The distribution of permanent deformation near strike-slip plate boundaries and the underlying controlling variables are commonly poorly understood. Here we examine the crustal deformation across the northern Dead Sea fault system based on paleomagnetic observations and mechanical modeling. We focus our investigation on the region of the Lebanese restraining bend where the fault system strikes obliquely to the general Sinai-Arabia plate motion. We construct a series of crustal elasto-plastic models in which kinematics is based on geodetic measurements, and the geometry of the plate boundary is constrained by gravity data. Both the observed regional vertical axis rotations and the model results display significant counterclockwise rotations (as much as ∼50°) confined to the northern Sinai microplate located west of the bend. On the other hand, relatively minor rotations (<∼10°) are displayed for the adjacent Arabian plate. Our results, validated by structural evidence, suggest that the northern Sinai microplate is mechanically weaker than the adjacent crust of the Arabian plate. This mechanical contrast, along with the oblique convergence and change of slip rate along the Dead Sea fault system, is required to simulate the observed rotations. We propose that the crustal mechanical contrast across plate boundaries is a key parameter responsible for the distribution pattern of permanent vertical axis rotations.
Asymmetric distribution of interseismic crustal deformation has been documented across major continental strike-slip plate boundaries, such as the San Andreas (California, USA), the North Anatolian (Turkey), the Great Sumatran (Indonesia), and the Altyn Tagh (Tibet) fault systems (e.g., Le Pichon et al., 2005; Fialko, 2006; Jolivet et al., 2008; Huang and Johnson, 2012). The asymmetric deformation has generally been interpreted in terms of an elastic-properties contrast across the plate boundary, however elastic deformation alone usually cannot explain the long-term crustal deformation (i.e., accumulated over several seismic cycles) patterns observed near plate boundaries (e.g., Nelson and Jones, 1987; Sonder et al., 1994). The mechanical properties of the crust may influence topography building, the formation of secondary faults, and seismic distribution. Although tectonically and geodynamically important, the relationship between the mechanical properties, the geometry of plate boundaries, plate motion, and the resultant permanent deformation accumulated near plate boundaries is still poorly resolved.
We analyzed the permanent vertical axis rotations observed across the northern Dead Sea fault system (DSFS) by constructing elasto-plastic models that take into account the plate kinematics and geometry as well as variations in the mechanical behavior across the plate boundary, i.e., Arabian plate versus Sinai microplate (Fig. 1). We demonstrate that a mechanically weaker northern Sinai microplate coupled with changes in the geometry of the plate boundary explains the observed asymmetrical pattern of permanent deformation.
THE NORTHERN DEAD SEA FAULT SYSTEM
The DSFS is a major continental strike-slip plate boundary that has accommodated left-lateral motion between the Sinai microplate and the Arabian plate since the Miocene (e.g., Garfunkel, 1981). Along Lebanon, the fault system bends ∼30° eastward, forming the Lebanese restraining bend (i.e., Yammouneh fault, Fig. 1). Geodetic studies reveal a northward decrease in the relative along-strike velocities from ∼4.1 mm/yr south of the bend (Hamiel et al., 2016) to ∼2.5 mm/yr north of the bend (Alchalbi et al., 2010; Fig. 1). The Roum fault branches westward from the main strand of the DSFS and marks a major discontinuity in the internal structure of Lebanon (Butler et al., 1998; Gomez et al., 2020). It evolves offshore of the Lebanese coast to a thrust fault system (Mount Lebanon thrust; Fig. 1), which, farther north, cuts back on land and connects with the Lebanese restraining bend (Elias et al., 2007; Carton et al., 2009).
ASYMMETRIC DEFORMATION NEAR THE LEBANESE RESTRAINING BEND
The northern Sinai microplate encompasses the stretched North African continental margin between what is now the stable Arabian plate in the east and the oceanic Herodotus Basin in the west (Granot, 2016). Extension of the margin during the Mesozoic extensively faulted northern Sinai (Dubertret, 1955; Fig. 1), which led to a mechanical contrast between the overall weaker northern Sinai microplate and the Arabian plate. Interseismic distributed deformation has been recorded west of the DSFS in the area limited by the Roum fault in the south, the Lebanese restraining bend in the east, and the Mount Lebanon thrust in the west and north (e.g., Gomez et al., 2020). In contrast, only minor deformation has been observed on the Arabian side of the plate boundary (e.g., Gomez et al., 2020). An asymmetric deformational pattern has also been shown by permanent counterclockwise (CCW) vertical-axis rotations of remanence magnetic directions (Ron, 1987; Henry et al., 2010; Fig. 1; see the Supplemental Material1) and river basins (Goren et al., 2015).
Previous attempts to explain how the distributed plate-boundary deformation is accommodated within the northern Sinai microplate (e.g., Freund and Tarling, 1979; Ron, 1987) have illustrated that the motion along the DSFS generated “bookshelf-type” rigid block rotations and differential motion between block-bounding shear faults. These approximately east-west–trending faults that cut through Lebanon (Fig. 1) are thought to be inherited Mesozoic structures currently active as dextral strike slip (Ghalayini et al., 2014). Alternatively, Henry et al. (2010) suggested that the crust domain located west of the restraining bend behaves as a single rigid block that rotates CCW in conjunction with sinistral slip motion along the DSFS. Either way, these kinematic models assume that deformation was accommodated on the edges of internally coherent and relatively large (102 to 104 km2) rotated blocks and thus predict voids and overlapping areas near the block edges. These, however, are not observed.
We computed a series of three-dimensional elasto-plastic models aimed at simulating the deformation surrounding the Lebanese restraining bend (Fig. 2). We assume elastic–perfectly plastic rheology and simulate the crustal deformation caused by the boundary conditions, geometry, and mechanical properties of the domains (see the Supplemental Material for more information regarding the model setup). The kinematic boundary conditions are constrained by geodetic data (Alchalbi et al., 2010; Hamiel et al., 2016). The boundary between the plates is defined by five vertical fault planes that freely slip in response to the imposed velocity boundary conditions. The western and eastern boundaries of the models are allowed to move freely only in the fault-tangential direction. At the bottom of the modeled blocks, vertical displacements are constrained to zero, whereas lateral motions are permitted.
The Poisson’s ratio of both plates is assumed to be constant and set to 0.25. We test a range of Young’s modulus values (35–75 GPa) for each plate and note that the effect of this variation on the predicted rotational deformation is negligible, and therefore focus our presented simulations on a constant Young’s modulus of 75 GPa. We also test a range of yield stresses, i.e., the transition from elastic to plastic deformation, for each plate (between 1 and 200 MPa) and examine both weak (relatively low yield stress) and strong (relatively high yield stress) crust. At stresses higher than the yield stress, the deformation is assumed to be perfectly plastic.
The vertical-axis rotation rates were derived by calculating the curl of the horizontal velocity field predicted for each model run. We calculated and compared the vertical and horizontal shear stresses in every element of our model and found that the vertical shear stresses are roughly an order of magnitude smaller. Therefore, we conclude that vertical-axis rotations induced by isostasy are an order of magnitude smaller compared to the rotations induced by plate motions, and thus they are neglected.
The modeling results reveal that when both plates share the same apparent crustal yield stress, nearly no rotational deformation is produced in either plate (Fig. 3). However, when a rheological contrast exists, deformation is distributed mostly within the weaker plate. Thus, to model the deformation observed west of the restraining bend, we must assume that the northern Sinai microplate is considerably weaker than the Arabian plate.
Models that encompass the rheological contrast predict varying degrees of CCW rotations throughout the northern Sinai microplate, having relatively high rotation rates concentrated near the Lebanese restraining bend, and gradually diminishing rates predicted westward toward the Mount Lebanon thrust belt (Fig. 3). Interestingly, the location of the predicted deformed region generally coincides with the observed major faults (i.e., Roum fault, Lebanese restraining bend, and Mount Lebanon thrust; Fig. 1) even though the Sinai microplate is modeled with homogeneous rock properties and the model is not constrained by the geometry or trace of these faults. Our models predict that the Arabian plate and parts of the Sinai microplate north and south of the bend should not have undergone significant rotational deformation.
COMPARISON BETWEEN MODELING RESULTS AND PALEOMAGNETIC OBSERVATIONS
To compare the modeling results against paleomagnetic observations, we calculate the predicted vertical-axis rotations for each paleomagnetic site (Fig. 4) by multiplying the modeled rotation rates by the age of the onset of rotation. We assume the rotational deformation in this region commenced during the Miocene along with the initiation of DSFS activity, which is estimated to have reached Lebanon by 17.4–10 Ma (e.g., Butler et al., 1998; Homberg et al., 2010; Nuriel et al., 2017). In view of that, Cretaceous sites formed prior to the formation of the plate boundary began to rotate when the motion along the northern DSFS commenced. However, for Miocene and younger sites, formed after the development of the Lebanese restraining bend, the rotation age corresponds to the age of the rocks.
Significant CCW rotations (as much as ∼50°; Figs. 3B–3D and 4) are confined to a domain located west of the bend, compared to relatively minor rotations (<∼10°) predicted for the adjacent Sinai and Arabian crust found east, north, and south of the bend. Despite small differences, the general rotational pattern predicted by our models is similar to that of the observations (Fig. 4). We conducted a misfit analysis in which we calculated the overall root mean square (RMS) for each model run at all paleomagnetic sites. The persistent RMS values (i.e., >∼18°) calculated for all models are probably due to the scatter of the remanence magnetic directions related to the paleosecular variations of the geomagnetic field, local structural complexities that were unaccounted for, and the uncertainty of the remanence direction of each site. The best fit (i.e., minimal RMS) is found for the model that has an apparent yield stress ratio of 2% between the Sinai microplate and Arabian plate (Fig. 3C).
DISCUSSION AND CONCLUSIONS
The detailed rotational mapping presented here for the crust surrounding the northern DSFS reveals a complex pattern of permanent deformation, which cannot be fully explained by the “bookshelf-type” kinematic rigid-block models (e.g., Freund and Tarling, 1979; Ron, 1987). Although our model does not include intraplate faults, it predicts that the area of extensive rotational deformation within the Sinai microplate is generally limited by major faults and is truncated by secondary faults (Figs. 3 and 4). Both the current continuum and previous discrete-block models illustrate how the bend of the DSFS in Lebanon gives rise to the regional deformation pattern. However, both the observations and modeling results indicate that the rotation field is best described by a spatially evolved deformation.
We suggest that the crust of the Sinai microplate west of the Lebanese restraining bend is mechanically weak relative to the adjacent Arabian crust, with a yield stress ratio between 0.01 and 0.05 between the northern Sinai microplate and Arabian plate. These ratios imply that the northern Sinai microplate has relatively small apparent yield stress values. Our model does not attempt to accurately quantify the complex crustal behavior. Instead, it is intended to simulate the general mechanical behavior of the plates relative to each other. We suggest that the preexisting intraplate, approximately east-west–striking secondary faults located west of the restraining bend (e.g., Dubertret, 1955) significantly weaken the overall strength of the Sinai crust and that a significant factor in the continuous deformation predicted by our models is, in fact, a smoothing of a discontinuous deformation field found across numerous small and intermediate faults. Additional evidence for the contrast in the mechanical behavior of the plates is shown by a contrast in the seismicity across the DSFS, revealing sparse earthquake data on the Arabian plate east of the restraining bend and a large number of seismic events distributed west of the bend (i.e., within Sinai microplate; Brax et al., 2019).
Our modeling results indicate that while the relatively strong Arabian plate moves northward along the Lebanese restraining bend, it pushes against the relatively weak Sinai microplate. The combined effect of the geometry of the plate boundary (i.e., restraining bend) and its kinematic behavior, together with the asymmetry in mechanical properties of the confining plates, results in prominent distributed vertical-axis rotations concentrated in the northern Sinai microplate west of the plate boundary. Additional support for the high strength of the Arabian plate comes from the northern boundary of the plate, where the Arabian indenter converges with the Anatolia microplate. There, a similar pattern of the asymmetric rotational field has been observed, whereby the relatively weak Anatolian crust has been considerably rotated while the Arabian crust remains almost undeformed (Piper et al., 2010). Our work suggests that the fragmentation of northern Africa into the Arabian plate and Sinai microplate during the Miocene might have occurred along, and possibly due to, the mechanical contrast that we infer. Finally, we suggest that such contrast in mechanical behavior across plate boundaries, e.g., across the San Andreas fault (Fulton et al., 2010), could explain the spatial distribution of surface deformation across other fault systems.
This study is supported by the Israeli Ministry of Science, Technology and Space, and by the Israeli Science Foundation grant 852/12. We thank Douwe van Hinsbergen, two anonymous reviewers, and editor Dennis Brown for their constructive and helpful reviews.