PUBLICATIONS - BGUrgranot/Publications/Dembo_15.pdf · DEMBO ET AL. INTRAPLATE DEFORMATION INDUCED BY FAULTS 1 PUBLICATIONS Journal of Geophysical Research: Solid Earth RESEARCH ARTICLE

Intraplate rotational deformation induced by faultsNeta Dembo1,2, Yariv Hamiel2, and Roi Granot1

1Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel, 2GeologicalSurvey of Israel, Jerusalem, Israel

Abstract Vertical axis rotations provide important constraints on the tectonic history of plate boundaries.Geodetic measurements can be used to calculate interseismic rotations, whereas paleomagnetic remanencedirections provide constraints on the long-term rotations accumulated over geological timescales. Here wepresent a new mechanical modeling approach that links between intraplate deformational patterns of thesetimescales. We constructmechanical models of active faults at their locked state to simulate the presumed to beelastic interseismic deformation rate observed by GPS measurements. We then apply a slip to the faults abovethe locking depth to simulate the long-term deformation of the crust from which we derive the accumulatedrotations. We test this approach in northern Israel along the Dead Sea Fault and Carmel-Gilboa fault system.We use 12 years of interseismic GPS measurements to constrain a slip model of the major faults found in thisregion. Next, we compare the modeled rotations against long-term rotations determined based on newprimary magnetic remanence directions from 29 sites with known age. The distributional pattern of site meandeclinations is in general agreement with the vertical axis rotations predicted by the mechanical model, bothshowing anomalously high rotations near fault tips and bending points. Overall, the results from northernIsrael validate the effectiveness of our approach and indicate that rotations induced by motion along faultsmay act in parallel (or alone) to rigid block rotations. Finally, the new suggested method unravels importantinsights on the evolution (timing, magnitude, and style) of deformation along major faults.

1. Introduction

Geodetic measurements provide constraints on the interseismic (tens of years) deformation state of the crust,while rock magnetic remanence directions provide evidence for the long-term rotational deformation accumu-lated over geological timescales. Bridging between the two timescales may help to better understand complexpatterns of intraplate paleomagnetic rotations often observed in the vicinity of fault zones [e.g., Otofuji et al.,2010; Titus et al., 2011]. This link may also provide new constraints on the structural settings of plate boundariesand the evolution of plate kinematics. Here we constrain the interseismic intraplate rotations using GPSvelocities translated to the reference frame of the rigid plate. The long-term intraplate rotations arederived from remanence magnetization directions assuming a geocentric axial dipole hypothesis andcorrected for the paleorotation of the plate.

Previous tectonic works have used various techniques to study crustal deformation over different timescales.For example, global kinematic studies combined geodetic data with marine geophysical data to estimatecurrent global plate motions [DeMets et al., 1990, 2010]. Other studies examined the intraplate crustaldeformation by direct calculation of present-day rotation rates from geodetic observations, and later comparedthem to rotations derived from paleomagnetic data [e.g., Walcott, 1984; Mattei et al., 2004, 2007; Otofuji et al.,2010; Titus et al., 2011]. This approach is applicable for tectonically active regions with fully creeping faults orfaults that have completed a full seismic cycle during the period covered by GPS measurements. However,for most tectonic regions where faults have not completed their seismic cycle and are locked to a certain depth,this comparison is not suitable. In such cases, the surface deformation accumulated during the interseismicperiod illustrates only a portion of the total deformation of the crust, which is ultimately recorded by themagnetization of rocks surrounding the fault zones.

Previous paleomagnetic and structural studies [e.g., Reches and Eidelman, 1995; Kimura et al., 2004; Shelef andOskin, 2010] have examined the long-term deformation that accumulated within fault zones (i.e., few hundredsof meters from the main fault trace). These studies have found that vertical axis rotations increase toward thefaults, reflecting drag folding (normal or reverse drag) within the fault zone. On a larger scale, rigid blockrotations have been frequently suggested to explain the regional distribution of vertical axis rotations in

DEMBO ET AL. INTRAPLATE DEFORMATION INDUCED BY FAULTS 1

PUBLICATIONSJournal of Geophysical Research: Solid Earth

RESEARCH ARTICLE10.1002/2015JB012264

Key Points:• A modeling approach for linkingintraplate vertical axis rotations overdifferent timescales

• Long-term large vertical axis rotationsoccur near fault tips and bendingpoints

• Intraplate deformation is related tofault activity and cannot be explainedby block rotations

Supporting Information:• Texts S1 and S2 and Figures S1–S3

Correspondence to:N. Dembo,[email protected]

Citation:Dembo, N., Y. Hamiel, and R. Granot(2015), Intraplate rotational deformationinduced by faults, J. Geophys. Res. SolidEarth, 120, doi:10.1002/2015JB012264.

Received 8 JUN 2015Accepted 15 OCT 2015Accepted article online 20 OCT 2015

©2015. American Geophysical Union.All Rights Reserved.

various tectonic regions [e.g., Beck, 1976;McKenzie and Jackson, 1983; Ron et al., 1984; Nur et al., 1986; Carlsonet al., 2013]. These models interpreted the observed paleomagnetic vertical axis rotations as rotations of crus-tal blocks that are bounded by rotated faults while they remain internally undeformed. Although this inter-pretation may well be valid as a first-order approximation, accumulating paleomagnetic observationsillustrate that rotational deformation may not be homogenously distributed within the defined blocks, lead-ing to the creation of ever more complex and crudely constrained structural models [e.g., Nelson and Jones,1987; Hernandez-Moreno et al., 2014].

In this study we present a new mechanical modeling approach to quantitatively compare interseismicgeodetic rotations with long-term intraplate paleomagnetically-derived rotations. First, we present ournew approach for calculating the expected long-term vertical axis rotations from a geodetically-basedmechanical model. Next, we test our approach in northern Israel, where faulting has prevailed alongside volcanicactivity since the Neogene, hence, offers records that enable us to study the relationship between the instanta-neous interseismic deformation (GPS measurements) and the long-term deformation (magnetic remanencedirections). We then compare our new remanence directions against rotational deformation patternsobtained from the mechanical modeling. Finally, we discuss the implications of our approach to the studyof the long-term structural and kinematic evolution of plate boundaries.

2. Modeling Approach

We construct a 3-D elastic dislocation slip model to relate interseismic rotations with long-term permanentrotations. We constrain the fault parameters based on GPS measurements, seismic data, and structuralmapping of active faults. Solutions for surface deformation due to dislocations in elastic half-space are readilyavailable for both homogeneous [Okada, 1985, 1992] and layered media [e.g., Wang et al., 2003]. Weperformed simulations of the deformation using the numerical approach developed by Wang et al. [2003].Each rectangular dislocation plane represents a single fault segment, defined by nine parameters: slip rate,longitude, latitude, length, width, locking depth and the strike, dip and rake angles. We assume a uniform slipalong the entire segment plane and Poisson ratio of 0.25.

Our methodology consists of twomodeling steps. First, we simulate the deformation rate within the interseis-mic period by applying a slip to the dislocations only below a specified locking depth while the top part of thefaults is locked (Figure 1a). We compare the surface velocities generated by the interseismic model againstthe observed GPS surface velocities, with the aim of reaching the model that best fits the GPS velocity field.The root-mean-square (RMS) between the observed and modeled velocity vectors is calculated during eachsimulation, and the best fitting model is the one that provides the lowermost RMS value. The second model-ing step involves modifying the best fitting interseismic model to simulate the long-term deformation rate ofthe crust. For that we assume that the faults are entirely, and uniformly, slipping (i.e., the faults above thelocking depth are activated, Figure 1b) and that they are tectonically stable (i.e., steady state). Mean vertical axis

Figure 1. Schematic illustrations of (a) a locked fault used to construct the interseismic slip model and (b) a slip model of afault slipping up to the surface that mimics the long-term conditions.

Journal of Geophysical Research: Solid Earth 10.1002/2015JB012264


rotation rates (ωz) are then calculated from the output surface velocities produced by the long-term deformationmodel (Figure 2). These rotation rates are defined as [e.g., Jaeger, 1962; Turcotte and Schubert, 2002]

ωz ¼12

∂Uy

∂x" ∂Ux

∂y

! "; (1)

where Ux andUy are themodeled horizontal velocities in the north and east directions, respectively. Equation (1)resembles the rotation rates of an embedded rigid vertical cylinder located along the surface. The predictedrotation rates at each paleomagnetic site are multiplied by the age of the site to obtain the expectedaccumulated long-term rotations. Finally, these rotations are compared against the observed rotationsderived from a paleomagnetic investigation. To the extent that remanence magnetic directions reflect thetrue original orientation of the sites, mismatch between the expected and observed long-term vertical axisrotations testifies for temporal tectonic changes (e.g., fault geometry and slip rate).

Deformation of the upper crust can be generally described by elastic models, both interseismically [e.g.,Savage and Burford, 1973; Savage and Lisowski, 1995] and coseismically [e.g., Massonnet et al., 1993; Fialkoet al., 2001]. Previous elastic slip models that account for the full seismic cycle, as well as models that includethe response for the long-term inelastic deformation of the lithosphere, generally predict similar surfacedeformation pattern for a given structural and kinematic setting [e.g., Tse and Rice, 1986; Savage, 1990;Thatcher, 1993, 2009]. Nevertheless, elastic models can only serve as the first approximation for the surfacevelocity field and hence rotational pattern. To further assess the viability of our modeling approach, weconducted various synthetic finite element models given elastic and elasto-plastic behavior. Comparisonbetween the long-term rotation fields predicted by an elastic half-space model and by the finite elementmodels (for a given synthetic fault) result in similar rotation patterns of all models (Figure S1 in the supportinginformation). A detailed description of the modeling parameters is found in Text S1 in the supportinginformation. The rather minor discrepancies found between the predictions made by the models are theamount of rotations and the exact location of the transition between clockwise and counterclockwise rotations.Small discrepancy between the elastic (Figure S1b) and elasto-plastic finite element models (Figure S1c) wasfound very close to the fault trace, where the deviatoric stress exceeds the yield stress. During the entire seismic

Figure 2. Surface vertical axis rotations caused in response to motion along synthetic faults. The (a, c, and e) rotation patterns predicted by elastic interseismicmodels of faults locked to a depth of 15 km are compared against (b, d, and f) rotation patterns calculated from fault that slip up to the surface. The models wereconstructed for three types of faults: a vertical sinistral strike-slip fault (Figures 2a and 2b), a normal fault with a dip-slip sense of motion (Figures 2c and 2d), and acombined oblique and sinistral slip along a fault with changing strike direction (Figures 2e and 2f). All faults were arbitrary set to a length of 200 km and using a slip rateof 5mm/yr.



cycle most of the upper crust surrounding the faults zones behaves elastically, while over geological timescalesa transition from elastic to inelastic deformation occurs, explaining some of the similarity between elastic andelasto-plastic models within these areas [e.g., Nicol and Wallace, 2007; Burov, 2007; Turcotte and Schubert,2002]. Overall, we conclude that although it is a simplified model, an elastic half-space model that accountsfor the long-term, multiple seismic cycles deformation, can generally explain patterns of the permanentdeformation. Finally, our modeling results should be considered only at distances greater than tens to hundredsofmeters from the center of fault traces (i.e., outside the fault zone) to avoid the areawhere the crust behaves asan inelastic material even during the seismic cycle period.

2.1. Synthetic Modeling

We illustrate our modeling approach by simulating the vertical axis rotation rates induced by synthetic lockedfaults, expressing the interseismic deformation, and faults that slip up to the surface, expressing the long-term deformation of the crust (Figure 2). All examined faults are set with a 5mm/yr slip rate and extendeddownwards to a depth of 1000 km (in order to mimic infinite fault width). The results from sinistral(Figures 2a and 2b), normal (Figures 2c and 2d), and a combination of both sinistral and oblique sinistral-normal motions (Figures 2e and 2f) indicate that the magnitude of vertical axis rotations considerably variesalong and near faults. Illustrations of the rotation fields expected near right-lateral faults are found in the sup-porting information (Figure S2). We note that the magnitude of rotations shown by these models linearlyrelates to the chosen slip rate (e.g., the rotation values should be doubled for a 10mm/yr slip rate).

The expected style of rotational deformation is strongly affected by the extension of faults to the surface(Figure 2). The magnitude and pattern of interseismic rotation rates show a very different behaviorcompared to that of the long-term rotation rates. A direct comparison of long-term rotations againstthe interseismic geodetic-based rotation rates is therefore not appropriate when the faults are lockedduring the interseismic period.

Our synthetic elastic modeling suggests that for all types of faults anomalously high long-term rotation ratesare associated with fault tips (Figure 2). The models also suggest that different types of faults (e.g., normalversus strike slip) lead to different patterns of surface rotations. Rotations around normal faults are confinedpredominantly to the fault tips, whereas around strike-slip faults rotations are distributed along the entirefault. The actual magnitude of rotations depends on slip rate, the position relative to the fault and the exam-ined time span (i.e., duration of tectonic activity). Furthermore, any change in fault geometry or sense andrate of slip between one segment and another is reflected in the calculated rotation pattern (Figures 2eand 2f). This behavior is evident by the expected rotations that appear near the bending point at Figure 2f.As different strike and slip directions characterize the segments that meet at this bending point, the rotationssurrounding them blend, resulting in a complex rotational pattern. Following is an examination of theseinferences in northern Israel, where the structural architecture of the crust as well as the accumulated verticalaxis rotations are relatively well constrained.

3. Carmel-Gilboa Fault System as a Case Study

Northern Israel contains tectonically-active plate boundaries. Available GPS observations [Al Tarazi et al., 2011;Sadeh et al., 2012] and a broad spread of exposures of Neogene basalts provide an ideal setting for investigatingboth the geodetic and paleomagnetic vertical axis rotations. In the next sections we briefly describe thegeological and tectonic setting of this region and then we present new paleomagnetic results andcompare them against the long-term rotations predicted by our modified GPS-based mechanical model.

3.1. Tectonic Setting of Northern Israel

Tectonic activity and crustal deformation in northern Israel occur mainly on the N-S trending, sinistral DeadSea Fault (DSF), and the NW-SE trending Carmel-Gilboa fault system (CGFS), which variably host sinistral andtop-to-NE normal faulting (Figure 3). The DSF is more than 1000 km long sinistral transform fault that formsthe boundary between the Arabian Plate and the Sinai Subplate [e.g., Eyal et al., 1981; Garfunkel, 1981]. Theformation of this fault zone dates back to the Early Miocene, around 16–20Ma [e.g., Quennell, 1958; Garfunkel,1981]. The CGFS was active since the Miocene, probably coinciding to the formation of the DSF [Freund et al.,1970; Garfunkel, 1981], and divided the Sinai Subplate into two tectonic domains [Ben-Avraham and Ginzburg,1990; Hofstetter et al., 1996; Sadeh et al., 2012]. The CGFS is composed of numerous approximately NW-SE



trending faults that branch out of the DSF from the central part of the Jordan Valley to the northern tip ofMount Carmel and extend northwestward into the Mediterranean continental shelf (Figure 3) [e.g.,Garfunkel and Almagor, 1984; Ben-Gai and Ben-Avraham, 1995; Hofstetter et al., 1996]. The main faults of thissystem are the Carmel and Gilboa Faults. The Carmel Fault is an oblique sinistral-normal fault [e.g., Ben-Gaiand Ben-Avraham, 1995; Achmon and Ben-Avraham, 1997; Sadeh et al., 2012]. The Gilboa Fault is a normal faultdipping 60° to the NE [Hatzor and Reches, 1990]. The Carmel and Gilboa Faults are associated with isolateduplifted structures suggesting that they were kinematically isolated since their formation. While the last large(M> 6) earthquake along the Jordan Valley segment of the DSF occurred in 1033 Common Era [Ambraseyset al., 1994; Hamiel et al., 2009], no historic large event was reported along the CGFS. The last moderate earth-quake (M5.3) that occurred in the study area took place north of the Carmel Fault in 1984 [Hofstetter et al.,1996], but it did not rupture the surface, altogether indicating that postseismic deformation plays a minor rolein the present deformation state of the crust. A recent geodetic study [Sadeh et al., 2012] showed that the cur-rent aseismic slip rate along the DSF decreases from 4.9 ± 0.7mm/yr south of the CGFS to 3.8 ± 0.7mm/yrnorth of the junction with the CGFS, suggesting that slip is transferred from the DSF to the CGFS and thatan active triple junction is located at the intersection between them. Previous paleomagnetic studies [Ronet al., 1984; Heimann, 1990] revealed a heterogeneous pattern of deformation northwest of the triple junction.They explained the observed rotations by rigid body block rotations acting on several crustal domains(Figure 5a) [Ron et al., 1984; Nur et al., 1989].

3.2. Long-Term Rotations

To define the long-term rotation pattern along the CGFS and its intersection with the DSF, we have sampledall fresh basaltic flows exposed in this region. Among the 29 volcanic Neogenic (16.3 ± 0.7 to 4.5 ± 0.4Ma,Table 1) paleomagnetic sites that were sampled, 22 sites were isotopically dated (Table 1 and Figure S3).

Figure 3. Shaded relief map of northern Israel showing the distribution of Neogene basalts, locations of the major faultsfound in the study area, and paleomagnetic sites (purple dots).



From each site 6 to 10 Sun compass-oriented cores were collected and then trimmed into standard sizedcylindrical specimens.

Paleomagnetic analyses were performed at the Paleomagnetic Laboratory at Ben-GurionUniversity of the Negev.A total of 225 specimens were progressively demagnetized either thermally in a magnetically shielded calibratedoven (internal magnetic field <10nT and temperature control of <5°), in 15 steps between 100°C and 600°C, orwith an alternating field (AF) demagnetizer in peak fields of 10 to 140mT (at 5 to 10mT intervals). Magnetizationwas measured using the JR-6A spinner magnetometer (sensitivity of 2×10"6A/m).

Both demagnetization treatments resulted in similar magnetic remanence directions and were successful inisolating straight magnetization components trending toward the origin of the orthogonal projection(Figures 4a and 4b). A principal component analysis [Kirschvink, 1980] was used to identify the primarycharacteristic remanent component and site mean magnetization directions were calculated using Fisherstatistics [Fisher, 1953]. We have rejected from further consideration specimens that their maximum angleof deviation reached 5° about the best fitted line (24 from a total of 225 specimens, Table 1). The resultingα95 uncertainty angles do not exceed 9° in any of the sites but mostly range between 2° and 5°. Fully thermaldemagnetization of most samples was achieved between 550°C and 580°C indicating low-Ti Magnetite andMagnetite as the main magnetic carriers. Mean median destructive field of 35.2 ± 14.1mT (Figure 4d) impliesthat the magnetic carriers mostly range from single domain to pseudosingle domain grain sizes.

Table 1. Paleomagnetic Results From Northern Israel—Site Mean Values, Statistical Parameters, and Long-Term Rotationsa

Site Latitude (deg) Longitude (deg) N0/N D (deg) I (deg) α95 (deg) κ Age (Myr) Rotation (deg) Rotation Rate (10"6 °/yr)

1 32.28345 35.54282 5/7 185.2 "58.1 7.1 115.6 5.555 ± 0.015b 1.93 0.3482 32.28318 35.54225 5/8 181.4 "10.5 8.1 90.6 5.425 ± 0.016b "1.87 "0.3453 32.31948 35.54989 7/9 178.7 "40.6 2.9 447.9 5.65 ± 0.02b "4.62 "0.8184 32.32166 35.54930 5/9 179.2 "39.3 4.2 327.6 5.8 ± 0.7c "4.12 "0.7105 32.33417 35.53961 8/8 187.0 "40.9 5.1 119.2 5.9 ± 0.1c 3.66 0.6216 32.44998 35.46577 6/7 153.1 "14.2 5.5 147.9 5.45 ± 0.02b "30.20 "5.5417 32.45045 35.46447 7/7 139.6 "57.2 2.6 555.8 4.8 ± 0.4c "43.53 "9.0688 32.44984 35.46479 5/8 147.1 "24.5 4.6 280.7 5.439 ± 0.007b "36.07 "6.6319 32.45474 35.45239 6/8 163.6 "35.4 3.4 388.0 4.5 ± 0.4c "19.47 "4.32610 32.53600 35.35924 9/9 0.1 31.7 3.4 231.1 14.14 ± 0.03b "4.19 "0.29611 32.55235 35.34049 7/7 211.2 "44.7 2.3 710.6 3.5–5.3f 28.10 5.302< R< 8.02912 32.55931 35.33693 8/8 197.5 "53.7 5.2 113.0 16.3 ± 0.7c 12.95 0.79413 32.56602 35.31932 7/7 207.0 "58.7 2.6 535.4 5.095 ± 0.015b 23.90 4.69114 32.50893 35.52020 7/7 358.0 47.0 4.0 230.0 3.5–5.3f "5.00 "1.429< R<"0.94315 32.52089 35.49057 7/8 149.5 "46.2 6.5 87.2 3.5–17.5f "33.50 "9.571< R<"1.91416 32.52627 35.48623 9/9 173.7 "55.2 1.9 713.7 9–17.5f "9.30 "1.033< R<"0.53117 32.54533 35.45639 8/8 336.2 41.6 3.1 323.8 9–17.5f "27.50 "3.056< R<"1.57118 35.53955 32.58850 8/8 10.1 27.3 4.9 128.2 10.1 ± 0.07d 6.93 0.68619 32.58648 35.53883 7/7 195.9 "53.8 4.1 219.4 10.1 ± 0.07d 11.93 1.18120 32.59268 35.52204 8/8 180.7 "52.0 1.6 1164.4 5.1 ± 0.07d "2.48 "0.48721 32.60895 35.45717 8/8 177.7 "47.3 2.4 513.9 6.4 ± 0.3e "5.73 "0.89622 32.62195 35.39988 7/7 335.5 16.0 2.1 824.1 12 ± 1e "28.65 "2.38723 32.56105 35.18993 6/9 143.3 "23.0 6.1 123.4 8.1 ± 0.6e "40.46 "4.99524 32.57903 35.16858 6/9 127.1 "61.5 4.1 269.4 9.1 ± 0.3e "56.78 "6.23925 32.59566 35.15788 7/7 152.8 "12.5 2.5 565.9 5.5–17.5f "30.9 "5.618< R<"1.76626 32.61275 35.12547 7/7 313.7 32.3 8.9 47.3 9.7 ± 3.5c "50.00 "5.15527 32.61330 35.19431 7/7 176.7 "61.1 2.4 647.8 8.2 ± 0.2e "7.08 "0.86328 32.61270 35.19395 6/6 187.5 "51.8 3.8 310.4 8.2 ± 0.2e 3.72 0.45429 32.69539 35.12309 8/8 6.7 29.9 2.5 484.5 5.5"17.5f 3.10 0.177< R< 0.564

aN: total number of measured specimens. N0: specimens included in statistics. D and I: site mean declination and inclination. α95: 95% confidence envelope. κ:precision parameter. Rotations stand for the vertical axis rotations obtained by calculating the angular distance between declination of the site magnetizationdirection and the expected magnetization direction [Besse and Courtillot, 2002]. Rotation rates are obtained by dividing the rotation calculated for each site by theage of the site. Statistics were calculated using PmagPy software package available at http://magician.ucsd.edu/Software/PmagPy. Basalt ages inmillions of years with2σ uncertainties.

bAr-Ar ages from this work (dating was performed by the New Mexico Geochronological Research Laboratory at the New Mexico Institute of Mining andTechnology).

cK-Ar ages from Shaliv [1991].dAr-Ar ages from Rozenbaum et al. [2015].eK-Ar ages from Y. Harlevan (Geological survey of Israel, unpublished data, personal communications, 2014).fAge estimated according to the mapped geological unit of the site.



Long-term vertical axis rotations were obtained by calculating the angular distance between the declinations ofthe sitemeanmagnetization direction and the expectedmagnetization direction (Figures 4c and 5 and Table 1).The expected direction was evaluated separately for each site according to the age of the site and the locationof the appropriate virtual geomagnetic pole of the moving African Plate [Besse and Courtillot, 2002].

The results reveal that basalts of similar ages have experienced rotations of a wide range of magnitudes(up to ~70° apart) either in clockwise or counterclockwise directions (Figure 6 and Table 1). No simple correla-tion was found between the age of the sites and their magnitude or sense of rotations (Figure 6). Large rotations(>20°) are observedmostly near the tips of fault segments while sites located further away (>~10 km) from thefaults generally experience negligible to minor rotations (Figure 5). All four sites located near the eastern tip ofCarmel Fault (Sites 23–26, Figure 5) have experienced counterclockwise rotation ranging from 30.9° to 56.8°.Conversely, Sites 11–13, which are located near the western tip of the Gilboa Fault, have clockwise rotatedbetween 13° to 28.1°. Near the eastern tip of Gilboa Fault Sites 6–9 have counterclockwise rotated between19.5° to 43.5°. Sites that are situated within 8 km from the DSF experience minor rotation (<7°) with the excep-tion of Site 19, which experienced about 12° clockwise rotation (Figure 5 and Table 1). Interestingly, these areasthat display similar rotations are composed of volcanic bodies formed millions of years apart, indicating thatpaleosecular variations of the geomagnetic field could not have contributed significantly to the results. To con-clude, the vertical axis rotations shown by our results reveal a pronounced heterogeneous distribution of rota-tions that seems to be related to their position relative to the active faults.

3.3. Mechanical Modeling and Comparison to the Long-Term Observed Rotations

A valid model of crustal deformation in northern Israel should reconcile GPS interseismic velocities with theheterogeneous pattern of paleomagnetic directions, which reflect long-term rotations. The interseismicvelocity field used for the investigation of northern Israel was derived from eight permanent GPS stationsand 60 campaign stations that were surveyed during three campaigns conducted between 1996 and 2008[Sadeh et al., 2012]. We translated the velocities relative to Arabia Plate (using the Arabia-ITRF2005 rotationparameters of Altamimi et al. [2007]) so that they could be compared against the modeling results, whichare based on the relative motions between Sinai and Arabia Plates (Figure 7). Fault geometries were basedon mapping of active and potentially active faults [Bartov et al., 2002; Sneh and Weinberger, 2014]. Dip anglesof both Carmel and Gilboa Faults were set to 60° [Hatzor and Reches, 1990; Hofstetter et al., 1996]. We haveestimated the remaining unknown fault parameters by minimizing the residuals between the displacementfield obtained by the dislocation models and the geodetic observations.

Figure 4. Orthogonal projections and magnetization curves of representative (a) alternating field and (b) thermal demagnetizations of twin samples from Site 11.Empty squares and black dots refer to the vertical and horizontal planes, respectively. (c) Equal area projection showing Site 11 means characteristic magnetiza-tion directions and the expected reference direction for this site according to themoving African Plate [Besse and Courtillot, 2002]. Both directions are shownwith α95confidence ellipses. The difference between the two declinations gives the amount of vertical axis rotation for the site. (d) Histogram of median destructive field(MDF) determined from AF demagnetization.



Figure 5. Site mean vertical axis rotations of the sampled paleomagnetic sites (black arrows). Wedges denote error (α95) ofsite mean magnetization directions. (a) Domains of rigid blocks defined by Nur et al. [1989]. (b) Vertical axis rotationscalculated based on the best fitting interseismic model (Figure 6). (c) Long-term vertical axis rotation rates calculated basedon the modified slip model. Abbreviations: CF, Carmel Fault; GF, Gilboa Fault; and DSF, Dead Sea Fault.



Following the one-dimensional dislocation model of Sadeh et al. [2012], initial estimations of slip rates and lock-ing depths along the DSF were constrained to range between 3.8–4.9mm/yr and 14.1–15.9 km, respectively.Having limited geological observations of the CGFS, we examined locking depths of 5 to 15 km together withslip rates of up to 1.5mm/yr. Although the resulted magnitude of rotations are strongly affected by the chosenslip rates and locking depths, the shape of the resulted rotation field is virtually insensitive to the chosenparameters. A detailed description of the interseismic modeling parameters and results is found in Text S2.

The rotation field obtained from the best fitting interseismic model (Figure 5b) reveals the largest magnitudes ofcounterclockwise rotations along the DSF and diminishing rotations away from the fault. These interseismically-modeled rotations and the observed long-term paleomagnetic rotations are not consistent (Figure 5b). Whereasthe interseismic rotation rates along the DSF are of largemagnitudes (up to ~3×10"6 °/yr), remanence directionsof 5.4–5.9Ma basalts unravel significantly smaller rotation rates there (<|0.85×10"6| °/yr). Clearly, the long-termrotation field cannot be explained simply by comparison against the interseismic deformation and hence needs aspecial care.

We have introduced the interseismic slip rates for the DSF and the Carmel and Gilboa Faults above their lock-ing depths and calculated the expected long-term rotation rates from the resulted velocity field. Comparisonbetween the observed and modeled long-term rotations (Figure 5c) shows mutual patterns of rotations nearfault tips and unrotated zones further away from the faults. Counterclockwise rotations are observed at theeastern tips of both Gilboa and Carmel Faults and clockwise rotations are observed at the western tips ofthese faults. Large vertical axis rotations also appear at the bending points of the faults. Altogether, these

Figure 6. Amount and sense of paleomagnetic rotations as function of site age. Uncertainties for rotations are based on α95angels, while age uncertainties resemble the dating uncertainties (Table 1). Empty circles show sites where no analyticalage is available and the age is estimated according to their mapped geological unit. No simple correlation is found betweenthe amount of rotations and the ages of the sites.



rotation patterns seem to reflect the combined oblique sinistral-normal and sinistral sense of slip (e.g.,Figures 2e and 2f). Interestingly, sites that are located within the fault zones, up to hundreds of meters fromthe fault traces (Sites 9, 11, 12, and 25), and sites located further away display similar rotations, suggestingthat probably none of our sites were strongly affected by fault zone deformation (i.e., drag on faults).

4. Discussion

Long-term variations of vertical axis paleomagnetic rotations were generally explained either by drag foldingin close proximity to the faults, within the fault zones [e.g., Reches and Eidelman, 1995; Kimura et al., 2004;Shelef and Oskin, 2010] or by simple blockmodels of isolated rigid crustal blocks that rotate uniformly about theirbounding faults [e.g., McKenzie and Jackson, 1983, 1986; Ron et al., 1984; Nur et al., 1986, 1989; Luyendyk, 1991].However, our paleomagnetic observations and modeling results from northern Israel reveal a heterogeneousintraplate pattern of rotations that present a challenge to the rigidly rotating block model previously suggestedfor this region (Figure 5a) [Ron et al., 1984; Nur et al., 1989]. The zones of anomalous rotations that we predict and

Figure 7. A comparison between the horizontal velocities observed with GPS (dark green arrows) [Sadeh et al., 2012] andpredicted velocities computed by the best fitting interseismic model (orange arrows). Black lines denote surface fault tracesof the major faults used to construct the elastic models. Sites enclosed within the dashed blue polygon are used forestimating the best fitting slip rate and locking depth along the Gilboa and Carmel Faults.



observe can be explained as a response to nonrigid deformation that accumulates over geological timescalesaround faults. Near the fault tips the stress is enhanced leading to large inelastic strain rates resulting in zonesof relatively large rotations. Further away from the faults, the stress and inelastic strain rate are small; thus, minorrotations are observed.

We showed that an elastic fault model that accounts for the complete seismic deformation generally explains pat-terns of permanent deformation. Differences between model predictions and paleomagnetic observations mayindicate a change in the tectonic stability (i.e., fault geometry, slip rates, and slip direction). Under a stable tectonicregime, we expect that the rotation rates calculated by our elastic models will correspond to the observed long-term rotation rates. Changes in the tectonic activity may account for different magnitudes and locations of therotating regions. Variations of fault geometry such as propagation of fault tips will cause the location of significantrotations to shift. Changes in the sense or rate of slip will affect the sense and/or magnitude of rotations.

While considering the misfit between the observed and predicted rotations in northern Israel (Figure 8), wefind that Sites 25 and 26 show a relatively largemisfit (between 55° and 70°) compared to the expected rotations.

Figure 8. Misfit between the paleomagnetic vertical axis rotations found in northern Israel and long-term modeledrotations. The modeled rotations are computed by multiplication of the rotation rates predicted by the long-term defor-mation model by the age of the corresponding site. (a) Errors in the vertical axis mostly result from uncertainty in the agesof the sites. Empty circles show sites where no analytical age is available and the age is estimated according to theirmapped geological unit. Averages of sites younger than 6.5 Ma (blue) and of sites older than 8Ma (red) are shown insquares. (b) Histograms showing the distribution of misfit within the two age groups (blue for<6.5 Ma and red for>8Ma).The data are divided into bins of 10°.



Interestingly, these sites are located in close proximity to the eastern tip of the Carmel Fault suggesting that therelatively large deviations may arise due to model singularity found close to the fault tips, or alternatively, thesedeviations may result from spatial propagation of the fault that may have occurred during its evolution. We alsonote that some of the randommisfit between the prediction and observed rotations found throughout the datamay arise due to paleosecular variations of the geomagnetic field and/or unmodeled secondary faults that werenot accounted for. In spite of that, even just considering the Carmel and Gilboa faults, not only do we reproducethe GPS data but also we do an acceptable job of explaining the paleomagnetic observations. A more detailedmodeling study that considers both the secondary faults of the region and the temporal evolution of the faultswould have probably resulted in a better fit to the observed rotations. The current state of geological knowledgeof the region precludes the construction of such model.

Sites younger than 6.5Ma show a rather small misfit (9.5° ± 7.1° on average, Figure 8a). The misfit of all siteswithin this age group, excluding Site 7, is smaller than 20°. By contrast, a greater misfit is observed for sitesolder than 8Ma (24.1° ± 11.2° on average, Figure 8a), even when excluding outliers (Sites 25 and 26) from con-sideration. This variation in misfit behavior correlates well with a dramatic change in plate kinematics thattook place in the northern part of the African Plate during the Late Miocene (Messinian). During this periodof time (~8Ma), a shift in the location of the Sinai-Arabia Euler pole has occurred [Joffe and Garfunkel, 1987;Marco, 2007]. Based on structural analysis of the DSF, two distinct slip phases were inferred to occur duringthe Miocene [Garfunkel, 1981]: an early Miocene slip phase (total of 65–70 km of slip) and a later Pliocene-Pleistocene slip phase (35–40 km of slip). Most of the structures along the DSF were formed during the sec-ond phase of motion [Garfunkel, 1981]. The approximately NW normal faulting of the CGFS was also inferredto be active in two similar phases [Shaliv et al., 1991]. This change in plate motion may explain why the older(>8Ma) paleomagnetic sites display relatively large misfit compared to the expected rotations calculatedbased on the present-day interseismic deformation and structural setting.

Following our approach and assuming a stable tectonic regime, we can utilize magnetic vertical axis rotations toestimate the total offset along the slipping faults. Moreover, vertical axis rotations measured at different locationshaving different ages can be useful for constraining the evolution of fault geometries. Our approach can be parti-cularly valuable in tectonically active regionswith slow slip rates as it provides an alternative tool for estimating sliprates that are too slow to be inferred from GPS measurements alone or regions with insufficient GPS data.

Finally, our new modeling approach has implications for paleomagnetic investigations aiming to constrainthe behavior of the geomagnetic field or used as the base for tectonic studies. For instance, our syntheticmodeling of a strike-slip faulting with 5mm/yr slip rate result in two separate areas of rotations confinedto the regions near the tips of the fault (Figure 2b). Taking this slip rate as an example, heterogeneous distri-bution of rotation rates above 1°/Myr are expected to be found up to roughly 65 km from the fault tips. Thesize of the rotated areas would linearly increase with slip rate. Moreover, normal faults induce smaller rotationrates confined to smaller regions around the tips of the faults (Figure 2d). Paleomagnetic studies that aim atstudying the paleosecular variations of the geomagnetic field or plate-scale tectonic motions should considertheir sampling strategy in light of these new insights.

5. Summary and Conclusions

We have shown that a direct comparison of long-term paleomagnetically-derived rotations againstinterseismic geodetic-based rotations is not appropriate when the faults are locked during the interseismicperiod. We have presented a new approach for connecting the rotations over these different timescales.Our two-step elastic modeling procedure involves modeling faults at their locked state to simulate interseis-mic deformation constrained by GPS measurements and then applying a slip to the faults above the lockingdepth to simulate the long-term deformation of the crust.

The rotational patterns calculated by the mechanical modeling predict highly heterogeneous distribution ofaccumulated vertical axis rotations around major fault segments. We have tested our approach in northernIsrael and found that the model is generally consistent with intraplate paleomagnetically-derived rotations.The largest rotations appear near fault tips and bending points and decrease with distance from the faults.The results clearly point to an intraplate style of deformation that is related to fault activity, which is notaccounted for by rigid block models.



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AcknowledgmentsWe thank Will Levandowski, ananonymous reviewer and the associateeditor for thoughtful and constructivereviews. Data to support this article areavailable in Table 1. This study wassupported by the Ministry of NationalInfrastructures, Energy, and WaterResources, grant 213-17-024, and theIsrael Science Foundation (ISF), grants1801/14 (Y.H.) and 852/12 (R.G.).

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