Abstract

Cap dolostones of the Ediacaran Doushantuo Formation (Yangtze Platform, South China) from various palaeo-water depths were studied to evaluate the extent of their diagenetic alteration and to assess temporal and spatial variations of seawater chemistry in the aftermath of the Marinoan glaciation. Diagenetic fluid overprint is common in cap dolostone lithologies. However, the mobilization of trace elements and the modification of Sr and O isotopic compositions are variable and were controlled by multiple stages of fluid overprint. The highest 87Sr/86Sr ratios (up to 0.7246) occur in cap dolostones from the palaeo-slope environment at the Huanglianba section, whereas cap dolostones deposited in platform settings and in one of the distal basinal settings reveal 87Sr/86Sr ratios close to the proposed late Neoproterozoic seawater composition (0.7077). Shale-normalized REE + Y patterns of carbonate leachates display enrichments of heavy over light REE and superchondritic Y/Ho ratios, typical of seawater. However, Y/Ho ratios in the cap dolostones are always lower than modern seawater values, which is interpreted to reflect dilution of the seawater signal by continent-derived meltwater influx during deglaciation. Negative Ce anomalies in carbonate leachates from platform and slope sections suggest that oxidized conditions existed in shallow marine environments shortly after the Marinoan glaciation, whereas positive or no resolvable Ce anomalies in basin settings indicate that the latter remained anoxic. Redox stratification of the Yangtze margin at the beginning of the Ediacaran is further supported by the relative enrichment of redox-sensitive trace metals in basinal sections. These data may indicate moderately anoxic (less than 10µM dissolved O2) and presumably manganous conditions during the deposition of cap dolostones in the deeper realms of the Yangtze basin.

Supplementary material: Supplementary data for this paper are available at https://doi.org/10.6084/m9.figshare.c.3770957

Two major low-latitude glaciations covered the Earth's surface to low latitudes during the late Neoproterozoic; these have been named the Sturtian and the Marinoan glaciations (Kennedy et al. 1997). Glaciogenic deposits formed during these two glaciations are capped worldwide by a sedimentologically and geochemically unique carbonate lithology with a thickness of only a few metres (Hoffman et al. 1998). These postglacial cap dolostones are thought to be a crucial piece in the puzzle of how the Ediacaran ocean became more oxic (Lenton et al. 2014; Lyons et al. 2014) and enriched in bioavailable metals (Anbar 2008). These processes finally laid the base for the evolution of life in the aftermath of the Marinoan glaciation and the beginning of the Ediacaran (e.g. Knoll & Carroll 1999; Yin et al. 2007). Striking geochemical results from marine sediment records of that time period suggest that the oceans of this period finally underwent a stepwise and protracted oxidation resulting in a stratified water column with an anoxic deep oceanic and an oxic upper oceanic realm (e.g. Kurzweil et al. 2015). Sahoo et al. (2016) postulated that these rapid environmental changes involving rapid oxygen rise in a biologically monotonous and mainly anoxic Ediacaran ocean may have stimulated evolutional innovations. However, the reasons for the oxygenation are still debated. Following the Snowball Earth hypothesis (Hoffman et al. 1998), rising CO2 levels turned the Earth into a greenhouse, causing glacial melting with an increased nutrient flux into the oceans and finally prompting higher primary productivity with subsequent burial of organic matter (Planavsky et al. 2010). Lenton et al. (2014) argued for the establishment of a positive feedback system of evolution of complex eukaryotes, benthic filter feeding, phosphorus removal and deep ocean oxygenation following the Marinoan glaciation.

Marinoan cap dolostones from various locations around the world typically display negative δ13Ccarb of −3 to −6‰ (e.g. Kaufmann et al. 1997; Halverson et al. 2005; Font et al. 2006; Jiang et al. 2007a; Nédélec et al. 2007), and extreme negative values (−41 to −48‰) have also been reported from a few sections of the Yangtze Platform in South China (Jiang et al. 2003; Wang et al. 2008; Lin et al. 2011). The genesis of cap dolostones is still much debated. Following Shields (2005) the main models for the formation of post-Marinoan cap dolostones include the following: (1) overturn and widespread upwelling of anoxic and organic carbon-rich deep oceanic water masses and oxidation of the latter (Grotzinger & Knoll 1995); (2) highly accelerated weathering rates during greenhouse conditions after the Snowball Earth event that led to an increase in seawater alkalinity and thus increased carbonate precipitation during transgressional periods (Kirschvink 1992; Hoffman et al. 1998; Spence et al. 2016); (3) oxidation of a large 12C-enriched pool of organic carbon (e.g. gas hydrates from permafrost soils) (Kennedy et al. 2001; Jiang et al. 2003); this model would also explain the rare observation of extremely low δ13Ccarb values; (4) abrupt deglaciation leading to the formation of a stratified ocean with a huge freshwater lens on the surface formed from meltwaters and the fast precipitation of cap dolomites (the ‘plumeworld hypothesis’ of Shields (2005)).

To complicate matters, it is still unclear whether the carbon isotopic compositions of Post-Marinoan cap dolostones from the Yangtze Platform record pristine seawater values at the time of their deposition or if the negative δ13Ccarb excursions found in these lithologies may be a result of post-depositional alteration. In this context Bristow et al. (2011) argued that the most extreme values (down to −48‰) are caused by the oxidation of hydrocarbon-rich fluids percolating through the sediment packages, and the detailed petrographic work of Lin et al. (2011) further confirmed that these extreme δ13Ccarb values occur only in late diagenetic calcite veins within dolostones and may be a result of late methane oxidation in the sedimentary basin.

In previous publications the trace element concentrations in Post-Marinoan cap dolostones from sections in China (Huang et al. 2009, 2011), Brazil (Font et al. 2006) and Ghana (Nédélec et al. 2007) were used to infer changes in the palaeo-ocean chemistry in the aftermath of the deglaciation. In this study, we take advantage of the large-scale distribution of early Ediacaran cap dolostones deposited at different water depths on the Yangtze Platform, South China, to assess the temporal and lateral variations in the chemistry of early Ediacaran seawater. By combining petrographic work, trace element variability, radiogenic Sr and stable C and O isotopic compositions, the purpose of this study is to (1) evaluate diagenetic alteration processes on cap dolostones from different geological settings and their impact on the isotopic and elemental compositions of the carbonates, (2) obtain insights into variations of early Ediacaran seawater oxygenation from platform to basin sections, and (3) aim for a better understanding of redox condition changes during the deposition of Ediacaran cap dolomites within the water and sediment bodies at the respective localities.

Geological setting

The basal Ediacaran marine sediments of the Doushantuo Formation were deposited along the SE margin of the Yangtze Block in variable depth environments (Zhou & Xiao 2007). Depositional environments of the rocks of the lower part of the Doushantuo Formation can be divided into three main subgroups: a shallow carbonate platform in the NW, a transitional belt of sediments deposited along the slope and a deep-water basin in the SE with depositional conditions below fair-weather wave base (Zhu et al. 2007). The marine deposits on the platform and in intra-platform environments (e.g. Jiulongwan, Hubei Province) consist of muddy carbonates and shales of the Doushantuo and overlying Dengying Formation (Vernhet 2007; Jiang et al. 2011; Zhu et al. 2011; Xiao et al. 2012). The Doushantuo Formation and overlying Liuchapo Formation of the distal slope and basinal sections in Guizhou and Hunan Provinces contain black cherts and shales and limited intervals of carbonate sedimentation (Vernhet 2007; Zhu et al. 2007). Parts of the slope and basin sequences were disturbed by submarine mass-flow events (Vernhet et al. 2006).

The first major stratigraphic unit of the Ediacaran (Sinian) in South China is formed by fine-grained carbonate layers, which form a sharp lithological contact with the underlying Marinoan glacial till. In the literature these globally occurring lithologies are often referred to as cap carbonates or cap dolostones. Zircons from volcanic ash beds at the base and above the cap dolostones on the Yangtze Platform were dated by Condon et al. (2005), yielding U–Pb ages of 635.5 ± 0.6 Ma (base) and 632.5 ± 0.5 Ma (just above the top). The Post-Marinoan cap carbonates in South China were deposited at variable depth depending on their palaeogeographical location along the SSE-stretching passive margin of the Yangtze Craton (Jiang et al. 2011). They commonly comprise microcrystalline dolomite layers of discrete thickness with distinctive sedimentary structures, such as tubes, tepee-like structures, ripples, peloids, rip-up and tubular structures (Jiang et al. 2003). Therefore, throughout this paper we prefer to use the term cap dolostones following Schrock (1948).

Cap dolostone samples for this study were taken from sections deposited in a platform environment at Xiaofenghe, Jiuqunao, Jiulongwan and Huajipo (Three Gorges area, Hubei Province), in the transitional slope belt at the Huanglianba section near Songtao (Guizhou Province) and in the basinal Yanwutan and Longbizui sections (Hunan Province, Fig. 1). According to Jiang et al. (2003), the facies of cap dolostones deposited on the Yangtze Platform can be divided into three sub-members with distinct sedimentological and petrological characteristics (Fig. 1): a strongly disrupted basal part (C1), a fine-grained, laminated carbonate with tepee-like structures (C2) and a fine-grained, laminated, parallel-bedded top layer (C3). However, these are descriptive sedimentological terms only, which cannot be used for time-equivalent correlations between sections. We therefore use these terms only for the following outcrop explanation, whereas we use a normalized height of all studied sections in our graphs for better comparison of the geochemical changes over the depositional height in each section.

Xiaofenghe section, Hubei Province

The Xiaofenghe section is located west of Xiaofenghe village at 30°56'29.5"N, 111°13'57.4"E. The cap dolostones crop out on the northern slope of the valley along a steep path close to the village. Deposition at Xiaofenghe presumably took place in an extremely shallow or lagoonal environment (Zhu et al. 2007; Xiao et al. 2012). The basal part C1 (0 – 1.6 m) is composed of a partly brecciated sparitic dolostone, the middle part C2 (1.6 – 2.3 m) is a finely laminated dolostone with tepee-like structures (Zhu et al. 2007) and the upper part C3 (2.3 – 4.8 m) contains laminated dark dolostones with cherty nodules and a 2 cm thick organic carbon-rich horizon at 3.75 m height. Major and trace element concentrations as well as isotopic data on acetic acid leachates of carbonates were published by Hohl et al. (2015a).

Huajipo section, Hubei Province

The Huajipo section (SW of Sandouping town), lies on a road transect south of the Yangtze river at 30°46′54.4"N, 111°02'02.1"E. The thickness of the cap dolostones is about 5 m. Layer C1 (0 – 0.75 m) consists of folded, massive dolostones with vertical cracks. A thin ash layer has been dated to 635.2 ± 0.6 Ma using U–Pb zircon geochronology (Condon et al. 2005). Layer C2 (0.75 – 2.5 m) consists of laminar bedded dolostones with variable bed thickness between 2 and 10 cm. The top part C3 (2.5 – 4.9 m) comprises massive thick-bedded and partially weathered dolostones. Jiang et al. (2003) and Bristow et al. (2011) obtained extreme negative carbon isotope values for calcite veins within these cap dolostones and argued for the oxidation of hydrocarbons (presumably from methane seeps) as a source for these signatures.

Jiuqunao (Jijiawan) section, Hubei Province

The Jiuqunao section (30°52′59.9"N, 110°52′45.4"E) is located on the southern banks of the Yangtze river a few kilometres upstream of the city of Yichang. The cap dolostone member is only 1.7 m in thickness. The basal part C1 (0.3 m thickness) crops out above a thin bentonite layer and consists of synsedimentary brecciated dolostones with several calcitic veins. Layer C2 (0.3 – 1.2 m) contains fine laminated dolomicrites with thin chert layers. The top of the section (C3; 1.3 – 1.7 m) is a dolostone with slump-fold structures. A second bentonite ash layer 5 m above the cap dolostones has been dated to 632.5 ± 0.5 Ma by Condon et al. (2005).

Jiulongwan section, Hubei Province

The Jiulongwan section (30°48′28.4"N, 111°03′47.2"E) is situated in the hills above Sandouping overlooking the Yangtze river and the Three Gorges Dam Scenic Area. The cap dolostones here overlie thick diamictites of the Nantuo Formation and have a total thickness of about 6.2 m. C1 (90 cm) consists of a highly ruptured dolomite breccia that is overlain by massive banked dolostones of C2 (0.9 – 2.75 m) followed by dark clay and organic-rich dolostones of C3 (2.35 – 6.2 m).

Huanglianba section, Guizhou Province

The Huanglianba section, located in Songtao county (28°11′34.3"N, 109°15′39.5"E), is located on the upper slope of the Yangtze Platform margin (Lu et al. 2013). The cap dolostones are exposed in a riverbed. The cap dolostones are 6 m thick and crop out in the riverbed in contact with the Nantuo diamictites. The basal part C1 (0 – 2 m) consists of carbon-rich dolomitic bindstones, whereas C2 (2 – 4.3 m) is composed of sulphide-bearing muddy dolostones with dark silica concretions. In layer C3 (4 – 6 m), a 25 cm thick carbon-rich layer is followed by recrystallized dark carbonates.

Longbizui section, Hunan Province

The basal Doushantuo Formation of the Longbizui section (28°29′57.9"N, 109°50′28.0"E) in Guzhang county was deposited in a slope to basin setting (Guo et al. 2013). The basal Doushantuo is not completely exposed (lack of exposure c. 2 – 3 m above the glacial deposits of the Nantuo Formation). Samples were taken from two large outcropping blocks of dolostones below a mudstone horizon of several tens of metres in thickness, similar to Doushantuo II lithologies in shallow-water sections of Hubei Province. Because of poor exposure, the lower part (equivalent to C1) was not sampled. Samples taken from C2 (5.25 – 5.9 m above diamictites) were generally finely laminated and of high organic content, whereas samples from C3 (5.9 – 6.5 m) were more disrupted, with calcitic veins and crack fillings.

Yanwutan section, Hunan Province

The Yanwutan section east of the city of Jishou (28°25′20.0"N, 110°28′42.1"E) is predominantly composed of mudstones and dolostones deposited under slope margin to basinal environments (Guo et al. 2007; Zhu et al. 2007; Ader et al. 2009). The cap dolostones of the Yanwutan section comprise c. 7 m of micritic dolostones on top of the Nantuo diamictites. Samples were taken from the basal part of C1 and the top part of C3. Major and trace element concentrations and isotopic compositions on acetic acid leachates of carbonates were published by Hohl et al. (2015b).

Petrographic features

A brief description of the microscopic structures that occur in the cap dolostones from Jiuqunao, Xiaofenghe, Huajipo, Huanglianba and Longbizui is given in Table 1 and in Figure 2. Only sample powder was available for analysis of Yanwutan samples and therefore we were not able to perform petrographic descriptions of the studied cap dolostones from this section.

Methods

All cap dolostones were collected as large hand specimens of c. 0.5 – 1 kg weight with focus on samples that contain macroscopically unweathered domains. After removing weathering rims and crushing, fresh sample chips of about 1 cm diameter were picked, embedded in Araldite resin, polished, gold-coated and pre-screened using BSE imaging on the SEM. Approximately 20 mg of sample powder was obtained by micro-drilling into the domain of rock chips that were presumed to be unaltered. Sample powders were treated with 1M acetic acid for at least 12 h at 70°C. Insoluble residues were separated by centrifugation and filtration through 0.45 µm cellulose acetate syringe filters. The supernatant was continuously dried in steps of 0.5 ml 3M HNO3 to evaporate remaining acetic acid. For inductively coupled plasma mass spectrometry (ICP-MS) analysis the nearly dry residue was dissolved in 1 ml 0.28M HNO3, weighed and diluted with 0.28M HNO3 to different concentrated sample solutions for trace element and major element analysis (see Hohl et al. (2015b) for more details). All measurements were performed on a Thermo Finnigan Element XR sector-field ICP mass spectrometer at Freie Universität Berlin using external calibration to a Phanerozoic marine calcite standard (CAL-S, Yeghicheyan et al. 2003; Hohl et al. 2015b) and drift correction methods by adding Co, In and Tl solutions of known concentration. The analytical setup used a Scott type quartz spray chamber and a 100 µl min−1 nebulizer. Sample time was 120 s with 20 samples per peak and 60 peak scans. Tuning of the mass spectrometer generally yielded low oxide generation rates of 2 – 5% for CeO+ and less than 1% for BaO+. Combined analytical precisions (1SD) are better than 10% for major elements and Sr and 5% for REE + Y and most other trace elements. Repeated analysis of Cal-S and J-Do1 carbonate reference materials indicated that our method is capable of obtaining reproducible and accurate major and trace element concentrations in the studied lithologies.

Aliquots of the dissolved samples were used for Sr separation on Sr Spec cation-exchange resin for 87Sr/86Sr analysis using thermal ionization mass spectrometry (TIMS) at Freie Universität Berlin. Repeated measurement of the NBS SRM-987 yielded 87Sr/86Sr = 0.710245 (±0.000020, 2SE, n = 12) corrected for mass fractionation using 86Sr/88Sr = 0.1194 (Nier 1938). Interferences of 87Rb on 87Sr were corrected assuming 85Rb/86Rb = 2.59265. 87Sr/86Sr ratios were also corrected for radiogenic ingrowth from 87Rb using the published depositional ages of c. 635 Ma (Condon et al. 2005), the Rb/Sr ratios determined by ICP-MS and a half-life of 87Rb of 4.88 × 1010 years. Rb/Sr ratios from Huanglianba section range from 0.003 to 0.011 and thus 87Sr/86Sr ratios were corrected, whereas samples from other localities were almost Rb free with Rb/Sr between 0.0002 and 0.001. Therefore, no corrections of the 87Sr/86Sr ratios were performed for the latter samples. In general, Rb corrections were minor and did not change the interpretation of the Sr isotope data.

Oxygen and carbon isotope ratio measurements were performed at the Museum für Naturkunde Berlin using a Thermo Finnigan Gasbench II coupled with a Thermo Finnigan Delta V isotope ratio mass spectrometer. Approximately 100 – 400 μg of carbonate powder was reacted with 30 μl of anhydrous phosphoric acid at 70°C for c. 1.5 h. Reference gas was pure CO2 calibrated against the Vienna Pee Dee Belemnite (V-PDB) standard by using IAEA reference materials (NBS 18 and NBS 19). We report isotope ratios as per mil deviation from the international reference material V-PDB in the delta notation according to Coplen (2011). The external errors of the measurements for both isotopic systems are better than 0.1‰ (1SD), based on the reproducibility of an in-house CaCO3 reference material (Jurassic Limestone).

Results

Major and trace elements

The major and trace elemental data of carbonate leachates from all studied sections are listed in Table 2 (YAW and NXF data have been given by Hohl et al. 2015a,b). Concentrations of Ca, Mg, Mn and Fe in acetic acid carbonate leachates were used to calculate normative dolomite molar fractions, assuming that Mg2+, Fe2+ and Mn2+ substitute for Ca2+ in CaCO3 forming stoichiometric dolomite. The analysed cap dolostones range from 12 to 97 mol% calculated dolomite fraction in the acetic acid leachates. Most of the proximal platform and slope samples are slightly less dolomitic with fractions between 50 and 60 wt%, whereas basin samples mostly contain >90 wt% dolomite fraction. The carbonate leachates have low Al concentrations (<500 µg g−1). Mn and Ba concentrations are highly variable, ranging from 0.07 to 1.34 wt% for Mn and 4 – 600 µg g−1 for Ba, respectively. Strontium concentrations in the carbonate leachates of the platform sections are generally low (<100 µg g−1), whereas slope and basin sections display concentrations ranging between 118 and 775 µg g−1 Sr. Mn/Sr ratios of the cap dolostones are often high (up to 177), with ratios below 10 being prevalent only in the slope section of Huanglianba.

Total REE concentrations in cap dolostone acetic acid leachates range from 0.11 to 6.75 µg g−1, showing higher total REE concentrations in the more calcitic lithologies of the platform sections relative to the more dolomitic basin and slope samples. Values for PAAS (Post Archean Australian Shale, McLennan, 1989)-normalized Ce/Ce* and Eu/Eu* were calculated using the equations (1) and (2) following Lawrence et al. (2006):  
formula
(1)
 
formula
(2)
These equations avoid using La and Gd for the calculation of CeN/CeN* and EuN/EuN*, as these elements may be naturally increased in the samples, and thus may cause apparent variations in REE anomalies (Bau & Dulski 1995; Ling et al. 2013). CeN/CeN* ratios in the platform sections are between 0.57 and 1.38 with a general trend to higher values to the top of the sections. CeN/CeN* ratios of carbonate leachates from the slope (0.73 – 1.42) are variable throughout the profile with no general trend. Basin sections show CeN/CeN* ratios between 1.03 and 1.3 in Yanwutan and Longbizui section carbonate leachates.

To correct Eu/Eu* ratios, we used 137Ba16O interference corrected 153Eu signals, applying the formula given by Dulski (1994). After the interference correction, the corrected ratios show no correlation with Ba/Sm ratios (supplementry material, Fig. A). However, in the case of one Ba-rich intra-platform calcitic vein in sample HJP 2.9 such corrections led to an underestimate of the Eu concentration, resulting in a negative Eu/Eu* anomaly (0.66) in comparison with the ambient dolomite lithology (1.7) (Fig. 3). The cap dolostones show either no or positive Eu anomalies, with values ranging from 0.95 in the Jiuqunao section to 2.43 in the Huajipo section, with a slightly decreasing trend from bottom to top in the platform and slope sections. This is consistent with previously published data from the platform by Huang et al. (2009). Eu/Eu* ratios in the distal basin sections are generally higher than in the proximal platform sections. However, Eu anomalies should be treated with caution as Eu concentration measurements by ICP-MS are affected by the above-mentioned Ba interference problems and inaccurate corrections may cause apparent anomalies (Jiang et al. 2007b; Viehmann et al. 2016).

Stable isotope data

Strontium, O and C isotopic compositions of cap dolostones analysed for this study are listed in Table 3. Data from the Yanwutan and Xiaofenghe sections were published earlier by Guo et al. (2007) and Hohl et al. (2015a,b). The cap dolostones show δ13Ccarb in the range from −1.1 to −5.9‰. One carbonate sample from Huanglianba at 4.6 m revealed an extremely low δ13Ccarb value of −30.6‰. The highest δ13Ccarb value (1.1‰) occurs near the top of the Yanwutan section (Guo et al. 2007). The δ18Ocarb values of Neoproterozoic marine carbonates are generally lower than those in modern carbonates, which is either due to a different composition of the seawater at that time or, more probably, due to diagenetic alteration and meteoric fluid–rock interaction (Brand & Veizer 1981). Most δ18Ocarb values from platform sections range between −5 and −9‰. A microcrystalline calcitic vein in Huajipo lithologies sampled by micro-drilling is lower in its oxygen isotope composition (−8.4‰) than the surrounding dolomite matrix (−7.2‰), which is indicative of meteoric alteration of vein material. Longbizui section shows a positive δ18Ocarb outlier (+5.7‰).

The variations of initial 87Sr/86Sr ratios of all carbonate leachates in this study range from 0.70767 to 0.71181 for intra-platform cap dolostones and from 0.70775 to 0.72419 for slope and basin cap dolostones. The least radiogenic values obtained in this study are consistent with other 87Sr/86Sr values reported in post-Marinoan cap dolostones from the Taoudeni basin in NW Africa (0.7077; Shields et al. 2007), the Karatau range in Kazakhstan (0.7083, Ohnemueller & Kasemann 2014), the Brazilian Araras Group (0.7071; Romero et al. 2013), and the Maiberg Formation, Namibia (0.7072, Halverson et al. 2007). In detail, the initial 87Sr/86Sr ratios of carbonates from the Jiuqunao section start at 0.71031 at the base, rise to 0.71165 in the middle of the section and drop to 0.71005 at the top. The Xiaofenghe and Huajipo sections show a similar behaviour of increasing radiogenic Sr up-section (0.70834 at the base, 0.70906 in the middle of the Xiaofenghe section, and 0.70767 at the base and 0.71050 at the top of the Huajipo section). The initial 87Sr/86Sr ratios in Huanglianba slope section are 0.72419 at the base and drop to 0.71687 at the top, revealing an opposing trend to less radiogenic compositions up-section. Basin cap dolostones in Longbizui range between 0.71279 and 0.71509. Yanwutan samples show a comparable behaviour to slope section samples, with declining values from 0.72033 at the base to 0.70770 at the top of the cap dolostones.

Discussion

Diagenetic alteration of Marinoan cap dolostones

This section will evaluate the effects of diagenetic modification on the studied cap dolostones. Therefore, trace elements such as Sr, Rb and Al, as well as Sr, O and C isotopic compositions, are used to infer whether the variations in the dataset are of pristine origin, for example owing to source effects (e.g. meltwater influx), or the result of post-sedimentary diagenetic overprint by fluid infiltration. Several researchers have described the influence of post-diagenetic modification on Phanerozoic carbonates (e.g. Brand & Veizer 1980, 1981; Derry et al. 1989; Banner & Hanson 1990) and typically observed elevated contents of Mn2+ and Fe2+ and decreasing contents of Sr2+ and Mg2+ compared with unaltered equivalents. These observations were interpreted to reflect dissolution of primary CaCO3 and precipitation of secondary calcite cements from meteoric fluids. Hence, Mn/Sr ratios are commonly used to assess the influence of diagenetic overprinting on carbonate rocks. Kaufman & Knoll (1995) have argued that Mn/Sr ratios below 10 are characteristic for unaltered samples, as these rocks might not have seen a substantial loss of fluid-mobile Sr. However, elevated redox-sensitive element concentrations in carbonates are not a useful tool for understanding diagenetic modification of Proterozoic carbonates, as these may have been deposited under more reducing redox conditions (e.g. ferruginous, manganous, anoxic, suboxic) compared with typical Phanerozoic carbonate rocks, which may result in variable element concentrations (e.g. Thomson et al 1998; Mucci 2004). Thus, the elevated Mn/Sr ratios obtained in many cap dolostones may have been caused by increased Mn concentrations in anoxic bottom water or porewater.

Our petrographic investigations show abundant calcite cement formation caused by dedolomitization processes along former fluid pathways or calcitic veins within the mainly subhedral to euhedral dolomite-bearing matrices (e.g. rhomb-shaped dolomite remnants and calcitic veins in Fig. 2a–c). Calcite cements are more common in platform carbonates. Higher calcite/dolomite ratios correlate with lower Sr concentrations in the samples. δ18Ocarb values are generally negative and, in the case of Yanwutan, decreasing values correlate with decreasing Sr concentrations (Hohl et al. 2015b), and thus may be explained by late meteoric alteration processes (Brand & Veizer 1981) or by mixing of seawater with meltwaters during deglaciation (Zhao & Zheng 2010).

The 87Sr/86Sr ratios of carbonate leachates from most cap dolostones from the present study are clearly elevated compared with generally accepted values of late Neoproterozoic seawater (e.g. Jacobsen & Kaufman 1999; Halverson et al. 2007). However, the 87Sr/86Sr ratios and Sr concentrations vary locally and temporally. Cap dolostones from all platform sections and a basin section (Yanwutan) display radiogenic 87Sr/86Sr along with depletions of Sr. Cap dolostones from the Longbizui (basin) and Huanglianba (slope) sections display higher Sr concentrations coupled with radiogenic Sr isotopic compositions (Fig. 4c), whereas O and C isotopes reveal no changes (except for a single positive δ18Ocarb value of +5.7‰). In summary, the obtained Sr isotope and concentration data from cap dolostones indicate a complicated and diverse evolution, and interpretations are complicated as primary and secondary effects on the dataset may compensate each other. However, we can state that radiogenic 87Sr/86Sr do not correlate with a higher concentration of silicate-derived elements such as total REE or Al, ruling out the influence of clay leaching during our chemical preparation.

Liu et al. (2013) discussed in detail the potential origin of radiogenic 87Sr/86Sr in Marinoan cap carbonates from the Nuccaleena Formation, South Australia, and found that they may be best explained by interaction of the carbonates with brines or hydrothermal fluids or may reflect values of glacial meltwaters mixing with the seawater. The latter hypothesis is further supported by the work of Ohno et al. (2008), which showed that radiogenic 87Sr/86Sr compositions occur together with light δ88Srcarb values in Marinoan cap dolostones from the Three Gorges region, indicating that the presumable Sr source was fine-grained deglaciation debris. The cap dolostones of the present study reveal 87Sr/86Sr compositions similar to earlier published values from the Yangtze Platform (Ohno et al. 2008; Sawaki et al. 2010). However, the local variations in isotopic compositions and concentrations of Sr led us to the conclusion that the budgets of Sr (and sometimes also O and other fluid-mobile elements; Hohl et al. 2015b) in cap dolostones of the Yangtze Platform might have been variably affected by late-diagenetic fluids. Their origin may be meteoric (as suggested by light oxygen isotopic compositions; Brand & Veizer 1981) or sedimentary basin brines (Banner & Hanson 1990; Cai et al. 2001; Hohl et al. 2015b).

Although fluid-mobile elements such as Sr or O in cap dolostones were strongly altered, some of the cap dolostones might still record pristine (or close to pristine) geochemical signatures of elements less susceptible to fluid overprint. For example, δ13Ccarb values do not correlate with radiogenic 87Sr/86Sr compositions (Fig. 4b). Only three samples from the platform sections and one sample from the basinal Yanwutan section show 87Sr/86Sr compositions close to the proposed Ediacaran seawater compositional range (0.7075 – 0.7080). To constrain the influence of fluids on the cap dolostones, we fitted the open-system fluid–rock mixing model of Jacobsen & Kaufman (1999) to our datasets. Following the approach of Hohl et al. (2015b), we used the isotopic compositions and elemental concentrations determined in the leachates of the presumably most pristine samples as a starting point and modelled the evolution of two possible fluid compositions (Fig. 4a–d). Our mixing model uses different fluid compositions because the data distribution can be explained only by a range of fluid compositions and multiple overprint of the carbonate rocks. We further computed the mixing with variable fluid–rock mixing ratios from 0.01 to 10. As a starting point (the presumably pristine marine Neoproterozoic carbonate composition) we used 87Sr/86Sr = 0.707, δ18Ocarb = 0, a primary Sr concentration of 200 – 350 µg g−1 and δ13Ccarb = 0 to + 5‰. These values were inferred from the most pristine samples of our dataset, whereas C concentrations used in the model (1200 µg g−1) were taken from Jacobsen & Kaufman (1999). Two different low concentration fluids (I and II) were modelled for a first-stage event (mixing with meteoric or freshwater–glacial meltwater) with δ18O = −15‰, δ13Ccarb = −6‰ and 87Sr/86Sr = 0.715, Sr = 30 µg g−1 and Ba = 200 µg g−1 for fluid I and 87Sr/86Sr = 0.725, Sr = 50 µg g−1 and Ba = 300 µg g−1 for fluid II respectively. However, the detailed nature of fluids I and II is unknown.

Mixing of 87Sr- and 16O-enriched glacial meltwaters with Ediacaran seawater as suggested in the so-called ‘plumeworld hypothesis’ (Shields 2005) or meteoric waters overprinting the carbonates are both reasonable processes to explain our data. According to Ohno et al. (2008), the correlation of light δ88Srcarb values with radiogenic 87Sr/86Sr ratios in Doushantuo cap dolostones from the Three Gorges region is best explained by a massive influence of fractionated continental Sr via meltwater runoff. However, this would explain only our modelled proximal platform realm and the Yanwutan section mixing trends for low-Sr concentration dolostones (fluids I and II) (Fig. 4c). Cap dolostones from the Huanglianba and Longbizui sections seem to have been influenced by an additional (secondary) fluid overprinting event. This overprint shifted Sr concentrations and isotopic compositions from the mixing trend observed in the platform sections and the Yanwutan section to higher (more concentrated and more radiogenic) values that cannot be attributed to meltwater influx alone (fluid–rock mixing pathways A and B in Fig. 4c). The nature of these Sr-rich and radiogenic fluids may have been sedimentary basin brines (e.g. Banner & Hanson 1990; Cai et al. 2001). To fit the unusual Sr evolution pathways determined in cap dolostone from basin and slope water environments from the Yangtze Platform we modelled two brines leading to a late-stage fluid overprint of the carbonate lithologies. These brines contained radiogenic Sr and high Sr concentrations according to our model and follow a different curvature in the 87Sr/86Sr–Sr plot than presumed early stage fluids (Fig. 4c). The modelling parameters used were 120 µg g−1 Sr and 86Sr/87Sr = 0.714 for brine A and 190 µg g−1 Sr and 86Sr/87Sr = 0.7255 for brine B.

Depositional environment and implications for the composition of early Ediacaran seawater

Here we discuss the significance of δ13Ccarb values and shale-normalized REE + Y abundance patterns of cap dolostone leachates as records of palaeo-environmental conditions. Except for samples from Jiulongwan (discussed below), δ13Ccarb values (Fig. 5) of the studied cap dolostones are between −3 and −7‰ (with one extremely negative outlier; −30.6‰), and resemble data from the Jiulongwan section cap dolostones studied by Huang et al. 2013; shown in Figs 5 and 7 for comparison), Namibia and Kazakhstan (Ohnemueller et al. 2014) and Brazil (Font et al. 2006; de Alvarenga et al. 2008). The δ13Ccarb data of the present study did not reveal systematic covariations with tracers that are easily affected by fluid–rock interaction (Fig. 4), arguing for the absence of a diagenetic or hydrothermal origin of the C isotope signal in the studied cap dolostones. Earlier data presented by Huang et al. (2013) show a strong positive correlation of δ18Ocarb with δ13Ccarb in Jiulongwan section cap dolostones (dashed trend line in Fig. 5), which was taken as an indicator for a strong diagenetic overprint and mobilization of carbon as it is difficult to produce such correlations in a primary depositional environment (Derry 2010, and references therein). In our dataset the O and C isotope values obtained for the Jiulongwan section (Fig. 5) reproduce the trend of Huang et al. (2013), whereas samples from other sections show no positive correlation between the two stable isotope systems. We therefore assume that despite the Jiulongwan data our obtained values are of primary origin, and represent the unique formation conditions of cap dolostones. The very low δ13Ccarb value recorded in cap dolostones of the Huajipo section (HJP −30.6‰) is similar to other strongly negative deviations in δ13Ccarb of the same locality occasionally reported in the literature (Jiang et al. 2003; Bristow et al. 2011). The origin of these very low carbon isotope compositions is still poorly understood. One explanation is that they formed as a result of early gas hydrate oxidation or oxidation of hydrocarbons redistributed by fluid–rock interaction during diagenesis. Whether this process took place during carbonate deposition or during diagenesis is still a matter of debate (Bristow et al. 2011; Lin et al. 2011).

Several studies have shown that ratios and patterns of REE + Y in leachates from pure carbonate phases may record the compositions of coeval seawater (Webb & Kamber 2000; Kamber & Webb 2001; Nothdurft et al. 2004). According to previous work done on Ediacaran carbonates from the Yangtze Platform, REE + Y analysis may provide insights into the palaeo-seawater oxidation state (Huang et al. 2009; Ling et al. 2013) and environmental changes, such as estuarine mixing (Hohl et al. 2015a). However, abundances and patterns of these elements must be evaluated carefully for the effects of diagenetic overprint and the influence of leaching of detrital phases such as clay minerals (Webb & Kamber 2000). In particular, clay minerals tend to have relatively high abundances of REE and shale-like abundance patterns that may strongly influence the original shape of REE patterns of marine carbonates. Furthermore, interferences on Eu (e.g. 135,137Ba16O) may obscure data for this element (Dulski 1994) and have to be corrected.

Shale-normalized REE + Y patterns of post-Marinoan cap dolostones from the present study display relative enrichments of the heavy REE (HREE) over the light REE (LREE) and positive Y anomalies (Fig. 3). Although a large variation in K and Al abundances (Fig. 6) in our acetic acid leachates argues for feldspar or ilite leaching, we did not observe any correlation of these elements with concentrations of the REE that behave conservatively (i.e. those that are not affected by the typical anomalies found in shale-normalized lanthanide patterns; supplementary material, Fig. C). To improve the overall data quality, REE data for samples with Al concentrations above 0.35 wt% were not considered (Ling et al. 2013). The same is true for samples with REE fractionations that cannot be attributed to formation in aqueous surface environments (PrN/YbN <1, Y/Ho <27; crosses in Figs 4 and 7). Tostevin et al. (2016a) further suggested the exclusion of data points that are below general marine Y/Ho ratios (<36, see horizontal line in upper part of Fig. 6). Despite two samples, the Y/Ho ratios of cap dolomites analysed for this study are between PAAS and modern open-marine seawater values (27 – 57, Fig. 6) but are often below the ‘clearly marine’ threshold of 36. Lawrence & Kamber (2006) showed that modern freshwater samples typically reveal flat shale-normalized REE + Y patterns with a strongly damped Y anomaly. However, by removing data with Y/Ho between 27 and 36, mixing processes of seawater with glacial meltwater influx can no longer be resolved. Alternatively, the smaller Y anomaly compared with modern seawater may reflect secondary modification of the REE + Y budget in the carbonate rocks by late fluid flow and REE addition. In our opinion, the latter explanation is not supported by the data, as total REE concentrations do not correlate with concentrations of typical fluid-mobile elements such as Sr or other ‘shale proxies’ such as Al or Rb concentrations.

Clear negative Ce anomalies (CeN/CeN* <0.9) in carbonates develop under suboxic to oxic conditions (e.g. Ling et al. 2013). As most platform carbonate leachates display negative Ce anomalies in the lower part of the cap dolostones (Fig. 7f), oxic conditions might have been prevalent shortly after the Marinoan glaciation. The absence of a clear negative Ce anomaly in basin cap dolostones suggests that oxic seawater conditions were limited to shallow-water settings and restricted basins on the Yangtze Platform, as Ce anomalies reflect only local oxygenation. Trace metal enrichments in deeper anoxic realms of the Ediacaran ocean show that atmospheric oxygenation before or after the Marinoan glaciation must have triggered a massive influx of redox-sensitive elements into the ocean (Sahoo et al. 2012, 2016). The CeN/CeN* ratios of almost all studied cap dolostone sections show a gradual increase from values lower than or close to unity at the base to values slightly higher than unity at the top (except Huajipo and Zhongling literature data from Huang et al. (2011); Fig. 7f). These changes probably reflect deeper deposition of the platform cap dolostones at a later stage of the proposed early Ediacaran transgression (e.g. Huang et al. 2013), with depositional conditions of these sections being below the chemocline.

Redox conditions during deposition of post-Marinoan cap dolostones

Although redox conditions on the shallow platform might have been already oxidizing at the beginning of the Ediacaran (negative Ce anomalies; Figs 6d, i and 7f) the redox state of the sediment porewaters may have been suboxic or even anoxic owing to consumption of oxygen during organic matter decomposition. Several researchers have shown that a varying redox front within the sediment may redistribute redox-sensitive elements according to their abundance and solubility (Cowie et al. 1995; Thomson et al. 1998; Mucci 2004). To assess how variable redox conditions affected the element and isotopic compositions of the carbonates we calculated enrichment factors based on the Al-normalized abundances of five redox-sensitive metals (Fe, V, Mo, U and Mn) in the carbonate leachates. The approach is similar to that used by Tribovillard et al. (2006) for organic-rich shales. Because the present study concerns carbonate rocks, the Al-normalized trace element data obtained on carbonate leachates were normalized relative to an appropriate carbonate rock standard. The lack of a wide range of carbonate reference materials that reflect variable environmental depositional conditions and the challenges in analysing low concentrations of trace metals in carbonate lithologies make it difficult to find a suitable reference material for comparison with geological samples. In the supplementary material (Fig. B) we present ranges of trace metal enrichment factors of four carbonate standards from the Geological Society of Japan (recent Porites coral (JCp-1; Inoue et al. 2004); Holocene giant clam (JCt-1; Inoue et al. 2004); Triassic Limestone (JLs-1; Imai et al. 1996) and Permian Dolomite (JDo-1; Imai et al. 1996)) relative to the CAL-S carbonate standard (Yeghicheyan et al. 2003). CAL-S is a pure micritic limestone that was deposited on a shallow platform during the Tithonian and shows REE + Y patterns similar to modern shallow seawater (Hohl et al. 2015a). The comparison shows that biogenic carbonate rocks have lower redox-sensitive trace metal concentrations whereas inorganic carbonate rocks show higher concentrations of these elements relative to CAL-S. We have chosen the CAL-S standard for comparison of our samples because it is representative for carbonate precipitates from oxidized seawater and data for a large range of trace elements are available.

Enrichment factors (EF) used in this study were calculated using equation (3):  
formula
(3)
where CElement is the concentration of the analysed element, HAsc is the carbonate acetic acid leachate and CAL-S is the limestone reference material (which is completely dissolvable in 1M acetic acid). Therefore, EF-Element >1 indicates an enrichment of this element in the carbonate phase relative to CAL-S and carbonates formed in Phanerozoic seawater (see Table 4). A decrease in enrichment factors of redox-sensitive metals suggests that these metals were incorporated into non-carbonate phases such as iron oxides, sulphides or organic matter. The CAL-S standard is certainly deposited under oxidized conditions, as is indicated by its low Fe (35 µg g−1) and relatively high U (0.77 µg g−1) contents. However, the exact dissolved oxygen amount in the seawater at the time of CAL-S deposition cannot be determined with certainty and therefore every enrichment factor given in this study represents an estimate relative to CAL-S.

Mn enrichments in carbonates may develop when MnO2 colloids dissolve under reducing porewater conditions (Cowie et al. 1995; Thomson et al. 1998) followed by Mn substitution for Mg into authigenic Mn carbonate (rhodochrosite) or other carbonate phases (e.g. Mn-rich dolomite). Mn enrichment factors in almost all samples exceed values given for biogenic and non-biogenic carbonate reference materials from different geological periods and depositional environments (Fig. 9b and d), arguing for the redox-controlled dissolution of Mn oxides and subsequent Mn incorporation into the carbonate lattice. Mn enrichments also correlate with high Mn/Fe, as well as increasing shale-normalized Ce/Ce* ratios.

In the lower parts of the platform-derived cap dolostone sections Fe, V, Mo and U are systematically depleted relative to the top (Fig. 8a–d). The enrichment factors of redox-sensitive metals from the slope section at Huanglianba (Fig. 8) show similar behaviour, whereas the basin sections at Yanwutan and Longbizui show systematic trace metal enrichment of the Longbizui samples compared with the Yanwutan samples (see Table 4). The low of V, U and Mo concentrations with concomitant negative Ce anomalies in carbonates of almost all studied sections (except the Longbizui basinal section; see Fig. 9a) argues against anoxic water conditions during the deposition of the Yangtze Platform cap dolostone units, as negative Ce anomalies form only in oxic water. Although the solubility of trace metals such as U and Mo should be higher under oxidizing conditions (Nozaki 2010) these redox-sensitive elements are depleted in the studied Neoproterozoic cap dolostones. The depletions in V, U and Mo concentrations together with negative but weaker (than those of Phanerozoic carbonate rocks) Ce anomalies therefore simply may reflect a lower concentration of dissolved oxygen in the Neoproterozoic oceans relative to modern surface oceans (Sperling et al. 2015). Enrichment of redox-sensitive metals in the Longbizui basin section (Figs 8 and 9), however, may be explained by ferruginous or even sulphidic conditions in deeper parts of the water column and subsequent incorporation of the metals into carbonate phases (Huang et al. 2011; Meyer et al. 2012).

Systematic relative enrichments of the redox-sensitive elements occur towards the top of the cap dolostone units from the basinal environment of the Yangtze Platform (Fig. 8). In contrast, in proximal platform sections of the Yangtze Platform, only V enrichment factors increase up-section (Fig. 8b). The enrichment of various trace elements up-section may have been caused by lateral fluid flow along faults and a longer retention time of these fluids beneath a hydrological clay-rich barrier in strata overlying the cap dolostones. Because the solubility of redox-sensitive trace metals such as Mo is higher under oxidizing conditions (Nozaki 2010), leaching and redistribution caused by basin fluids overprint may take place only if these fluids were of oxic nature. In contrast, Mn will be redistributed only by the reductive dissolution of manganese(IV) oxide (MnO2) colloids (Thomson et al. 1998). If the clay mineral-rich Doushantuo II member acted as a barrier to trace element redistribution throughout the Yangtze Platform (Derkowski et al. 2013) this should have led to similar patterns of redox-sensitive element enrichments at different localities of the Yangtze Platform. This is not consistent with the observation of variable trace metal enrichments between proximal platform and distal slope and basinal sections, and rather than fluid flow redistribution of redox-sensitive metals a primary origin may explain the observed enrichment patterns, as we discuss below.

The common occurrence of sedimentary (anhedral) sulphides in slope and basinal cap dolostone and of framboidal pyrites in cap dolostones of the Jiulongwan section (intra-platform basin) is consistent with sulphidic conditions in these settings (see Table 1 and Fig. 2e and f). Positive shale-normalized Ce anomalies in the same samples are strong indicators for the dissolution of Mn oxides, which typically occurs under moderately anoxic conditions (less than 10µM dissolved O2; Johnson et al. 1992; Canfield & Thamdrup 2009; Tostevin et al. 2016b). The positive Ce anomalies were mostly found in distal samples (slope and basin), showing true marine Y/Ho ratios (>36; Fig. 6d). The magnitudes of the Ce anomalies show a positive correlation with Fe enrichments and Mn/Fe ratios (Figs 9a, e and 10). This may be best explained by the dissolution of Fe–Mn oxides under intermediate manganous water conditions prevalent at 635 – 630 Ma in the distal (basinal) parts of the Yangtze Platform, whereas only iron speciation data may help to clarify whether truly ferruginous conditions were prevalent at this time and locality. Enrichments of Mn above values of the Permian dolomite reference material JDo-1 and shale-normalized Ce/Ce* ratios that are far above modern oxic conditions (Fig. 9a and b) further argue for a stratified water column with manganous bottom water conditions where the dissolution of MnO2 would release CeIII+ into seawater. This observation goes along with the oxidation of a deep-water dissolved organic carbon pool indicated by a positive correlation of Mn enrichments with δ13Ccarb values (R2 = 0.76). However, the enrichment of redox-sensitive Mo in the same anoxic basinal section samples (Fig. 9c and d) would be consistent only if oxic weathering on the continents released sufficient amounts of Mo, U and V into the deeper ocean shortly after the Marinoan glaciation (e.g. Chen et al. 2015; Och et al. 2016).

The best explanation for the local enrichments of redox-sensitive elements in carbonate leachates of post-Marinoan cap dolostones may therefore lie in variable redox conditions in different palaeo-environments of carbonate deposition (Fig. 10). The oxic weathering influx of redox-sensitive trace metals (such as V, U and Mo) into the early Ediacaran ocean and the scavenging of CeIV+on organic colloids or Mn oxides and hydroxides in oxic surface waters was followed by variable deposition and accumulation of these elements in various environments from suboxic shallow platform to presumably manganous proximal restricted basins and deep distal basins. This influx in metals may have been important for contemporary and subsequent biological inventions that led to the evolution of animals during the late Neoproterozoic (Anbar 2008), and the redox stratification of the water column and the observed hints for meltwater mixing with the upper layer are consistent with the plumeworld hypothesis of Shields (2005) with a high-alkalinity oxic meltwater lens above anoxic bottom waters.

Conclusions

Data on fluid-mobile elements and their isotopes indicate that Ediacaran cap dolostones from platform, slope and basin depositional environments of the Yangtze Platform, South China, underwent variable fluid–rock interaction and mixing with fluids from different sources. A first-stage mixing event may be attributed to meltwater with radiogenic Sr isotopes but low Sr concentration. In contrast, late fluid overprinting occurred in some slope and basin sections of the Yangtze Platform, which may be attributed to continental basin brines with radiogenic Sr isotopes and elevated Sr concentrations. In the course of these processes, O isotopic compositions were usually shifted to lower values following modelled fluid–rock mixing pathways. Most carbon isotopic compositions of cap dolostones show no temporal variability nor any correlation with tracers of fluid–rock interaction.

Pristine marine REE + Y patterns and negative Ce anomalies together with moderately negative δ13Ccarb values of proximal platform settings may reflect pristine seawater compositions at those localities and show that shallow Ediacaran seawater was already oxidized shortly after (or before) the Marinoan glaciation. Sedimentary sulphides and Mn enrichments together with redox-sensitive metal enrichments (Mo, U and V), positive shale-normalized Ce anomalies and the lightest δ13Ccarb values in carbonates of the distal basinal sections argue for reductive dissolution of Mn-oxides and organic colloids under presumably manganous conditions (less than 10µM O2) at that time. As a consequence, redox-sensitive trace metals and Ca2+ were incorporated into deep-water manganous dolomites, which further supports previous redox-stratified models for a redox-stratified continental margin during the Ediacaran (e.g. Li et al. 2010; Tostevin et al. 2016b). The influx of trace metals into the ocean in the aftermath of the Marinoan glaciation may have been crucial for subsequent biological inventions that led to the evolution of the first animals during the Ediacaran.

Overall, mixing of seawater with meltwater (indicated by suppressed Y/Ho anomalies and perhaps Sr isotopes) in oxic surface water overlying presumably manganous bottom waters further argues for the plumeworld hypothesis presented by Shields (2005).

Acknowledgements

We thank M. Feth and K. Hammerschmidt for their support in the laboratory, W. Bäro for pre-processing of samples from Huanglianba, and Members of FOR 736 for their help during collection of the samples in the field. Many thanks go to A. Bekker and two anonymous reviewers for comments on two earlier versions of this paper, which led to substantial improvements. We thank I. Wilson for his proof reading. Finally, we would like to thank the editors Graham A. Shields-Zhou and V. Vandeginste for helpful discussion and support for this paper.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)