WSNs can be inferred from the number of message transmissions. Thus, we can deduce that WSC gives the best speed/energy alternative for event-centric WSNs.

VII. CONCLUSION & FUTURE

In this paper, we characterized a new class of event wireless sensor networks, in which every node is an information provider to clients interested in specific events. We introduced WSC, a new dissemination scheme based on Network Coding that allows fast, decentralized homogenous data propagation from the nodes detecting the events to the entire network. Our performance evaluation compares WSC with SPIN, Gossiping and flooding: three major dissemination algorithms for wireless sensor networks. We demonstrate the advantages of using WSC in terms of bandwidth efficiency, outperforms all the other algorithms, and offers the fastest propagation (convergence time), thanks to its smart exploitation of the shared nature of the wireless medium

In our study, we do not treat the storage efficiency of the information among the network. Therefore and in continuation of this work, we plan to extend WSC distributed event storage solution in which the information not distributed to all the nodes but to a set of them high information availability and a low energy consumption. , in which every node is an information provider to clients interested in specific events.

VIII. REFERENCES

a new dissemination scheme based on , decentralized and the nodes detecting the events to the entire network. Our performance evaluation compares WSC with SPIN, Gossiping and backoff-based flooding: three major dissemination algorithms for wireless sensor networks. We demonstrate the advantages of using where WSC widely and offers the fastest data thanks to its smart wireless medium. he storage efficiency of the information among the network. Therefore and in the continuation of this work, we plan to extend WSC to a in which the information are distributed to all the nodes but to a set of them, keeping a energy consumption. WSN for different event occurrence frequencies (150 nodes)

Fig. 1 -

 1 Fig. 1 -Event-centric WSN overview II. BACKGROUND

Fig. 7 -

 7 Fig. 7 -Convergence time for different number of nodes

[ 1 ]

 1 Y. Sankarasubramaniam, O. B. Akan, I. F. Akyildiz. to-sink reliable transport in wireless sensor networks." MobiHoc'03, June 2003, Annapolis, Maryland, USA. [2] C. Intanagonwiwat, R. Govindan, and D. Estrin. "Directed Diffusion: A Scalable and Robust Communication Paradigm for Sensor Networks." ACM MobiCom'00, August 2000, Boston, Massachusetts.

Fig. 6 -

 6 Fig. 6 -Convergence time of the EC

YFig. 8 -

 8 Fig. 8 -ܰ ௦ for differe

  of a message by any node.

	receives a new message ܯ ሺ݆ሻ from ܽ, ݆ ∈ ܦ ሻ, if this message is a not been encoded), ܽ enqueues the coding queue ܳ ௨௧ ሺܽሻ as depicted has already received the message ሺܯ ሺ݆ሻ ∈ However, if the message is already
	what we call a Super-coding operation as

TABLE I

 I

	Simulation time Mobility model MAC protocol Capacity Trans. rang. Max. num. concurrent evt. ܧ Evt. occurrence frequency ߤ Avg. num. of src. nodes ܦ ௩ Buffering period ܶ ௨ Coding queue ܳ size Decoding queue ܳ ௨௧ size Message size	-SIMULATION SETTINGS 600 ݏ ݁݊ܰ 802.11ܾ 0.5 ݏܾܯ ~50 ݉ 50 0.1| 0.5 | 1 | 5 | 40 ݏ/.ݐݒ݁ 2 | 6 adaptive 500 × ݁ݖ݅ݏ_݃ݏܯ 500 × ݁ݖ݅ݏ_݃ݏܯ 64 kb