The Dead Sea Transform (DST) fault system is an active tectonic boundary separating the African and Arabian plates. Extending from the Gulf of Aqaba to southern Turkey, a total length of approx. 1100 km, it dominates the seismicity of Israel, the Palestinian Authority, Lebanon, and Syria (Fig. 1a and b). The DST is a left-lateral strike-slip fault with a total offset of 105 km (Garfunkel, 2014). The average long-term slip rate is 4 to 5 mmyr-1 (Bartov et al., 1980). Geodetic slip rates along the Israeli part of the DST range from 3 to 5 mmyr-1 (Hamiel et al., 2016; Sadeh et al., 2012).

Splaying northwest from the DST is the Gilboa Fault and farther northwest towards the Mediterranean the Carmel Fault. Both comprise an active zone generalized as the Carmel Fault Zone (CFZ). The DST segments are capable of producing M 6 and M 7–7.5 events (Shamir et al., 2001; Hamiel et al., 2009), and the CFZ is capable of producing up to M 6.5 earthquakes (Grünthal et al., 2009).

The Israel Seismic Network (ISN), established in 1983 and upgraded over the years, consists of a mixture of different instrumental and operational stations, including short-period stations (14 in total), broadband stations (24 in total), and a large broadband array (part of the Comprehensive Nuclear Test Ban Treaty). The deployment of the ISN does not cover areas of increased seismic hazard, e.g., densely populated zones and soil sites, or areas designated by the Israel Seismic Code (IS413) as being suspected of extreme ground motion amplification, such as the Zevulun Valley (Fig. 1b). Currently, the seismic network is upgraded within the TRUAA project (an early warning system), with up to 69 strong motion accelerometers and 12 broadband seismometers added to ISN (Kurzon et al., 2020a). However, most of the instrumentation are placed along the DST and Carmel Fault to provide early warning and not in densely populated or industrialized areas where the seismic risk is tangible. Based on demographic projections (the Taub Center for Social Policy Study in Israel; for URL see data and resources) the population of Israel is expected to grow from 9.05 million in 2021 to 12.8 million in 2040, and combined with the increasing demand for housing and infrastructures, the seismic risk is expected to grow.

The Israel seismic catalog covers 36 years of measurements (1985–2021) and includes more than 23 300 events (Wetzler and Kurzon, 2016a), but only 15 of them are of M>5 (Figs. 1a and 2). Moving back in time, Israel's pre-instrumental catalog spans over 3000 years (Agnon, 2014; Zohar, 2019) with many catastrophic events, such as the 749 (M>7), 1202, (M>7.5), 1759 (M>7), and the 1837 (M>7) earthquakes, among others. In total, 14 M>7 events were cataloged by Ambraseys (2006) in the past two millennia. Recent geodetic studies (Hamiel et al., 2016; Sadeh et al., 2012) identified a slip deficit on specific segments of the DST, such as the Jordan Gorge Fault (JGF) and the Jordan Valley Fault (JVF), equivalent to an M>7 earthquake.

The geological structure of Israel exhibits strong spatial heterogeneity over short scales (Fig. 3a and b). Deep pull-apart basins (up to 10 km) filled with soft sediments (Vs∼600–800 ms-1) accompany the active DST system, from south to north: the Dead Sea Basin, Beit Shean Valley (BSV), the Sea of Galilee (SG), and the Hula Valley (Rosenthal et al., 2019). Along the CFZ, the Zevulun, Harod, and Jezreel valleys are formed. The vulnerability of Zevulun Valley is particularly crucial because of its dense population and the high concentration of strategic industrial infrastructure (Shani-Kadmiel et al., 2020).

The Israeli coastal plain, one of the most densely populated regions of the country (on average, 9000 people per square kilometer), is underlain by a westward-thickening sedimentary wedge (SW). In the Judea foothills area, east of the SW, a strong reflector exists between the sandstones and clays (Pleistocene Kurkar group, Vs∼300 ms-1) and the hard carbonate rocks (the Cretaceous Judea group, Vs∼2000 ms-1). In the coastal plain, the Kurkar group overlays the soft carbonates (Avedat group, Vs∼900 ms-1) and clastic sediments (the Bet Guvrin Formation, Vs∼800 ms-1) (refer to Fig. 3b). The depth of the Kurkar group base reflector is typically several tens of meters. Further to the west, a prominent reflector is a contact between the clays (Pliocene Yafo Formation, Vs∼600 ms-1) and top of the Judea group (Gvirtzman et al., 2008). These two reflectors, when shallower than 250 m, were used for the latest update of the Israel Building Code IS 413 (Israel Standards Institution, 2013) to delineate areas of a high potential of ground motion amplification (Gvitzman and Zaslavsky, 2009). This situation further complicates the process of developing an empirical GMM for Israel.

The impact of inter-basin sources along the DST on regional ground motions was examined by Shimony et al. (2021). This work clearly showed that regional ground motions are determined by source–path coupling effects in the strike-slip basins before waves propagate into the surrounding areas. Ground motions are determined by the location of the rupture nucleation, the near-rupture lithology, and the local structures. Shimony et al. (2021) focused on symmetric sub-shear ruptures and did not model rupture directivity or super-shear rupture velocities, both known to amplify regional ground motions.

Under specific conditions, super-shear ruptures and directivity occur on bi-material faults (Shi and Ben-Zion, 2006). Specifically, for subsonic propagation, symmetrically initiated bilateral rupture evolves after some propagation distance to a unilateral rupture in the positive direction, which is the direction of slip on the compliant side of the fault containing the softer layer. The magnitude of this effect increases with propagation velocity and the degree of material contrast across the fault. At super-shear propagation speeds, along a bi-material fault, the propagation direction is reversed.

The DST is a mature left-lateral fault with a 105 km offset, resulting in a strong material contrast between the hard layers on the Jordan side (east) and the soft layers on the Israeli side (west). Thus, the rupture can potentially propagate unilaterally southwards, discharging most of the seismic energy into Israel or northward in super-shear mode. The Jordan Gorge Fault and the Jordan Valley Fault (both active faults of the DST) specifically can produce an earthquake with rupture propagating in super-shear velocity since they border deep sedimentary basins, characterized by a large shear wave velocity contrast along the rupture propagation path. Thus, to quantify the seismic hazard ensuing from bi-material faults, it is necessary to study the two propagation directions: both sub-shear and super-shear velocities.

Ground motions in this research were modeled using the SW4v2 software (Petersson and Sjogreen, 2014, 2017a, b), developed for large-scale simulations of seismic wave propagation on parallel computers.

The velocity model covers the northern and central part of Israel (Fig. 4a) and includes the main DST trough and the following basins/structures, from south to north: Beit Shean Valley (BSV), Belvoir basalts (BB), Sea of Galilee (SG), Korazim structural saddle (K), Golan basalts (GB), and Hula Valley (HV). Along the CFZ, we model the major sedimentary basins of Jezreel Valley (JV) and Zevulun Valley (ZV). The coastal plain is underlain by the westward-thickening sedimentary wedge (SW). Geographically, the model extends from the city of Ashdod in the south (31.8∘ N, 34.6∘ E) to the Hula Valley in the north (33.23∘ N, 35.72∘ E) and from the Mediterranean Sea in the west to the Golan basalts in the east. Figure 4b–d illustrate the north–south and east–west cross-sections of the velocity profiles. The numerical domain spans 159 km in the north–south direction and 124 km in the east–west direction. It covers almost 80 % of the Israeli population and a significant part of the population of the Palestinian Authority.

Subsurface geometry and the characteristics of the DST trough were obtained from Rosenthal et al. (2019), with modifications for the Hula Valley, obtained from the density log of the Notera 3 borehole (Rybakov et al., 2003). The sedimentary wedge structure retrieved from Gvirtzman et al. (2008) and the Zevulun Valley structure was set using data from Gvirtzman et al. (2011). The basement depth along the model is based on Ben-Avraham et al. (2002). Five physical quantities describe the viscoelastic material model used in this research: shear wave velocity (Vs), pressure wave velocity (Vp), density (ρ), and seismic quality factors (Qs, Qp) for each point in the computational space. The missing parameters were assessed indirectly by using the correlation presented by Brocher (2008). The main units with their respective velocity, density, and quality factors are shown in Table 1.

Seismic sources were modeled using the distributed slip model (DSM) developed by Shani-Kadmiel et al. (2016). DSM is a kinematic model which describes the rupture patch as an elliptic surface with maximum slip at the nucleation point, decaying toward the edges as a pseudo-Gaussian function (Fig. S2 in the Supplement). Shani-Kadmiel et al. (2016) present validation of the DSM using macroseismic reports of the 1927 Jericho earthquake, showing good agreement between the reported and simulated ground motions. Rupture patch size and displacements were scaled following the relations presented in Wells and Coppersmith (1994). All sources were modeled as left-lateral, vertical strike slips (a dip of 90∘ and rake of 0∘), with a strike of 3∘ for sources on the DST and a strike of 325∘ for the CFZ. The moment rate time function of each point on the rupture patch was set to a GaussianInt pulse (Petersson and Sjogreen, 2017b) with a central frequency of f0=0.4 Hz and a maximum frequency of fmax=1 Hz.

The depth of the model was set to 28 km corresponding to the maximum seismogenic depth in this region (Wetzler and Kurzon, 2016a). We assigned a minimum shear wave velocity of 608 ms-1 for the uppermost sedimentary layer due to the computational limitations of our system. Grid spacing was set to 76 m in accordance with the minimum shear wave velocity and the maximum frequency of the source. We set the simulation time to 120 s to allow the slowest waves to propagate across the entire computational domain. The main parameters of the numerical setting are summarized in Table 2.

To examine the variability in ground motions from moderate M 6 and strong M 7 earthquakes, we concentrated on earthquake events nucleating on active segments of the DST system, with known slip deficit, and along the CFZ. We modeled a symmetric bilateral rupture on the Jordan Gorge Fault (JGF-B), Jericho Fault (JF), Carmel Fault Zone (CFZ), and the Shemona Fault (SF), a southward unilateral rupture on the JGF (JGF-U), and a super-shear rupture on the Jordan Valley Fault (JVF) (Fig. 3).

The hypocenter for the DST events was placed in the middle of the seismogenic depth: 11 and 13 km for the M 6 and M 7 models, respectively; for the M 6 CFZ, the value was set to 12 km. The rupture patch was designed to be contained in uniform lithology to prevent super-shear rupture speeds in the shallow parts of our model. Therefore, rupture speed for each scenario was set to 0.9 VS of the lithology surrounding the nucleation zone. The only exception was the JVF scenario for both M 6 and M 7, in which we modeled super-shear effects. For this scenario, the rupture nucleates within the hard rock with a sub-shear speed of 1800 ms-1 and evolves into a super-shear rupture when it ruptures the sediments with a shear wave velocity of <900 ms-1. The rupture velocity of each scenario corresponds to the local variations in the sediment's depth. Following the transition of the nucleation zone from the shallow crystalline basement in the south and west parts of the model to the thick Mesozoic and Cenozoic sediments in the north and the east, the rupture velocity decreases from 3195 ms-1 along the Shemona, Carmel, and Jericho faults to 1800 ms-1 along the JGF and JVF faults. As a reference, we simulated a simple two-layered reference model (Ref) on the JGF, with mechanical properties similar to the regional setting, following Aldersons et al. (2003). The scenarios are summarized in Table 3.

For each simulation, we attained a set of 129 synthetic ground motion records (three components each; north–south, east–west, and vertical) from the network deployed in the computational domain. Next, we calculated the PGV values for each scenario at each station as the maximum value over the three components. We decided to exclude some of the M 7 near-source records (stations 104, 105, and 106 for the JVF scenario and stations 122, 123, and 129 for the JGF-B, JGF-U, and Shemona scenarios) due to high strain values and possible nonlinear effects not compatible with the linearity assumption of our model. In total, our ground motion database consists of 645 and 633 synthetic records for M 6 and M 7 models, respectively. Figure 5 presents our results in terms of PGV as a function of distance. We used different markers for records from the sedimentary structures of the Zevulun Valley and the sedimentary wedge to differentiate them from the remaining data.

The next step was to formulate a parametric ground motion attenuation model (AM) for the two magnitudes based on our simulations. Such a model will provide an estimate for the median ground motions and their variability. The general parametric form of the AM for both M 6 and M 7 is based on the CB14 function and presented in Eq. (1): 1ln⁡Y=aln⁡RRUP2+b+cln⁡Vs,surfVs,ref+dZ2+e±σ, where Y is ground motion intensity measure (IM). Due to the bandwidth of our numerical models (0.1 to 1 Hz), we formulated the AM in terms of PGV. We used the closest distance to the fault rupture plane (RRUP as defined in CB14) as the initial explanatory variable. To improve the accuracy of the model, we incorporated two additional variables into the regressions: surface shear wave velocity at the site (VS,surf) and the depth to VS=2 kms-1 (Z2), which is the depth to the hard Mesozoic sediments (top Judea group) considered the primary reflector in the region. Model coefficients are denoted a, b, c, d, and e, and σ is the standard deviation. The VS,ref is the shear wave velocity corresponding to the Judea group in the computational domain, which in our model equals 2000 ms-1.

The process of minimizing the residuals as a function of each explanatory variable can be found in the Supplement (Fig. S3 in the Supplement). We used VS,surf instead of the more common VS30 as our grid resolution is 76 m, preventing us from accurately determining the time-averaged shear wave velocity in the top 30 m of each site in our model. The coefficients and the total standard deviation for each model are summarized in Table 4.

We then examined the simulated data and the contribution of each scenario to the AM variability. We calculated the within-event (δW) and between-event (δB) residuals (see Al Atik et al., 2010) for each magnitude and distance: 2δWi,j=ln⁡PGVi,jsim-ln⁡PGVim,3δBi=ln⁡PGVim-ln⁡PGVAM, where PGVi,jsim is the simulation value for event i and recording j, PGVim is the median for event i, and PGVAM is the AM median value. The total residual is the sum of the within- and between-event residuals.

The residuals are presented in Fig. 6: total (Fig. 6a and b), within-event (Fig. 6c and d), and between-events (Fig. 6e and f). The total residuals (Fig. 6a and b) show a large underprediction of the PGV from the JVF scenario (orange) on which we modeled a super-shear rupture, up to a ratio of 2.5 and 2 in the Zevulun Valley (orange triangles), for M 6 and M 7, respectively. However, the AM also exhibits overpredictions: the PGVs from the scenarios nucleated in the crystalline basement (SF, JF, and CFZ), with rupture speed=3195 ms-1, are overpredicted down to a ratio of more than -1 (in natural logarithm, ln, units).

Some within-event residuals exhibit distance dependency; for M 7, the JVF (super-shear) and JGF-U (directivity model) residuals increase with rupture distances greater than 20 km. The JVF residuals also demonstrate the same distance dependency for M 6; however, the effect is less prominent when compared to M 7.

The effect of the rupture directivity (JGF-U) is demonstrated by comparing the Zevulun Valley and the sedimentary wedge within-event residuals (Fig. 6c and d). While in a symmetric rupture (JGF-B) the seismic energy dissipates equally into the northern and southern parts of the model, in an asymmetric rupture (JGF-U), more energy propagates toward the south, resulting in stronger ground motions at the sedimentary wedge (Fig. 5). However, the ground motions are less intensive at the Zevulun Valley compared to the symmetric rupture. As a result, the within-event residuals for Zevulun Valley are higher for the JGF-B scenario compared to the JGF-U scenario, while for the sedimentary wedge, the opposite is true. Most clearly, the JVF between-event residuals are the highest for both M 6 and M 7 with a ratio of 1 (Fig. 6e and f).

We further studied the single station variation of ground motions and quantified the misfit between the simulated PGV and the AM PGV. We calculated the mean ground motion and its standard deviation at each station. The residuals for single station k were calculated as follows: 4δk=ln⁡PGVksim-ln⁡PGVkAM, where PGVksim and PGVkAM are the simulated and predicted mean PGV at station k, respectively. Figures 7 and 8 show the mean simulated and mean AM PGVs for M 6 and M 7, respectively. For each station, we also plotted the standard deviation using a scaled diameter circle.

Both figures show that simulated ground motion variability at a single station is large and not fully covered by the AM. For example, simulated ground motions at station 129 located on the Hula Valley exhibit a significant standard deviation. For M 6, it is the largest value (green triangle) of 0.17 ms-1 compared to 0.09 ms-1 (indigo) predicted by the AM, while for M 7, the largest standard deviation is 0.59 ms-1 (orange triangle) compared to 0.02 ms-1 (light green triangle) observed at station 127 located on the Zevulun Valley. As a result, there is a large discrepancy between the simulated and AM values at specific stations.

In general, as expected from normal log distribution, higher mean PGV values are accompanied by a larger standard deviation for both magnitudes. It is of significance for seismic hazard assessment as outlier ground motions at specific sites, mainly from M<7 earthquakes, could be a significant source of damage (Minson et al., 2020)

To examine the agreement between our simulations and an instrumental, global GMM, we calculated the total residuals between PGVs from our simulations and PGVs predicted by the CB14 model. We chose the CB14 model as it is planned to supersede the CB08 model used in the Israel Building Code (413). The CB14 PGVs were calculated for a strike-slip fault, for which we used the surface shear wave velocity as the Vs30 parameter and the basin response term Z2 as Z2.5. Figure 9 shows the total residuals for the AM and CB14 models as a function of distance (RRUP). For both magnitudes, the AM (mean and standard deviation) oscillates near the zero-model bias (dotted horizontal black line). However, it deviates when approaching the region containing rupture distances typical of the Zevulun Valley. The effect is more noticeable for M 7. Figure 9 also shows that the CB14 is less consistent and performs differently for each magnitude. While for M 6 the GMM mostly overpredicts (negative values) the simulated PGV (until reaching ZV and SW rupture distances zones), for M 7 it mostly underpredicts them (positive values), except for large distances, by up to a factor of 2 and above. In addition, the residuals calculated with respect to CB14 exhibit a significant standard deviation of the mean ground motion, with considerably larger variability for M 7.

It is important to note that, by averaging the PGVs, we subdue the performance of both models at individual stations/rupture distances; thus, we cannot analyze the residual's spatial variations at a specific location. However, it is sufficient to demonstrate that the global model deviates considerably from simulated ground motions.

Another important intensity measure is the significant duration (Ds 595), the time interval between 5 % to 95 % of the cumulative seismic energy (Arias Intensity) at a site. Figure 10 shows the simulated and empirical Ds 595 values as a function of rupture distance. The typical increase in the empirical model with distance is captured in the reference (laterally homogenous) model. However, for all other models, the significant duration remains nearly constant at rupture distances larger than 20 km. In addition, the empirical GMM mostly underpredicts the simulated values between 2 and 50 km for both magnitudes.

We postulate that this is caused by the complex geological setting of our model. The impact of geological complexity is reflected in Ds 595 values from near-source stations, Zevulun Valley (triangles), and the sedimentary wedge (rectangles). At near-source stations, the significant duration is large due to the effects of deep sedimentary structures along the DST, which also prolongs the path duration of the ground motions in other sites (Shimony et al., 2021), resulting in long significant duration with almost no path dependency. On the contrary at the Zevulun Valley and the SW, the energy accumulates faster than in other sites as the ground motions are amplified, reaching 95 % of the total energy over a shorter duration. Interestingly, the significant duration in Zevulun Valley is lower than in the sedimentary wedge. As we expect deep sedimentary structures to prolong shaking duration, it may sound counterintuitive. However, it is explained by the relative proximity of the Zevulun Valley to the rupture. Whereas in Zevulun Valley, most of the energy arrives as a pulse at the beginning of the record, the energy at the more distant sedimentary wedge accumulates more gradually and reaches its maximum almost at the end of the record, resulting in longer Ds 595 values. In general, there is no large deviation between the simulated significant duration for M 6 and M 7. However, the empirical model shows a longer duration for M 7. This resemblance in source duration is related to the DSM settings and more specifically to the source fundamental frequency, which in our study is the same for both magnitudes and is a subject for testing in future works.