Effect of density uncertainties in cosmogenic 10Be depth-profiles: Dating a cemented Pleistocene alluvial fan (Carboneras Fault, SE Iberia)

Quaternary Geochronology 6 (2011) 186e194

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Research Paper

Effect of density uncertainties in cosmogenic 10Be depth-profiles: Dating a cemented Pleistocene alluvial fan (Carboneras Fault, SE Iberia) Ángel Rodés a, *, Raimon Pallàs a, Regis Braucher b, Ximena Moreno a, Eulàlia Masana a, Didier L. Bourlés b a b

Departament de Geodinàmica i Geofísica, Facultat de Geologia, Universitat de Barcelona, Martí i Franquès s/n, 08028 Barcelona, Spain CEREGE, UMR 6635, Université Paul Cézanne CNRS-Aix Marseille Université BP80, 13545 Aix en Provence, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 March 2010 Received in revised form 4 October 2010 Accepted 20 October 2010 Available online 10 November 2010

Cosmonuclide depth-profiles can be used to calculate both the age of landforms and the rates at which erosion has affected them since their formation. Results are heavily dependent on the selection of the appropriate density of the material exposed to cosmic radiation. In materials where density has changed significantly through time, as in alluvial sediments affected by post-depositional calcrete cementation, the uncertainties in density must be accurately modelled to produce reliable results. We develop new equations for an accurate account of density uncertainties and to test the effect of density gain due to cementation processes. We apply them to two 10Be depth-profiles measured in an alluvial fan deformed by the Carboneras Fault (SE Iberia). When a linear increase of density through time is considered, model results yield an age ranging from 200 ka to 1 Ma within 1s confidence level. Ó 2010 Elsevier B.V. All rights reserved.

Keywords: Cosmic ray exposure dating Denudation Geochronology Numerical model Paleoseismology Calcrete

1. Introduction Cosmonuclide exposure dating is a dependable technique in landscape evolution studies (Gosse and Phillips, 2001). The concentration of cosmonuclides (e.g. 10Be) measured at the surface of a given landform depends, among other parameters, on the amount of cosmonuclide lost by erosion, and on the time of exposure to cosmic radiation. If erosion is assumed to be negligible for the period of exposure, an exposure age can be deduced from the cosmonuclide concentrations found in superficial materials (Lal, 1991). Moreover, where erosion is not negligible, it is possible to deduce an exposure age and an erosion rate using numerical modeling of cosmonuclide concentrations from a series of samples taken along a depth profile (Siame et al., 2004). Advances in Accelerator Mass Spectrometry (AMS) in recent years have increased the precision in 10Be concentration measurements. Thus, as a result of more precise measurements and the increased speed of computer processors there is now room for improvement in the conceptual models used to interpret concentration depth-profiles. Exposure ages and erosion rates for a given

* Corresponding author. Tel.: þ34 93 403 40 29; fax: þ34 93 402 13 40. E-mail address: [email protected] (Á. Rodés). 1871-1014/$ e see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.quageo.2010.10.004

surface have been calculated in the literature by chi-square inverse modeling of the measured cosmonuclide concentration depthprofiles, assuming no variation of the material density (Siame et al., 2004; Braucher et al., 2009; Nissen et al., 2009). However, where post-depositional processes produce density variations through time (for example by calcrete formation), the assumption of constant density may produce significant age inaccuracies. A meticulous processing of density uncertainties and of density evolution is therefore necessary to obtain reliable chronological results from cosmonuclide depth-profile modeling. The aims of this paper are (1) to assess the precision of age and erosion estimation for depth-profiles affected by density uncertainties, (2) to develop a model for 10Be depth-profiles, taking into account the variations in sediment density through time, and (3) to apply the new model to constrain the age of the Pleistocene El Puntal fan (Carboneras Fault). 2. Modeling density variations and uncertainties in depth-profiles

10

Be

To numerically estimate the age and the erosion rate experienced at a depositional landform surface, Siame et al. (2004) and Braucher et al. (2009) used the chi-square inverse approach to fit synthetic 10Be depth-profile models to measured 10Be datasets,

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

assuming no variation in the material density. In this work, we use the same approach but we introduce the modifications required to account for density variations through time. Moreover, we present a way of considering the density data as a gaussian distribution in the chi-square inverse approach.

values of k correspond to a constant-density gain. Eq. (5) can be solved as:

Cðx;3;tÞ ¼

2

The Be concentration (C) at a depth x (g cm ) from the top surface of a deposit, which has been eroding at a constant rate 3 (g cm2 a1) since its formation (t years ago), was described by Lal (1991) as:

dC dC x ¼ Pe L þ 3  lC dt dx

(1)

where P is the surface production rate in at g1 a1, which can be calculated using the CRONUS-Earth online calculator (Balco et al., 2008), L is the attenuation length of the cosmic radiation (g cm2), and l is the 10Be decay constant (a1). Eq. (1) may be solved as:

 3 P x
Cðx;3;tÞ ¼ 3 e L 1  et ðlþLÞ Lþl

CðCInher: ;x;3;tÞ


  Pspal: L x t lþL 3 spal: spal: 1e ¼ CInher: þ 3 e Lspal: þ l
  x
t lþL 3 Pstop Lstop stop 1e þ 3 e Lstop þ l
  t lþL 3 Pfast L x fast e fast 1  e þ 3 Lfast þ l

(3)

where the first addend is the 10Be inherited from the exposure of matter to cosmic rays before its deposition:

CInher: ¼ Cðx;0Þ $elt

(7)

Considering inheritance and production of 10Be due to spallation, stopping muons and fast muons, the variable-density 10Be concentration model will be:

CðCInher: x;3;tÞ ¼ CInher:

!l " #  3 Pspal: e kLspal: ðkx 3Þ k l ekt ðkx 3Þ ðkx 3Þ G ; þ ; k kLspal: kLspal: k kLspal: kLspal: " # 3   l  Pstop e kLstop ðkx 3Þ k l ekt ðkx 3Þ ðkx 3Þ G ; ; þ kLstop k kLstop kLstop k kLstop l ! " # k  3 l ekt ðkx 3Þ ðkx 3Þ Pfast e kLfast ðkx 3Þ G ; ; þ k kLfast kLfast k kLfast kLfast (8)

2.2.1. c2 fit modeling Depth-profile sampling provides a set of data of N 10Be concentrations (Ci) measured in samples obtained from several profile depths (xi). Numerical modeling was performed to calculate the time (t), inheritance (CInher.) and erosion rate (3) values that fit the data obtained from the sampled profiles. To fit the models (Eqs. 3 and 8) into the data, it is necessary to compute them with an inverse method, especially if uncertainty boundaries need to be demarcated in the CInher.-3-t space. We used the same c2 fit-based inverse method employed by Siame et al. (2004) or Braucher et al. (2009). This method defines the solution in the CInher.- 3-t space by minimizing the c2 value:

1 σ values

If we consider that the density of the sediment decreases or increases constantly with time due to diagenetic processes, the 10Be concentration can be described by:

2σ s values Forbidden values 68.27 % of allowed values 95.45 % of allowed values 4.55 % of allowed values

0.10

0.08

Probability

2.2. Variable-density model

Chi-square distribution (7 (8 degrees of freedom)

0.06

0.04

0.02

(5)

where k is the rate of sediment density loss in g cm3 a1. This factor can be expressed as:

r0  r1 t r1

l

(4)

In the case of alluvial fan deposits, this inherited Be may be formed (1) during the deposition of the quartz grains in the source area, (2) during the exhumation of the source area, and (3) during the transportation of the quartz grains from the source area to the deposition site.

k ¼

r k1 er dr

kL

10

dC dC x ¼ Pe L þ ð3 þ kxÞ  lC dt dx

ðkx3Þ

ZkL

ekt ðkx3Þ

(2)

Depth can also be expressed as x ¼ r$z , where z is the current profile depth in cm and r is the mean density of the rock or sediment in g cm3. Considering that the production of 10Be is due to spallation, stopping muons and fast muons, which have different attenuation lengths and production rates, the 10Be concentration can be expressed as:

#  l " 3  P ekL ðkx  3Þ k l ekt ðkx  3Þ ðkx  3Þ G ; ; k k kL kL kL kL

 l 3  P ekL ðkx  3Þ k ¼ k kL kL

2.1. Constant-density model 10

187

(6)

where r1 is the current density (g cm3), r0 is the initial density and t is the age of the depositional surface in years. Therefore, negative

0

5 χ2 best fit

10

15

20

χ2 values

Fig. 1. Strategy followed to choose c2 values corresponding to 1s and 2s confidence levels over a chi-squared distribution. 1s values vary from c2min to a c2 value that restricts the distribution area to 68.27% of all possible distribution values (i.e. the part of the distribution beyond c2min ). 2s values restrict the distribution area to 95.45% of allowed values.

188

c2 ¼

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194 N X Ci  CðCInher: ;x;3;tÞ i¼0

!2 (9)

sið3;tÞ

where Ci are the measured concentrations from the N samples at xi depths, CðCInher: ;x;3;tÞ is the concentration predicted by the model, and si(3,t) are the uncertainties of the samples, explained below. In the case of two depth-profiles from the same landform (N þ M samples, same age t, same inheritance (CInher.), and two erosion rates 31 and 32), solutions are located in the CInher.-31-32-t space. The c2 function for two-profile models is:

c2 ¼

N X Ci  CðCInher: ;x;31 ;tÞ i¼0

sið31 ;tÞ

!2 þ

M X Cj  CðCInher: ;x;32 ;tÞ j¼0

sjð32 ;tÞ

!2 (10)

As the data are subject to measurement errors and as the samples have been affected by biological and diagenetic processes not

considered in the models, they never fully fit the model, but only one solution that minimizes the c2 value can be obtained (Braucher et al., 2009). This solution, which is defined by the maximum likelihood CInher.-3-t combination, is called c2 best fit value ðc2min Þ. To estimate to what degree a model reflects the distribution of the data, the quality factor of the c2 best fit value is reported. Pugh and Winslow (1966) defined the quality factor of a c2 fit as:

Qf ¼ 1  P

y c2min

; 2 2

!

(11)

where y is the degrees of freedom of the model (number of samples minus the number of modelled parameters). The quality factor varies from 0 to 1, with higher values meaning better fitting (Pugh and Winslow, 1966). The CInher.-3-t values that fit the data within 1s or 2s confidence level (i.e., 68.27% or 95.45%) are obtained from the c2 distribution, as shown in the example of Fig. 1.

Fig. 2. Location of 10Be depth-profiles 1 and 2 in the El Puntal alluvial fan. The sampling area is located on the NW flank of the La Serrata range, a horst-like structure bounded by two parallel traces of the left-lateral Carboneras Fault.

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

189

Fig. 3. Anthropic outcrops excavated in the El Puntal alluvial fan, where depth Profiles 1 (2.8 m deep) and 2 (1.8 m deep) were sampled. Note the regularity of the fan surface in A, and the cementation of deposits associated with calcrete formation in A and B.

2.3. Uncertainties

3. Field example: El Puntal alluvial fan, Carboneras Fault

When fitting the models Eq. (9) or Eq. (10), we consider not only the uncertainties related to concentration measurements (sC) but also those related to depth estimation (sx), both as independent random errors:

The left-lateral Carboneras Fault (SE Iberia) displays ample geomorphological evidence of Quaternary tectonic activity both in its onshore and offshore sections (Bousquet, 1979; Goy and Zazo, 1986; Bell et al., 1997; Faulkner et al., 2003; Gràcia et al., 2006; Moreno et al., 2009). Deformed Quaternary sedimentary units of known age imaged in offshore seismic profiles suggest vertical slip rates ranging from 40 to 140 m/Ma (Moreno et al., 2009). In its central section, the onshore Carboneras Fault splits into two parallel traces forming the La Serrata SW-NE linear range (Fig. 2). The El Puntal alluvial fan, which flanks the La Serrata range to the NW, corresponds to second oldest generation of alluvial deposits deformed by the Carboneras Fault. This fan generation is considered to be of Middle Pleistocene age on the basis of relative chronology (Moreno et al., 2009), calcrete crust development (Dumas, 1969), and soil development (Schulte and Julià, 2001). Diagenetic characteristics of these deposits are common in semiarid climates. Outcrops in the El Puntal alluvial fan show uniform nodular and laminated calcrete crusts developed at sub-superficial horizons (down to c. 50 cm depth), whereas at deeper levels sediments range from weakly to strongly cemented (Fig. 3). The source area of the El Puntal alluvial fan in the La Serrata range mainly consists of deformed Miocene and Pliocene deltaic calcarenites and conglomerates with a high content of quartz

sið3;tÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2C þ s2x

(12)

If inheritance is considered as an input parameter, concentration measurement error includes not only errors related to the sample concentration measurement, but also the uncertainty in the estimation of inheritance:

sC ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2sample þ s2Inher:

(13)

As CInher. is considered constant with depth, the concentration uncertainty due to x error may be expressed as:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2 dCðx;3;tÞ
sx ¼ sr $zsample þ szsample $r dx

(14)

where the first addend corresponds to the error in density estimation, and the second addend reports the depth range where each single sample was collected (See Appendix A).

Table 1 Location and mean density of profiles studied. 10Be production rates due to spallation, stopping muons and fast muons (Pspal., Pstop and Pfast, respectively) have been calculated with the CRONUS-Earth online calculator v. 2.2, according to Balco et al. (2008). Profile

Latitude (N)

Longitude (W)

Elevation (m)

Mean density (g cm2)

Pspal. (at g1 a1)

Pstop (at g1 a1)

Pfast (at g1 a1)

PUN-1 PUN-2

36.86315 36.86425

2.19352 2.19150

110 117

2.2  0.3 2.1  0.3

4.35 4.38

0.0985 0.0989

0.0855 0.0857

190

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

Table 2 The El Puntal sample depths and 10Be concentrations. The value of the blank sample was 1014 atoms of 10Be/Be. Concentration uncertainties include the blank concentration uncertainty, measurement error and spectrometer standard error. Sample

Number of pebbles used

50 80 90 150 80 90 150 400 100 150 200 200 100

3.1. Methods

10

Depth (cm)

Be concentration (at g1)

267  5 195  5 141  5 95  5 46  6 33 163  4 135  3 97  3 58  3 32  2 33 >1000

518525 184334 264741 430387 732225 1069913 200185 280303 335545 485063 577632 820548 26380

Aprox. PUN01 PUN02 PUN03 PUN04 PUN05 PUN06 PUN07 PUN08 PUN09 PUN10 PUN11 PUN12 GRA02

pebbles and granules. Dacites, andesites, volcanic breccia and Miocene marlstones appear as secondary lithologies.

            

91090 8525 8419 19731 21527 41572 11087 12459 10311 14172 26009 23676 2949

Between 50 and 400 quartz pebbles (2e10 cm of diameter) from each sample were crushed and sieved to yield 250e1000 mm grains. The samples were then put through a Franz magnetic separator to remove any magnetic material. To eliminate carbonate, samples were digested with chlorhydric acid for 48 h, using organic oil as an antifoaming agent. After washing the oil residue, 3 to 6 Hexafluorosilicic acid digestions were performed for 3e6 days. Remaining quartz grains were cleaned using sequential HF dissolutions to remove any potential atmospheric 10Be (Brown et al., 1991; Kohl and Nishiizumi, 1992; Cerling and Craig, 1994). Between 15 and 30 g per sample of clean quartz cores were then completely dissolved in HF and spiked with 300 mg of 9Be carrier (Bourlès, 1988; Brown et al., 1992). Beryllium was separated by successive solvent extractions and alkaline precipitations (Bourlès, 1988; Brown et al., 1992).

Fig. 4. Sample concentrations vs. current effective depth expressed in g cm2. Error bars include concentration and depth uncertainties in A and B; and also density uncertainties in C and D. A, B) Best fits of models that only consider concentration and depth uncertainties. C, D) Best fits of models that consider concentration, depth and density uncertainties. The best fits of variable-density models are depicted by dashed lines. Constant-density model results that fit the measured 10Be dataset within 1s confidence level are depicted by gray areas.

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

Measurement of 10Be concentrations was performed at the ASTER AMS facility at Aix-en-Provence (France) in 2009. All 10Be concentrations are calibrated against the National Institute of Standards and Technology standard reference material 4325 by using an assigned value of 2.79  0.03  1011 and using a 10Be halflife of 1.36  0.07  106 years (Nishiizumi et al., 2007). 10Be concentrations in quartz were calculated following Balco (2006).

191

10

Be production rates corresponding to both sites were deduced from the location data using the CRONUS-earth online calculator v.2.2.1 (Table 1). All the computations used the same constants as CRONUS-earth online calculators (hess.ess.washington.edu), explained in Balco et al. (2008), Balco (2009, 2010). Therefore, in all our calculations, a decay constant of 4.9975 107 a1 (Chmeleff et al., 2010) and a spallation attenuation length of Lspall. ¼ 160 g cm2 (Balco et al., 2008) were used. The local muon attenuation lengths Lstop ¼ 1303 g cm2, and Lfast ¼ 2193 g cm2 were calculated from our field data (location and depths) using CRONUSearth online calculator v.2.2.1 Matlab code. The computation of 10Be concentration models was performed using a computer algebra system software. 3.2. Data collection and results Two small anthropic outcrops excavated across the El Puntal alluvial fan (SW Serrata range) were selected for 10Be depth profile sampling (Figs. 2 and 3, Table 2). Both outcrops are located c. 1 km from the fan apex, where the fan surface is well preserved, and where there are no significant signs of erosion or incision. They are mainly made up of cross-bedded pebble conglomerates with a variable matrix content (Fig. 3). Laterally, and also at the bottom in outcrop 1, major erosional discontinuities divide these high energy torrential facies from gravels with a higher matrix content. Profiles 1 and 2 were sampled at different depths (Table 2, Fig. 1). Six samples were collected from each profile: PUN01 to PUN06 from outcrop 1, and PUN07 to PUN12 from outcrop 2 (Fig. 4). In addition, a deep sample (GRA02, Table 2) was collected from a quarry in the Pliocene conglomerates close to the apex of the alluvial fan. The high energy sediment facies sampled in Profiles 1 and 2 are consistent with fast transportation and are in agreement with the proximity of the Carboneras fault, the trace of which is located less than 1 km upstream (Fig. 2). This suggests that the potential 10Be inheritance component formed during transportation of quartz grains is probably negligible. However, most of the source area of these deposits is formed by Pliocene conglomerates that could have a certain concentration of 10Be due to the exposure of the quartz grains prior to their burial (Pliocene) and/or during exhumation (Pleistocene). The first source of inheritance is represented by the GRA02 concentration and was introduced into the models as a minimum value of the variable CInher. (Fig. 5 A). The irregular cementation pattern of sediments in the outcrops studied implies a variation in sediment density from 1.8 g cm2 (uncemented gravels) to 2.5 g cm2 (gravels with well developed calcrete crust). Bulk density measurements yielded a mean density of 2.2 g cm2 for outcrop 1 and 2.1 g cm2 for outcrop 2, and 1s density uncertainties of 0.2 g cm2 were considered.

Fig. 5. Probability distribution of each variable according to models. Densities are expressed in g cm3 x axis correspond to values of each variable CInher., age (t) and erosion rates (31and 32). For each single value of each variable, the best fit of each model was calculated. The y axis represents the cumulative probability of the calculated best fit (c2(variable)min) with respect to the total distribution over the best value c2min , as shown in Fig. 1. Models not considering density uncertainties are indicated by gray lines and variable-density models are represented by dashed lines. A) Probability distribution of inheritance according to models. A minimum value of CInher. ¼ CGRA02 was introduced. CInher. values predicted by variable-density model (dashed) are similar to those predicted by the constant-density models that considers the initial density. B) Probability distribution of age according to models. Behaviour of variable-density model with respect to age probability distribution is similar to the constant-density model that considers the mean density through time (c. 2 g cm3). C) Probability distributions of erosion rates according to models. As all the models predicted similar probability distributions, some of them were not represented.

Table 3 Two-profile models results (y ¼ 11 samples - 4 parameters ¼ 7 degrees of freedom). Model in the first 3 rows and model in the penultimate row consider no density uncertainties. Models in the first 6 rows do not consider variation of densities through time. r1 is the current mean density, 2.2 g cm3 for Profile 1 and 2.1 g cm3 for Profile 2. Initial density (g cm3)

Final density (g cm3)

c2min

Qf

CInher.,best (103 at g1)

31,best e 32,best

(104 g cm2a1)

tbest (ka)

1.8 2.0

1.8 2.0

r1

r1

11.6 12.6 12.1 3.1 4.1 4.9 12.6 4.3

0.16 0.14 0.14 0.75 0.68 0.67 0.13 0.71

44 45 45 39 37 27 26 73

0.0e3.9 5.4e8.1 5.9e8.9 2.2e6.1 5.8e8.8 6.3e9.2 6.4e8.9 0.0e4.7

243 535 774 307 676 1152 651 248

1.8  0.2 2.0  0.2 r1  0.2 1.8 1.8  0.2

1.8  0.2 2.0  0.2 r1  0.2

r1 r1  0.2

192

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

Given that geomorphological evidence indicates that both profiles must reflect the same age, only two-profile models were constructed, using 11 samples to compute 4 parameters, hence, implying 7 degrees of freedom. To evaluate the relevance of density when fitting the models to the 10Be depth profile datasets, the following cases were considered: (i) constant densities without uncertainty, (ii) constant density with uncertainty, and (iii) variable density with current uncertainty. Constant-density models shown in Fig. 5 and Table 3 consider initial (1.8 g cm2 for uncemented gravels), mean (2.0 g cm2) and current densities. The variable-density model was computed with an initial density r0 of 1.8  0.2 g cm2. Results of variable-density models are also shown in Fig. 6.

similar effect can be observed in a buried depth profile. However, unlike the erosion process, the density gain implies a higher production of cosmogenic nuclides at depth while keeping the same production near the surface. Fig. 7A shows that deep nuclide concentrations are more sensitive to density variations whereas shallow nuclide concentrations are more sensitive to burial or erosion processes. Fig. 7B shows that concentrations obtained from the variabledensity model are only slightly different from those obtained by a constant-density model using the time averaged density. The use of a constant-density model with the time averaged density could be a reasonable approach despite the fact that the profile obtained from the variable-density model has a greater curvature.

4. Discussion

4.2. El Puntal alluvial fan

4.1. Variable-density model behaviour

The deepest sample PUN01 (Profile 1) shows an abnormally high concentration of 10Be (Fig. 4). Considering the stratigraphic erosional discontinuities observed in outcrop 1, this high concentration value can be interpreted as corresponding to an older

If an initial density lower than the current density is used, the curvature of the theoretical concentration depth profile increases. A

A

B

C

D

Fig. 6. Projections of the best fit result (black dots) and the CInher.-31-32-t hyper-volume corresponding to variable-density model results that fit the data within 1s confidence level. Owing to the simplicity of the relationship between 31 and 32 (which is almost linear, as shown in graph B), only four 2D projections are represented. Graph A indicates that inheritance and erosion rate behave almost as independent parameters; and graphs C and D show that the age is sensitive to erosion rate and inheritance. The inset graph in D represents source area erosion rate vs. CInher. values. CInher. values are calculated considering a Pliocene inherited amount of 10Be (CGRA02) and the 10Be accumulated during exhumation, which depends on the source area erosion rate. Shaded areas correspond to results that are improbable because of indirect estimates: CInher. in A and D, and erosion rates in B and C.

Á. Rodés et al. / Quaternary Geochronology 6 (2011) 186e194

Fig. 7. Examples of depth concentrations according to constant and variable-density models, with an exposure age of 500 ka. A. Effects of density gain and erosion in theoretical cosmogenic concentration depth-profiles. B. Comparison between a variable-density model considering a density evolution from 1.6 to 2.4 g cm3 and constant-density models considering initial, final and time averaged densities. All models are calculated for sea level, high-latitude production rates and attenuation lengths of Pspal. ¼ 4.5 at g1 a1, Pstop ¼ 0.096 at g1 a1, Pfast ¼ 0.085 at g1 a1, Lspal. ¼ 160 g cm2, Lstop ¼ 1510 g cm2 and Lfast ¼ 4320 g cm2.

193

Mathematically this implies that, in Eq. (12), sx obtains higher values than sC as depth increases. When this uncertainty is considered, a higher variability of models fit the data within 1s confidence level than when it is not (Fig. 4A and B vs. C and D). As shown in Fig. 5, the increase in model freedom when considering density uncertainties affects the inheritance and ages predicted by the models, but does not significantly affect the erosion rate predictions. Best fits of models that consider a density variation through time show similar quality factors (Table 3) but slightly different probability distribution ranges of inheritance and age (Fig. 5). However, probability distributions of free parameters in variabledensity models are similar to those predicted by constant-density models using a time averaged density. Therefore, to ignore the density evolution of these sediments by using the current density would result in an overestimation of the age and of the inheritance. Predicted values of inheritance (Fig. 5A) imply erosion rates higher than 50 m/Ma in the source area of the El Puntal fan, which is in the La Serrata range (inset graph in Fig. 6D). In general, the erosion rates in the uplifted range of La Serrata are not expected to be much higher than the dip-slip rates of the Carboneras Fault (c. 40e140 m/Ma, according to Moreno et al. (2009)). Hence, at a conservative estimate, erosion rates higher than 200 m/Ma are not expected in the source area of the El Puntal fan, which implies a lower limit of c. 50,000 at g1 for inheritance. According to the variable-density model, these values for inheritance correspond to ages T1,000,000 a (Fig. 6D). Therefore, according to the estimates of the La Serrata erosion rates, the age of the El Puntal alluvial fan is probably lower than 1 Ma. All the results of the models reflect a higher erosion rate in Profile 2 than in Profile 1 (Fig. 6B). The models indicate that since the abandonment of the alluvial fan, thicknesses of 0e2.8 m and 0.6e4.5 m have been lost by erosion at the tops of Profiles 1 and 2, respectively. This relatively large contrast in denudation within the restricted area of sampling can be ascribed to the proximity of an active channel to outcrop 1, which since the abandonment of the fan surface could have increased erosion due to diffusion processes in neighboring areas. However, the highest values of surface lowering predicted by the models (2.8 and 4.5 m) are probably not realistic considering the smooth surface of the El Puntal fan (Figs. 2 and 3A). Fig. 6C shows that the highest erosion rate values, and thus the greatest lowerings, correspond to the oldest ages in the 10Be models. Hence, the regularity of the El Puntal Fan surface suggests that the oldest ages predicted by the model may not be realistic in line with the constraints deduced from inheritance estimates. 5. Conclusions

alluvial surface. Hence, PUN01 was treated as an outlier and was not computed in the models. Studying the pedogenic carbonate coatings in a semi-arid Mediterranean climate during the Pleistocene and the Holocene, Badía et al. (2009) observed that the gain in carbonate in fluvial terraces was regular through time. This suggests a linear increase in density with time in alluvial sediments, as contemplated in our variable-density model. According to the density evolution reflected in this model, the El Puntal alluvial fan would have a most probable age of 248 ka (Table 3), with a 1s confidence level ranging between 214 and 1625 ka, as indicated by the black dashed line in Fig. 5B. As shown in Table 3, all models that consider density uncertainties obtained a significantly better quality factor than models not considering density uncertainties, suggesting that density uncertainty is a relevant factor that must be taken into account when fitting data and models. Fig. 4 shows that the uncertainty of x (expressed in g cm2) increases with depth due to the uncertainty in density. For deep samples, x uncertainty is more relevant than the concentration uncertainty when fitting the model to the data.

Although inheritance is the most important factor in restricting the age of a depositional landform, the density of a deposit is also a crucial factor in modeling cosmogenic nuclide depth-profiles to interpret precise concentration measurements. In cases where the distribution of density is not well constrained, an adequate propagation of the vertical error is needed to obtain realistic confidence level boundaries (sx in Eqs. 12 and 14). In landforms made up of cemented sediments, models that do not take into account the increase in density due to diagenetic processes are expected to significantly overestimate landform ages. The variable-density model presented here, which considers a uniform density gain, can be used to yield more realistic age estimates. Comparison of results between variable and constantdensity models shows that, if a constant-density model is used to fit data from cemented sediments, a time averaged density must be considered. Once the 10Be inheritance is constrained by indirect estimation of erosion rates in the source area, 10Be data modeling of two depth profiles indicates that the El Puntal alluvial fan has an age ranging

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from 214 ka to c. 1 Ma within 1s confidence level. This is the first numerical age constraint on the second oldest generation of alluvial fans associated with the Carboneras Fault zone. Acknowledgements This study has been sponsored by Spanish National Project EVENT (CGL2006-12861-C02-02) and supported by the ConsoliderIngenio 2010 programme, under CSD2006-0004 “Topo-Iberia”. The French AMS national facility ASTER (CEREGE) is supported by the INSU/CNRS, the French MESR, IRD and CEA. We are grateful to M. Arnold, G. Aumaître and K. Keddadouche for 10Be AMS measurements. Appendix. Supplementary material Supplementary data related to this article can be found online at doi:10.1016/j.quageo.2010.10.004. Editorial handling by: R. Grun References Badía, D., Martí, C., Palacio, E., Sancho, C., Poch, R.M., 2009. Soil evolution over the Quaternary period in a semiarid climate (Segre river terraces, northeast Spain). Catena 77, 165e174. Balco, G., 2006. Converting Al and Be Isotope Ratio Measurements to Nuclide Concentrations in Quartz. Cosmogenic Nuclide Lab, University of Washington. http://hess.ess.washington.edu. Balco, G., 2009. 26Al-10Be Exposure Age/erosion Rate Calculators: Update from v. 2.1 to v. 2.2. Cosmogenic Nuclide Lab, University of Washington. http://hess.ess. washington.edu. Balco, G., 2010. 26Al-10Be Exposure Age/Erosion Rate Calculators: Update of Constants File from 2.2 to 2.2.1. Cosmogenic Nuclide Lab, University of Washington. http://hess.ess.washington.edu. Balco, G., Stone, J.O., Lifton, N.A., Dunai, T.J., 2008. A complete and easily accesible means of calculating surface exposure ages and erosion rates from 10Be and 26Al measurements. Quaternary Geochronology 3, 174e195. Bell, J.W., Amelung, F., King, G.C.P., 1997. Preliminary late quaternary slip history of the carboneras fault, Southeastern Spain. Journal of Geodynamics 24 (1e4), 51e66. Bourlès, D.L., 1988. Etude de la géochimie de l’isotope cosmogénique 10Be et de son isotope stable 9Be en milieu océanique. Application à la datation des sediments marins. Ph.D. thesis, Paris-sud Centre d’Orsay. Bousquet, J.-C., 1979. Quaternary strike-slip faults in southeastern spain. Tectonophysics 52 (1e4), 277e286. Braucher, R., Del Castillo, P., Siame, L., Hidy, A.J., Bourlés, D.L., 2009. Determination of both exposure time and denudation rate from an in situ-produced 10Be depth

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