Displacement history of a limestone normal fault scarp, northern Israel, from cosmogenic 36C1

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. B3, PAGES , MARCH 10, 2001 Displacement history of a limestone normal fault scarp, northern Israel, from cosmogenic 36C1 Sara Gran Mitchell, 1'2 Ari Matmon, 3'4 Paul R. Bierman, 1 Yehouda Enzel 3 Marc Caffee, 5 and Donna Rizzo 6 Abstract. The abundance of cosmogenic 36C1, measured in 41 limestone samples from a 9 rn high bedrock fault scarp, allows us to construct the 14 kyr fault displacement history of the Nahef East normal fault, northern Israel (300 rn above sea level, N33 ø latitude). The Nahef East fault is one of a series of fault scarps located along the 700 rn high Zurim Escarpment, a major geomorphic feature. Samples at the top of the scarp have the highest nuclide concentrations (79 x 104 atoms (g rock)- ); samples at the base have the lowest (11 x 104 atoms (g rock)- ). Using chemical data from the samples, Nahef East fault scarp geometry, and surface and subsurface production rates for the 36Cl-producing reactions, we have constructed a numerical model that calculates 36C1 accumulation a scarp through time, given a series of unique displacement scenarios. The resulting model 36C1 concentrations are compared to those measured in the scarp samples. Faulting histories that result in a good match between measured and modeled 36C1 abundances show three distinct periods of fault activity during the past 14 kyr with over 6 vertical meters of motion occurring during a 3 kyr time period in the middle Holocene. Smaller amounts of displacement occurred before and after the period of most rapid motion. The episodic behavior of the Nahef East fault indicates that the average displacement rate of this fault system has varied through time. 1. Introduction which a Ca- and Cl-containing surface becomes exposed due to normal faulting [Noller et al., 1996; Zreda and Noller, Few methods can decipher the seismic history and dis- 1998]. In general, exposed rock surfaces receive a higher cosplacement rate of a fault if the only remaining evidence of mic ray dosing than buried surfaces. Similarly, rock with a seismic activity is a bedrock scarp [McCalpin, 1996]. Weathhigh concentration of a particular nuclide's target element, ering features on carbonate scarps may reflect relative ages of such as Ca for 36C1, will have a correspondingly high nuclide displacement events [Stewart, 1996], but such features often concentration (Appendix A). Using interpretive models, nucannot be used to resolve seismic history in detail sufficient to clide abundance can be interpreted as an age of exposure and distinguish paleoseismic events or calculate recurrence inter- thus can be used to date vertical motion on a fault scarp. vals. The horizontal component of fault motion is not detectable Cosmogenic dating of fault scarp surfaces is a viable and using cosmogenic nuclide analysis because it does not create potentially powerful new method for determining paleoseis- vertical offset. Therefore the following discussion of faulting mic histories of bedrock scarps [Noller et al., 1996; Zreda and and displacement assumes all motion is dip slip and thus rep- Noller, 1998]. The increasing precision of cosmogenic isotope resents minimum total displacement values. In addition, bemeasurements and continued refinement of 36C1 depth-pro- cause nuclide production rates are calculated using vertical duction models [Liu et al., 1994; Dep et al., 1994; Stone et al., shielding depths, the numerical model considers vertical fault 1998] and production rates [Zreda et al., 1991; Stone et al., motion only, regardless of the angle of displacement. There- 1996, Phillips et al., 1996] allow estimation of the rate at fore we use the term displacemento refer to the purely vertical component of fault motion. We have determined the displacement history of a carbon- 1Department of Geology, University of Vermont, Burlingtom ate normal fault scarp located in northern Israel, using in situ Vermont. produced cosmogenic 36C1. Here we describe the processes by 2Now at the Department of Earth apd Space Sciences, University of Washington, Seattle, Washington. which 36C1 accumulates beneath a dynamic surface and pre- 3Institute of Earth Sciences, Hebrew Univers;,ty, Jerusalem, Israel. sent in detail a numerical model we use to interpret data from 4Now at the Department of Geology, University of Vermont, Bur- the Nahef East fault scarp. We discuss how this model allows lington, Vermont. us to extract likely histories of fault motion and the implica- 5Center for Accelerator Mass Spectrometry, Lawrence Livermore tions of this temporal pattern to seismology in general and to National Laboratory, Livermore, California. the geomorphic evolution of the Galilee region in particular. ødepartment of Civil and Environmental Engineering, University of Vermont, Burlington, Vermont. Copyright 2001 by the American Geophysical Union. Paper number 2000JB Study Area The Nahef East fault scarp is located in the Beit-Hakerem Valley, Galilee region, northern Israel (Figure 1). This region /01/2000JB $09.00 has been undergoing N-S extension since the Miocene, al- 4247

2 4248 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING area Israel o o 30 km km deposits ;..._ Upper ' Sample Transect r Quaternary Cenomanian Senonian chalk -.. Cenornanian Lower O "TOP" (TOP250A, Samples TOP250B, -- Turonian dolom it e Cretaceous Lower TOP125) :-.::. Upper Cenomanian- Turonian limestone Normal Fault Figure 1. (a) Location, (b) topography and (c) geology of the Nahef East fault scarp. Location of TOP sample shown by open circle in Figure i c. Digital shaded relief image from Hall [ 1991 ]; geologic map after Geologic Survey of Israel [ 1965]. though there has been little historic seismicity [Freund, 1965, 1970; Gaffunkel et al., 1980; Ron et al., 1984; van Eck and Hofstetter, 1990]. The Nahef East fault scarp is one of several relatively short (2-6 km long), en echelon scarps that extend subparallel to the large (700 m high) Zurim Escarpment (Figure 1). Morphometric analysis of Zurim Escarpment slope profiles indicates that the escarpment began forming --6 Myr before present (B.P.) and reached approximately today's relief by 4 Myr B.P. [Mattnon et al., 1998]. The small bedrock scarps therefore represent a relatively recent renewal of the extensional tectonic and seismic activity that has affected this region for the past few million years. The Nahef East fault scarp can be traced for-5 km, and its vertical offset, which is the current vertical distance between the top and base of the scarp, varies from 1.5 to 11.1 m (Figure 2) [McCalpin, 1996]. At its western edge the fault is directly beneath the town of Nahef (population 4000). The footwall consists of variably dolomitized limestone of the Turonian to Cenomanian Sakhnin Formation, which we refer to as carbonate; the hanging wall consists of Senonian chalk from the Mount Scopus Group [Freund, 1965], which we refer to as chalk. On the basis of the stratigraphic thickness of these two units the total vertical throw on the Nahef East fault is between 50 and 300 m [Freund, 1959; Kafri, 1997]; however, only the last 10 m of displacement are represented by today's topography. Similar to other carbonate fault scarp systems, displacement on the Nahef East scarp is distributed in places across more than one fault plane [Stewart and Hancock, 1991]. Among all the small scarps located along the Zurim Escarpment, the Nahef East scarp is the least degraded. The condition of the Nahef East scarp made it the best choice for this study for two reasons: first, scarp erosion and degradation complicates the interpretation of cosmogenic isotope measurements. Second, the condition of the Nahef East scarp relative to the other nearby scarps indicates that it was exposed most recently. Therefore its paleoseismic history likely represents the most recent scarp-forming seismic activity in the vicinity. For in situ cosmogenic nuclides to provide paleoseismic information on a bedrock scarp, the scarp must be exposed by faulting rather than other processes, such as differential erosion of the hanging wall. Three observationsupport exposure resulting from faulting rather than stripping. First, the surface drainage system on the hanging wall is too poorly developed to remove much material; the sample transect is located near the local drainage divide, and what surface flow does origi-

3 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING I.._.12 E10 Sample Transect E ' 3. Methods 3.1. Field Methods ½ 8 In winter 1998, we measured the Nahef East fault geomeo try and collected samples. Using a Trimble 4400 real-time - 6.=o kinematic (RTK) global positioning system (GPS), we sur- $ 4 2 veyed several thousand topographic data points on both the hanging wall and footwall of the fault system. To measure west east 0 -- I surficial vertical displacement along the fault, we surveyed 30 I I I I I t I I 0 2OO cross sections, each m long and oriented perpendicular Horizontal distance from NW end of fault (m) to and across the scarp (Figure 3). From these cross sections Figure 2. Characteristics of the Nahef East fault scarp. B to B' we measured the vertical offset along the scarp (Figures 2 and corresponds to Figure 3. Vertical offset is the difference in eleva- 4). tion between the top and bottom of the scarp. The sample transect We chose a sample location near the northwest end was not taken from the scarp where the vertical offset was highest because in that location the scarp was slightly degraded. In the ( N, E, Israel Map Grid) of the scarp. At this location the scarp is planar and displays only minor modificaregion from 1000 m and eastward the fault divides into several tion by weathering (Figure 5). This weathering includes -4 different scarps; only the most distinct of these scarps was sur- cm deep rills as well as some minor pitting, but does not veyed. Only 2 km of scarp were surveyed because the town of include any major block failure or sheet exfoliation. In the Nahef covers the western portion of the fault. sample location the scarp is 9 vertical m high and dips 51ø (Figures 2 and 4). Where we sampled, the majority of disnate on the slopes above the scarp flows into the limestone karst surface. Second, near the sample transect a splay of the fault forms a sharp, 2 m high scarp that displaces two carbonate surfaces of equal composition and erodibility. Third, for the 9 m high scarp to have been created solely by erosion placement is accommodated on a single fault plane. Samples were taken from the scarp face at 30 cm downdip intervals using a rock drill (Table 1). The extracted cores were 2.54 cm in diameter and ranged from 4 to 10 cm long. At each 30 cm interval we took three to four cores, resulting in at least since the late Pleistocene (as mandated by the 36C1 data), a 150 g of sample. At two elevations on the scarp we took a chalk erosion rate of >75 m Myr - is required, unreasonably replicate set of samples -1 m west of the main sample transect high considering the absence of chalk deposits down gradient in the valley. (SG300R and SG600R). Two samples taken from the upper footwall surface (SGTOP and the three TOP replicates), were B A' A to A' is sample transect o o o- Nahef East Fault ß small dots aregps cross-section topo points o o o o- o o o- contour interval = 2 rn coordinates are Israel Map Grid easting (meters) Figure 3. Topography of the Nahef East fault scarp and the surrounding area (Israel Map Grid, contours in meters above mean sea level), constructed from several thousand GPS data points. A to A' are the ends of the scarp cross section sampled for 36C1 (Figure 4), B to B' are marked on the displacement versus distance diagram (Figure 2). Small dots are data points taken for 22 of the 30 transects used to measure scarp geometry (Figure 2). The remaining transects were measured to the east.

4 ß 4250 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING Scale J 20,...f m Z Vertical offset = 9 m Chalk (Senonian). Limestone (Turonian) Scale % chalk slab SG000 SG-090 SGTO P,,,,,,,,, Figure 4. (a) Scarp cross section at sampling location. Vertical offset is calculated by measuring the vertical distance between the top and bottom of the scarp (Figure 2). Section A to A' is shown on Figure 3. (b) Close up diagram of the Nahef East fault scarp, showing a small slab of chalk covering the base of the scarp. Samples with minus sign in their identification indicate they were taken from below the chalk. Scarp sample locations are marked by tick marks; sample SGTOP is marked with an open circle. used to estimate the long-term erosion rate of the limestone (Figures I and 4). We also measured the density of a sample from the hanging wall chalk for cosmic ray shielding calculations Analytical Methods Four different analyses of the carbonate samples are necessary for measuring 36C1 and parameterizing 36C1 production rates (Table 1). Chlorine extraction procedures were modified from Stone et al. [1996]. We processed samples in batches of eight, including two full procedural blanks in each batch. The 36C1/C1 ratios of the AgC1 precipitates from rock samples were measured using accelerator mass spectrometry (AMS) at Lawrence Livermore National Laboratory. The blanks have consistently low 36C1/C1 ratios (8.0 x 10-5 to 1.7 x 10-6) compared to the measured sample ratios (7.1 x 10-3 to 0.8 x 10-3) (Tables 1 and 2). Four full laboratory replicates (TOP250B, SG780D, SG540D, and SG480D) were processed by dissolving the same rock in two different batches in order to de- termine measurement precision (mean 36C1 concentrations are 74.1 _+ 6.8, 39.4 _+ 5.4, 27.1 _+ 2.4 and 25.5 _+ 2.8, x 104 atoms 36C1 (g rock) -, respectively) (Figure 6). SG-030 and SG-030b are two separate rock cores taken from the same position and processed separately (mean 36C1 concentration is 13.2 _+ 1.3 x 104 atoms 36C1 (g rock)' ). TOP125 is a smaller grain-size rock aliquot from the same sample that produced TOP250A and TOP250B. Total chloride in each sample was measured using mercury (H) thiocyanate absorbance spectroscopy [Florence and Farrar, 1971 ] with a Lachat Quik-Chem automated ion analyzer. The chloride concentrations of the samples were measured twice and calibrated with six internal standards via two different methods: hand-digitized peak area and the calibration internal to the Quik-Chem (also based on peak area). The blanks contained an average of 0.2 _+ 0.1 pg (g solution -1) chloride. Chloride measured in the sample solutions was cot- Figure 5. Photograph of the Nahef East fault scarp, looking to the northwest. The Zurim Escarpment is in the distance (top left) Note the presence of house directly above the scarp, and the light-colored, unweathered scarp recently exhumed from beneath the chalk slab. Geologist (in bottom left) is 1.6 m for scale.

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6 4252 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING Table 2. Isotope and Chemical Data From Procedural Blanks o o u o oo 0 0,--, '-' O. O Blank a 36C1/C1 ratio b Average C1 in x 10 '15 Blank, c lag (g solution) ' C1 Added as Carrier, a lag (g solution) ' B4a B4b B5a B5b B6a B6b B7a B7b B8a B8b B9a B9b B 10a B 10b a Number in blank identification indicates batch. ' Ratio error from AMS uncertainty only. c Some C1 was measured in blank solutions before carrier addition, although this was only a small percentage of the C1 added as carrier. a Carrier is a weak NaC1 solution, -2 g of carrier were added to each blank after aliquot removal but before AgC1 precipitation. rected for the amount of chloride contained the batch-spe- cific blanks. Major element chemistry (Ca and Mg) was measured on dissolved rock aliquots using a Perkin-Elmer Optima 3000 inductively-coupled plasma atomic emission spectrometer (ICPAE). Potassium was also measured and was below detection limits in every sample, < 0.1 lag (g solution) -. Ca and K were each measured using a single wavelength ( and nm, respectively). Mg was quantified using four different wavelengths ( , , , and nm); the reported Mg concentration for each sample is an average. Each sample was analyzed twice at two different concentrations; the high concentration samples were used to quantify Mg and K, and the low concentration samples were used to quantify Ca. Each procedural blank was analyzed at the high concentration, and each contained < 0.1% of the Ca and Mg measured in the rock samples. For analyses made on both concentrations, Ca and Mg values were corrected using separate sets of three internal standards. We used these ICPAE measurements of Ca and Mg and stoichiometric relationships to ensure the quality of our analyses. Wholerock yields from the ICPAE data averaged _+ 5.3%. Samples with a yield 5% greater or < 100% were reanalyzed. The normalized amounts of Ca and Mg from the second analysis were similar to the original analysis, even if the yield was significantly different. We infer that the error was in dilution or sample introduction and not in the ICPAE measurement of Ca and Mg. We then normalized the calculated Ca and Mg content in each sample to the actual measured mass of dissolved rock, considering carbonate stoichiometry. Normalized Ca and Mg contents of the three replicate samples agree well (average l c = 0.37 %). Trace elements (U, Th, B, Gd, Sm, and Li) were measured at Dartmouth College using ICP-masspectrometry (ICP- MS). Separate rock aliquots for each sample were dissolved using ultrapure HNO3 in acid-washed HDPE vials. A blank of

7 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING ' atoms 36CI (g rock) '1 Figure 6. Measured 36C1 abundance (104 atoms 36C1 (g rock) - ) as a function of depth in Nahef East limestone samples. Error bars are 20 AMS analytical error. the ultrapure acid and nanopure water was below detection limits for all analyzed elements. 4. Data 4.1. Fault Displacement Data Vertical displacement on the Nahef East fault scarp varies from 1.5 to 11.5 meters (Figure 2). The greatest amount of displacement has occurred near the western end of the fault, where the trace is lost beneath the town of Nahef. In most places the Nahef East fault separates the Cenomanian-Turo- nian carbonates from Senonian chalk; however, in places the fault bends and cuts through the Sakhnin Formation. Though the fault trace is usually a single surface, it sometimes becomes a fault array with smaller amounts of displacement distributed among several different planes Isotopic and Chemical Data Isotopic, major, and minor element data were collected from the 41 samples as well as five replicates (Table 1). The 36C1 concentrations are highest in samples collected from the upper carbonate surface (SGTOP, TOP250A, TOP250B, and TOP125), the result of accumulation during slow erosion. The 36C1 content decreases down the scarp, from 79 to 11 x 104 atoms (g rock) '. As expected, samples with a Ca content lower of similar altitude and latitude (Wombeyan Park Reserve, Australia, S34 ø, 620 m above mean sea level) have 36C1 con- centrations of 93 to 124 x 104 atoms (g rock) ', indicating the limestone at our site in Israel is eroding more quickly than the limestone in Australia [Stone et al., 1998]. In our samples, mass percent Ca ranges from 25 to 40 (mean is _ 4.0%) and mass percent Mg ranges from 11 to 0.3 (mean is 2.8 +_ 2.9%). Chloride content ranges from 5 to 35 tg g' (mean is _ 9.0 tg g' ). More than half of the samples have < 10 pg g- chloride. These chloride values are significantly less than those measured at the Wombeyan site, where several samples have > 100 tg g' C1 [Stonet al., 1998]. Chloride in the Nahef East samples is also less than the average C1 concentration (150 tg g' ) in carbonates worldwide [Fabryka-Martin, 1988]. Boron in the Nahef East fault scarp samples is low; samples average 0.7 +_ 0.8 pg g', and many are below ICP-MS detection limits. Sm, Gd, and Th are all < 0.2 tg g'. U ranges from 1.7 to 6.9 tg g', averaging 4.3 +_ 0.9 tg g-. Because of the low C1 content of most samples the 4øCa reactions (spallation and muon capture) dominate 36C1 production at and below the surface (Figure 7 and Appendix A). 5. Numerical Modeling of 3C1 Accumulation on an Active Fault Scarp Because of the complexity of subsurface 36C1 accumulation near an active normal fault, measured nuclide abundances cannot be resolved into a unique displacement history using the analytical expressions typically employed for surface exposure dating; rather, an iterative solution is required, one that considers not only the multiple, depth-dependent 36C1 production pathways (Appendix A) but also the complex sample 35C1(n,7)36CI spallationn _ ""'-' \ 40Ca(p.-,o036CI ' than their neighbors generally have a correspondingly low Ca spallation Total Production 36C1 content (Table 1 and Figure 6) In order to determine lateral consistency of 36C1 measurements, two sets of samples were taken 1 m apart but at the ' ' same elevation (300 and 300R; 600 and 600R). Each pair has Production Rate (atoms 36CI yr '1) consistent 36C1 values when Ca content is normalized (means Figure 7. c rates of 36C1 production at depth for the seven are 20 _+ 1 and 27 _+ 1 x 104 atoms 36C1 (g Ca) -, respectively). production pathways, assumin ]0 ppm C1 in pure c citc The two rock samples taken from the upper limestone surface (CaCO3). Spalladon of 4øCa is the dominant production pathway (SGTOP and the average of all TOP samples) agree well, in the upper 3 m; 4øCa muon capture dominates below 3 m, Stone containing 70 +_ 1 and 71 _+ 7 x 104 atoms 36C1 (g rock) -, re- et ½1. []998]. Actual production rates for individual samples vary spectively. In comparison, limestone samples from a surface accordin to chcmic composition. o Cl(n,U-fission) CI,,! 35C1(n,7)36Cl fast p, 35C1(n,7)36CI stopped - 1ooo_

8 4254 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING dosing history resulting from episodic fault motion. We have m Myr' ), the equations in Appendix A, and each sample's inibuilt a numerical model to automate these calculations and tial vertical distance beneath the upper footwall surface. Such run it using MATLAB 5.6 software. calculations assume that before faulting begins, the samples The model incorporates the seven different depth/produc- are brought toward the surface beneath a steadily eroding, tion rate relationships germane to the production of 36C1 in rock (Appendix A). It is parameterized using measured sample chemistry and scarp geometry of the Nahef East fault and allows the user to vary the rate of footwall erosion and the timing and magnitude of fault displacement. The model can horizontal rock-air interface (i.e., there is no scarp forming yet). The numerical model also contains a simple geometric correction for sample thickness (thickness of cm) and scales production rates to the altitude and latitude of the sample locality (N33 ø, 300 m) [Lal, 1988]. be downloaded from the ftp folder at all files included in the folder are required for the model to 5.2. Accumulation of 3 C1 on Tilted Surfaces operate correctly. These files include data sets and subfunctions as well as a short description of the model structure Steady State Erosion Rate of Upper Limestone Surface and Prefaulting Nuclide Abundance In order to model accurately the accumulation of 36C1 during faulting we need to estimate initial 36C1 abundance as a function of depth prior to displacement. This abundance is controlled by the rate at which the footwall upper surface erodes, an estimate of which can be made by collecting and analyzing surface samples (SGTOP and TOP replicates 250A, 250B, and 125) away from the scarp. The 3 C1 inventory on m Myr 'l 29 m Myr 'l m Myr -o approximate 36CI of top o 600- samples 800 Nuclide production rates on tilted surfaces are less than production rates on horizontal surfaces. A tilted surface receives cosmic rays directly from only a fraction of the sky. For example, a vertical cliff will receive direct cosmic rays from one half of the hemisphere; the production rate of cosmogenic nuclides from direct dosing on a vertical surface is therefore one half that of a horizontal surface. The neutron flux has an angular intensity that varies owing to atmospheric thickness, and the muon flux varies angularly both in intensity and energy spectrum [Stone et al., 1998] (Appendix A). A proportion of the cosmic ray flux will strike a tilted surface directly, while cosmic rays from the remaining portion of the sky can travel through the back side, meaning through the footwall, of a normal fault scarp, before reacting with rock on the scarp surface. The fraction of cosmic rays interacting and below a steadily eroding surface is in equilibrium with 36C1 production and nuclide loss by erosion and radio decay (Figure 8) [Dockhorn et al., 1991; Bierman et al., 1995; Stone et al., 1998]. The 3 C1 content measured in both rock samples directly with a tilted surface is a function of the surface angle and including the three replicates can be used to estimate the and the angle-flux relationships for each of the different erosion rate for the upper limestone surface. The average ero- cosmic ray particles [Stone et al., 1998; Dunne et al., 1999]. sion rate for these two samples is 29 _+ 3 m Myr - (Appendix The Nahef East fault scarp dips 51 ø at the sample location A). (Figure 4). On the basis of the relationship between the sur- We solve for the initial, prefaulting 3 C1 concentrations in face angle and corresponding neutron flux, 88.5% of neutrons each sample using the calculated steady state erosion rate (29 travel through the chalk or strike the carbonate stirface directly, and the remaining 11.5% travel through the footwall before reaching the surface [Stone et al., 1998; Dunne et al., 1999]. The tilt scaling for muons is more complicated than the scaling for neutrons because muons hitting Earth's surface vary in both abundance and energy depending on the incidence angle. More muons strike Earth's surface from the zenith, but muons arriving from the horizon have higher ener- gies and can therefore travel further underground before stopping [Stone et al., 1998; Crookes and Rastin, 1973; Bilokon et al., 1989]. Geometric calculations were made to correct for 36C1 production rates from muons on tilted surfaces using the muon flux information found in Stone et al. [1998]. These calculations result in -90.5% of muons traveling through the hanging wall to reach the scarp surface, while only -9.5% must first travel through the footwall. The MATLAB 5.6 model incorporates these surface angle/flux factors as it numerically integrates production rates during faulting IO0 36CI (104 atoms (g rock) '1) Figure 8. Concentrations of 36C1 in the uppermost samples as they are exhumed at different erosion rates. An erosion rate of 2.9 cm kyr - results in a 36C1 concentration of 70.2 x 104 atoms (g rock) ' in SGTOP and a 36C1 concentration of 71.3 x 104 atoms (g rock) ' (the average 36C1 concentration) in TOP. Samples were taken from an elevation of 300 m, 33 ø latitude. All seven production pathways (Figure 7) were used to calculate the erosion rate Accumulation of CI During Faulting The 36C1 accumulation model accounts for cosmic rays that travel through both the hanging wall and footwall and therefore through a thickness of rock that varies through time. This thickness depends on the direction from which the cosmic rays reach the fault scarp surface and create 36C1. During faulting, even as samples are subaerially exposed, they remain shielded with respect to the footwall; this footwall shielding depth is the vertical distance between the sample and the upper footwall surface. For the purpose of calculating production rates, the shielding depth is always multiplied by the den-

9 _ Depth: I 200 cm cm Depthc -I... Depth C = 82 cm I Depth C = 0cm Depth C = 0cm 3OO MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING cm 164 cm f Displacement 20% 10 Erosion 0 -! kyr B.P. Depth L = 173 cm Figure 9. Sample shielding depth throughoutime with respect to each fault block for a hypothetical, 12 kyr, two-event exposure history. In this situation, erosion rate is 29 m Myr -.(a) At!2 kyr B.P., sample depth is 200 cm with respecto both chalk and limestone. (b) At 9 kyr B.P., 9 cm of both chalk and limestone have eroded, resulting in a sample depth of 191 cm. (c) At 6 kyr B.P., 9 more cm of erosion, faulting event 1 : 100 cm vertical displacement. Sample depth is now 182 cm for limestone, 82 cm for chalk. (d) At 3 kyr B.P., 9 more cm erosion, faulting event 2: 200 cm vertical displacement. Sample depth is 173 cm for limestone, 0 cm for chalk (fully exposed). (e) "Today," 9 cm erosion, sample depth 164 cm for limestone, 0 cm for chalk. (f) Centimeters of exhumation resulting from erosion and displacement through time. Only erosion affects sample depth for limestone; both erosion and displacement affect sample depth for chalk. The model does not take into account a slab of chalk ir- regularly covering the lowest meter or two of the scarp (Figures 4 and 5). Because the extent of the slab is highly irregular and, where it exists, it is thin (0 to 30 cm), it will add noise to the data but does not change the overall model results; its presence slightly reduces 36C1 concentrations in our lowest... : ::."., ½ ½ 5 4( :5s½.;. ½ 4,?;,g'"'½< ½ 1 D e pt h = three samples. Also, because the sampled scarp face is planar and appears quite fresh, we assume that the scarp face has not :.:.:.x...:+$:..:... :: eroded enough to affect significantly the model results. We did not take samples from the uppermost 0.8 vertical m of the scarp face where pitting and rounding of the scarp suggested significant erosion MATLAB Model Mechanics Given a faulting scenario (a time/displacement history), the MATLAB 5.6 model integrates 36C1 production and decay for each sample, accounting for changing irradiation geometry (depth below the surface) and thus changing rates of 36C1 production over time. Initial abundance of 36C1 in each sample is set by the steady state erosion rate. Then, using the chemical composition of each sample, the model calculates the number of 36C1 atoms produced and losto decay in 10 year time steps (Figure 10). During each time step, the displacement scenario and erosion rate are used together to calculate hanging wall and footwall shielding depth values and thus 36C1 production rates for each sample. The model then moves on to the next timestep, and the process is repeated. Initial model runs indicated that displacement did not start before 20 kyr B.P.; therefore each individual model run included 2000 ten year time steps. Because of the complex interrelationships between isotope production and the timing and magnitude of changing shield- Sample-dependent variables Depth-dependent variables INITIAL 36CI ABUNDANCE sample Ca, chemistry CI, ' ON erosio rate U, Th, displacement B, Gd, Sm 36CI PRODUCTI - history (7 pathways) : 36Cl ABUNDANCE I timestep - 10yr c ABUNDANCES CALCULATED FOR ALL SAMPLES AT EACH TIMESTEP sity of the rock (2.75 g cm '3) to create a density-normalized shielding depth (g cm'2). Figure 10. Conceptual model of MATLAB 5.6 program. Start- The shielding depth with respecto the hanging wall, also density-normalized, is the vertical distance between the individual sample and the horizontal chalk surface. The hanging wall shielding depth is therefore dependent on both the rate of fault displacement and the rate of chalk erosion, which we assume, in the absence of other data, to be the same as the carbonate erosion rate (29 m Myr- ; Figure 9). Once the hanging wall has moved down past an individual point on the scarp, the hanging wall shielding depth there becomes zero. 36CI decay ing with initial abundances, the model uses the chemical characteristics of each sample (sample-dependent variables) and the erosion rate and displacement history of the scarp as a whole (depth-dependent variables) to calculate 36C1 production rates for each sample in each time step. The model calculates the number of 36C1 atoms produced in each sample and then the number of 36C1 atoms that decay during thatime step. Then, the model moves forward a time step, incorporates any changes in depth for each sample, and repeats the process until all the time steps have passed.

10 4256 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING 000 a Displacement History Nuclide Abundances Residuals 0 qo q, ' 200 &' ' : b , r 200- o D ca I I I I I d crøeeø ' i i Time (kyr B.P.) 0 i I i i i CI (104 at. (g rock) -1) Percent Deviance Figure 11. Three different displacement scenarios with resulting model 36C1 values and residuals (percent difference between measured and model 36C1 values). Model 36C1 are open circles; measured 36C1 dat are small dots. (a) Steady creep from 9 to 1 kyr B.P. results in model 36C1 values that are too low for much of the scarp. (b) A single rupture event occurring at 6.5 kyr B.P. results in model 36C1 values that are too low at the top of the scarp and too high at the base. (c) The best fit scenario from the six-event series (with maximum displacement in the mid-holocene) results in a reasonable fit down the entire profile. ing depths for rock on the scarp face, there are many time/ displacement scenarios consistent with measured 36C1 abun- these samples was never affected by faulting) and three labodances. Thus, rather than trying to figure out when individual earthquakes occurred, our modeling was directed toward finding a robus temporal pattern of displacement. We considratory replicates (SG780D, SG540D, and SG480D). These replicates never closely matched in scenarios that fit most other points quite well. ered both steady creep and episodic displacement. Starting creep at different times over the past 20 kyr, we modeled 5.5. Model Results scarp formation over time frames ranging from 4 to 20 kyr Evaluating model outputs suggests that the Nahef East B.P. We also generated six distinct series of episodic disfault scarp was formed not by steady creep but by at least placement scenarios, differing in the number of events n used three and probably more earthquakes. Displacement scenarios to generate the observed displacement (n = 1-6). Within each resulting from small numbers of events (n < 3) or from steady series, event sizes are the same and the minimum temporal creep generate model 36C1 values that are clearly less spacing between events was 500 years. tent with measured data than model results from the best fit- For both of these analyses we calculated a "goodness of ting six-event scenario (Figure' 11). None of the one- or twofit" parameter F for each scenario by summing the absolute difference between model and measured 36C1 values: event scenarios produced a 36C1 profile resulting able F value. For the three-event series, 6 of 15 scenarios pro- F =,136 Cl Measured-36 C1Model[. (1) We have designated a 95% confidence level for the entire profile by summing the 2o error limits for the samples. Therefore all displacement scenarios resulting in an F less than the calculated 95% confidence limit are considered viable. Several samples were excluded from this analysis, including the samples taken from the upper limestone surface (the 36C1 in consis- in an accept- duced model 36C1 profiles consistent with measured abun- dances within the error limit; however, all three-event scenar- ios that have acceptable F values generate 36C1 concentrations that are systematically too low at the top of the scarp profile. Of the 20 steady creep scenarios, one had an acceptable F value (Figure 11). The model 36C1 values generated from this scenario (displacement occurring constantly from 9 to I kyr

11 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING 4257 Normalized F... 95% confidence 1000 E 800 E o Events Events 6 Events ß 'o 400 E I I Number of Events (.D Time (kyr B.P.) Figure 14. Cumulative displacement versus time for best fit histories of four, five, and six events. All three of these histories show most displacement occurs in a relatively short period of time, centered around 5 kyr BP. Lesser amounts of displacement occur in the time periods and kyr B.P. Figure 12. Lowest residual (F) value for each displacement history series. For comparison, F values have been normalized to the lowest residual. Higher numbers of events result in better F values; however, the change in F decreases with an increasing num- ber of events Events n=157 5 Events n = Events n = 220 n n_bbbon... RO 100- n 50- n,,,,,,,, Time (kyr B.P.) Figure 13. Distribution of displacement events occurring through time for the four-, five-, and six-event series. All displacement scenarios shown have an acceptable F value. The number of acceptable scenarios n for each series is included in each histogram. The height of each bar corresponds to the number of scenarios containing an event happening in each time interval. The best 25% of scenarios for each series (scenarios with the lowest F) are shown in black. All three series show a large amount of displacement between 4 and 7 kyr B.P. B.P.) fit best near the center of the profile but fit relatively poorly (and outside 95% error boundaries) at both the top and bottom of the profile (Figure 11). This scenario, however, also places the fault activity in the middle Holocene. The systematic poorness of fit for the majority of episodic displacement scenarios involving small numbers of events leads us to believe that the scarp probably records more than three events. For n = 4, 5, and 6 events, we ran 180, 205, and 235 scenarios, respectively, many of which are consistent with measured abundances; in general, models using larger numbers of events do not display the systematic differences between model and measured results. The lowest F value for each series indicates that the overall degree of fit can become markedly better when the number of modeled displacement events increases from one to five, but the difference in the lowest F value between n = 5 and n = 6 is minor in comparison (Figure 12). This result indicates that increasing the number of earthquakes further, at least while retaining a 500 year minimum time interval between events, will not result in more precisely defined displacement histories. The best fit scenarios from the different series (n > 3) indicate three separate periods of seismic activity and a variable displacement rate on the Nahef East fault (Figures 13 and 14). The best fitting 25% of the acceptable scenarios in each series help constrain the boundaries of these three time periods (Figure 13). The measured 36C1 data, when interpreted using our model of isotope production, are most consistent with rapid and significant displacement in the mid-holocene ( kyr B.P.) with lesser amounts of displacement in the Late Pleistocene (13-11 kyr B.P.) and late Holocene ( kyr B.P.) Sensitivity Analysis We have tested the sensitivity of our model to changing boundary conditions and assumptions. For example, if the erosion rate of the footwall were 10% higher, model ages would be -2 kyr older but still indicate three periods of activity. Our modeling is robusto random uncertainties measured 36C1 and target element abundance of individual

12 4258 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING 2OO as early as kyr B.P., while samples on the lowest meter of scarp record no more than 4 kyr of exposure (Figure 15). These age limits are reflected in discrete event scenarios that resulted in acceptable 36C1 profiles and suggest an integrated displacement rate for the Nahef East fault of m kyr OO 800 individual sample exposure ages in this region are not possible 6. Discussion Our 36C1 analysis of Nahef East fault scarp samples con- strains the fault's seismic history and earthquake potential. This information allows us to consider the uplift pattern of the Zurim Escarpment specifically and fault behavior in extensional terranes in general Evidence Supporting CI Assessment of the Timing and Nature of Fault Motion looo There is robust supportin geologic evidence for both sig nificant middle Holocene shaking near the Nahef East fault and for discrete motion on the Nahef East fault during the late Earliest possible exposure (kyr B.P.) Holocene. This geologic evidence strongly suggests that epi- Figure 15. Each sample's earliest possibl exposure age based sodic movement and earthquakes rather than aseismicreep on individual prefaulting isotope accumulation and surface ex- built the Nahef East fault scarp, further buttressing our finding posure accumulation rates, assuming a single large event exposes (section 5.5) that multievent displacement scenarios best fit each sample. Because this analysis does not take into account the the measured 36C1 data. possibility of many events and therefore the complexity of co- A cave on the Zurim Escarpment preserves deposits that seismic, subsurface 36C1 accumulation, Figure 15 does not repre- record strong, presumably seismic, shaking. Located 4 km sent actual exposure ages. Instead, it gives the early temporal north of the Nahef East fault, the cave contains earthquakeend-member for the exposure age of each sample. There are three damaged artifacts and human remains of the Chalcolithic era zones of earliest possible exposure; the top four samples could (6-7 kyr B.P.). U-Th dating of samples collected from the have been exposed early, while the central 6-7 m could not have been exposed prior to 10 kyr B.P. The bottom 2 m of scarp could bases of stalagmites, found on cave debris interpreted to be not have been exposed prior to 6 kyr B.P. coseismic, indicates that strong shaking and subsequent damage occurred just prior to 6.2 kyr B.P. (M. Bar-Matthews, personal communication, 1999). This date is consistent with the period of rapi displacement we identified in the 36C1 record. samples because we evaluate model results in terms of total Although the archeological record does not reveal the magniprofile variance and because adjacent sample abundances are tude of displacement, it mandates that shaking and thus fault well correlated. motion must have been significant. Because the Nahef East Our modeling assumes uniform displacement with a mini- fault has the freshest, youngest-looking scarp on the Zurim mum of 500 years between earthquakes; however, it is Escarpment, it is reasonable to suggest that the cave preserves evidence of Nahef East fault motion. unlikely nature behaved so consistently. To test the model's sensitivity to nonuniform displacements, we generated a small The base of the scarp near the sampled transect is covered series of scenarios by varying displacement size and interval. discontinuously for over 100 m laterally, by a thin (<30 cm) We find that good fits to measure data can be obtained by in- slab of chalk 1-2 m high (Figures 4 and 5). Where the chalk is creasing the displacement of a mid-holocenevent to nearly not present, the limestone is discolored to a similar height. 4.5 m, or by replacing large events with clusters of small (10 This slab likely represents the fault surface during most recent cm) events. However, even if we use different size events and motion on the Nahef East fault; during this last displacement vary their timing, scenarios consistent with the 95% confi- event the fault plane extended through the chalk instead of at dence limit continue to result in the same three distinct peri- the border between the chalk and the limestone. The presence ods of activity as those restricted to uniform displacements. of the discontinuous chalk slab located at the base of the scarp Though this series of scenarios was not comprehensive, all supports our 36Cl-based inference of a late Holocene earthscenariosuggest rapid displacement in the middle Holocene quake and suggests that displacement during this event was 1- with lesser displacement before and after. 2 m, consistent with model results (Figure 14). We can use measured 36C1 abundances and our model to estimate the maximum amount of time any sample has been 6.2. Spatial and Temporal Patterns of Displacement exposed at the surface, thus constraining the maximum age The simplest models of earthquake recurrence assume that for displacement that formed the Nahef East scarp. Assuming crustal strain builds at a constant rate and is released periodia single large event that exposes the entire scarp instantane- cally (as an earthquake) in either a time-predictable (varying ously with no subsurface 36C1 production, we calculate the slip) or slip-predictable (varying time) manner [Shimazaki exposure durationecessary to produce the measured 36C1 and Nakata, 1980]. The behavior of the Nahef East fault, the abundances. Samples near the top of the scarp (SG960, youngest and least weathered of several similarly sized and SG930, SG900, and SG870) have greater maximum exposure similarly oriented fault scarps on the Zurim Escarpment, vioages than samples near the base and could have been exposed lates both constant slip models. Although Nahef East earth-

13 MITCHELL ET AL.' COSMOGENIC 36C1 FAULT SCARP DATING 4259 Scenario Framework Space-time diagram for segment behavior displacement vs. time for individual segments A + variable displacement rate on individual segments Displacement occurs X 5 regularly X y rate constant for entire displacement escarpment Y I I + seismic overlap between I I I = different segments at all Z Z I "> 11_ i I times time time + variable displacement Displacement varies, no on individual segments X I I I two segments active at ß - once + variable displacement Y rate for entire Y I I = I B escarpment / _l + no seismic overlap Z I I U ]-- ]- I between different seg- ments time time C + variable displacement on individual segments X i I Displacement varies,..= there two active may or segments may not at be once + variable displacement rate for entire Y I I I. X Y escarpment = Z I +seismicoverlap Z I [ I between different segmeats at some times time time I Figure 16. Space-time and displacement rate diagrams of different short- and long-term models of tectonic activity resulting in the behavior pattern of the Nahef East fault and the geomorphic expression of other nearby scarps. X, Y, and Z represent individual fault segments. (a) Displacement rate variable on single segments, constant for entire escarpment. (b) Displacement rate variable for entire escarpment, no seismic overlap between different segments. (c) Displacement rate variable for entire escarpment, different segments active at the same time. quakes appear to occur in clusters spaced similarly in time, 4 Conversely, displacement could occur on different seg- + 2 kyr B.P., displacement rates on the Nahef East fault have ments at the same time; for example, when the displacement was less on the Nahef East fault in the late Holocene, addivaried significantly with a distinct peak in the rate of surface tional motion was accommodated on a different fault elsedisplacement occurring kyr B.P., the middle Holocene (Figures 13 and 14). There were periods of lesser movement where in the region (Figure 16). The absence of any recorded in the late Pleistocene (13-11 kyr B.P.) and late Holocene seismicity in a long historic record and the distinct relative ( kyr B.P.) as well. Our finding is not unique; many ages of mapped fault scarps argue against this model. These other palcoseismic studies have found episodic or clustering observations imply that one segment is active at a time and behavior in fault systems [e.g., Sieh et al., 1989; Schwartz, that escarpment-wide displacement and uplift rates do, in fact, 1989; Niemi and Hall, 1992; Grant and Sieh, 1994]. vary temporally. These models could be tested explicitly by There are several possiblexplanations for the fluctuation 36C1 dating of other Zurim Escarpment fault scarps. of seismic activity on this single fault segment (Figure 16) Long-Term Escarpment Evolution Fault segments along the Zurim Escarpment could have a distinct life cycle, with faulting beginning slowly, accelerating Cosmogenic analysis of the Nahef East fault scarp, coupled midcycle, then decreasing until the segment is no longer ac- with geologic mapping, provides data useful for understandtive (Figure 16). Fault motion is then transferred acrosstruc- ing the formation of the Zurim Escarpment in particular and tural gaps to another fault segment, possibly after some period large bedrock escarpments in general. Our best-fitting model of quiescence during which strain is accumulated. This model scenario suggesthat the 9 m high section of the Nahef East is supported by the observation that scarps along the Zurim fault scarp took ~ 14 kyr to form, resulting in an average dis- Escarpment range from very fresh (Nahef East fault) to ex- placement rate of 0.7 m kyr '. If the Zurim Escarpment had tremely weathered (other nearby scarps). If this hypothesis been uplifted at this rate, its 700 m of relief could have been correct, then the Nahef East Fault is now in that period of di- created in about a million years; however, the amount of relief minishing activity and does not pose a significant seismic and stratigraphic throw shown by the faults on the Zurim risk; if displacement were to occur again, it would be less in- Escarpment demands long-term periodicity in seismic activtense than the late Holocene seismic episode. ity.

14 4260 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING In the upper 3 m of the Earth'surface, spallation of 4øCa atoms by fast secondary neutrons is the dominant 36Cl-creating reaction in calcite. These neutrons react with 4øCa nuclei, producing 36C1. The rate at which this spallation occurs de- All scenarios consistent with the measured 36C1 data sug- pends on the flux of secondary neutrons at the surface, which (up to 6 m) occurred during is a function of the altitude and latitude of the sample [Lal, gest that significant displacement a 3 kyr period in the middle Holocene. Using the maximum vertical displacement method for calculating earthquake magnitudes [Wells and Coppersmith, 1994] and the largest individual displacement event that still results in a good fitting 36C1 profile (4.7 m), the resulting maximum earthquake on the Nahef East fault would be M = 7.1 (moment magnitude scale). An earthquake in the six-event series (1.6 m) would have a moment magnitude of 6.8. The discovery of rapid, mid-holocene displacement, probably spread out over a few thousand years, suggests that once fault motion begins, more earthquakes might soon follow. The production of 36C1 from 4øCa spallation decreases ex Prospects for Cosmogenic Isotope Dating ponentially with depth. Production at depth z due to 4øCa spallation P,(z) is dependent on the surface production rate P,(0), the mass fraction concentration of target element [Ca], the shielding depth z (g cm'2), which is the depth in centimeters multiplied by the rock density (2.75 g cm -3, measured in five limestone samples), and an attenuation length (A, = 160 uring 36C1 in samples collected from Ca- or Cl-containing g cm '2) for cosmic ray neutrons, The paucity of prehistoric earthquake displacement data limit our ability to determine seismic risk and study fault behavior in active fault systems [Berryman and Beanland, 1991; depolo et al., 1991; Stewart, 1996]. This and other studies [Noller et al., 1996; Zreda and Noller, 1998] show that meas- bedrock scarps is an effective method for determining the age of motion on normal faults. Fault scarp dating is not limited to 36C1; bedrock scarps containing quartz (i.e., sandstone, gran- ite, quartzite, or rhyolite) could be dated using WBe and 26A1 On the Zurim Escarpment, as on many others, the cumulative vertical relief of the various extant scarps (< 50 m) does [e.g. Nishiizumi et al., 1991; Bierman, 1994]. Scarps exposing not come close to the total vertical relief (700 m). Further- olivine or pyroxene could be dated using 3He [Kurz et al., more, stratigraphic offset mandates at least m of over- 1990]. Cosmogenic 4C has also been applied all displacement between units in the hanging wall and foot- in carbonate rocks [Handwerger et al., 1999]. Any uneroded wall of just the Nahef East fault, 5-30 times the surface offset bedrock scarp with a simple exposure history (without burial observed today. The Nahef East fault and others must have or nontectonic exhumation) is a candidate for cosmogenic nubeen active in the past, forming scarps that eroded before the clide dating. next long-term cycle of seismic activity began. This observed Provided that exposure histories are simple and scarps are discrepancy between stratigraphic and surface offset supports in good condition, cosmogenic dating will determine scarp morphometric evidence that the majority of escarpment to- ages more precisely and more accurately than measuring relapography formed long ago. Early faulting created scarps that tive weathering characteristics. Nuclide measurement can had up to 4 Myr to erode before the recent renewal of tectonic constrain the timing of displacement, even when geomorphic activity created the scarps seen today [Matmon et al., 1998, clues, such as distinct weathering horizons, are absent. If dis- 1999]. crete displacement events are indicated by the morphology of the scarp face, modeling the ages of events from nuclide 6.4. Seismic Hazard of the Zurim Escarpment Fault abundances becomes much simpler because displacement size System can be estimated independently. However, an interpretive Earthquakes occurring in northern Israel (on the Dead Sea model is still required to calculate subsurface isotope accu- Transform fault, not on extensional faults) in recent centuries mulation during the development of the scarp. Calculating (e.g., the M = 6.4 Safed earthquake of 1837 and the M = 6.2 ages directly from the scarp surface, without such a model, Jericho earthquake of 1927) caused serious damage in popu- will overestimate the age of ruptur events, especially for carlated regions [van Eck and Hofstetter, 1990; Ben-Menahem, bonate rocks in which subsurface production from muons can 1981 ]. Considering that over 80,000 people live within 30 km account for a large portion of the measured 36C1. of the Zurim Escarpment (and the many other similar escarpments located throughouthe Galilee), the potential for severe Appendix A: 3 icl Production Mechanisms damage and loss of life is high. There are seven different reactions that create 36C1 in car- The Beit-Hakerem Valley is an area of significant seismic hazard because our data indicate that a large amount of disbonate rocks. The relationships between rock chemistry, sample depth, and 36C1 production rates associated with these replacement occurred in a relatively short period of time. The actions are discussed here. Symbol definitions and units can size and morphology of the escarpment and the presence of be found in Table A1. old, weathered scarps indicate that the region has been seismically active for years [Matmon et al., 1998]. These A1. Spallation of 4øCa two observations indicate that seismic activity is likely to occur in the future. However, the region has not been seismically active within the past 2 kyr, consistent with nuclide data suggesting that several thousand years may pass between active episodes on the Nahef East fault. 1991]. to fault scarps Although surface production rates of 36C1 by 4øCa spallation (P,(0)) have been calibrated by a number of researchers (Table A2), some disagreement remains. We have chosen to use the production rates of Stone et al. [1996, 1998] because the calibrations were done on Ca-rich mineral separates and carbonates and thus are based on Ca reactions exclusively. We have not considered changes in production rates over time due to fluctuations in Earth's magnetic field because the associated error is less significanthan the other errors inherent to our model and data. p36clsp(z) = Psp(O)[Ca]exp -z/asp atoms 36C1 yr '.(A1) The production of 36C1 resulting from 4øCa spallation at

15 MITCHELL ET AL.' COSMOGENIC 36Cl FAULT SCARP DATING 4261 Table A1. Symbols and units. from 4øCa spallation: -z/asp Symbol Definition, Value Assigned and Units N36Cl(Ca ) = Psp (0)[Ca]exp X +œp/asp General Symbols z depth (g cm -2) atoms 36C1 (g rock) - yr '. (A2) density (2.75 g cm '3) erosion rate (cm yr ' ) A2. Muon Capture by 4øCa x 10 '6 years ' (36C1 decay constant) Whereas 4øCa spallation is the predominant 36C1 t36c x 106 years (36C1 half-life) mechanism in the very shallow subsurface (< 3 m), negative muons are less reactive than neutrons and therefore penetrate 6Cl from 4øCa spallation further into rocks [Spannagel and Fireman, 1972; Charalam- P( v)(o) 48.8 (atoms (g rock) ' yr - )(surface production bus, 1971]. Three meters and deeper beneath the surface, rate of 36C1 from 4øCa spallation) (Table A2) negative muon capture by 4øCa is the dominant 36C1 produc- Asp 160 gcm -2 attenuation of neutrons in rock [Liu et tion mechanism in low-chlorine rocks such as those we samal., 1994] pled. The production rate of 36C1 at depth from muons 6Cl frotn scl Thermal Neutron Capture P([t-,Ca (Z), has been parameterized by Fabryka-Martin, [1988] P(n,sv)(O) 560 fast n (g air) ' yr ' (stopping rate of neutrons and Stone, et al. [ 1998]: at ground level) [Liu et al., 1994] f35 fraction of thermal neutrons captured by 35C1 /}[t-,ca) (z) = P - (z)[ca]yca atoms 36C1 (g rock) - yr -,(A3) pre-exponential term for production of neu- where F t_ is the negative muon stopping rate (stopped la' g trons in pure calcite [Liu et al., 1994] yr - ) at depth z, [Ca] is the mass fraction of Ca in the rock, and pre-exponential term for production of Yca is the number of atoms 36C1 produced per stopped la- in neutrons in pure calcite [Liu et al., 1994] each respective sample [Stone et al., 1998]. Yca was scaled for Lth 33.0 _+ 0.8 (g cm -2) characteristic length for neu- each sample using the muon capture probabilities of each of tron diffusion in limestone 6Cl from Negative Muon Capture on 4øCa the major elements in carbonate rocks (Ca, Mg, O, and C) and the calibrated Yca value of atoms 36C1 (g rock) - yr - for P( t,ca) production rate of 36C1 from muon capture (sur- pure calcite Iron Egidy and Hartmann, 1982; Knight et al., face production rate is 5.0 (atoms (g rock) ; Stone et al., 1998]. yr -l)[stonet al., 1998] The stopping rate of negative muons with respecto depth q'.-(z) stopped g- (g rock) '1 yr - intensity of stopped muons at depth z is approximated by Stone et al. [1998], with a fifth-order polynomial, which follows the form: Yca atom (stopped g-)- 36C1 yield from captured muons in pure calcite Neutron Production Following Negative At- Capture P(n,[t-) atoms (g rock) - yr -1(production rate of 36C1 from thermal neutrons from muon capture) Ys neutron (stopped g-)-i (average neutron yield from g- capture in calcite) P(rad) 36C1 Production by Fast Muons (p 6Cl,.f) atoms (g rock) -1 yr - (production rate of 36C1 P(n,,l) from thermal neutrons from fast muon slowing (bremsstralung) q (z) muon cm -2 yr - (fast muon flux at depth z) 1 neutron (disintegration) - (average neutron yield per photodisintegration) 36Cl Production by ( a;n) Reactions and U Fission 36C1 production from (%n) reactions and U fission (atoms (g rock)-' yr - ) x 10-7 yr ' decay constant of U average neutrons emitted per spontaneous fission of U 238 n yr - (neutron yield from U-produced t radia- tion) loglo[ Pg- (z)] = a + blog10(z) + c[log10(z)] 2 + production ß..f[loglo(z)] 5 stopped la' (g rock) 4 yr ' (A4) for the coefficients (a, b, c... f) defined by Stone et al. [1998]. Ihis polynomial approximation is inaccurate for z < 100 g cm-2; we assign the 100 gcm -2 value of qj _ to all z < 100 g cm -2. The surface production rate of 36C1 due to negative muon capture in pure calcite is atom 36C1 g (calcite) -1 yr - at sea level and high latitude [Stonet al., 1998]. A3. Thermal Neutron Capture by 35C1 Another 36C1 production mechanism the incorporation of a thermal (low energy) neutron into a 35C1 nucleus. The production rate of 36C1 by thermal neutron capture is dependent on the percentage of thermal neutrons absorbed by 35C1, a factor lmown as f35, as well as the abundance of thermal neutrons moving through the rock. There are many different reactions that produce tl',ermal neutrons, including spallation, muon capture, bremsstrahlung reactions (¾ radiation), and ra- diogenic U fission and U-Th (o0 decay [Fabryka-Martin, 1988; Liu et al., 1994; Bierman et al., 1995; Stone et al., 1998]. For rock such as ours with low chlorine (< 10 lag n yr -I(neutron yield from Th-produced t radiation) 36C1 production from thermal neutron activation is less significant than production from spallation and muon capture of 4øCa ' depth z below a steadily eroding surface will eventually reach A3.1. Spallation thermal neutrons. The spallation of atan equilibrium between 36C1 production and loss of 36C1 by oms in the atmosphere and rock by secondary fast neutrons radioactive decay and erosion of the upper surface. The ero- releases additional neutrons. These neutrons eventually lose sion rate e (cm yr - ) results in a nuclide abundance N36Cl(ca) their kinetic energy through collisions with other atoms and

16 4262 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING Table A2. Production Rates From 4øCaa Study Site Altitude Latitude Duration Production Rate, b atoms (g Ca) - yr - Yokoyama et al. [1977] Maserik and Reedy [ 1995] Stone et al. [ 1996] Zreda et al. [ 1991 ] Swanson et al. [ 1994] Stone et al. [ 1996] Phillips et al. [ 1996] c 4øCa Spallation Only Aiguille du 3840 m 47 ø modem 68 _+ 14 Midi high latitudes sea level > 60 ø modem 64.6 Tabernacle Hill 1445 m 41 ø 17.3 kyr to present Total Production From Ca Tabernacle Hill 1445 m 39 ø 17.3 kyr to present 54.8 _+ 5.0 Puget Sound sea level 48 ø 15.5 kyr to present 89.5 _+ 5.6 Tabernacle Hill 1445 m 41 ø 17.3 kyr to present 53.6 _+ 1.8 various 1oca- sea level to 20o-80 ø 60-2 kyr tions 2600 a After Stone et al. [ 1996]. t, Scaled to sea level and high latitude. c Phillips et al. [ 1996] took many samples at varying elevations, latitudes, and spanning a range of exposure ages. The other studies focused on a single outcrop. become thermalized. Liu et al. [1994] describes 36C1 produc- of neutrons produced by that flux Yf (currently assumed to be tion at depth from spallation thermal neutrons P(sp, n)(z), 1 neutron per disintegration), and the fraction of neutrons captured by 35C1 0r35) [from Stonet al., 1998]: P(sp,n) (Z) = Pn,sp (O) f 35(kl exp -z/asp + k2 exp -z/lth ) atoms 36C1 (g rock) - yr '. (A5) Neutrons near the rock/atmosphere interface tend to escape the rock before they can be thermalized; therefore thermal neutron production decreasesharply in the tens of centimeters nearest the rock surface (k and k2 are preexponential terms that account for the change in production rate just below the surface; Lth is the neutron diffusion length in limestone, g cm -2)[Bierman et al., 1995; Dep et al., 1994; Liu et al., 1994]. The equilibrium concentration of 36C1 due solely to spallation thermal neutrons based on nuclide production and decay N36Cl(sp, n), at a given erosion rate is quantified, N36Cl(z ') = l sp,n)(o)f351klexp-z/asp ' Z+œP/Asp q k2exp-z/lth Z+eP/Ltn 1 that an equal number of fast muons are received gles in the upper hemisphere els through the footwall and 71.7% travels through /}g-,ca) (z)= tpg_ (z)ysf35 atoms 36C1 (g rock) - yr -. (A7) P(la-,,/) (z) = 5.8x 10-6 Yf ln(0.104z) t + (z) f35 atoms 36C1 (g rock) - yr ', al., 1998]. The production of 36C1 beneath the surface via this reaction Ptn_a)(z) is dependent on the flux of high-energy muons traveling through the rock at the given depth (z), the where the number of 36C1 atoms produced per year from raamount of gamma radiation produced by the flux, the number diogenic reactions (Ptraa)) is the product of the radiogenic (A8) where ß is approximated by Stone et al. [1998], with another fifth-order polynomial. Because of the low C1 levels in the Nahef East fault scarp samples (and the low production rate of thermal neutrons from bremsstrahlung radiation), fast muonproduced thermal neutrons contribute only a very small amount of 36C1 to the samples. Because of the low f35 of the Nahef East fault scarp samples and the relatively few 36C1 atoms produced from bremsstrahlung radiation we did not calculate a correction factor for the 36C1 produced from the slowing of fast muons on tilted surfaces. Instead, we assumed from all anand that 28.3% of the flux travthe hangatoms 36C1 (g rock) '1.(A6) ing wall (51 ø/180 ø and (180ø-51 ø)/180 ø, respectively). A3.2. Negative muon capture. When negative muons are A3.4. Radiogenic neutrons. U-Th alpha decay, with its captured by elements such as C1, C, Ca, and O, the nucleus releases neutrons that are then thermalized [Fabryka-Martin, 1988; Bierman et al., 1995; Stone et al., 1998]. The produc- production is noncosmogenic and is dependent solely on the tion of thermal neutrons at depth by muon capture P([t-,Ca)(Z) is chemical composition of the rock, the resulting 36C1 dependent on the rate at which muons are stopped in the rock trations are independent of sample depth and erosion rate. ß t-(z), the neutron yield per stopped muon Ys, and the per- For (ct,n) reactions, neutron production PNto n depends on cent of thermal neutrons captured by 35C1, f35: the concentration of U and Th and various light elements in the rock [Fabryka-Martin, 1988], subsequent (ct,n) reactions, and 238U fission produce thermal neutrons that can be captured by 35C1. Because this neutron PN(a,n ) = X[U]+Y[Th] n yr - concen- Because samples collected for this study contained only trace amounts of 35C1, the contribution to 36C1 production by muon where X and Y are neutron yield factors calculated using capture-produced thermal neutrons are < 5% at the surface methods described by Fabryka-Martin [ 1988]. and 20% at 2000 g cm '2. A3.3. Bremsstrahlung radiation. The slowing of high- fission. This rate is determined by the atomic concentration of energy muons in rock produces bremsstrahlungamma pho- 238U (N238), its decay constant gs, and the average number of ton radiation. This radiation can cause nuclear disintegrations, neutrons released per spontaneous fission [Fabryka-Marreleasing thermal neutrons [Fabry;ca-Martin, 1988; Stone et tin, 1988]: (A9) PNtn, 238u) is the rate at which neutrons are produced by 238U PN(n,238U) = N238). n yr ' (A10)

17 neutron production rate and f35: P(rad)--(PN(n238,U ) +PN(n,a) 35 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING 4263 atoms 36C1 (g rock) - yr -. (A11) The steady state, background concentrations of 36C1 in each cent areas since Upper Cretaceous times, Geol. Mag., 102, , Freund, R., The geometry of faulting in the Galilee, Isr. J. Earth Sci., 19, , Garfunkel, Z., I. Zak, and R. Freund, Active faulting in the Dead Sea Rift, Tectonophysics, 80, 1-26, Geologic Survey of Israel, Geologic Map of Israel, 1:250,000, Jerusample resulting from these two radiogenic sources is calcu- salem, lated by determining the concentration of 36C1 at which radio- Grant, L, B., and K. Sieh, Paleoseismic evidence of clustered earthactive decay equals production. For these low C1, low U quakes on the San Andreas fault in the Carizzo Plain, California, rocks, radiogenic nuclide contribution is < 5% of the total 36C1 J. Geophys. Res., 99, , content, even in the deepest samples collected for this study. Hall, J., Shaded image relief map of Israel, Geol. Surv. of Isr., Jerusalem, Handwerger, D. A., T. E. Cerling, and R. L. Bruhn, Cosmogenic 4C Acknowledgments. This research was funded by Hebrew Uniin carbonate rocks, Geomorphology, 27, 13-24, versity, an Israeli Atomic Energy Commission grant to Y. Enzel, an Kafri, U., Neogene to Quaternary drainage systems and their rela- NSF MRI EAR grant to P. Bierman, a University of Vertionship to young tectonics: lower Galilee, Israel, Rep. GSI/1/97 mont SUGR/FAME grant to S. Mitchell and P. Bierman, and an NSF Geol. Surv. of Isr., Jerusalem, Graduate Research Fellowship to S. Mitchell. C. Massey and D. Glu- Knight, J. D., C. J. Orth, M. E. Schillaci, R. A. Naumann, F. J. Hartek assisted in the field. ICP-MS samples were analyzed by B. Klaue mann, J. J. Reidy, and H. Schnewly, Coulomb capture ratios of at Dartmouth College, with support from J. Blum. J. Larsen assisted negative muons in N2 + 02, NO and CO, Phys. Lett., A, 79, 377- with C1 and ICP analyses. Analyses of 36C1 were done at Lawrence 379, Livermore National Laboratory (under DOE contract W-7405-ENG- Kurz, M.D., D. Colonder, T. W. Trull, R. B. Moore, and K. O'Brien, 48). J. Stone greatly assisted with the geometric and chemistry Cosmic ray exposure dating with in situ produced cosmogenic corrections for the numerical model. We thank A. Gillespie, T. Ito, 3He: Results from young Hawaiian lava flows, Earth Plan. Sci. and an anonymous reviewer for their constructive reviews. Lett., 97, , Lal, D., In situ-produced cosmogenic isotopes in terrestrial rocks, References Annu. Rev. Earth Planet. Sci., 16, , Lal, D., Cosmic ray labeling of erosion surfaces: In situ production Ben-Menahem, A., Variation of slip and creep along the Levant Rift rates and erosion models, Earth Planet. Sci. Lett., 104, , over the past 4500 years, Tectonophysics, 80, , Berryman, K. R., and S. Beanland, Variation in fault behavior in dif- Liu, B., F. M. Phillips, J. T. Fabryka-Martin, M. M. Fowler, and W. ferent tectonic provinces of New Zealand, J. Struct. Geol., 13, D. Stone, Cosmogenic 36C1 accumulation in unstable landforms, 1, , Effects of the thermal neutron distribution, Water Resour. Res., Bierman, P. R., Using in situ cosmogenic isotopes to estimate rates of 30, , landscapevolution: a review from the geomorphic perspective, J. Maserik, J., and R. C. Reedy, Terrestrial cosmogenic-nuclide pro- Geophys. Res., 99, , duction systematics calculated from numerical simulations, Earth Bierman, P. R., A. Gillespie, M. Caffee, and D. Elmore, Estimating Planet. Sci. Lett., 136, , erosion rates and exposure ages with 36C1 produced by neutron Matmon, A., E. Zilberman, and Y. Enzel, Morphometric analysis for activation, Geochim. Cosmochim. Acta, 59, , determining the age of escarpments: an example fi'om the Galilee, B ilokon, H., G. Cini-Castagnoli, A. Castellina, B. Piazzoli, G. Man- northern Israel, Report GSI/31/98, Geol. Surv. of Isr., Jerusalem, nocci, E. Meroni, P. Picchi, and S. Vernetto, Flux of the vertical negative muonstopping at depths hg/cm, d. Geophys. Matmon, A., Y. Enzel, E. Zilberman, and A. Heimann, Late Pliocene Res., 94, 12,145-12,152, and Pleistocene reversal of drainage systems in northern Israel: Charalambus, S., Nuclear transmutation by negative stopped muons and the activity induced by cosmic-ray muons, Nuc. Phys., A, 166, , Tectonic implications, Geomorphology, 28, 43-59, McCalpin, J.P., Paleoseismology, 588 pp. Academic, San Diego, Calif., Crookes, J. N., and B.C. Rastin, The absolute intensity of muons at Niemi, T. M., and N. T. Hall, Late Holocene slip rate and recurrence 31.6 hg cm -2 below sea level, Nuc. Phys.,B, 58, , of great earthquakes on the San Andreas fault in northern Califor- Dep, L., D. Elmore, J. Fabryka-Martin, J. Masarik, and R. Reedy, nia, Geology, 20, , Production rate systematics of in-situ-produced cosmogenic nu- Nishiizumi, K., C. P. Kohl, J. R. Arnold, J. Klein, D. Fink, and R. clides in terrestrial rocks: Monte Carlo approach of investigating Middleton, Cosmic ray produced løbe and 26A1 in Antarctic rocks: 35Cl(n,T)36C1, Nuc. Inst. Methods Phys. Res., B, 92, , Exposure and erosion history, Earth Planet. Sci. Lett., 104, 440- depolo, C. M., D. G. Clark, D. B. Slemmons, and A. R. Ramelli, Historic surface faulting in the Basin and Range province, western North America: Implications for fault segmentation, J. Struct. Geol., 13, , Dockhorn, B., S. Neumaier, F. J. Hartmann, C. Petitjean, H. Faester- 454, Noller, J., M. G. Zreda, and W. R. Lettis, Use of cosmogenic C1-36 to date late Quaternary activity of the Hebgen Lake Fault, Montana, Geol. Soc. Am., Abstr. Programs, 28, 300, 1996 Phillips, F. M., M. G. Zreda, M. R. Flinsch, D. Elmore, and P. mann, G. Korschinek, H. Morinaga, and E. Nolte, Determination Sharma, A reevaluation of cosmogenic 36C1 production rates in of erosion rates with cosmic ray produced 36C1, Hadrons Nuclei, terrestrial rocks, Geophys. Res. Lett., 23, , , , Ron, H., R. Freund, Z. Garfunkel, and Z. Nur, Block rotation by Dunne, J., D. Elmore, and P. Muzikar, Scaling factors for the rates of production of cosmogenic nuclides for geometric shielding and attenuation depth on sloped surfaces, Geomorphology, 27, 3-12, Fabryka-Martin, J. T., Production of radionuclides in the Earth and their hydrogeologic significance, with emphasis on chlorine-36 and iodine-129, Ph.D. dissertation, 400 pp., Univ. of Ariz., Tucson, Florence, T. M., and Y. J. Farrar, Spectrophotometric determination of chloride at the parts-per-billion level by mercury (II) thiocyanate method, Anal. Chim. Acta, 54, , Freund, R., On the stratigraphy and tectonics of the Upper Cretaceous in the western Galilee, Bull. Res. Counc. lsr., G8, 43-50, Freund, R., A model of the structural development of Israel and adjastrike-slip faulting: Structural and paleomagnetic evidence (Israel), J. Geophys. Res., 89, , Schwartz, D. P., Paleoseismicity, persistence of segments, and temporal clustering of earthquakes; Examples from the San Andreas, Wasatch, and Lost River fault zones, Proceedings of Conference XLV; A Workshop on Fault Segmentation and Controls of rupture initiation and termination, U.S. Geol. Surv., Open File Rep., , , Shimazaki, K., and T. Nakata, Time-predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, , Sieh, K., M. Stuiver, and D. Brillinger, A more precise chronology of earthquakes produced by the San Andreas Fault in southern California, J. Geophys. Res., 94, , Spannagel, G., and E. L. Fireman, Stopping rate of negative cosmic ray muons near sea level, J. Geophys. Res., 77, , 1972.

18 4264 MITCHELL ET AL.: COSMOGENIC 36C1 FAULT SCARP DATING Stewart, I. S., A rough guide to limestone fault scarps, d. $truct. Geol., 18, , Stewart, I. S., and P. L. Hancock, Neotectonic normal fault zones in the Aegean region, J. Struct. Geol., 13, , Stone, J. O., G. L. Allan, L. K. Fifield, and R. G. Cresswell, Cosmo- genic chlorine-36 from calcium spallation, Geochim. Cosmochim. Acta, 60, , Stone, J. O., J. M. Evans, L. K. Fifield, G. L. Allan, and R. G. Cresswell, Cosmogenic chlorine-36 production in calcite by muons, Geochim. Cosmochim. Acta, 62, , P. R. Bierman and A. Matmon, Department of Geology, Univer- Swanson, T. W., R. C. Finkel, L. Harris, and J. Southon, Application sity of Vermont, Burlington, VT (pbierman@zoo.uvm.edu; of 36C1 dating based on the deglaciation history of the Cordilleran zoo.uvm.edu) ice sheet in Washington and British Columbia, Geol. Soc. Am., M. Caffee, Lawrence Livermore National Laboratory, Livermore, Abstr. Programs, 26, 512, CA (mcaffee@llnl.gov) van Eck, T., and A. Hofstetter, Fault geometry and spatial clustering Y. Enzel, Institute of Earth Sciences, Hebrew University, Jerusa- of micro earthquakes along the Dead Sea-Jordan rift fault zone, Tectonophysics, 180, 15-27, yon Egidy, T., and F. J. Hartmann, Average muonic coulomb capture probabilities for sixty-five elements, Phys. Rev. A, 26, , Wells, D. L., and K. J. Coppersmith, Empirical relationships among magnitude, rupture length, rupture area, and surface displacement, Bull. Seismol. Soc. Am., 82, , Yokoyama, Y., J. L. Reyss, and F. Guichard, Production of radionuclides by cosmic rays at mountain altitudes, Earth Planet. Sci. Lett., 36, 44-50, Zreda, M., and J. Noller, Ages of prehistoric earthquakes revealed by cosmogeni chlorine-36 in a bedrock fault scarp at Hebgen Lake, Science, 292, , Zreda, M. G., F. M. Phillips, D. Elmore, P. Kubik, P. Sharma, and R. Dorn, Cosmogenic chlorine-36 production rates in terrestrial rocks, Earth Planet. Sci. Lett., 105, , 199!. lem, Israel, (enzel@vms.huji.ac.il) S. Gran Mitchell, Department of Earth and Space Sciences, University of Washington, Seattle, WA (sgml@u.wa.shington. edu) D. Rizzo, Department of Civil and Environmental Engineering, University of Vermont, Burlington, VT (drizzo@emba.uvm. edu) (Received October 12, 1999; revised September 27, 2000; accepted October 6, 2000.)