Stud. Geophys. Geod., 57 (2013), 647668, DOI: 10.1007/s11200-013-0809-7 647 © 2013 Inst. Geophys. AS CR, Prague

Numerical relationships between magnetic parameters measured in Quaternary sediments and global paleoclimatic proxies

ALFREDO PERALTA1, VINCENZO COSTANZO-ALVAREZ1, EDUARDO CARRILLO2, LEONARDO EVERT

DURÁN1, MILAGROSA ALDANA1 AND DANIEL REY3

1 Universidad Simón Bolívar. Dpto. Ciencias de la Tierra, Caracas, Venezuela (vcosta@usb.ve, maldana@usb.ve)

2 Universidad Central de Venezuela. Instituto de Ciencias de la Tierra, Caracas, Venezuela (eduardo.carrillo@ciens.ucv.ve)

3 Departamento de Geociencias Mariñas e Ordenación do Territorio, Universidad de Vigo, Spain (danirey@uvigo.es)

Received: January 28, 2013; Revised: August 1, 2013; Accepted: August 27, 2013

ABSTRACT

The complexity of most geological and geophysical problems prompts sometimes the use of non linear mathematical methods to handle them. An adaptive neuro fuzzy inference system (ANFIS) that combines fuzzy logic with neural networks, is applied here to study a paleoclimate section from the Quaternary sedimentary fill of the Lake Mucubají (western Venezuela). The purpose of this work is to find a set of numerical relationships that could predict the possible connections between oxygen isotope ( 18O) values from two different locations in the northern hemisphere (Ammersee in southern Germany and an ice core from the Greenland Ice Core Project - GRIP) and rock-magnetic parameters measured in Mucubají samples (i.e. mass-specific magnetic susceptibility - χ, magnetic remanence S-ratio, mass-specific saturation isothermal remanent magnetization - SIRM and anhysteretic remanent magnetization - ARM). The best inferences in terms of coefficient of determionation R2 and the Root Mean-Square Error (RMSE) are obtained using those magnetic data as input that include information about magnetite grain size distributions, e.g., SIRM and ARM in FIS structures [1χ, 4ARM] and [4ARM, 1SIRM]. A comparison between Ammersee and GRIP actual data, as well as their corresponding inferences for the FIS structure [4ARM, 1SIRM], reveals a reasonable good inference of global trends for both records, overlooking the regional and/or local paleoclimate forcings that might have affected Ammersee. A better correlation between global isotope paleoclimate records and magnetic proxies, is perhaps prevented by the role played by local and regional paleoclimate and tectonism in Mucubají. We also argue that the ratio of ARM over SIRM appears to be related in a complex way to the onset and to the end of the Younger Dryas. Our novel approach to the assessment of a specific paleoclimate case study shows the potential of the ANFIS technique in solving problems where traditional univariate and multivariate linear regression methods could prove inadequate.

Ke y wo rd s : Holocene, Neuro Fuzzy System, paleoclimate, rock magnetic properties

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1. INTRODUCTION

The use of univariate or multivariate linear regression analyses is a common practice when it comes to correlate different paleoclimate proxies (e.g., Volkman et al., 1995; Mourguiart et al., 1998; Harris and Mix, 1999, 2002; Hodell et al., 2001; Poage and Chamberlain, 2001; Jones et al., 2001; Kowalski, 2002; Johnson and Ingram, 2004; Sturm et al., 2007 and Bowen, 2008, among others). Nevertheless, in most cases geological and geophysical systems encompass complex sets of dispersed data that prompt the use of alternative non linear ways to handle them. One of these possible alternative means could be the use of a computing tool such as the ANFIS (adaptive neuro fuzzy inference system), a hybrid algorithm that combines neural networks with fuzzy logic. The ANFIS has been employed in the past in different areas of geosciences and diverse geological settings (e.g., Muller et al., 1998, 1999; Huang and Leung, 1999; Gautam and Holz, 2001; Nikravesh and Aminzadeh, 2001; Huang et al., 2001; Janakiraman and Konno, 2002; Finol and Jing, 2002; Tutmez et al., 2006; Ziaii et al., 2009; Hurtado et al., 2009; Rajaee et al., 2010; Tahmasebi and Hezrkhani, 2010; Singh et al., 2010 and Zoveidavianpoor et al., 2013, among others). However, the only application of this computational tool to a paleoclimate study is so far that by Da Silva et al. (2010) who found a set of non linear relationships between Miocene global climatic changes (benthic foraminifera 18O) and magnetic parameters (i.e. S-ratios and susceptibility) measured in a Colombian stratigraphic well.

In this work we apply the ANFIS to the study of some rock magnetic experimental data (magnetic susceptibility χ, magnetic remanence S-ratio, mass-specific saturation remanent magnetization SIRM and anhysteretic remanent magnetization ARM) measured in a composite paleoclimate section that includes two stratigraphic intervals of a single core drilled in the Quaternary sedimentary fill of the Lake Mucubají (western Venezuela). Magnetic parameters (i.e. magnetic susceptibility) have been widely used as paleoclimate proxies in the past, since the early works by Shackleton and Opdyke (1973) and Kent (1982), up to the numerous studies on loess (e.g., Zhu et al., 2001; Retallack et al., 2003; Balsam and Chen, 2004), lake sediments (e.g., Geiss and Banerjee, 1997; Hu et al., 2000) and marine sediments (e.g., Alexander et al., 1993; Brachfeld and Banerjee, 2000; Moreno et al., 2002).

Our goal is to look for a set of numerical relationships that could predict, in a satisfactory way, the likely connections between paleoclimate proxies (i.e. 18O) and the magnetic data that might describe the variations of types and concentrations of magnetic minerals (i.e. χ and S-ratios) and/or their grain size distributions (mass-specific SIRM and ARM). The Lake Mucubají could be considered as an appropriated natural laboratory for the ANFIS study proposed here, since its geological history reveals that it has undergone a series of events related to tectonic and climate changes, encrypted in the lithological and magnetic properties of a rapidly accumulated continuous stratigraphic sequence (Carrillo et al., 2008).

The two isotope paleoclimate records used in our computational tests are the 18O ratios of precipitation of a glacial lake environment at Ammersee (southern Germany), reported by the National Oceanic and Atmospheric Administration (NOAA) from deep-lake ostracods (von Grafenstein et al., 1999), and the 18O database of the Greenland Ice

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Core Project (GRIP). Both datasets have the ideal decadal resolution that allows an appropriated correlation with the temporal scale of our paleoclimate section in Lake Mucubají. Although it is reasonable to believe that δ18O from Ammersee might be influenced by the effects of regional and local paleoclimate forcings in mid Europe, they seem to be also properly tuned to global climate changes in the northern hemisphere when compared to their Greenland´s counterparts, even for some fine scale features produced by rapid temperature shifts (von Grafenstein et al., 1999).

2. GEOLOGICAL SETTING

The Lake Mucubají is part of a network of glacial lakes located in the western Venezuela Andean range (Fig. 1). This lake was affected by the Andean tectonic through the Boconó Fault, and by alternated glacial and interglacial periods (Carrillo et. al, 2008). It is located at 3550 m above sea level surrounded by moraines, has a perimeter of 2.3 km, 785 m length, 540 m width, 16 m of maximum depth and a total water volume of 1.5 millions of m3 (Carrillo et. al, 2008).

The northern end of the SouthAmerican continent is framed by a dextral transform system that accommodates the relative movement between the Caribbean and the South American plates. The average displacement in this network of faults is 2 cm/yr (Pérez et

Fig. 1. Regional geographical and structural setting of the Lake Mucubají in western Venezuela (after Carrillo et al., 2008, © 2007 Elsevier B.V.).

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al., 2001). The Boconó fault releases more than a half of this stress whereas the rest is released by other faults in the region such as Oca - San Sebastián - El Pilar system (Audemard et al., 1999). Sedimentary deposits, dating from the last glacial maximum (Pleistocene), are particularly abundant in the central section of the Boconó fault. Previous studies have established a relationship between the tectonic activity in the moraines and interglacial periods in lake sediments (Giegengack et al., 1976, Schubert, 1982; Giegengack, 1984). On the other hand, Salgado-Labouriau and Schubert (1976), Rull (1996) and Mahaney et al. (2000) have focused their studies on glacial and post glacial sediments in order to monitor possible climate and vegetation changes in the region and to compare them with global climate changes. These researchers consider that the last glacial period that affected this part of the country is equivalent to the last glacial maximum.

Figure 2 shows a bathymetric map of the Lake Mucubají with the location of the 4 cores studied by Carrillo et al. (2008). We worked with a section of the composite core MUCL-02-02, extracted from a depth of approximately 11 m. Fig. 3 (modified after Carrillo et al., 2008) presents a scheme of these four cores with their most important lithological features. The three main lithological units described from base to top by Carrillo et al. (2008) are:

Unit I: characterized by the presence of sandy and shale siltstones, with lamination or thin inter stratiphication. Some layers have basal horizons with fine to medium-grained sands (quartz, muscovite and feldspars). The bottom part of this unit is a layer of coarse-grained and massive shale that underlines another layer of coarse-grained sands.

Unit II: characterized by mainly sandy to silty shales with abundant particles of organic matter with thin stratiphication. Radiocarbon ages for this unit, from the MUCL-02-01, show that the transition between Units I and II coincides with the beginning of the last glacial maximum.

Fig. 2. Bathymetric map of the Lake Mucubají showing the location of core MUCL 02-02 used in this study (after Carrillo et al., 2008, © 2007 Elsevier B.V.).

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Unit III: does not show a clear stratiphication and has mainly silt, shale and abundant organic matter. The upper meter of MUCL-02-03 has a high amount of fine-grained detritus of aquatic plants. This unit also reveals the presence of diatomea shells (Carrillo et al., 2008).

3. SAMPLING AND EXPERIMENTAL TECHNIQUES

Samples were taken continuously every 2.5 cm and prepared in cubic plastic boxes. Out of the 96 samples available, we only worked with the 64 ones that seem to be purely related to the paleoclimate record and do not appear to have been largely affected by regional and/or local tectonism. As a matter of fact, we eliminated those stratigraphic levels at the top and bottom of the section (32 samples) that correspond to instantaneous and turbiditic events. That is to say major changes in sediment textures and composition produced by shock induced deposits and reworking features such as slumps and liquefaction, and likely related to earthquakes at the nearby Boconó Fault (Carrillo et al., 2008).

Fig. 3. Scheme of the four cores drilled in the Lake Mucubají. This figure shows the main lithostratigraphic features in these cores as well as the intersection 14C ages in years (BP) obtained from the calibration curve and the 14C conventional ages using 2 (95%) intervals (modified after Carrillo et al., 2008, © 2007 Elsevier B.V.). The thick box between 400 and 600 cm in MUCL 02-02 shows the paleoclimate section used in this study, which is encompassed by intersection 14C ages 12890 BP in MUCL 02-02-02B and 10890 BP in neighboring MUCL 02-02-01.

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Figure 3 shows our paleoclimate section (gray box) in MUCL 02-02 (Unit II) that is within two 14C intersection ages, namely12890 BP (top of a reworking event in MUCL 02-02-02B) and 10890 BP (bottom of the following younger reworking event in MUCL 02-02-01) (Fig. 3). According to Carrillo et al. (2008) these ages come from thin layers of fine-grained organic matter that probably accumulated, from lighter suspended particles, at the latest stages of major turbiditic events related to seismic-tectonic activity in the region (i.e. slumps). We have chosen this rather homogeneous 160 cm-thick layer of laminated silty clays as our paleoclimate section to further minimize the possible role of regional and/or local tectonics upon the rock magnetic data.

Figure 4a shows the two δ18O paleoclimate records that are linked to the rock magnetic proxies of the Lake Mucubají, namely Ammersee (southern Germany) reported by the National Oceanic and Atmospheric Administration (NOAA) (von Grafenstein et al., 1999) and the database of the Greenland Ice Core Project (GRIP). In addition, Figs 4b,c,d,e show the profiles of χ, S-ratio, mass-specific SIRM and ARM respectively, measured at different levels of the two Mucubají cores that we have analyzed (i.e. MUCL 02-02-02B and MUCL 02-02-03B).

From these profiles some shared trends between the magnetic parameters and their corresponding paleoclimatic proxies are easy distinguishable. Indeed, at the Lake Mucubají where the main drainage into the lacustrine basin came from its tributaries, the magnetic susceptibility must have been related to the terrigenous input that characterized warm and humid (surface runoff) periods such as the onset of the Holocene (i.e. higher χ and δ18O values). Conversely, in cold weather (i.e. Younger Dryas) the intensity of the alteration probably decreased together with the magnetic susceptibility and their corresponding δ18O values.

Our first step was to tie up the Lake Mucubají magnetic proxies with a δ18O dataset that seems to mirror somehow the climate variability in the time period encompassed by our section (i.e. NOAA δ18O inferred from deep-lake ostracods at Ammersee in southern Germany, von Grafenstein et al., 1999). It is important to bear in mind that there is quite a number of detailed δ18O paleoclimate records available, from different geographical locations, that could be equally suited as comparison patterns for the numerical tests we performed using Lake Mucubají rock magnetic data. One of these records comes from the Caripe basin (Lin et al., 1997) located approximately 2N and 600 km east of Mucubají. However, in our particular case, the choice of Ammersee does not obey to a geographical proximity criterium, but rather to its geological and depositional characteristics. Indeed, although Cariaco is close to Lake Mucubají we have to take into account that it is a deep pull-apart marine basin, subjected to anoxic conditions of sediment accumulation. Thus there is no guarantee that the local and regional features of Cariaco paleoclimate data would resemble, better than Amersee`s, the so far inexistent δ18O record for Lake Mucubají. On the other hand, Ammersee data come from a lake formed by glaciers melting, in a very similar setting to the one that prevailed in Mucubají at the end of the Pleistocene and beginning of the Holocene. Moreover, these data have the appropriated decadal time resolution needed to compare with the minimum time-window encompassed by our rock magnetic parameters.

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Since the δ18O record for Ammersee might be influenced by the effects of regional and local paleoclimate forcings at its location in mid Europe, which are climatically different to those at near-tropical latitudes, we also compared Mucubají magnetic parameters with the global paleoclimate δ18O record obtained from an ice core drilled in central Greenland as part of the joint European Greenland Ice Core Project (GRIP). The Ammersee paleoclimate record shows global trends too since it allows a precise and even a fine scale lateral correlation with the δ18O proxies of the GRIP dataset (i.e. the youngest Dansgaard-Oeschger event) within the time period 5000 to 15000 years (von Grafenstein et al., 1999). Lea et al. (2003) also compared the Cariaco paleoclimate sea surface temperature (SST) record, calculated from the Mg/Ca values of surface-dwelling

Fig. 4. a) Profiles of 18O for the 1289010890 BP age interval, inferred from ostracods in the Ammersee (crosses) after von Grafenstein et al. (1999), and from an ice core drilled for the Greenland Ice Core Project (diamonds). b) Magnetic susceptibility [108 m3/kg], c) mass-specific ARM [103 Am2/kg], d) mass-specific SIRM [103 Am2/kg] and e) magnetic remanence S-ratio along stratigraphic levels measured in Lake Mucubají (MUCL 02-02-03-B and MUCL 02-02-02-B). Those levels that correspond to instantaneous and turbiditic events, at the top and bottom of the section, were eliminated from these profiles leaving only the paleoclimate record. A 32 cm gap (approximately 400 years) between MUCL 02-02-03-B and MUCL 02-02-02-B, as well as the limit at the end of the Younger Dryas and the beginning of the Holocene, are also shown. The 18O are linked to magnetic data in Lake Mucubají through an intersection 14C age of 12890 BP measured at MUCL 02-02-02B and the next youngest intersection 14C age available of 10890 BP measured at neighboring core MUCL 02-02-01 (after Carrillo et al., 2008), assuming a constant accumulation rate of 0.08 cm/yr.

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planktonic foraminifera, with the δ18O global records of Greenland GISP II ice core and the atmospheric methane from the GRIP itself, demonstrating that there has been a synchroneity of tropical and high latitude Atlantic temperatures over the past 25000 years.

The global δ18O data from Ammersee and the GRIP in Fig. 4a, are age-linked to the rock magnetic profiles by the 14C intersection ages of the two major turbiditic events that bracket our paleoclimate section between 12890 and 10890 BP (Fig. 3). We also presupposed a constant sedimentation rate of 0.08 cm/yr for this 160 cm-thick section that was accumulated in a 2000 years time period. Although the assumption of a constant accumulation rate may not be entirely true due to the existence of a possible erosional contact around 480 cm in MUCL 02-02 (Fig. 3), we still believe it is a reasonable hypothesis considering the range of the uncertainties we are handling. Carrillo et al. (2008) have previously anchored a major rise of the magnetic susceptibility in MUCL 02-02-03B to the temperature transition between the end of the Younger Dryas and the beginning of the Holocene, described by regional and global paleoclimate records from Greenland and the Cariaco Basin. Incidentally, such a correlation is preserved for our rock magnetic data without need of any further adjustment, when the constant accumulation rate of 0.08 cm/yr assumed for MUCL 02-02-02B, is extended over MUCL 02-02-03B.

Each 2.5 cm sample along our paleoclimate section would represent an approximately 31 years time-window, although there is an about 400 years gap between 12000 and 12400 BP (i.e. the equivalent of 13 samples missing between MUCL 02-02-02B and MUCL 02-02-03B). Since the stratigraphic/temporal resolution of the δ18O data, for both Ammersee and GRIP, is approximately 0.85 cm during 11 years, we averaged these values every 31 years in order to assign a single δ18O mean of either paleoclimate record to the sets of rock magnetic data (i.e. χ, S-ratio and mass-specific SIRM and ARM) measured at each stratigraphic level in Lake Mucubají.

For the measurement of the magnetic susceptibility at room temperature, we employed a Bartington MS2 System with a MS2B. The readings of magnetic susceptibility were repeated 5 times and a standard deviation of less than 10% was calculated for each sample-average (Fig. 4b). We also measured the mass-specific saturation isothermal remanent magnetization (SIRM) and S-ratio ( 0.3T 3TIRM IRM , after Bloemendal et al., 1992), in a Molspin minispin rock magnetometer with a sensitivity better than 1 107 emu/cm3 at 24 s time constant (Figs 4c,e). In these experiments the SIRM was acquired after an ASC IM-10-30 pulse magnetizer with interchangeable coils, capable of generating fields in excess of 28 kGauss. The mass-specific anhysteretic remanent magnetization (ARM) was determined in a LDA-3 AF demagnetizer using a 100 mT initial AF peak field and a DC field of 50 μT (Fig. 4d). We also carried out thermomagnetic susceptibility experiments in air atmosphere, of various representative samples. The equipment used for these experiments was a CS-3 temperature control unit and a KLY-3S Kappabridge that allows continuous susceptibility and temperature readings of a sample during heating to 700C and then cooling back to room temperature.

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4. RESULTS

4 . 1 . R o c k m a g n e t i c r e s u l t s

Figure 5 shows thermomagnetic cycles (heating and cooling), measured in air atmosphere and obtained for selected samples at 441 cm, 451 cm, 465 cm and 481 cm. The heating curves show a well defined Curie point of 580C that reveals the presence of magnetite in these samples. In addition, all the 580C drops are preceded by a small increase of the magnetic susceptibility, probably a Hopkinson peak. Since susceptibility values are higher after cooling, we argue that new magnetite must have formed during laboratory heating.

Lithostratigraphic analyses performed in these rocks and their link to paleoclimate changes, seem to be indicative of their mostly primary (granitic) nature (Carrillo et al., 2008). There is some evidence for the presence of hematite (small tails of the thermomagnetic curves that go beyond 580C) that could have formed by chemical alteration of magnetite in both the source and the sedimentary rocks. Frank and Nowaczyk

Fig. 5. Thermomagnetic susceptibility curves (heating and cooling) measured in air atmosphere for samples from a) 441 cm, b) 451 cm, c) 465 and d) 481 cm.

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(2008) demonstrated, for a well-constrained experiment that uses synthetic samples with variable contents of magnetite upon hematite, that the amount of hematite can be quite significant in samples with S-ratio as high as 0.8 calculated according to the definition of Bloemendal et al. (1992). This could be the case of Mucubají samples as shown in the profile of Fig. 4e.

4 . 2 . C o m p u t a t i o n a l r e s u l t s

Once the correlation between the paleoclimate section and the δ18O values was obtained, we used an adaptive neuro fuzzy inference system (ANFIS) to find some numerical relationships that could link magnetic and paleoclimate proxies. The ANFIS is a computational tool that builds a system of fuzzy inference, out of a set of input and output variables. The parameters of the membership functions, that assign fuzzy values to the input variables and to the fuzzy rules, are adjusted via neural retropropagation algorithms allowing the system to learn from the data that is employing. For this work we applied the command ANFIS from MATLAB 6.5 that enables the use of fuzzy rules with AND and OR links, 11 different membership functions and either network or group partitions.

The five layers ANFIS employed here are equivalent, under some constrains, to a Takagi-Sugeno-Kang (TSK) model (Finol and Jing, 2002) that consists of a set of fuzzy if/then rules:

Ri: If x1 is Ci1 and x2 is Ci2 and … and xn is Cin

Then 1 1 2 2 0...i i i in n iy c x c x c x c

The output values yi are linear or constant function of the input variables xj (j = 1, 2, …, n). Ri (i = 1, 2, …, m) is the i-th fuzzy rule; Ci1, …, Cin are the antecedent linguistic variables and ci1, …, cin the consequent parameters (Da Silva et al., 2010 and Hurtado et al., 2008).

To train our fuzzy model we used δ18O values as output and χ, S-ratio, mass-specific SIRM and ARM as input variables. The hybrid method we employed to train the system combines a retropropagation neural network with the least square method. The maximum error allowed between inferred and actual values is previously fixed (tolerance error). The epochs are the number of iterations that the program runs and that could go from 1000 to 10000 depending on the diminution of the error in each case. Therefore, the training of the ANFIS adjusts the parameters of both the fuzzy rules and the membership functions up to the point in which the maximum number of iterations is reached, or the training error keeps within the level of tolerance.

Besides the possibility of establishing numerical relationships and predictive formulae, we also tried to discriminate the combinations of magnetic parameters that enable the best inference of the δ18O. The first computational trials we carried out used only one magnetic property as input variable and 2, 3 or 4 membership functions with their corresponding fuzzy rules. These tests were repeated with every experimental magnetic parameter. Afterwards, we checked the quality of the inference obtained using various

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pairs of these parameters as input variables. Once more we employed a maximum of 4 fuzzy rules, and a Gaussian membership function.

In order to test the flexibility of the system we limited the number of fuzzy rules to no more than 4. To infer both the δ18O Ammersee Lake and GRIP actual data we trained the system with only 60% of the data available randomly chosen and evenly distributed along

Fig. 6. Five best ANFIS inferences for the 18O of Ammersee (von Grafenstein et al., 1999), using a maximum number of 4 rules, for each number and/or combination of input variables, and after training the system with 60% randomly chosen datasets of magnetic parameters measured in a section of Lake Mucubaji MUCL 02-02. Solid lines stand for the inferred data whereas the circles represent the actual 18O mean values from Ammersee record. Scatter plots of inferred versus actual 18O show a better clustering of these data points, around the unitary-slope straight line, as the quality of the inference improves. a) [3], b) [4, 1S-ratio], c) [2, 2SIRM], d) [1, 4ARM], e) [4ARM, 1SIRM]. Fuzzy rules and parameters of the membership functions are shown in Table 1.

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the whole section. The output (inferred δ18O values) was then compared with its experimental counterpart and the performance of the fitting was tested using the coefficient of determination R2 and the Root Mean-Square Error (RMSE).

Figure 6 depicts some of the best inferences (minimum RMSE and maximum R2) of Ammersee δ18O paleoclimate record, using no more that 4 rules for each number and/or combination of input variables, and obtained after completing a large number of computational tests. Table 1 shows the parameters of the Gaussian membership functions [ 1 2h , Center], their corresponding fuzzy rules and the quality of the inference measured

from the RMSE and R2 values. The inferred 18O shown in Fig. 6a are obtained using χ as the sole input variable and 3 fuzzy rules (R2 = 0.426, RMSE = 0.779). The other best inferences are the ones shown in Fig. 6b for the FIS structure [4χ, 1S-ratio] (R2 = 0.406, RMSE = 1.013); Fig. 6c for the FIS structure [2χ, 2SIRM] (R2 = 0.575, RMSE = 0.813); Fig. 6d for the FIS structure [1χ, 4ARM] (R2 = 0.659, RMSE = 0.587) and Fig. 6e for the FIS structure [4ARM, 1SIRM] (R2 = 0.559, RMSE = 0.663).

These same structures were then tested with the GRIP data that yield the results shown in Fig. 7 and Table 2 (3χ: R2 = 0.785 and RMSE = 0.305; [4χ, 1S-ratio]: R2 = 0.426 and RMSE = 1.30; [2χ, 2SIRM]: R2 = 0. 545 and RMSE = 1.195; [1χ, 4ARM]: R2 = 0.594 and RMSE = 0.846 and [4ARM, 1SIRM]: R2 = 0.611 and RMSE = 0.826).

Scatter plots of inferred versus actual δ18O (Figs 6 and 7) show how the clustering of these data points, around the unitary-slope straight line, gets better as the quality of the inference improves.

5. DISCUSSION

From the various computational trials we carried out to infer the δ18O paleoclimate records of Ammersee and GRIP, using just one single input variable at a time and up to 4 fuzzy rules, mass-specific susceptibility χ yields the optimal results for the FIS structure 3χ (Tables 1 and 2). However, a qualitative examination of Figs 6a and 7a reveals that the ability of the ANFIS to infer 18O throughout the whole section is still inadequate (Tables 1 and 2). This is probably due to the fact that there is not a univocal correlation between χ and global paleoclimate proxies. Indeed, magnetic susceptibility values might have been also affected by the presence of paramagnetic minerals in these rocks. Moreover, χ values are not very sensitive to changes in particle sizes of magnetite either. Thus, in order to test the ANFIS and to compensate for the effects of those factors that might have an influence on the information contained in the magnetic susceptibility profile, we combined χ with other input variables such as S-ratio and mass-specific SIRM and ARM.

The S-ratio measures the relative contribution of low (e.g., magnetite) and high (e.g., hematite and goethite) coercivity minerals to the total saturation isothermal remanent magnetization. From Figs 6b and 7b, as well as Tables 1 and 2 it seems clear that even the best ANFIS result, obtained after including this parameter in all the computational tests carried out for a maximum of 4 rules per number and/or combination

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Tab

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0.77

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1.01

3

0.81

3

0.58

7

0.55

9

Fuzz

y R

ules

If

[2

.324

, 15.

17]

18

O =

0.2

19

15.5

5 If

[10.

39, 4

6.08

]

18O

= 2

.372

34.3

6 If

[9.9

51, 4

9.90

]

18O

= 0

.739

11

39.5

If

[5

.31,

9.6

93]

S

(0.0

0196

5, 1

.031

)

18O

=

3.87

16

1.92

S+10

.43

If

[6

.126

, 14.

36]

S

(0.0

0196

5, 1

.031

)

18O

=

7.51

17

3.86

S+83

.50

If

[1

2.09

, 33.

30]

S

(0.0

0196

5, 1

.031

)

18O

=

0.47

06

21.0

4S+

27.8

0 If

[4.9

59, 5

5.2]

S

(0

.001

965,

1.0

31)

18

O =

0.

7218

16.2

S+15

.58

If

[1

8.81

8, 6

.206

] S

IRM

[6

48.6

87, 1

04.7

00]

18

O =

0.03

37SI

RM2

4.38

If

[18.

818,

6.2

06]

SIR

M

[649

.005

, 163

1.76

1]

18

O =

16

.557

0.23

3SIR

M+

188.

71

If

[1

4.69

8, 6

.098

6]

SIR

M

[648

.687

, 104

.700

]

18O

=

34.2

02

0.49

0SIR

M+

956.

23

If

[1

4.69

8, 6

.098

6]

SIR

M

[649

.005

, 163

1.76

1]

18

O =

2.8

86

0.17

78SI

RM+

122.

76

If

(1

0.03

, 62.

19)

ARM

[1

.198

, 0.0

2528

]

18O

= 0

.149

80

.536

ARM1

4.19

If

(10.

03, 6

2.19

) A

RM

[2.0

47, 1

0.26

]

18O

=

0.03

70

.281

8ARM

7.2

5 If

(10.

03, 6

2.19

) A

RM

[3.8

78, 1

7.82

]

18O

=

0.61

24

2.79

ARM6

3.96

If

(10.

03, 6

2.19

) A

RM

[4.0

14, 2

6.79

]

18O

=

26.1

63

4.2A

RM2

50.1

If A

RM

[1.0

63, 0

.377

5]

SIR

RM

(104

.6, 1

632)

18O

=

0.40

16

0.00

4884

SIRM

13.

21

If A

RM

[2.2

11, 1

0.6]

S

IRM

(1

04.6

, 163

2)

18

O =

0.

3924

0.00

1487

SIRM

5.2

8 If

ARM

[3

.837

, 17.

73]

SIR

M

(104

.6, 1

632)

18O

= 4

.870

0.02

503S

IRM8

9.04

If

ARM

[3

.737

, 26.

83]

SIR

M

(104

.6, 1

632)

18O

= 1

07.8

4.98

7SIR

M1

8.3

FIS

Stru

ctur

e

[3]

(3

)

[4,

1S-

ratio

] (4

, 1)

[2,

2SI

RM]

(2, 2

)

[1,

4AR

M]

(1, 4

)

[4AR

M, 1

SIRM

] (4

, 1)

NIV

1 2 2 3 3

A. Peralta et al.

660 Stud. Geophys. Geod., 57 (2013)

of input variables, give rise to a rather coarse inference (i.e. FIS structure [4χ, 1S-ratio]). This apparently weak association of S-ratio to the Ammersee and GRIP paleoclimate records is probably due to its limited variability, between 0.88 and 1, along the whole section.

Fig. 7. Five best ANFIS inferences for the 18O of the GRIP, using a maximum number of 4 rules, for each number and/or combination of input variables, and after training the system with 60% randomly chosen datasets of magnetic parameters measured in a section of Lake Mucubaji MUCL 02-02. Solid lines stand for the inferred data whereas the circles represent the actual 18O mean values from the GRIP record. Scatter plots of inferred versus actual 18O show a better clustering of these data points, around the unitary-slope straight line, as the quality of the inference improves. a) [3], b) [4, 1S-ratio], c) [2, 2SIRM], d) [1, 4ARM], e) [4ARM, 1SIRM]. Fuzzy rules and parameters for the membership functions are shown in Table 2.

Magnetic parameters of Quaternary sediments and global paleoclimatic proxies

Stud. Geophys. Geod., 57 (2013) 661

Tab

le 2

. Th

e sa

me

as in

Tab

le 1

, but

for t

he G

reen

land

Ice

Cor

e Pr

ojec

t dat

a.

R2

0.30

5

0.42

6

0.54

5

0.59

4

0.61

1

RMSE

0.78

5

1.03

0

1.19

5

0.84

6

0.82

6

Fuzz

y R

ules

If

[7

.429

, 10.

292]

18O

= 0

.019

40.0

0 If

[5.0

26, 3

9.82

8]

18

O =

0.

1553

2.72

9 If

[11.

680,

61.

337]

18O

=

0.12

33

0.21

3

If

[4

.837

, 9.8

04]

S

(0.0

96, 1

.0)

18

O =

0.3

49

1.45

2S4

5.50

1 If

[3.0

41, 2

4.56

9]

S

(0.0

096,

1.0

)

18O

= 0

.812

87.6

40S

145.

28

If

[1

0.00

0, 4

1.34

9]

S

(0.0

096,

1.0

)

18O

=

0.08

66

2.44

5S+

26.2

0 If

[7.6

46, 6

2.02

9]

S

(0.0

096,

1.0

)

18O

=

0.66

41

57.3

68S+

59.3

86

If

[1

2.45

7,

2.33

4]

SIR

M

[648

.378

, 104

.726

]

18O

= 1

.762

0.02

4SIR

M5

6.36

4 If

[12.

457,

2.

334]

S

SIRM

[6

49.9

13, 1

631.

535]

18O

=

26.7

09

0.51

5SIR

M+

163.

226

If

[1

3.69

1, 5

1.55

2]

SIR

M

[648

.378

, 104

.726

]

18O

=

2.85

10

.008

SIRM

+44

.464

If

[13.

691,

51.

552]

S

IRM

[6

49.9

13, 1

631.

535]

18O

= 0

.721

0.04

3SIR

M7

.012

If

(8

.995

62.

188)

A

RM

[0.8

68, 1

.177

]

18O

= 0

.166

0.34

4ARM

41.

391

If

(8

.995

62.

188)

A

RM

[2.8

88, 1

1.78

9]

18

O =

0.

1310

.176

ARM2

3.91

1 If

(8.9

95 6

2.18

8)

ARM

[3

.996

, 17.

233]

18O

= 0

.989

7.17

4ARM

176

.611

If

(8.9

95 6

2.18

8)

ARM

[4

.058

, 26.

841]

18O

=

28.4

70

28.2

52AR

M6

4.87

1

If A

RM

[0.8

46, 1

.229

] S

IRM

(1

00.1

72, 1

631.

893)

18O

=

0.23

4ARM

0.0

06SI

RM4

0.30

8 If

ARM

[2

.697

, 11.

181]

S

IRM

(1

00.1

72, 1

631.

893)

18O

= 0

.158

ARM0

.003

SIRM

27.

914

If A

RM

[3.8

78, 1

7.61

1]

SIR

M

(100

.172

, 163

1.89

3)

18

O =

16.

998A

RM0

.047

SIRM

300

.461

If

ARM

[3

.840

, 26.

394]

S

IRM

(1

00.1

72, 1

631.

893)

18O

= 1

71.6

99AR

M8

.060

SIRM

11.

747

FIS

Stru

ctur

e

[3]

(3

)

[4,

1S-

ratio

] (4

, 1)

[2,

2SI

RM]

(2, 2

)

[1,

4AR

M]

(1, 4

)

[4AR

M, 1

SIRM

] (4

, 1)

NIV

1 2 2 2 2

A. Peralta et al.

662 Stud. Geophys. Geod., 57 (2013)

As a further step in our computational trials we used, together with χ, the mass-specific SIRM as an input variable (FIS structure [2χ, 2SIRM]) since this magnetic parameter contains information about magnetite grain size distribution. Figs 6c and 7c, as well as Tables 1 and 2, show that the use of mass-specific SIRM, instead of S-ratio, improves the inference of the 18O suggesting that magnetite granulometric variations might be linked to paleoclimate changes too. Moreover, we also tested two other FIS structures that include mass-specific ARM (i.e. [1χ, 4ARM] and [4ARM, 1SIRM]). These trials lead to the optimal 18O inferences from all the computational tests we performed using a maximum of 4 rules per number and/or combination of input variables. They also give rise to the highest number of clusters out of the data available (Tables 1 and 2, as well as Figs 6d,e and 7d,e). Although both SIRM and ARM depend on magnetite granulometries, the former appears to be particularly sensitive to the presence of multidomain grain size distributions of this mineral, whereas the latter to the pseudosingle-single domain range.

In Fig. 8a we show, in a single plot, the Ammersee and GRIP δ18O actual values used to train the ANFIS. When these two datasets are closely compared, we find that both of them keep a difference that averages 27% along the whole section. Major deviations from this mean could be due to the fact that whereas Ammersee data might reflect regional and local changes in precipitation at the mid-latitudinal position of southern Germany, the GRIP data are mostly a global paleoclimate record. Similarly, figure 8b shows that the same gap of 27% is preserved between the optimal inferences of the 18O, for both Ammersee and GRIP datasets, when Mucubají magnetic proxies are employed as input variables using the FIS structure [4ARM, 1SIRM] (Tables 1 and 2 and Figs 6e and 7e). Moreover, 27% is nearly the same difference between the RMSE obtained for these two inferences (Tables 1 and 2).

It is noteworthy that, for the synthetic δ18O shown in Fig 8b, deviations from the 27% average of the percentile differences between these two datasets, have much less dispersion than those corresponding to the actual data (Fig. 8a). This result suggests that the magnetic proxies from Lake Mucubaji, used as input variables to train the ANFIS, provide a good inference of the global trends in both datasets but overlook the fine scale regional and/or local features that affected Ammersee 18O record. Even so, these inferences cannot be improved beyond the range from 61 to 66% (i.e. maximum R2 for both Ammersee and GRIP paleoclimate records) suggesting that global climate change alone does not explain all the variability in the magnetic records, but local and regional paleoclimate forcings and/or tectonic activity in Lake Mucubají might played a significant role too. Furthermore, it is important to bear in mind that neither the Ammersee nor the GRIP data necessarily represent the actual 18O for Lake Mucubaji, which have not yet been measured.

From a simple lateral correlation of cores at the Lake Mucubají, Carrillo et al (2008) claimed that there is not a systematic influence of grain size (whole rock) on magnetic susceptibility data. Thus they concluded that this paleoenvironmental proxy is rather linked to the intensity of alteration of a single source of sediments. However, since mass-specific ARM depends on both the concentration of magnetite and the size distribution of the fine-grained fraction of this mineral, we argue that the magnetic granulometric

Magnetic parameters of Quaternary sediments and global paleoclimatic proxies

Stud. Geophys. Geod., 57 (2013) 663

features of these sediments must be also related, in a complex way, to the global climate changes that affected the region. In order to demonstrate this hypothesis we directly compared an ARM SIRM profile (and its first derivative) with the 18O data (Fig. 9).

Fig. 8. a) Ammersee (crosses) and GRIP 18O (diamonds) mean values averaged in age windows of about 31 yrs around the dates assigned to each Mucubají depth level and assuming a constant accumulation rate of 0.08 cm/yr. These values, used to train the ANFIS, are compared in a single plot versus their corresponding radiocarbon intersection ages (after Carrillo et al., 2008). Deviations from an average difference of about 27% between these two datasets are also shown along the whole section. b) The optimal inferences of the 18O, for both Ammersee and GRIP datasets, obtained by using Lake Mucubají magnetic proxies as input variables and the FIS structure [4ARM, 1SIRM], are compared in a single plot versus stratigraphic level.

A. Peralta et al.

664 Stud. Geophys. Geod., 57 (2013)

The ARM SIRM ratio not only compensates for variations in concentrations of magnetite but is also a granulometric indicator that tends to increase as the grain sizes of this mineral decrease. The first derivative was calculated to highlight the variations of this parameter throughout the whole section. It is noticeable that temperature transitions at the onset and the end of the Younger Dryas, coincide with those stratigraphic levels that display a wavelet-like behavior of the ARM SIRM profile and its first derivative. Such peculiar features might be the record of short events of wavering energy variations associated to major global climate changes, in the context of a rather stable depositional regime. Although it is not clear the nature of the regional and/or local mechanisms that could have promoted changes in these parameters, we believed they might be related to grain flows that occurred during flooding events (Carrillo et al., 2008) throughout times of climatic instability at the beginning of both the Younger Dryas and the Holocene.

6. CONCLUSIONS

From the multiple computational trials we carried out, using just one single magnetic input variable at a time and up to 4 fuzzy rules, magnetic susceptibility (i.e. concentration of magnetite) gave rise to the best correlation between inferred and actual 18O for both Ammersee lake and GRIP datasets. However, there is not a univocal link between χ and global paleoclimate proxies in these rocks due perhaps to the effects of the paramagnetic fraction and the varying magnetite grain size distributions throughout the paleoclimate

Fig. 9. Profiles of ARM SIRM and their first derivatives, compared with the 18O paleoclimate records of Ammersee (crosses) and GRIP (diamonds). First derivatives of the ARM SIRM were calculated to highlight changes in magnetite particle size distributions related to the major temperature transitions that bracket the Younger Dryas.

Magnetic parameters of Quaternary sediments and global paleoclimatic proxies

Stud. Geophys. Geod., 57 (2013) 665

section. Thus, although magnetic susceptibility could be considered as a reliable paleoenvironmental proxy linked to the intensity of alteration of a single source of sediments in Lake Mucubají, it does not seem to fully reflect the sedimentary features related to global climate changes.

A rather coarse inference of the 18O for both Ammersee and GRIP, is obtained when S-ratio is used, together with χ, as an input variable for the ANFIS. In contrast, magnetic parameters such as SIRM and ARM, that include information about grain size distribution of magnetite in these rocks, improve the inference of 18O. These results suggest that magnetic granulometries might be also related, in a complex way, to paleoclimate changes.

The Ammersee and GRIP δ18O actual values, used to train the ANFIS, keep an average difference of about 27% along the whole section. Deviations from this mean might reflect regional paleoclimate forcings in the location of Ammersee, contrasting with the rather global nature of the GRIP data. The optimal 18O inferences using a FIS structure [4ARM, 1SIRM] for both Ammersee and GRIP datasets, as well as their corresponding RMSE, also show an average difference of 27% when compared with respect to each other. However, the dispersion of their percentile differences around this mean value, is lower than the one corresponding to the actual Ammersee and GRIP δ18O. Thus we argue that Lake Mucubají magnetic data, used as input variables, provide a good inference of the global paleoclimate trends, bypassing the regional and/or local features of Ammersee 18O record. Moreover, local and/or regional paleoclimate and tectonism in Lake Mucubají might have affected in some extent these magnetic proxies, otherwise directly linked to global climatic changes.

A wavelet-like behavior of the ARM SIRM profile and its first derivative coincide with the time limits that bracket the Younger Dryas when compared with their corresponding paleoclimate proxies. We argue that a complex relationship between magnetite granulometries and climate transitions could be linked to global temperature changes.

This novel approach to the assessment of a paleoclimate problem, applied to the lacustrine Quaternary sediments of Lake Mucubají, shows the scope of the ANFIS technique in handling geological problems where traditional linear regression methods prove to be limited.

Aknowledgments: Samples were generously provided by Christian Beck (Université de Savoie,

France) and Franck Audemard (FUNVISIS, Venezuela). We would also want to thank the enormous logistic and experimental support provided by Corina Campos (Universidad Simón Bolívar, Venezuela) and Kais Mohamed (Universidad de Vigo, Spain). This research was partially funded by LOCTI research grants to V. C-A and M.A.

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