Sensitivity of seismic hazard results to alternative seismic source and magnitude-recurrence models: a case study for Jordan

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1 Geodinamica Acta ISSN: (Print) (Online) Journal homepage: Sensitivity of seismic hazard results to alternative seismic source and magnitude-recurrence models: a case study for Jordan Nazan Yılmaz & M. Semih Yücemen To cite this article: Nazan Yılmaz & M. Semih Yücemen (2015) Sensitivity of seismic hazard results to alternative seismic source and magnitude-recurrence models: a case study for Jordan, Geodinamica Acta, 27:2-3, , DOI: / To link to this article: Published online: 16 Oct Submit your article to this journal Article views: 375 View Crossmark data Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at

2 Geodinamica Acta, 2015 Vol. 27, Nos. 2 3, , Sensitivity of seismic hazard results to alternative seismic source and magnitude-recurrence models: a case study for Jordan Nazan Yılmaz a * and M. Semih Yücemen b a Earthquake Department, Disaster and Emergency Management Presidency, Ankara, Turkey; b Civil Engineering and Earthquake Studies Departments, Middle East Technical University, Ankara, Turkey (Received 20 February 2014; final version received 18 June 2014) Influence of different models and assumptions with respect to seismic source modelling and magnitude distribution on seismic hazard results is examined, taking Jordan as a case study. Four alternative models, which are based on different combinations of seismic source models and magnitude-recurrence relationships, are considered. Seismic hazard curves obtained at four different sites in Jordan according to these four models are compared. In order to display the magnitude of spatial variation of peak ground acceleration (PGA) values obtained from these models, difference maps for return periods of 475 and 2475 years are constructed. Logic tree method is applied to aggregate the results calculated based on different models and assumptions. Then, best estimate seismic hazard maps for PGA and spectral acceleration at 0.2 and 1.0 s corresponding to return periods of 475 and 2475 years are plotted. Keywords: probabilistic seismic hazard; sensitivity; seismic source model; magnitude distribution; Jordan 1. Introduction Probabilistic seismic hazard analysis (PSHA) methodology has been utilised in the last 45 years by adapting the developments in the models describing the temporal, spatial and magnitude distribution of earthquakes, as well as attenuation characteristics of the ground motion. Point, line (fault model), area (source zone model), twodimensional dipping plane (i.e. fault with subsurface geometry), three-dimensional volumetric source (i.e. area source with depth), background area source and spatially smoothed seismicity models are alternative seismic source models for spatial distribution of potential earthquakes. Exponentially distributed magnitude, characteristic earthquake and maximum magnitude (purely characteristic earthquake) models are often used to describe magnitude-recurrence relationship. Poisson and renewal models are used to model the occurrence of earthquakes in the time domain. A case study, involving the assessment of seismic hazard for Jordan, is conducted in order to investigate the spatial sensitivity of seismic hazard results to alternative seismic source and magnitude-recurrence models. Most parts of Jordan, especially the regions along the Dead Sea-Jordan rift valley, are subject to significant seismic threat. The Dead Sea transform fault system (DSTFS) which extends in approximately south-north direction near the western boundary of Jordan has produced destructive earthquakes since ancient times (Ben-Menahem, 1979). The DSTFS was formed as a result of the breakup of the Arabian Plate from the African Plate (Barazangi, 1983). Deformation in this boundary is intense and complex with faults trending not only sub-parallel to the transform but also oblique to it (Bender, 1974). 2. Case study: seismic hazard assessment for Jordan The earlier probabilistic seismic hazard studies in the region are limited in number and they date back to the development of seismic hazard maps for Palestine (Ben-Menahem, 1981; Shapira, 1981). Later, a number of studies were conducted for the estimation of seismic hazard in Jordan. Yücemen (1992) conducted a very comprehensive study for the assessment of the seismic hazard in Jordan and its vicinity using probabilistic and statistical methods. Seven seismic sources, which include line sources for the well-defined faults and area sources for the others, were delineated in that study. The results were presented in the form of seismic hazard maps displaying iso-acceleration and iso-intensity contours corresponding to different return periods. In that study, the major problems were the identification of seismic source zones, delineation of faults, assessment of the fault parameters and the non-availability of attenuation relationships derived based on local data. In a later study conducted by Yücemen (1995), the problems associated with the location of seismic source zones were addressed in full and a model was described to quantify and incorporate explicitly the errors made in the demarcation of the source zone boundaries. The basic concept introduced in that model was the assumption of random source zone boundaries instead of deterministic ones. To demonstrate the application of the proposed model, seismic hazard was computed at three different cities in *Corresponding author. nazan.yilmaz@afad.gov.tr 2014 Taylor & Francis

3 Geodinamica Acta 189 Jordan. The sensitivity of results to the location uncertainty was examined. Besides, a comparison against the previous results was made. In the last two decades, a number of studies (Al-Tarazi, 1992; Batayneh, 1994; Husein Malkawi, Al-Homoud, & Liang, 1995; Fahmi, Husein Malkawi, & Al-Zoubi, 1996; Jiménez, 2004; Jiménez, Al-Nimry, Khasawneh, Al-Hadid, & Kahhaleh, 2008) were conducted for the development of seismic hazard maps for Jordan and its vicinity. The probabilistic methodology and the computational algorithms were not different than the ones utilised by Yücemen (1992, 1995); however, these studies involved more information and expert opinion for the delineation of seismic sources. Accordingly, more reliable seismic source models and seismicity parameters were used in these studies. Also, Al-Tarazi and Sandvol (2007) conducted a study for seismic hazard evaluation along the Jordan-Dead Sea transform based on spatially smoothed seismicity model and characteristic earthquake concept. Three alternative models were used to produce probabilistic seismic hazard maps for the region. Models 1 and 2 were based on spatially smoothed seismicity model for earthquakes with magnitudes greater than 3.0 for the time period and magnitude range between 5.0 and 7.0 for the time period B C and A.D. 2003, respectively. No seismic source zones were used in these two models. In Model 3, contribution of the large events with magnitude equal to or greater than 7.0 to the seismic hazard was calculated by assigning them to major faults as characteristic events having a narrow magnitude range. The results obtained from Models 1 to 3 were combined to form a single probabilistic seismic hazard map. The maps showing the peak ground acceleration (PGA) with 10% probability of exceedance in 50 years were produced for each one of the three models as well as for the combination of them Seismic database and seismic sources Two major steps of PSHA are the delineation of seismic sources and the assessment of the earthquake occurrence characteristics for each seismic source. Therefore, the past earthquake catalogues and tectonic structure of the region of interest must be studied to determine the locations and magnitude-recurrence relationships of seismic sources that may generate the future seismic activity. To carry out a seismic hazard analysis for Jordan, the seismicity of the rectangular region bounded by N latitudes and E longitudes is studied. For this region, two earthquake catalogues which are presented in Jiménez (2004) are used. First earthquake catalogue includes the earthquakes that occurred between the years 0 and In this study, the historical events that occurred between the years 0 and 1899 are not taken into consideration due to the incompleteness in smaller magnitudes. The magnitudes of the events between the years 1900 and 1989 are given in local magnitude (M L ) scale. The earthquake magnitudes in body wave magnitude (m b ) scale, mostly for the events with M L 4.0, as well as those in surface wave magnitude (M s ) scale for some events are also presented. The second earthquake catalogue includes the events that occurred between the years 1990 and The magnitudes of these events are given in M L scale. PGA and spectral acceleration (SA) at 0.2 and 1.0 s (SA (0.2 s) and SA (1.0 s)) are selected as the basic parameters for the seismic hazard evaluation. The instrumental data for strong earthquakes are scarce in the Levant region and the available attenuation relationships for strong motion and intensity have been generally derived based on very few instrumental records (including data gaps both in distance and magnitude), intensity data and isoseismal information and in some cases, accelerations are mainly derived from seismogram records (Jiménez et al., 2008). Thus, in this study, the attenuation equations developed by Ambraseys, Simpson, and Bommer (1996) for Europe and adjacent regions are utilised. Since no information is available about the site conditions all over Jordan, all computations are carried out for rock site condition. Therefore, ground motion prediction equations proposed by Ambraseys et al. (1996) for rock site condition, which is shown below, are used in this study: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi log PGA ¼ 1:48 þ 0:266M s 0:922 log d 2 þ 3:5 2 (1) log SA ð0:2sþ¼ 1:21 þ 0:284M pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 0:922 log d 2 þ 4:2 2 log SA ð1:0sþ¼ 3:17 þ 0:508M pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 0:885 log d 2 þ 4:3 2 where PGA, SA (0.2 s) and SA (1 s) are in g; d is the shortest distance to the surface projection of fault rupture in km. In Ambraseys et al. (1996), standard deviations associated with the attenuation equations derived for log PGA, log SA (0.2 s) and log SA (1.0 s) are given as 0.25, 0.27 and 0.32, respectively. In the attenuation equations given above, the magnitude values should be in terms of M s scale. Therefore, the magnitudes of earthquakes in the catalogue are converted from M L to M s using the equation derived by Jiménez (2004) based on the earthquake catalogue compiled for the seismic hazard assessment of Jordan as given below: M s ¼ 1:11M L 0:50 (4) Poisson model assumes independence between earthquakes. Therefore, secondary events, i.e. foreshocks and aftershocks, are removed from the earthquake catalogue in order to form an alternative seismic database. Various methods are proposed in the literature to identify secondary events. One simple procedure, based on the assumption that earthquakes which fall into the space (2) (3)

4 190 N. Yılmaz and M.S. Yücemen Table 1. Space and time windows to identify secondary events (after Deniz, 2006; Deniz & Yücemen, 2005). Moment magnitude (M w ) Width of space window (km) Width of time window (days) and time windows of another larger magnitude earthquake are identified as secondary events, is utilised here. For this purpose, the time and space windows proposed by Deniz (2006) and Deniz and Yücemen (2005) for earthquakes with moment magnitudes equal to or greater than 4.5, as given in Table 1, are used. In order to implement the space and time windows proposed by Deniz (2006) and Deniz and Yücemen (2005), the magnitudes of earthquakes in the whole catalogue should be converted to the moment magnitude, M w, scale. The conversion is performed using the equation derived by Deniz and Yücemen (2010) based on earthquakes recorded in Turkey, which is given as follows: M w ¼ 1:57M L 2:66 (5) The minimum earthquake magnitude, m 0, to be considered in seismic hazard analysis is set equal to 4.0 in M s scale. Therefore, earthquakes with magnitude, M w < 3.7, which corresponds to 4.0 in M s scale according to Equations (4) and (5), are removed from the earthquake catalogue. For magnitudes that are not given in Table 1, linear and log-linear interpolations are applied for the time and space windows, respectively (Deniz & Yücemen, 2005). Also earthquakes with magnitudes greater than 6.0 are assumed to be main shocks although they may be identified as secondary events of another main shock. The resulting earthquake catalogue includes 175 main shocks, which can be treated as independent events. In this study, two different models, namely area and line, are used for the main seismic sources that affect Jordan. For the location of seismic sources, the information given in the report by Jiménez (2004) is used. The locations of area and line sources are shown in Figure 1. Information on these seismic sources and their seismicity parameters are given in the following sections Alternative models Different seismic source models combined with different magnitude-recurrence relationships are applied to calculate seismic hazard for Jordan. These models are explained in the following sections Model 1 In this model, the area sources shown in Figure 1(a) are used by assuming exponential magnitude distribution, given below, for all of them. f M ðmþ ¼ kbe bðm m 0Þ m 0 m m 1 (6) 0 otherwise k ¼ 1 e b ðm 1 m 0 Þ (7) h i 1 where f M (m) is the probability density function for magnitudes, m 0 and m 1 are lower and upper bound magnitudes and k is the normalising constant, which adjusts the value of the cumulative distribution function to unity at magnitude, m = m 1. Figure 1. Locations of (a) area sources and (b) line sources used in this study (after Jiménez 2004).

5 Geodinamica Acta 191 In this model, m 0 is taken as 4.0 for all sources. The annual rate of earthquakes with magnitude equal to or greater than m 0, ν, and the parameter of the exponential magnitude distribution, β, are assessed based on the information given by Jiménez (2004). However, a certain degree of cross-checking has also been done using some of the other references (Al-Tarazi, 1992; Batayneh, 1994; Fahmi et al., 1996; Yücemen, 1992). The depths of seismic sources, except those defined for Cyprus and Gulf of Suez, are assumed to be 20 km based on the study of Al-Tarazi and Sandvol (2007). The depth for the Cyprus seismic source is taken as 40 km which is the average value of the depths of the earthquakes that are in the earthquake catalogue including only the main shocks and fall into this source. Similarly, the depths of two seismic sources defined for Gulf of Suez, namely Gulf of Suez- North and Gulf of Suez-South, are taken as 25 km which is consistent with the study of Al-Tarazi and Sandvol (2007). In the earthquake catalogue, there are some events that cannot be associated with any one of the seismic sources identified in this model. These activities are treated as the background seismicity and their effect is smeared uniformly over the whole region. For the background seismic source, the value of β is taken from the study of Yücemen (1992). The seismicity parameters of the seismic sources in Model 1 are listed in Table 2. Table 2. Parameters of seismic sources considered in Model 1. Source No.* Name of source m 1 ν (per year) β Depth (km) 1 Dead Sea-Jordan River Wadi-Araba Yamune-Roum Palmira Gulf of Aqaba Gulf of Suez-South Gulf of Suez-North Sirhan Faults Farah Haifa Wadi Karak SE Maan East Gulf of Aqaba Central Sinai North East Gaza SE-Mediterranean SE-Mediterranean SE-Mediterranean Cyprus Background *These numbers correspond to the source numbers shown in Figure 1(a). Table 3. Parameters of seismic sources considered in Model 2 and Model 3. Source No. Name of source Type of source model Fault type m 1 ν (per year) β Depth (km) 1 Dead Sea-Jordan River Line Strike-Slip Wadi Araba Line Strike-Slip Northern Faults Line Strike-Slip Gulf of Aqaba Line Strike-Slip Gulf of Suez Line Strike-Slip Sirhan Faults Line Strike-Slip Farah Haifa Line Strike-Slip Wadi Karak Line Strike-Slip SE Maan Line Strike-Slip East Gulf of Aqaba Line Strike-Slip Central Sinai Line Strike-Slip North East Gaza Line Strike-Slip * SE-Mediterranean 1 Area * SE-Mediterranean 2 Area * SE-Mediterranean 3 Area * Cyprus Area Background Area *These numbers correspond to the source numbers shown in Figure 1(a) while others correspond to the source numbers shown in Figure 1(b).

6 192 N. Yılmaz and M.S. Yücemen Model 2 and Model 3 In Model 2, all seismic sources, except SE-Mediterranean 1, SE-Mediterranean 2, SE-Mediterranean 3 and Cyprus, are modelled as line (fault) sources as shown in Figure 1(b). m 0 is again taken as 4.0 for all sources. Similar to Model 1, a background area source with uniform seismicity is defined to take into account the seismic activity that cannot be related with any one of the seismic sources in this model. Exponential magnitude distribution is assumed for all sources. In Model 3, the same seismic sources and seismicity parameters are used; but, characteristic earthquake model proposed by Youngs and Coppersmith (1985) is assumed for all line sources (faults) with m In the characteristic earthquake model proposed by Youngs and Coppersmith (1985), magnitudes are assumed to be exponentially distributed up to the magnitude level m. Above this magnitude, the characteristic earthquake lies with a uniform distribution between (m 1 Δm c ) and m 1. In order to apply this model in their analysis, Youngs and Coppersmith (1985) made some simplifying assumptions. They assumed Δm c to be equal to 0.5 magnitude unit, m = m 1 Δm c and frequency of characteristic part of the distribution equals to the frequency of the exponential part at (m 1.0). Applying these assumptions and renormalising the probability density function so that the total area under it equals to unity, the probability density function of magnitude for the characteristic earthquake model takes the following form: f M ðmþ ¼ kbe bðm m 0Þ m 0 m m 1 0:5 kbe bððm Þ m 0Þ m 1 0:5 m m 1 (8) where h k ¼ 1 e bðm 1 0:5 m 0 Þ þ be bðm m0þ 0:5 i 1 (9) The parameters of the seismic sources for Model 2 and Model 3 are listed in Table Model 4 All seismic sources are modelled as line (fault) sources as shown in Figure 1(b). Purely characteristic earthquake (or maximum magnitude) model is used for the sources with m If a fault is considered to be purely characteristic, only earthquakes of specified maximum magnitude are expected to occur on the fault. In this case, these earthquakes rupture the entire fault or a series of its segments. In Model 4, for the faults whose slip rates are available, the activity rates of their maximum magnitude events (characteristic earthquakes) are calculated using the seismic moment balancing concept. This method is preferred because the length of the available earthquake catalogue was not long enough to predict the frequency of characteristic earthquakes. Seismic moment, first introduced by Aki (1966), describes size of an earthquake with static fault parameters as follows: M 0 ¼ lad (10) where M 0 is the seismic moment, μ is the rigidity or shear modulus of the crust (usually taken as dyne/cm 2 ), A is the rupture area on the fault plane undergoing slip during the earthquake and D is average displacement over the slip surface. The seismic moment rate, M0 0, or the rate of seismic energy release can be calculated from the time derivative of Equation (10) as follows: M 0 0 ¼ las (11) where S is the average slip rate along the fault. Seismic moment can be calculated from the moment magnitude, M w, using the following equation (Hanks & Kanamori, 1979): M w ¼ 2=3 log M 0 10:7 (12) or M 0 ¼ 10 1:5M wþ16:05 (13) Table 4. Parameters of seismic sources considered in Model 4. Source No. Fault name Fault type Model type Slip-rate (mm/year) ν (per year) m 0 m 1 β Average depth (km) 1 Dead Sea -Jordan River Strike-slip Purely characteristic Wadi Araba Strike-slip Purely characteristic Northern Faults Strike-slip Purely characteristic * Gulf of Aqaba Strike-slip Purely characteristic Gulf of Suez Strike-slip Purely characteristic Sirhan Faults Strike-slip Purely characteristic * Farah Haifa Strike-slip Exponential Wadi Karak Strike-slip Exponential SE Maan Strike-slip Exponential East Gulf of Aqaba Strike-slip Exponential Central Sinai Strike-slip Exponential North East Gaza Strike-slip Exponential SE Mediterranean Reverse Purely characteristic * Cyprus Strike-slip Purely characteristic *Rate is calculated from characteristic earthquake model proposed by Youngs and Coppersmith (1985).

7 Geodinamica Acta 193 Figure 2. Seismic hazard curves obtained for the sites located in (a) Amman, (b) Azraq, (c) Aqaba and (d) Irbid. Figure 3. Contributions of the different seismic sources to the seismic hazard obtained from (a) Model 1, (b) Model 2, (c) Model 3 and (d) Model 4 at the site located in Amman.

8 194 N. Yılmaz and M.S. Yücemen The activity rate of earthquakes with magnitude, M w, can be calculated from the combination of Equations (11) and (13) in the following form; m M ¼ M 0 0 las ¼ M :5M (14) wþ16:05 Based on the study of Ambraseys (2006), an average slip rate of 4.5 mm/year is assigned to the faults that constitute the main Dead Sea fault system and extend in approximately south-north direction. This value is also consistent with the slip rate distribution given by Mahmoud, Reilinger, McClusky, Vernant, and Tealeb (2005). For the Gulf of Suez and Cyprus faults, the slip-rate distribution of Mahmoud et al. (2005) is applied. The seismic moment in the denominator of Equation (14) is calculated from M w scale. But, maximum magnitudes of the faults considered in this study are given in M s scale. Hanks and Kanamori (1979) stated that Equation 12 given in terms of M w is also valid for M s within the range of 5.0 M s 7.5. Except the Cyprus fault, maximum magnitudes of the faults for which slip rates are available are in this range. In addition, Ambraseys (2001) proposed the following equation for Eastern Mediterranean and Middle East Region to calculate the seismic moment from M s scale, for M s greater than 6.0: log M 0 ¼ 16:07 þ 1:5M s (15) The constants in Equation (15) are approximately the same with those given by Hanks and Kanamori (1979) in Equation (13). Accordingly, the maximum magnitudes of the faults are not converted from M s scale to M w scale in calculating the activity rates of maximum magnitude earthquakes through Equation (14). For the rest of the faults with m 1 6.5, whose slip rates are not available, the activity rates of maximum magnitude events are taken to be equal to the rates associated with characteristic earthquakes over the interval (m 1, m 1 0.5) in the characteristic earthquake model Figure 4. Seismic hazard maps obtained from (a) Model 1, (b) Model 2, (c) Model 3 and (d) Model 4 for PGA at 10% probability of exceedance in 50 years (475 years return period).

9 Geodinamica Acta 195 proposed by Youngs and Coppersmith (1985). For the faults with m 1 < 6.5, exponential magnitude distribution is used and m 0 is set equal to 4.0. The parameters of the faults in Model 4 are listed in Table 4. The earthquakes that are not assigned to any one of the specific faults are assumed to be potential seismogenic sources and the contribution of these events to seismic hazard is calculated using the spatially smoothed seismicity model of Frankel (1995) (it is to be noted that in Models 1 3, the background seismic activity is assumed to be uniformly distributed). In the spatially smoothed seismicity model, it is assumed that future earthquakes will occur in the vicinity of the locations of past earthquakes. In this model, earthquakes are spatially distributed to cells of a grid. Then, cumulative number of earthquakes, n i, with magnitude greater than minimum magnitude, M ref, in each cell, i, is counted and converted from cumulative to incremental values. These values are spatially smoothed by multiplying them by a Gaussian function having a correlation distance, c. For each cell, the spatially smoothed value, ñ i, is calculated using the following equation (Frankel, 1995): Figure 5. Maps showing the spatial variation of the difference between the PGA values obtained from Model 2 and Model 1 for a return period of (a) 475 years and (b) 2475 years and locations of area seismic sources (dashed black lines) and line sources (black lines). Figure 6. Maps showing the spatial variation of the difference between the PGA values obtained from Model 3 and Model 2 for a return period of (a) 475 years and (b) 2475 years and locations of line sources (black lines).

10 196 N. Yılmaz and M.S. Yücemen P n j e ðd ij=cþ 2 j ~n i ¼ P (16) e ðd ij=cþ 2 j where Δ ij is the distance between the ith and jth cells. The radius of the smoothing region is set equal to 3c. For each site, the values of ñ i are binned with respect to their distances from that site, so that N k denotes the total of ñ i values for cells within a certain distance increment of the site. The annual exceedance rate of ground motion level, u 0, at a specific site is determined from a sum over distance and magnitude according to the following equation (Frankel, 1995): kðu [ u 0 Þ¼ X X 10 ½logðN k=tþ bðm 1 M ref ÞŠ Pðu [ u 0 =D k ; M 1 Þ k l (17) where k is the index for the distance bin, l is the index for the magnitude bin and T is the temporal length of the earthquake catalogue used to determine N k (in years). P(u > u 0 /D k, M l ) is the probability that u at the site will exceed u 0 for an earthquake at a distance D k with magnitude M l and it is dependent on the attenuation relationship and the standard deviation of the ground motion for any specific distance and magnitude combination. In implementing the spatially smoothed seismicity model, the earthquakes with magnitudes between 4.0 and 6.5 in the catalogue including only main shocks are used. Also, the earthquakes related with the faults having m 1 < 6.5 are eliminated from the catalogue. The slope of the Gutenberg Richter magnitude-recurrence relationship, b, is computed as 0.71 based on this data-set. area sources coupled with exponential magnitude distribution (Model 1) resulted in the lowest annual exceedance probabilities for PGA values greater than 0.03 g at all sites. On the other hand, modelling the faults, except Cyprus, SE-Mediterranean 1, SE-Mediterranean 2 and SE-Mediterranean 3, as line sources with exponential magnitude distribution (Model 2) gave higher seismic hazard results compared to Model 1 as expected, since the seismic activity rates that are distributed over the areas in Model 1 are assigned to the fault lines in Model 2. The use of characteristic earthquake model proposed by Youngs and Coppersmith (1985) for major faults with m (Model 3) resulted in higher 2.3. Seismic hazard computations and discussion of results Seismic hazard analyses are carried out based on the models described in the previous section. In all analyses, earthquake occurrences are assumed to be independent events both in time and space and modelled as a homogeneous Poisson process. EZ-FRISK (Risk Engineering, 2005) software is used to calculate seismic hazard nucleating from the main seismic sources (line and area sources) and background seismic source with uniformly distributed seismicity. On the other hand, the computer program developed by USGS (Frankel et al., 1996) is used to quantify the seismic hazard based on the spatially smoothed seismicity model. For Model 4, the results of analyses obtained from these two computer programs are combined externally. Four cities that are located in different regions of Jordan, namely, Azraq, Amman, Irbid and Aqaba are considered. The sites corresponding to these cities are marked on Figure 1(b). Figure 2 shows seismic hazard curves obtained for PGA at these sites according to the four models explained in the previous section. It can be observed from this figure that modelling the faults as Figure 7. Maps showing the spatial variation of the difference between the PGA values obtained from Model 4 and Model 3 for a return period of (a) 475 years and (b) 2475 years and locations of line sources (black lines) and epicentres of earthquakes considered in the spatially smoothed seismicity model.

11 Geodinamica Acta 197 seismic hazard results compared to the exponentially distributed magnitude assumption. This is due to the increased rate in large magnitude earthquakes consistent with the characteristic earthquake model. Compared to Model 3, modelling all faults as line sources and applying purely characteristic earthquake (maximum magnitude) model for magnitude distribution of faults with m 1 6.5, combined with spatially smoothed seismicity model for earthquakes with magnitude, m < 6.5 (Model 4) resulted in lower exceedance probabilities up to certain PGA levels. For the PGA values greater than these levels, the opposite trend is observed. The contributions of the different seismic sources to the seismic hazard at these sites are evaluated for PGA. Because of space limitation, only the seismic source contribution graphs obtained for Amman are presented in Figure 3 and discussed here. The highest contributing seismic source to the seismic hazards at the site located in Amman is the Dead Sea-Jordan River in Models 1 3. The background seismic activity modelled as spatially smoothed seismicity contributes the most to the seismic hazard estimated based on Model 4. In addition to the analyses carried out for the four sites explained above, seismic hazard analyses are carried out to construct seismic hazard maps for Jordan in terms of PGA, SA (0.2 s) and SA (1.0 s) for return periods of 475, 1000 and 2475 years. The rectangular region bounded by N latitudes and E longitudes is divided into grids with spacing of in latitude and longitude. Seismic hazard computations are carried out at each grid point according to each one of the set of assumptions classified as Models 1 4, in order to display the spatial distributions of PGA, SA (0.2 s) and SA (1.0 s) values corresponding to 475, 1000 and 2475 years return periods. Because of space limitation, only the seismic hazard maps for a return period of 475 years in terms of PGA obtained using the four different models are presented in Figure 4. It should be mentioned that only the values given within the national boundaries of Jordan, drawn by thick black lines in these maps, are reliable. This is because some of the additional seismic sources that may contribute to the seismic hazard at the sites located outside of the national boundaries of Jordan are not taken into consideration in seismic hazard calculations. The differences among these four models, in terms of PGA, are calculated at each grid point in the region within the boundaries of Jordan through the following equation: Difference ð%þ ¼ PGA j PGA i 100 (18) PGA i where PGA i and PGA j are PGA values obtained from the ith and jth models, respectively. The difference in positive sign (+) indicates that the jth model gives higher PGA values than the ith model and that with negative sign ( ) represents the opposite trend. The spatial variation of these differences is shown in Figures 5 7. Figure 5 shows the spatial variation of the difference in PGA values obtained from Model 2 with respect to Model 1 for return periods of 475 and 2475 years [i.e. i = 1, j = 2 in Equation (18)]. It is observed from this figure that modelling seismic sources as line sources results in an increase in PGA values especially at the regions near to the western boundary of Jordan. The higher increases are concentrated at the regions along and near vicinity of line sources. On the other hand, compared with the line source model, modelling seismic sources having low annual activity rate (i.e. Sirhan, Wadi Karak, SE-Maan and East Gulf of Aqaba faults) as area sources causes an increase in PGA values at the regions near the boundaries of area sources. Figure 8. Logic tree formulation for the combination of different assumptions (CEM(Y&C): Characteristic Earthquake Model proposed by Youngs and Coppersmith (1985), PCEM: Purely Characteristic Earthquake Model. The values given in the parentheses are the subjective probabilities assigned to the corresponding assumptions.).

12 198 N. Yılmaz and M.S. Yücemen Figure 6 shows the spatial variation of the difference in PGA values obtained from Model 3 with respect to Model 2 for return periods of 475 and 2475 years [i.e. i =2, j = 3 in Equation (18)]. It is seen from this figure that characteristic earthquake model proposed by Youngs and Coppersmith (1985) gives higher PGA values compared with those obtained from the truncated exponential magnitude distribution. In Model 3, characteristic earthquake model is used for seismic sources with m Accordingly, the increase in PGA values is higher along Dead Sea-Jordan River, Wadi Araba, Gulf of Aqaba and Sirhan faults. The spatial variation of the difference in PGA values obtained from Model 4 with respect to Model 3 for return periods of 475 and 2475 years [i.e. i =3, j =4in Equation (18)] is shown in Figure 7. In Model 4, purely characteristic earthquake (maximum magnitude) model is used for the faults with m and their annual activity rates are calculated from their maximum magnitudes, annual slip rates and rupture areas. Additionally, the contribution of earthquakes with magnitude between 4.0 and 6.5 to the seismic hazard is computed by applying the spatially smoothed seismicity model. Model 4 gives lower PGA values around the Dead Sea-Jordan River Figure 9. Best estimate seismic hazard maps of Jordan for PGA (in g) corresponding to (a) 10% probability of exceedance in 50 years (475 years return period) and (b) 2% probability of exceedance in 50 years (2475 years return period). Figure 10. Best estimate seismic hazard maps of Jordan for SA at 0.2 s (in g) corresponding to (a) 10% probability of exceedance in 50 years (475 years return period) and (b) 2% probability of exceedance in 50 years (2475 years return period) and locations of faults.

13 Geodinamica Acta 199 fault. In Model 4, this fault is assumed to generate only earthquakes with magnitude equal to 7.5. Since the earthquakes with magnitudes between 4.0 and 6.5 are used as background seismic activity, events that have magnitudes between 6.5 and 7.5 and those considered in Model 3 for this fault are not included in Model 4. Also, compared with the activity rates assigned to characteristic magnitudes (i.e. magnitude range between 7.0 and 7.5) associated with this fault in Model 3, the rate calculated for its maximum magnitude earthquakes in Model 4 is lower. Similarly, Model 3 gives higher PGA values for a return period of 475 years around the Sirhan faults. Although the activity rates of characteristic events calculated from the characteristic earthquake model of Youngs and Coppersmith (1985) are lumped totally on maximum magnitude earthquakes in the purely characteristic earthquake model, this region is far away from the area where the epicentres of earthquakes cluster. On the other hand, the PGA values computed from Model 4 are higher than Model 3 around the Wadi Araba fault. For this fault, the activity rate of maximum magnitude earthquakes is greater than the rate of the characteristic earthquakes (i.e. magnitude range between 6.1 and 6.6) computed according to the characteristic earthquake model. The decrease in PGA values around the eastern boundaries of Jordan in Model 4 with respect to Model 3 is attributed to the use of the spatially smoothed seismicity model in Model 4, since in this region, the earthquake epicentres are extremely sparse. such high values resulting from extreme closeness (less than 10 km) to the faults are excluded, maximum PGA values for Jordan are about 0.3 and 0.5 g for return periods of 475 and 2475 years, respectively. If high values for SA are excluded in the same way, the maximum SA values at 0.2 s are 0.8 and 1.4 g and those at 1.0 s are 0.3 and 0.7 g for return periods of 475 and 2475 years, respectively Best Estimate seismic hazard maps for Jordan The results of the analyses carried out in the previous section are aggregated through the use of the logic tree formulation as presented in Figure 8. This figure shows the assumptions made in modelling of main faults and models used for magnitude distribution as well as the weights assigned to each one of these assumptions. The logic tree has four different branches which represent the four different models, named as Models 1 4as explained previously. By multiplying the seismic hazard results computed for each model by the corresponding subjective probability, given in Figure 8, and adding these values, a weighted average seismic hazard curve, called as the best estimate, is constructed at each grid point. The seismic hazard maps constructed based on these best estimate seismic hazard curves are called as the best estimate seismic hazard maps. Figures 9 11 show the best estimate seismic hazard maps for Jordan for PGA, SA (0.2 s) and SA (1.0 s) corresponding to return periods of 475 and 2475 years. It can be observed from Figures 9 11 that high PGA and SA values concentrate at the western boundary of Jordan, where the faults that form the main Dead Sea transform system are situated in this region. In order to visualise this, all of the faults are superimposed on the best estimate seismic hazard map for SA (0.2 s) for a return period of 2475 years as shown in Figure 10(b). If Figure 11. Best estimate seismic hazard maps of Jordan for SA at 1.0 s (in g) corresponding to (a) 10% probability of exceedance in 50 years (475 years return period) and (b) 2% probability of exceedance in 50 years (2475 years return period).

14 200 N. Yılmaz and M.S. Yücemen 3. Summary and conclusions In this study, sensitivity of seismic hazard results to alternative models is examined for Jordan by utilising four different combinations of models in terms of seismic sources (area or line sources) and magnitude distributions (exponential, characteristic earthquake or purely characteristic earthquake models). The influence of these combinations, which are referred to as Models 1 4, on seismic hazard results is investigated at four sites located in Azraq, Amman, Irbid and Aqaba. In addition, spatial sensitivity of seismic hazard results to these models is examined for PGA corresponding to return periods of 475 and 2475 years. The results obtained from different models are aggregated using the logic tree method. The best estimate seismic hazard maps for PGA and SA at 0.2 and 1.0 s corresponding to return periods of 475 and 2475 years are presented. Based on the results obtained from this study, the following conclusions can be stated: (1) A line (fault) source model with exponential magnitude distribution may give higher seismic hazard values than the corresponding area source model. Higher differences are concentrated at the regions along and near vicinity of line sources. But, in the case of low annual activity rate, modelling a seismic source as an area source rather than line source may result in higher seismic hazard values at the regions near the boundaries of area source. (2) Based on the same seismicity parameters (i.e. ν and β), the characteristic earthquake model proposed by Youngs and Coppersmith (1985) yields higher seismic hazard results than the classical truncated exponential distribution for the line (fault) source model. (3) The use of the purely characteristic earthquake model for faults combined with the spatially smoothed seismicity model for background seismic activity or characteristic earthquake model proposed by Youngs and Coppersmith (1985) may yield different seismic hazard results. Characteristic earthquake model proposed by Youngs and Coppersmith (1985) may give higher seismic hazard results in regions where the activity rates of maximum magnitude earthquakes of faults are lower than the rates assigned to characteristic events in the characteristic earthquake model. The same trend may be observed when a gap exists between the upper bound magnitude of background seismic activity and the maximum magnitude earthquake of faults. (4) In cases where the period of available earthquake catalogue is not sufficiently long to predict the frequency of maximum magnitude earthquake and paleoseismicity data is not available, the activity rates of the maximum magnitude earthquakes can be calculated using the seismic moment balancing concept requiring information on slip rates, rupture areas and maximum magnitudes. This study points out that the modelling of faults by area sources instead of line sources may underestimate seismic hazard especially in the near vicinity of faults. Besides, appropriate magnitude distribution consistent with characteristics of faults should be used, since the results are dependent on these assumptions. These observations justify the importance of basing the seismic hazard studies on faults with properly assessed parameters. In this study, the activity rates of maximum magnitude earthquakes of faults are calculated from the geometry of the faults (length and width), their slip rates and maximum magnitudes. In order to improve the results, investigations should be carried out to obtain the parameters of the faults (width, slip rate, mean recurrence interval of maximum magnitude earthquakes etc.) for each segment separately. In addition, instead of the Poisson model, the renewal model can be used to predict the probability of future earthquake occurrences, especially for the main active faults, like the Dead Sea-Jordan River. But this requires further investigations to obtain data on the additional parameters used in the renewal model. In addition, all ground motion parameters predicted in this study are based on rock site conditions. 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