Distribution and provenance of heavy minerals from recent sediments of Green Lake, North Brazil, revisited with multivariate and geostatistical analysis

Geostatistical and multivariate statistical analyses were applied to heavy mineral data from an Amazonian fluvial-lake system near the Tapajós River mouth to investigate the spatial distribution and source-area of sediments. Twenty-one points were investigated, and the physical characteristics of the Green Lake deepest point were determined. Sand accumulates in the lake margins and mud quantity increases towards the lake center. Heavy mineral assemblage is composed of zircon, tourmaline, kyanite, rutile, staurolite, anatase, sillimanite, garnet, and spinel. Tourmaline, staurolite, and spinel are more abundant in the southeast area of the lake, while kyanite is dominant in the north area and zircon is in the whole lake except in its southeast area. Zircon - tourmaline and zircon - staurolite pairs are negatively correlated (r= -0.947 and -0.775, respectively), while tourmaline - staurolite and sillimanite - anatase pairs have a positive correlation (r= 0.628 and 0.675, respectively) which indicate different source rock types. Geostatistical analysis grouped the heavy minerals in three grups: Group 1 (tourmaline – staurolite – spinel - kyanite) and Group 2 (garnet – rutile – sillimanite - anatase) related to metamorphic source rocks ranging from medium to high grade, and Group 3 (zircon) related to acid igneous source rocks. The heavy mineral assemblage of Green Lake is analogous to the assemblage of the Alter do Chão Formation, indicating that this formation is the source of sediments of Green Lake.


INTRODUCTION
The study of the spatial distribution and composition of recent sediments is common in oceanographic re-search, as well as in studies of estuaries, lakes and modern fluvial environments (Brito et al., 2009;Dadalto and Albino, 2009;Leandro et al., 2014;Tavares et al., 2010;Veronez Jr. et al., 2009). In Amazonian sys-tems, this technique is used to understand the source and transportation of suspended load sediments (Guyot et al., 2007;Viers et al., 2008) and dissolved solids (Moquet et al., 2016). However, only a few studies focus on the provenance of sand in lake environments (e.g. Sawakuchi et al., 2018).
Multivariate statistics have a great application in sciences, especially in environmental sciences. It is used for grouping and differentiation of n-groups (Ebqa'ai and Ibrahim, 2017;Matiatos, 2016;Yıldırım and Tokalıoğlu, 2016). It is employed for interpolation using a spatial correlation function data without bias and with minimal variance (Vieira, 2000). Despite its efficiency, its application in determining heavy mineral distributions is limited (Aguiar Neto et al., 2016;Ochoa et al., 2013).
Regions having different relief and erosion rates composed of different Precambrian to Cenozoic rocks are drained by Brazilian Amazon rivers (Tassinari et al., 2000;Wittmann et al., 2011). Hence, mixing of sediments along these rivers is common, which makes it difficult to ascertain sediments source and distribution.
Determination of spatial distribution of heavy minerals along rivers and lakes is a difficult task (Aguiar Neto et al., 2016;Derkachev and Nikolaeva, 2007;Frihy et al., 2022;Nascimento Jr. et al., 2015;Nascimento Jr. et al., 2017). Studies of geospatial distribution of heavy minerals in the Brazilian Amazon are sparse. This research aims at testing the application of multivariate techniques in the Green Lake sediments.
Heavy minerals in the Amazon River are of immature Andean origin (Landim et al., 1983) whereas the ultrastable mineral assemblage of the Tapajós River interpreted as cratonic (Gozzi, 2019). In the Green Lake, sediments of the Amazon River and the Tapajós River, are mixed (Mendes et al., 2020), which makes it difficult the determination of the source and the heavy mineral spatial distributions. The main objective of this research is to determine the spatial distribution of the heavy minerals in order to assess their provenance and testing the applicability of multivariate and geostatistical analysis.

GEOLOGICAL SETTING
The Green Lake micro-basin is formed at the Tapajós and Amazon rivers' confluence due to the seasonal discharge variations of these rivers ( Fig. 1A-C). The monthly average discharge varies from 4,000 to 30,000m -3 s -1 in the Tapajós River and from 105,000 to 235,000m -3 s -1 in the Amazon River (ANA, 2018). Differences in the discharge of these two rivers creates a hydraulic barrier at the mouth of the Tapajós River. This bar prevents the suspended load sediments of the Tapajós River to enter the Amazon River (Meade et al., 1991).
The changes in the flow rates of the Tapajós and the Amazon rivers are due to the seasonal variations in rainfall, which is characteristic of tropical regions. When the Amazonian rainfall period is short, the Green Lake becomes hydrologically isolated from the Tapajós River (Fig. 1E). On the other hand, if precipitation increas-es, the discharge of the Tapajós River increases, and it incorporates the Green Lake area resulting in both rivers behaving as a unified fluvial system (Fig. 1F). In such situations, as sediment distribution along rivers depends on the rock and soil types, vegetation cover, declivities, topography and rain regime, it becomes difficult to comprehend the sedimentary processes occurring within the Green Lake (Carvalho, 2008).
Cretaceous siliciclastic rocks of the Alter do Chão Formation have been considered the probable source of the heavy minerals of Green Lake (Mendes et al., 2020;Ribeiro et al., 2017). However, these researches failed to demonstrate a preferred spatial distribution of its heavy minerals and a relation between the Green Lake bottom sediments and the ones from the Amazon River or the Tapajós River.

MATERIALS AND METHODS
A planimetric map with the spatial distribution of the sampling points was used (Fig. 1C). Graduated rules and Secchi discs measurements were performed to determine the lake depth. A Van Veen Grab sampler was used to collect 21 sediment samples. These samples were sieved and divided into mud and sand fractions. Green Lake's physical parameters were measured using an OAKTON multiparameter meter.
The heavy minerals were extracted from the very fine-to fine-sized sand (63-125µm) -as most of the heavy minerals occur in this size interval (Morton and Hallsworth, 1999)-with bromoform. The heavy minerals were identified, characterized and quantified under polarized microscope based on the count of a minimum of 300grains/line (Galehouse, 1971). The Zircon-Tourmaline-Rutile (ZTR) index (Hubert, 1962) was used to determine the mineralogical maturity.
Geospatial concentration maps were constructed using the SURFER® software (Golden Software) through a kriging algorithm for interpolating data points. The kriging tool was chosen because it guarantees an excellent trend description and represents the best choice when the number of observations is limited, as in this case.
The multivariate statistical analysis was done using the SPSS software (SPSS Inc., Chicago, IL, USA). Correlation matrices were used to identify heavy mineral relations. In this analysis, Pearson's product-moment correlation coefficient (r) was applied. The Principal Component Analysis (PCA) was used to group heavy minerals and to assess the composition of their source rocks. The PCA components were transformed using varimax rotation with Kaiser normalization.
PCA has been successfully used in the identification of pollutants. Different applications for the PCA use available data and require no factor weighting (Lu et al., 2010;Tokalıoğlu and Kartal, 2006;Yongming et al., 2006). Due Origin of the Green Lake sediments -a reassessment 4 its applicability and excellent results, PCA was applied to heavy mineral data (Cascalho, 2019;Derkachev and Nikolaeva, 2007;Ryan et al., 2007).
Different heavy mineral associations were identified by Cluster analysis (Derkachev and Nikolaeva, 2007;Ryan et al., 2007). The similarity measurement used in the cluster analysis was performed according to Ward's method, as this methodology agglomerates observations in different homogeneous groups with minimum variances. The results are displayed as a dendrogram created with hierarchical clustering, and the values of the distance between clusters are presented.

RESULTS
The Green Lake is V-shaped with two arms oriented in NE-SW and NW-SE directions. It is deepest at the confluence (5.5m). The lake bottom is relatively flat and slightly deeper at the center ( Fig. 2A). Sand accumulation takes place mainly in the marginal portions of the lake with grain size decreasing towards the lake center ( Fig. 2B), where there is predominantly mud accumulation (Fig. 2C). In the deepest point of the lake (LV-19), physical-chemical parameters show low variation (Table 1). The measured ranges are 0.5°C for temperature, 0.71mg/L for dissolved oxygen, 0.74µS for electrical conductivity, 0.53 Nephelometric Turbidity Units (UNT) for turbidity, and 0.27 for pH.

Heavy Minerals
Zircon, tourmaline, kyanite, rutile, staurolite, anatase, sillimanite, garnet, and spinel form the heavy minerals assemblage (Mendes et al., 2020, Fig. 3). This assemblage is considered moderate to stable even though the calculated ZTR index value, above 90%, indicates an abundance of stable heavy minerals (Mendes et al., 2020). Mineralogical similarities, variations in spatial distribution, and significant changes in the heavy mineral assemblage were noted The range of variation is more significant for zircon (68.1-90.2%), tourmaline (3.2-22.2%), and staurolite (0.5-6.4%) as standard deviation values are greater than 1.5. For the other heavy minerals, the variations are insignificant and the standard deviation values are less than 1.0 ( Table 2).
The zircon grains are prismatic bipyramidal in shape. They are characterized by slightly worn facets, inclusions, and zoning. Tourmaline grains are subangular to rounded, having equidimensional prismatic shapes. The kyanite grains are irregular prisms presenting impact and spearhead dissolution marks. The angular staurolite grains show impact and dissolution marks. The sillimanite grains are colorless and prismatic. Garnets and spinel grains occur in a few samples, constituting up to 0.5%. They commonly show corrosion features.

Geostatistical Analysis
The heavy mineral distribution maps (Fig. 4) show that tourmaline, staurolite, and spinel grains occur in larger quantities in the southeastern part of the lake; anatase and sillimanite grains predominate in the southeastern and northern regions; whereas the zircon grains are most present in the north-central region. The other minerals do not show a preferential distribution.    Origin of the Green Lake sediments -a reassessment 6

Correlation analysis
Pearson correlation coefficient (r) indicates that only some of the heavy mineral pairs are correlated (Table 3).

Principal components analysis
Due to the complexity of correlation results (positive and negative), we have performed PCA additional analyses on heavy minerals to aid in delineating their provenance.
By extracting eigenvectors and eigenvalues from the correlation matrix, the number of main significant components and the percentage of total variance they explain (Table 4) were determined. Four statistically significant components explain 79.6% of the total variance obtained by the linear discriminant function equations (Table 5). Opaque, mica, and authigenic minerals were excluded from the linear discriminant calculation. The four eigenvectors present values greater than 1 and the first two represent 53% of the total variance. It indicates that these two eigenvectors are the most important and capable of discriminating the studied sediments.
The first eigenvector constituted 33.8% of the total variance and presented greater weights for zircon, tourmaline, Table. 2. Percentual composition and statistical parameters of transparent and nonmicaceous heavy minerals, very-fine sand fraction (63 -125 µm) from Green Lake bottom sediments. Zir = zircon; Tou = tourmaline; Rut = rutile; Kya = kyanite; Sta = staurolite; Ana = anatase; Sil = sillimanite; Gar = garnet; Spi = spinel; ZTR = Zircon + Tourmaline  Origin of the Green Lake sediments -a reassessment 7 and staurolite. The second eigenvector presented 18.77% of the total variance and the greatest weights are for anatase and sillimanite. The third eigenvector constituted 13.7% of the total variance and presented the greatest weights for rutile and spinel. The fourth eigenvector explained 13.2% of the total variance and presented the greatest weights for kyanite and garnet.
The communality values above 0.6 indicate that the number of factors is acceptable and validates the factor FIGURE 4. Geospatial heavy minerals distribution maps, Green Lake, Brazilian Amazon. For legend, see Table 2.  o l o g i c a A c t a , 2 0 . 5 , 1 -1 4 ( 2 0 2 2  Origin of the Green Lake sediments -a reassessment 8 model used (Hair Jr. et al., 2014). A principal component plotting was performed (Fig. 5). In the 2D plot, the tourmaline-staurolite and sillimanite-anatase pairs have an opposite direction relative to zircon (Fig. 5A). In the 3D plot, three relationships were made with Kya-Spi-Sta-Tou; Gar-Rut-Sil-Ana and Zir (Fig. 5B).

Cluster analysis
The heavy mineral values were standardized using z-scores and the Euclidian distances between the heavy mineral values were calculated. The hierarchical cluster grouping is presented as a dendrogram. The dendrogram indicates the existence of three subgroups: the first one contains only zircon; the second one contains tourmaline, kyanite, spinel, and staurolite; and the third one contains garnet, rutile, anatase, sillimanite (Fig. 5C).

DISCUSSION
The grain size of the Green Lake sediments varies between mud and coarse sand (Mendes et al., 2020), which is a sedimentary characteristic of Amazonian lakes . To determine the spatial distribution of heavy minerals, the application of classical and modern analytical techniques was required. In addition, distribution modeling was applied to understand changes in provenance, morphological characteristics, control during transportation, and recent or past climates (Morton andHallsworth, 1994, 1999).
The geostatistical and multivariate statistical techniques are efficient tools for identifying distribution patterns of the heavy mineral assemblage of the Green Lake and assessing the sediment source. Despite their efficiency, the application of these techniques in heavy minerals studies is uncommon (Derkachev and Nikolaeva, 2007;Ochoa et al., 2013;Ryan et al., 2007). PCA has been widely used in a variety of studies to reduce the number of parameters and facilitate correlation analysis between variables (Tokalıoğlu and Kartal, 2006). The kriging grouping (Fig. 4) combined with PCA assisted in determining the main heavy minerals groups and in interpreting the sediments source.
In this work, it was assumed that a significant positive correlation between heavy mineral pairs (Tour-Sta, Sil-Ana)   suggests a common or combined source, and a negative correlation (Zir-Tou, Zir-Sta) suggests mixing of sources. The other mineral correlations (Kya, Rut, Gar, Spi) are not well defined.
The results of this study suggest that the Green Lake heavy minerals can be classified into three groups (Tables 3; 4; Figs. 4; 5): Group 1 (Tou-Sta-Spi-Kya), Group 2 (Gar-Rut-Sil-Ana), and Group 3 (Zir). This classification indicates that the sediments are from at least two different rock types: metamorphic rocks, Groups 1 and 2, and acid igneous rocks, Group 3. Based on the PCA analysis (Table  4), internal variations were associated with the degree of metamorphism (Fig. 5B). Despite the metamorphic origin, temperature and pressure variations in the minerals' formation reflect stability of the minerals under the weathering conditions.
Variations in the degree of correlation in Groups 1 and 2 indicate changes from medium to high-grade metamorphic source rock types. The occurrence of kyanite and sillimanite indicate metapelites as source rock because they are rich in aluminum (Winter, 2014). Minerals in Group 1 show significant correlation indicating medium-grade metamorphic rocks as common source. Generally, these metamorphic minerals are common in schists, meta-schists, and gneisses (Deer et al., 1997). Group 2 minerals are common in highgrade metamorphic rocks. Group 3, composed by zircon only, did not have a significant correlation with any other group, suggesting their source is different from Group 1 and 2. Origin of the Green Lake sediments -a reassessment 10 Three possibilities are proposed to explain the variations and spatial distribution of the Green Lake heavy minerals: i) fluvial dynamic interaction between the Tapajós River and the Amazon River; ii) internal dynamics of the lake related to the physicochemical variables and iii) variations in the source of the sediments.
Due to its higher discharge, the Amazon River flows into the Tapajós River (Freitas et al., 2017;Medeiros Filho, 2015;Medeiros Filho et al., 2016), and, thus, it may introduce sediments into the Green Lake. However, the immature heavy mineral assemblage of the Amazon River is mainly composed of hypersthene, augite, and amphibole derived from Andean source rocks (Landim et al., 1983;Lima Jr. and Nogueira, 2013). This assemblage differs from the Green Lake heavy mineral assemblage in terms of mineral species and mineral proportion. Therefore, the possibility of the Amazon River controlling the Green Lake heavy mineral assemblage was disregarded.
Hydrographic studies on the Tapajós River have been focused on physical-chemical analyses (Sousa et al., 2009), heavy metals (Maia et al., 2016), carbon content (Bertassoli Jr. et al., 2017) and description of heavy mineral assemblages (Gozzi, 2019). Despite its the importance, only a few studies on sediment characterization of the Tapajós River have been performed (Medeiros Filho, 2015;Medeiros Filho et al., 2016).
In order to state that the Tapajós River introduces sediments into the Green Lake, it is necessary to demonstrate that the sediment dispersal pattern in the lake is controlled by the Tapajós River. This relationship is well-defined during the Amazonian winter when the Tapajós River flows into the Green Lake (Fig. 1F), and the Amazonian summer, when Green Lake is isolated from the Tapajós River (Fig. 1E). However, sediment transport of Tapajós River is hampered by the hydraulic-barrier effect in the confluence of Tapajós and Amazon rivers (Nascimento et al., 1976).
Provenance studies at the confluence of the Madeira and Amazon rivers suggest that the Madeira River contributes with heavy minerals derived from a cratonic source and, the Amazon River provides andalusite-rich Andean sediments (Nascimento Jr. et al., 2015). At the Xingu and Amazon rivers confluence, there is a dominance of unstable heavy minerals (epidote, hypersthene, amphibole) whereas upstream along the Xingu River stable/ultra-stable heavy minerals (zircon, tourmaline, rutile) dominate (Souza, 2018). If identical geological context occurs at the Amazon and Tapajós river confluence (Fig.1A), one would expect that the heavy mineral assemblage of the Tapajós River was unstable like the one in the Xingu River, however, this is not the case.
The species and relative proportions of the Green Lake heavy minerals differ from those downstream of the Tapajós River, so it is unlikely to consider the Tapajós River introduces sediments into the Green Lake. Geospatial distribution of the Green Lake heavy minerals is another evidence the Tapajós River cannot be the source of these sediments. The concentration of the heavy minerals is low in the western and southwestern portions of the lake (Fig.  4), which is where the Tapajós River flows into the lake. Therefore, this low concentration suggests an insignificant heavy minerals transportation into the lake.
Low Zr and Hf values in the Tapajós River, near Alter do Chão and Santarém areas, indicates deposition of zircon grains, which are related to an earlier Green Lake deposit (Medeiros Filho et al., 2016). This is an additional evidence to disregard the Tapajos River as the supplier of sediments to the Green Lake. As the Green Lake heavy mineral assemblage is not similar to that of the Tapajós River, other sedimentary sources were considered. df 1 = -0.966zir + 0.890tou -0.265rut + 0.087kya + 0.869sta -0.183ana -0.053sil -0.297gar + 0.006spi df 2 = -0.017zir -0.160tou + 0.158rut + 0.186kya -0.105sta + 0.871ana + 0.874sil -0.416gar -0.028spi df3= + 0.135zir -0.238tou + 0.684rut -0.158kya + 0.046sta -0.022ana + 0.267sil + 0.289gar -0.852spi df 4 = + 0.005zir -0.141tou -0.278rut + 0.872kya + 0.109sta -0.087ana + 0.231sil + 0.547gar -0.101spi TABLE 5. Linear discriminant function equations used for separation of mineral groups. For legend, see Table 2 The area surrounding Green Lake is composed of friable rocks of the Alter do Chão Formation. This formation is known for its siliciclastic composition (conglomerate, sandstones and mudstones). High degree of weathering results in feldspar hydrolysis -a common phenomenon under hot and humid climate conditions like that one in the Amazon region-and kaolinite neoformation (Mendes et al., 2013). The Green Lake heavy mineral assemblage is similar in species and relative concentration to that of the Alter do Chão Formation (Mendes et al., 2013(Mendes et al., , 2015(Mendes et al., , 2020. The Green Lake heavy mineral assemblage is mainly controlled by recent/modern weathering and erosion of the rocks surrounding the lake, the Alter do Chão Formation. This weathering modifies the original mineral assemblage by eliminating less stable heavy minerals. In this case, application of discriminant equations (Table 5) proved to be an important tool to determine the relationship between the heavy mineral assemblage of the Alter do Chão Formation and the one found in the Green Lake.
Low pH values, electrical conductivity, and dissolved oxygen in the Green Lake contribute to the mortality of organisms, thereby, generating carbonic acids which, in turn, increase the corrosion potential. ZTR minerals are not affected by superficially pH conditions and shallow diagenesis, but garnet and spinel, as well as other unstable minerals, are sensitive and easily dissolved in this weathering environment (acid pH) (Morton, 1984). Some of the superficial textures of the heavy mineral grains indicating chemical dissolution in the Green Lake heavy minerals corroborate this interpretation (Mendes et al., 2020).
The recent ultra-stable mineral assemblage of Green Lake (ZTR> 90%) suggests that most of the original minerals were eliminated. This feature is corroborated by the low abundance of unstable minerals in the lake sediments. The heavy mineral dissolution and modification may, to some extent, be responsible for the spatial distribution pattern of heavy minerals in the Green Lake -when only one sediment source is considered.

CONCLUSIONS
Researches on provenance and spatial distribution of bottom sediments in Amazonian fluvial lakes are rare. This study aims to understand the spatial distribution and source rocks of the Green Lake sediments through geostatistical and multivariate statistical analysis. The Green Lake heavy mineral assemblage demonstrates various spatial distribution patterns. Using PCA and cluster analysis, three heavy mineral groups were identified. Group 1 and 2 suggest sediment contribution from medium to highgrade metamorphic source rocks, while Group 3 suggests sediments originating from acid igneous source rocks. From these results, the authors concluded that the Green Lake bottom sediments come from weathering and erosion of the outcrops of Alter do Chão Formation that are surrounding the lake. The bottom sediments of this lake were not a contribution of either the Tapajós River or the Amazon River. Factors related to the surface weathering of the Amazonian region, pH, dissolved oxygen amounts, and electric conductivity made the Green Lake water acidic. This feature has increased the corrosion potential of the lake water and, hence, caused dissolution of unstable heavy minerals, resulting in their observed geospatial distribution pattern.

CONFLICT OF INTEREST
On behalf of all authors, the corresponding author states that there is no conflict of interest.