Astronomical Cycles of the Late Permian Lopingian in South China and Their Implications for Third-Order Sea-Level Change

WANG Xiuqi, ZHANG Xunhua, GAO Fei, and ZHANG Minghua

Astronomical Cycles of the Late Permian Lopingian in South China and Their Implications for Third-Order Sea-Level Change

WANG Xiuqi1), 2), 3), ZHANG Xunhua2), *, GAO Fei2), and ZHANG Minghua4)

1)College of Marine Geosciences, Ocean University of China, Qingdao 266100, China 2)Qingdao Institute of Marine Geology, China Geological Survey, Qingdao 266071, China 3)Qingdao Jimo Municipal Transport Bureau, Qingdao 266200, China 4) The Brigade of Geological Survey of Ganxi, Bureau of Geologic Exploration and Mineral Development of Jiangxi Province, Nanchang 330002, China

The late Permian (Lopingian) was a crucial climate transition period from the late Paleozoic Ice Age to the early Triassic of exceptionally high temperatures. However, the origins of the third-order sea-level changes during the Lopingian Epoch remain unclear. Here, we presented astronomically calibrated gamma-ray (GR) log and non-U GR (computed gamma ray or CGR) curves from the clastic and carbonate successions of well GFD-1 in the Pingle Depression of South China for studying the sea-level oscillations during the Lopingian. Spectral analyses of the 405kyr-calibrated GR and CGR time data revealed periodicities close to about 405, about 100, about 44.2, about 35.1, about 21, and about 17.5kyr, supporting the existence of Milankovitch forcing in the sedimentary records. A high-resolution astronomical time scale and high-resolution sedimentation rate curve of the Lopingian from well GFD-1 were constructed by cyclostratigraphic analysis. The eccentricity and obliquity amplitude modulation cycles suggested long periodicities of about 2.4 and about 1.2myr, respectively. In the Wuchiapingian greenhouse of the Lopingian, the about 2.4myr eccentricity oscillation controlled ‘weak’ glacio-eustasy and/or aquifer eustatic changes related to the global third-order sea-level changes and that a lowstand (W2) was initiated by an eccentricity oscillation minimum. In contrast, during the Changhsingian, which exhibited a cooling event, an about 1.2myr obliquity cycle was probably strong, with the sea-level records highlighting the link between the ‘icehouse’ sea-level lowering (C2 and C1) and the obliquity nodes. Moreover, dynamic sedimentary noise model as an indicator of sea-level showed local third-order sea-level variations, the coevolution trends in the orbital power, global and local sea-level changes, and sedimentation rate had significant implications for establishing the global nature and synchronicity of these million-year-scale eustatic records and reconstructing the temporal depositional history at a regional scale. In addition, the volcanism and tectonism that continued into the early-middle Wuchiapingian probably led to a series of climate changes that drove the hydrological cycles not paced by the Milankovitch cycles.

Lopingian; Milankovitch cycle; third-order eustasy; long-period astronomical cycle; sedimentation rate

1 Introduction

The Lopingian of the Permian represents the last epoch of the Paleozoic Era and is bracketed by the end-Gua- dalupian and end-Permian mass extinctions and volcanisms, which are associated with dramatic environmental changes (Racki and Wignall, 2005; Shen., 2010a). It was a remarkably transitional period from the late Paleozoic Ice Age (Chen, 2013) to the early Triassic of exceptionally high temperatures (Sun, 2012). The Chinese basalt eruptions that began during the latest Capitanian may have triggered the Phanerozoic sea-level minimum (Hallam and Wignall, 1999). During the fol-lowing Lopingian, third-order sea-level variations (Snedden and Liu, 2010) with a million-year-scale and medium-high amplitudes (>25m and even >75m) occurred (Miller, 2005; Li., 2018). However, the origins of these subsequent sea-level drops remain yet unknown.

Global sea-level variations result from changes in the ocean basin capacity and seawater volume (Haq, 2014). The changes in the ocean basin capacity are related to low-frequency (<10−6per year) variations in the sea-floor spreading rate (Miller, 2005). However, the variations in the seawater volume are dominated by the higher-frequency (>10−6per year) high-amplitude eustatic oscillations (up to 200m) associated with the astronomically forced growth and decay of the continental ice sheets and other high-frequency but low-amplitudes (5–10m) eus- tatic processes (Li., 2018a). Variations in Earth’s orbital parameters (eccentricity, obliquity, and precession) have been shown to be a significant driver of paleoclimate change in geological time (Hinnov and Hilgen, 2012; Chen., 2019a, 2019b). The amplitude modulation cycles of the eccentricity (about 2.4myr) and obliquity (about 1.2myr) are now considered to be responsible for the major climate changes in the Cenozoic and Mesozoic Eras (Zachos., 2001). Moreover, these long-term cycles and/or tectonic processes (Boulila., 2011) apparently also have a significant effect on the third- order sea-level changes (Matthews and Frohlich, 2002; Lirer., 2009; Huang., 2010). For instance, Boulila. (2011) suggested that astronomically controlled third-order eustatic sequences during the Cenozoic ice house and Mesozoic greenhouse corresponded to an about1.2 myr obliquity modulation cycle and an about 2.4myr eccentricity modulation cycle, respectively. Further, Li. (2016a) reported that the myr scale, the high-amplitude global sea-level variations were affected by obliquity forcing during the Early Triassic. However, the instability of the orbital modulation cycles owing to the chaotic behavior of the solar system in the Paleozoic Era may hinder efforts to establish the relationship between the orbital forcing and the global and even local third-order eustatic sequences (Laskar., 2004; Fang., 2015), and such surveys have only begun to address this era (De Vleeschouwer., 2014; Fang., 2017).

For investigating the reservoir and production capacity of shale gas in South China, a systematic coring well called well GFD-1 was drilled by the China Geological Survey in the Pingle Depression of the lower Yangtze Craton. The total coring interval was about 1500m and ranged from the early Triassic Daye Formation to the middle Permian Maokou Formation. This well provides an opportunity for deciphering the changes in the paleo-sea-level records in the Lopingian marine-continental transitional facies and marine deposition, which is different from the previous researches only emphasizing the marine strata or the terrestrial strata. In this study, a cyclostratigraphy analysis of the Lopingian deposits from well GFD-1 was performed using gamma-ray (GR) log and non-U GR (computed gamma ray or CGR) curves. The goals of this study were: 1) to identify the astronomical forcing in the sequences of the stratigraphic cycles and elucidate the evolution of the sedimentation rates along a stratigraphic succession, 2) to establish a high- resolution astronomical time scale (ATS) for well GFD-1 by tuning the sedimentary records to the astronomical solution, and 3) to elucidate the long-period astronomical terms during the Lopingian as well as the correlation between the orbital forcing, global and local third-order eustatic sequences, and high-resolution sedimentation rate.

2 Geological Setting

The Pingle Depression is a sunken belt in South China and lies in the north of Jiangxi Province (Yang., 1994; Song., 2003) (Fig.1). Through the south boundary along the Pingxiang-Guangfeng deep fracture zone, it is adjacent to Cathaysia Block (Song., 2003; Xie., 2018). To the north, the Pingle depression is bounded by the Yifeng-Jingdezhen deep fracture belt that is a part of the Jiangnan rift zone (Wang., 2019). The eastern and western boundaries of the depression are the provincial boundaries of Anhui Province and of Hunan Province, respectively.

The Pingle Depression was lifted by the Dongwu orogenic movement, after which the Lopingian settings were deposited (BGMRJP, 2014). The unconformity boundary of the Guadalupian and the Lopingian (GLB) is considered an overlapping interface of the second-order and third-order sequences, with paleosol layers, paleokarst, limestone gravel layers, and aluminaceous mudstone being unconformable evidences around the GLB in the Pingle Depression (Qin., 2015). The Ganjiang fault divided the Pingle Depression into the Pingxiang sag and the Leping sag in the west and east, respectively (Li., 2003) (Fig.1c). In the Pingxiang sag, the Shigang-Lashi deep fault that formed during the Caledonian is the boundary for the simultaneous heterogeneous deposition in the Leping formation of the Lopingian (Chen., 2001). To the south, the coal-bearing clastic rocks of the Leping formation (P3) developed in the marine-conti- nental transitional facies depositional environment, which can be divided further into the Guanshan, Laoshan, Shizishan, and Wangpanli members, in ascending order. The sedimentary facies mainly include shallow sea shelves, coastal plains, tidal flats, swamps, barrier-la- goons, and delta fronts (Xu., 2011; Yu., 2016). To the north, terrestrial-marine transitional strata developed only in the Guanshan member and the lower part of the Laoshan member, and the overlying strata called the Qibaoshan formation (P3; stratigraphically equivalent to the upper part of the Laoshan, Shizishan, and Wangpanli members) was a set of shallow marine sediments with mudstones, silty mudstones, siltstones, micritic limestones, siliceous limestones, and siliceous rocks (Deng., 2005). The Changxing formation above the P3/P3with conformity was formed in the marginal marine environment with marine carbonate deposits (Li., 2003; Qin., 2015).

Well GFD-1 is located at latitude 115˚40´N and longitude 28˚30´E in the middle of the Pingle depression (Fig. 1c). This study focused on coring intervals at 450–1238 m, with correspond to the lower Daye formation of the early Triassic (450–495m), the late Permian Changxing formation (495–725m), and the Leping formation (725– 1238m) (Fig.2). These three sets of strata were deposited continuously. The Daye formation consisted of a sequence of thick gray argillaceous limestones. The Chang- xing formation was dominated by chert-nodule-bearing gray thick bioclastic limestones and siliceous limestones. The Leping Formation was characterized by dark-gray or black mudstones, gray sandstones, and sand-shale interbeds intercalated with thin coal seams.

Fig.1 (a) Late Permian paleogeography showing location of South China (from http://www. scotese.com), (b) Late Permian paleogeographic configuration of South China showing location of Pingle Depression (pink star) (modified from Wu et al., 2012), and (c) Map showing location of Pingle Depression, tectonic units, and well GFD-1 (blue pentagon) (modified from Regional Geology of Jiangxi Province, 2014).

3 Method

3.1 Paleoclimate Proxies for Cyclostratigraphy

The GR log of boreholes is a valuable tool for digitizing stratigraphy for the analysis of paleoclimate trends and climatic cycles (Schnyder., 2006; De Vlees- chouwer., 2017; Li., 2019). The radiogenic isotopes of potassium (K), uranium (U), and thorium (Th) are the three primary sources of the gamma rays emitted from deposits (Ruffell and Worden, 2000; Schnyder., 2006). K, U, and Th are concentrated in a number of sedimentary host minerals such as clays and feldspar (Li., 2016a; Fang., 2019). In addition, U can be present in high contents in organic matter that has been deposited under anoxic conditions (Brumsack, 2006; Schnyder., 2006; Fang., 2019). Moreover, non-U GR curve (.., CGR (API)=16.32×K(%)+3.93 ×Th(ppm), Rider, 1999; Kumpan., 2013), which can reveal the variations in the clay content, can also be employed as a quantitative proxy for cyclostratigraphic ana- lysis (Li., 2016b; Li., 2018b; Cong., 2019). The total GR log and Th and K logs which covered 450m to 1238m in the GFD-1 well, were measured by Schlumberger Oilfield Services at a sampling resolution of 0.05m. In total, 15761 sample points for the GR series and 15761 data points for the CGR curve were obtained.

Fig.2 Composite histogram of well GFD-1 with members, lithostratigraphy, data series in the stratigraphic domain, and filter output curves. Interpreted about 405kyr orbital eccentricity cycles are extracted from GR (initial values, red lines) and CGR (initial values, blue lines) series using Gaussian filters with passbands of 0.016±0.0025cyclesm−1 (450–680m), 0.025±0.005cyclesm−1 (680–950m), and 0.03±0.01cyclesm−1 (950–1238m), respectively. AP (green arrow), anchor point (Burgess et al., 2014); T, Triassic; SZS: Shizishan member; ULS, upper Laoshan sub-member; MLS, middle Laoshan sub-member; LLS, lower Laoshan sub-member; E, the about 405kyr eccentricity cycle.

3.2 Upper Permian Astronomical Parameters

Considering that the La04 and La10 astronomical solutions (Laskar., 2004; 2011) are restricted to the last 250Ma (Li., 2018a), the Berger94 solution (Berger and Loutre, 1994) was used. Linear interpolation of the Berger94 solution at 259Ma (Berger and Loutre, 1994) yielded seven theoretical astronomical terms: about 405kyr for long eccentricity(E), about 125kyr(e1) and about 95kyr(e2) for short eccentricity (with an average of 100kyr), about 44.2kyr(O1) and about 35.1kyr(O2) for obliquity, and about 21kyr(P1) and about 17.6kyr(P2) precession cycles, with the ratio of the orbital parameter periods being approximately 23.0:7.1:5.4:2.5:2.0:1.2:1.0.

3.3 Time-Series Analysis

A secular trend was removed from the logging series. The spectral analysis was performed using the 2π multi- taper method (MTM) power spectrum (Thomson, 1982) and the robust autoregressive AR (1) red noise model (Mann and Lees, 1996). Evolutionary fast Fourier transform spectral analysis was also performed on the logging series to generate the power spectra from many segments of the depth series and detect all the cycle frequencies of interest (Weedon, 2003; Meyers and Hinnov, 2010). The about 405kyr long orbital eccentricity cycles were extracted from the logging depth series using the Gaussian bandpass filter. The GR and CGR depth records were transformed into time series based on the interpreted about 405kyr cycles from the higher-resolution log data as the age model. Amplitude modulation (AM) analysis can detect the long-term periodicities related to secular resonance (Fang., 2015) (.., about 1.2 or about 2.4myr) and determine whether the sediment cycles have astronomic origins (Watkins., 1999). The analysis steps performed were as follows: first, the secular trend was removed from the calibrated data series, which was then subjected to Taner-Hilbert bandpass filtering to extract the AM curves; Then, the extracted amplitude curves were analyzed spectrally using periodograms at a higher resolution than that for the MTM.

Instead of using conventional ‘ratio methods’, one can employ the correlation coefficient (COCO) and evolutionary correlation coefficient (eCOCO) approaches, which are objective statistical methods similar to the average spectral misfit (ASM) method of Meyers and Sageman (2007) and its evolutionary extension eASM (Meyers, 2014), for simultaneously testing the astronomical forcing of paleoclimate data series and mean sedimentation rate (Li., 2018c, 2019). The COCO estimates the correlation coefficient () between the power spectra of a sedimentary proxy series in the depth domain and an astronomical solution in the time domain, converting the proxy series from depth to time for a range of ‘test’ sedimentation rates (Li., 2018c). In the eCOCO approach, a sliding window is applied to the paleoclimate proxy data for tracking the changes in the sedimentation rate along the stratigraphic and determining the best fit sedimentation rate (Li., 2018c). These two methods involve the following parameters: correlation coefficient (COCO, eCOCO), null hypothesis (0and e0), and number of contributing astronomical frequencies. Among them, null hypothesis represents the assumption of no astronomical forcing and indicates the probability that a specific correlation coefficient value can occur by chance (Li., 2018c). Also, the number of astronomical parameters contributing to the correlation coefficient of each test sedimentation rate is evaluated (Li., 2018c). In general, the most likely sedimentation rate has the highest correlation coefficient (), the lowest null hypothesis and maximum number of astronomical parameters.

The sedimentary noise model allows one to explore the 100s kyr-myr scale sea-level oscillations embedded within the paleoclimate proxies that are sensitive to water-depth-related noise. Thus, this model can be used to reconstruct the geologic history of the local sea-level for understanding the origins of eustasy within the desired time frame (Li., 2018a). This model uses two complementary approaches (Li., 2018a): dynamic noise after orbital tuning (DYNOT) and the lag-1 autocorrelation coefficient (1). The former is designed to measure the noise in the proxy while the latter is an independent noise indicator for the relative sea-level changes. When the sea-level is relatively low, the water-depth-related noise at a fixed-slope location in the marginal marine environment is stronger than that at times of relatively higher sea levels. This leads to a higher DYNOT ratio and a lower1value and vice versa (Li., 2018a). This model has been discussed in greater detail by Li. (2018a). Moreover, the above-discussed analytical methods have been implemented in the software Acycle (version 1.2) (Li., 2019) (https://github.com/mingsongli/ acycle).

4 Results

4.1 GR and CGR Variations

In well GFD-1, the GR values range from 8.95 to 397.00API while the CGR values range from 2.17 to 197.24API (before the removal of the secular trend). The coal-bearing clastic rocks with a variety of lithological changes that developed in the marine-continental transitional facies sediments gradually changed into carbonates from the marginal marine environment, indicating that transgression and regression occurred during the time of the studied interval. As shown in Fig.2, from bottom to top, the correlation between GR curve and lithology of the Leping formation was shown as follows: the Guanshan member was fluvial and lacustrine sediments with low sea-level relatively, silty mudstone (corresponding to high GR values) and medium sandstone (corresponding to low GR values) were developed in the lower part, mudstone and argillaceous siltstone with high GR values were mainly developed in the middle and upper part, the thick-bedded box-shaped coarse sandstone and medium sandstone were deposited at the top of the Guanshan member, and the GR values decreased. The Laoshan member experienced the process of sea-level rise and then fall and could be divided into three parts: the lower Laoshan sub-member was a shallow sea shelf facies deposit. Sand-bearing micritic limestone and bioclastic limestone with low GR values were occurred in the lower part, gradually rising sea level allowed the development of thin layered mudstone, carbonaceous shale and coal seams, the increase of clay mineral and organic matter content led to the high GR curve values. The middle Laoshan sub-member was sub-abysmal basinal facies with the highest sea level of Leping formation, and the shallow sea shelf facies of the upper Laoshan sub-member indicated the decrease of sea-level. Large section of pure shale with high organic matter content resulted in the increasing GR values. The GR curve of the middle-upper Laoshan sub-members had high values, but with decreasing sea-level, the increase of sandy content and the decrease of organic matter and clay content at the top of the Laoshan member caused low GR values. The Shizishan member in the lowstand developed barrier island facies, which was mainly composed of fine-grained quartz sandstone (corresponding to low GR values) and argillaceous siltstone (corresponding to high GR values), the GR value fluctuated with the change of clay content. The Wangpanli member was tidal-flat facies with variable lithology. Quartz sandstone and feldspar quartz-sandstone with mudstone, silty mudstone with fine siltstone, carbonaceous shale, sand-mudstone interbedded and several thin coal seams were developed in this member. High clay and high organic carbon content corresponded to high GR values while high sandy content led to low GR values. Clay and organic content gradually increased from bottom to top, which caused the increasing tendency of GR values. The Changxing formation and Daye formation were all shallow marine platform carbonate sedimentation. The former was mainly dominated by siliceous limestone with low GR values, some high GR values in strata represented the high clay content. The latter mainly developed argillaceous limestone with higher clay concentration, and GR values were significantly higher than that of the Changxing formation. The GR and CGR values exhibited similar cyclic patterns, with higher values corresponding to clastic rocks and argillaceous limestones with more clay minerals or organic matter and lower values being associated with sandstones, siliceous limestones with less clay mineral or organic matter.

4.2 Cyclostratigraphy in Depth Domain

4.2.1 Analysis of evolutionary correlation coefficient

Multiple COCO peaks suggested the sedimentation rate could be variable. Three peaks, namely, those at about 8.0, about 10.5, and about 16.5cmkyr−1with correlation coefficient= 0.43, emerged from the COCO analysis of the GR datasets (Fig.3a). All three sedimentation rates had0significance levels lower than 0.1%, suggesting that the assumption of no astronomical signal be rejected at the 99.9% level (Fig.3b), and all seven astronomical frequencies were used in the estimation. (Fig.3c). Two peaks at about 25 and about 32cmkyr−1also appeared in this analyse (Fig.3a). Among them, theand0value of peak at about 32cmkyr−1were similar to the above three peaks, but the peak at about 25cmkyr−1had the lowervalue and higher0value than those of three peaks above. Furthermore, both two peaks only had six astronomical frequencies which were used in the COCO, respectively. That meant peaks at about 8.0, about 10.5, and about 16.5 cmkyr−1were more reliable than the other two at about 25 and about 32cmkyr−1. The eCOCO analysis indicated that the sedimentation rate ranged from about 11 to about 5cmkyr−1(average of about 8cmkyr−1) for depths of 1238–950m and then increased to about 12 to about 8 cmkyr−1(average of about 10cmkyr−1) for 950–680m. At the depth of 680– 450m, the rate increased again with the range from about 13 to about 21cmkyr−1(average of about 17cmkyr−1) (Fig.3e). The jumps in the sedimentation rate after about 950, about 680, and about 500m may be linked to the changes of depositional environment. Three lines of potential sedimentation rate exhibitedvalue greater than 0.6 and have0significance levels of less than 0.5%, with more than six terms contributing astronomical frequencies (Figs.3d, e, and f).

For the whole section (1238– 450m), the results of the COCO and eCOCO analyses together suggested that the variation characteristics of sedimentation rate can be divided into three subsets (1238– 950, 950– 680, and 680– 450m), about 8.0, about 10.5, and about 16.5cmkyr−1corresponded to the average rate of each subset, respectively. Further, discontinuities were observed in the sedimentation rates around depths of about 950, about 680, and about 500m (Fig.3).

Fig.3 COCO and eCOCO analyses of detrended GR depth series (less a 205m ‘loess’ trend). (a) correlation coefficient spectrum, (b) null hypothesis test, (c) number of contributing astronomical frequencies, (d) evolutionary ρ shown with sedi- mentation rate (SR) variations in depth domain, (e) evolutionary H0 shown with SR variations in depth domain; white solid line with arrows represents major trend in variations in sedimentation rate, and (f) evolution of number of contributing astronomical frequencies. Sliding window is 100m. Number of sliding steps is 30 (i.e., 1.5m). Tested sediment accumulation rate ranges from 1 to 40cmkyr−1, with a step size of 0.1cmkyr−1. Number of Monte Carlo simulations performed is 2000.

4.2.2 Spectral analysis

Considering the large variations of the sedimentation rate, the untuned GR and CGR datasets were divided into 3 non-overlapped intervals (based on eCOCO results in Fig.3e) for spectral analysis in depth domain, filtering and astronomical calibration. To interpret the wavelengths of significant spectral peaks in terms of possible astronomical periods, their ratios were compared to that of the Late Permian Milankovitch cycles (see Section 3.3; Berger and Loutre, 1994).

In Subset 1 (450–680m), the power spectra of the untuned GR series exhibited wavelengths of 62.5, 15.38, 7.41, 5.44, and 3.31 above the 99% confidence level, these were interpreted as the E, e, O1, O2, and P1 astronomical cycles, respectively (Figs.4a, b); The spectral analysis of the untuned CGR dataset showed that the wavelengths of 62.4, 7.25, 5.44, and 3.26–2.75m (>95% CL) represented E, O1, O2, and P, respectively (Fig.5a, b). The broader cyclic variations in this subset than those in subset 2 and 3 confirmed average sedimentation rate (about 17cmkyr−1) during this part is highest in the whole section. In Subset 2 (680–950m), the wavelengths of 40, 12.05–10.2, 4.35, 3.48, and 1.72m (>99% CL) in the GR series power spectra were ascribed to the E, e, O1, O2, and P2 (Figs.4c, d); The wavelengths of 40, 12.35, 4.35–3.46, and 2.13–1.75m (>95% CL) in the CGR series power spectra represented the E, e1, O (combined O1 and O2), and P (combined P1 and P2) (Figs.5c, d). The average sedimentation rate of this subset was about 10cmkyr−1. In subset 3 (950–1238m), the GR series was characterized by cyclic variations with wavelengths of35.71, 9.23–8.23, 3.89, and 1.82m above the 95% confi- dence level (Figs.4e, f); the power spectra of the CGR series displayed the similar wavelengths of 35.7, 9.23, 3.89, and 1.82m above the 95% confidence level (Figs.5e, f). Comparison of the ratios of these cycle wavelengths with the ratios of Milankovitch frequencies implied that these cycles represent E, e, O1, and P1, respectively with a mean accumulation rate of about 8cmkyr−1.

Fig.4 2π MTM power spectra and FFT spectrogram of untuned GR depth series. (a) and (b) subset 1(450–680m): series with a 100m sliding window, less a 205m ‘loess’ trend, (c) and (d) subset 2 (680–950m): series with a 60m sliding window, less a 205m ‘loess’ trend, and (e) and (f) subset 3 (950–1238m): series with a 60m sliding window, less a 205m ‘loess’ trend. Significant peaks are labeled in meters. CL, confidence level.

Fig.5. 2π MTM power spectra and FFT spectrogram of untuned CGR depth series. (a) and (b) subset 1 (450–680m): series with a 100m sliding window, less a 422m ‘loess’ trend; (c) and (d) subset 2 (680–950m): series with an 80m sliding window, less a 94m ‘loess’ trend, and (e) and (f) subset 3 (950–1238m): series with an 80m sliding window, less a 101m ‘loess’ trend. Significant peaks are labeled in meters. CL, confidence level.

4.3 Cyclostratigraphy in Time Domain

4.3.1 Astronomical calibration and spectral analysis

The about 405kyr long eccentricity cycle is caused by the motions of orbital perihelia of Jupiter and Venus. Due to the stable orbits of Jupiter and Venus, it has been consistent through at least the entire Phanerozoic (Laskar., 2011). Therefore, about 405kyr cycle is possible to utilize this cycle for astrochronology prior to the Mesozoic Era (.., Wu., 2013; Fang., 2015). The three subsets of log-transformed logging series were astronomically calibrated via the inferred about 405kyr cycles. The time-calibrated GR spectrum exhibited dominant peaks at 405, 101, 44.1, 35.5, 21.5, and 17.5kyr above the 99% confidence level (Fig.6a). Further, the CGR spectrum exhibited similar peaks at 405, 100, 44.9, 34.8, 21, and 17.5kyr above the 95% confidence level (Fig.6b). The spectral characteristics were consistent with those of the predicted late Permian astronomical parameters (see Section 3.3; Berger and Loutre, 1994) and corresponded to the long eccentricity, short eccentricity, short obliquity, and precession cycles, respectively. Therefore, the cyclostratigraphic interpretation was supported in both the depth domain and the time domain.

Fig.6 Spectral analysis in time domain. 2π MTM power spectra with robust red noise models of about 405kyr-tuned time series. (a) GR series, less a 2550kyr ‘loess’ trend, and (b) CGR series, less a 2550kyr ‘loess’ trend, with significant peaks labeled in kiloyears. CL, confidence level.

4.3.2 Floating astronomical time scale (ATS)

Owing to the absence of radioisotopic date constraints, the geochronology of the study interval is not known with accuracy. Zeng. (2015) compared typical conodontic moleculeandof the Permian with the hybrid group of Triassic bivalves and Permian brachiopods, suggesting that the top boundary of the Changhsingian is about 3.67m higher than that of Chang-xing formation in this study area. Considering the Permian-Triassic boundary (PTB) has been dated at 251.904Ma by Burgess(2014) and the top boundary of Changxing formation in the well GFD-1 is at the depth of about 494.3m (based on the changes in the lithology and well logging interpretation), we here anchored the 490.63m datum to the numerical age of 251.904Ma (PTB) for providing a useful constraint to construct more precise astronomical solutions in the Paleozoic, and a floating ATS was constructed using the interpreted about 405kyr eccentricity cycles of the GR and CGR series (Fig.2). The 450–1238m section of data series consists of more than 19 long eccentricity cycles with a total duration of about 7.71Ma and ranges from 251.644Ma to 259.354Ma. Thus, the average sedimentation rate is about 10.2cmkyr−1, which is consistent with the average value (about 10cmkyr−1) obtained from the COCO and eCOCO analyses. In addition, referring to the International Chrono- stratigraphic Chart (ICC, version 2012), the age of Guadalupian-Lopingian (GLB) is 259.9±0.4Ma, so the intact Lopingian duration is about 8Ma, which is slightly longer than that in the well GFD-1 (about 7.45Ma). This is because the Dongwu movement resulted in the erosion and loss of some Lopingian strata, with the apparent GLB unconformity. Totally, evidences of duration and sedimentation rate all can verify the existence of about 405kyr cycle in spectral analysis for the succession. Moreover, the floating time scale can be shifted if a more precise geochronology could be obtained.

4.3.3 Amplitude modulation (AM) analysis

The results of the AM analysis of the about 405kyr- calibrated GR time series and that of the calibrated CGR series were analogous and indicated the presence of long- term cyclicities (Fig.7). The amplitude changes in the interpreted long eccentricity and short eccentricity all exhibited a primary periodicity of about 2.4myr based on the time records (Figs.7a, b, d, and e), while a primary periodicity of about 1.2myr was observed based on the period of the obliquity cycles (Figs.7c, f). These two long-term cycles had similar periodicities to those in the Cenozoic Era, suggesting these cycles were not affected by the chaotic motion of the inner planets and remaining 2:1 secular resonance (Laskar., 2004; Burgess., 2014).

Fig.7 Amplitude modulation (AM) analysis of long eccentricity, short eccentricity, and obliquity signals and periodograms. Blue solid lines define AM envelopes. Numbers of all peaks (red points) in periodograms are labeled in kiloyears. a(1), b(1), and c(1) show AM envelopes of long eccentricity, short eccentricity, and obliquity. Taner filters of about 405kyr-calibrated GR time series extracted using passbands of 0.00246±0.001, 0.009±0.001, and 0.025±0.002cycleskyr−1, respectively. a(2), b(2), and c(2) are power spectra (black solid lines) of AM envelopes shown in a(1), b(1), and c(1); d(1), e(1), and f(1) show Taner filters of about 405kyr-calibrated CGR time series extracted using passbands of 0.00246±0.001, 0.009±0.001, and 0.025±0.003cycleskyr−1, respectively; d(2), e(2), and f(2) are power spectra of AM envelopes shown in d(1), e(1), and f(1).

4.3.4 Modeling dynamic sedimentary noise

The GR datasets tuned to the interpreted about 405kyr cycles were used to model the dynamic sedimentary noise for an independent, high-resolution sea-level reconstruction (Li., 2018a). That the DYNOT and1values showed similar patterns suggested that significantly enhanced noise occurred during the Wuchiapingian and Changhsingian (Figs.8c, d). By combining the results of the AM analysis and the modeling of the sedimentary noise, the correlation between the astronomical climate forcing, the time series of the Late Permian global sea- level records, and the local sea-level variations in South China was found.

5 Discussion

5.1 Orbital-Forced Global Third-Order Eustatic Sequences in the Late Permian

The driving forces for the million-year-scale, large global sea-level changes during the late Permian Lopingian remain unclear, partly because the time scale is uncertain. The astronomically tuned GR and CGR series now provide an integrated time scale for the Lopingian. This time scale implies that the main oscillations seen in the global sea-level records are related to the orbital modulation cycles (Fig.8).

With the disappearance of the Permo-Carboniferous Ice Age (Gonzfilez-Bonorino and Eyles, 1995; Crowell, 1999), the late Permian entered a post-glacial period (Hallam and Wignall, 1997). The enhanced plume outgassing, significant increase inCO2and massive methane release caused by end-Guadalupian volcanisms provided the background conditions for global warming during the Wuchiapingian (Wignall, 2001). During this ‘greenhouse world’ period with either small and ephemeral or no ice sheets, the sensitivity of the large polar ice sheets to obliquity forcing may not have been strong, and the about 2.4myr astronomical cycles controlled ‘weak’ glacio-eustasy and/or aquifer eustatic changes related to the rapid, large sea-level changes (Boulila., 2011; Li., 2016a; Wendler and Wendler, 2016). Thus, we infer that the high-amplitude global sea-level variations in the Wuchiapingian (Snedden and Liu, 2010) were probably affected by eccentricity forcing and that sequence boundary (SB) W2 seems to correspond to eccentricity modulation cycles with a minimum of about 2.4myr (Figs. 8b, f). However, as can be seen from Fig.8, the falling sea-level (W2) lags slightly behind this minimum, which reflects the non-simultaneous response among the climate, glaciers and sea-level change. Since the climate change caused by the earth’s orbit is a gradual changing process, while the expansion and melting of glaciers are relatively slow, the changes of sea-level and climate may not be completely consistent. Due to the limited chronological resolution in the stratum, this problem seems intractable in the Paleozoic era. On the other hand, there is no equivalent SB corresponding to the about 2.4myr eccentricity minimum in the strata under SB W2. These mismatches may be due to non-orbital climate processes (Lovell, 2010; Boulila., 2011). The end-Guadalupian volcanisms and the concomitant tectonic movements could have led to a series of climate changes that drove the hydrological cycles not paced by the Milankovitch cycles (Li., 2018a).

Fig.8 Temporal framework, and the correlation between long-period orbital cycles, global sea level, dynamics noise model and variations in sedimentation rate. Temporal framework is constructed by astronomical tuning of GR data series from well GFD-1, the age (251.904Ma) of PTB comes from Burgess et al. (2014), and the age (254.2±0.1Ma) of Wuchiapingian-Changhsingian boundary comes from ICC (version 2012). (a), about 1.2myr from about 405kyr-calibrated GR and CGR time series (red and blue solid curves) extracted from bandpass filter output using passband of 0.00083±0.0001cycles kyr−1, respectively; (b), Global third-order eustatic sea level changes and sequence boundaries (W2, C1, and C2) (Snedden and Liu, 2010); (c) and (d), DYNOT and ρ1 models of GR series from well GFD-1. Confidence levels are estimated by Monte Carlo analysis with 5000 iterations; (e), Sedimentation rate variations from eCOCO map (white solid line with arrows); (f), about 2.4myr from about 405kyr-calibrated GR and CGR time series (red and blue dashed curves) extracted from bandpass filter output using passband of 0.00042±0.0001cycleskyr−1, respectively; SR, sedimentation rate.

A cooling trend in the Changhsingian has been identified based on various climate proxies (Chen., 2013). These include the occurrence of distinct peri-Gondwanan cool water brachiopod elements and the absence of compound corals in the Changhsingian strata (Shen., 2006, 2010b), conodonts data (Mei., 2002), diversity of biotic and lithologic proxies (Kozur, 1998; Beauchamp and Baud, 2002), the carbonate platform evolution on the Gondwana shelf (Pakistan; Mertmann, 2003), ice-lava contacts in the initiation phase of Siberian flood magmatism (Jerram and Widdowson, 2005) and biogenic cherts beneath polar sea ice (Beauchamp and Baud, 2002). Chumakov and Zharkov (2003) have stated that this brief-term phenomenon from the late Wuchiapingian induced glacial and glaciomarine facies in the circumpolar belts ‘with small-scale permanent or intermittent glaciation centers’. During epochs of persistent glaciations, the obliquity signature is strongly expressed in the depositional sequences in the form of the control of the waning and waxing of the polar ice sheets (Zachos., 2001; Westerhold., 2005; Boulila., 2011). Thus, we suggest that the obliquity forcing controlled the glacio-eustasy of the sea-level changes and that SBs C1 and C2 are correlated to the nodes of the about 1.2myr obliquity modulation exactly in the Changhsingian ‘icehouse world’ (Figs.8a, b). Generally, the influence of obliquity should be most pronounced in the high latitudes (Herbert, 1986). The good correspondence between SBs (C1 and C2) and nodes in the Upper Permian formation at a low latitude indicates that obliquity forcing can also exert the significant influence on paleoclimatic change near the Equator, and the third-order eustatic events maybe more sensitive to obliquity forcing in the ‘icehouse world’ than that to eccentricity modulation cycles in the ‘greenhouse world’.

5.2 Orbital-Forced Regional Third-Order Sequences in the Late Permian

The reconstruction of the geologic history of the sea-level usually relies on the marginal marine depositional sequences. In the Pingle Depression, for the Wuchiapingian, which has a marine-terrestrial transitional facies sedimentary environment, a third-order sequence boundary between the Wangpanli member and the Shizishan member that is marked by a small unconformable surface has been observed (Gong., 2002; Qin. 2015). This is consistent with the major lithologic changes from sandstone beds to the interbedding of sandstone, siltstone, and mudstone sediments. However, with respect to the marginal marine depositional sequences of the Changhsingian, it is hard to identify the sedimentary features representing a sea-level fall, because the unconformable surfaces may be subtle and even ‘conformable’ (Li., 2018a), thus hindering the reconstruction of the local sea-level geologic history of the Lopingian.

Instead of sequence stratigraphy, which relies on a subjective assessment of the sequence hierarchical order and the identification of unconformable surfaces, the sedimentary noise model used for the investigated interval in this study provides a high-resolution time frame for sea-level changes by estimating them directly from the stratigraphy. DYNOT and1sea-level models exhibited similar patterns suggests that significantly enhanced noises occurred in the studied section (Fig.8α, β, γ, δ, and ε). Sources of noises that affect climate and sea-level proxies can be classified as follows: water-depth related noise such as storms, tides, bioturbation, and unsteady depositional rate; other factors such as tectonics and volcanism (Li., 2018a). Two noticeably high noises (Fig. 8δ and ε) are observed during the early Wuchiapingian as per the model. The Dongwu tectonic movement and Emeishan province flood basalt eruptions began during the late Capitanian and the latter ended by about 257Ma in the middle Wuchiapingian in southwestern China (Shellnutt., 2012) which could affect the long-term trend in the sedimentary noise and/or drive the pace of the hydrological cycles pace not the Milankovitch cycles (Li., 2018a). The noise at ‘δ’ location is lower than that at ‘ε’, reflecting the weakening volcanism. These geological events, which are irrelevant to the water-depth-related noise, could have contributed to the ‘noise’ estimated using the DYNOT and1models but cannot be removed from the two models (Li., 2018a). In addition, the other three significant increased noises (Fig.8α, β, and γ) occurred in the section after 257Ma. Because the effects of volcanic and tectonic movements on this part of the formation were negligible and no volcanic ash bed was found in the whole section, these noises were not controlled by regional events. More importantly, these three noises correspond well to SBs W2, C1, and C2, respectively (Figs.8b, c, and d), which reflects that they probably meant relatively low sea-levels and were correlated to the major global third-order eustatic changes that occurred during the Lopingian, establishing the global nature and synchronicity of these millions-year-scale third-order eustatic records (Figs.8a, b, c, d, and f).

It is noticed that a high-resolution sedimentation rate history can also be used to interpret the regional deposition history (Wu., 2014; Ma., 2017). The COCO and eCOCO analyses confirmed the link between the sedimentation rate and the sea-level changes: increasing sedimentation rates occurred at shallower depth than about 950, about 680, and about 500m with the lowest rates indicate falls in the regional relative sea-level (Li., 2018c; Cong., 2019)，respectively and these correspond exactly to the SBs W2, C1, and C2 (Figs.8b, e). During the period of sea-level rise, the sedimentation rate decreased and the eccentricity power increased or the obliquity power declined. These coevolution trends in the orbital signals, global and local sea-level changes, and sedimentation rates, determined from the depth-to-time transformation function, could have significant implications for identifying the sequence boundaries and reconstructing the temporal depositional history at a regional scale.

6 Conclusions

The GR and CGR series of sedimentary sequences from the Pingle Depression in South China provided solid evidences for Milankovitch forcing during the Lopingian of the Late Permian. It is clear that the global and local third-order sea-level variations during this period were driven by long-period astronomical cycles. In addition, other probable factors (.., volcanism and tectonics) cannot be ruled out as additional sea-level drivers in the sedimentary records. Based on the results obtained, we could draw the following conclusions from the study:

1) The about 405kyr long eccentricity cycle calibrations show that the short eccentricity, main obliquity, and precession exhibit periodicities of about 405, about 100, about 44.2, about 35.1, about 21, and about 17.5kyr, respectively, during the Lopingian. The primary periodicities of about 2.4 and about 1.2myr for the long eccentricity and obliquity amplitude modulation cycles are similar to those in the Cenozoic and Mesozoic Eras.

2) It has been proposed that long-period orbital modulations control third-order sea-level changes. In the Wuchiapingian greenhouse of the Lopingian, the about 2.4myr eccentricity oscillation controlled ‘weak’ glacio-eustasy and/or aquifer eustatic changes related to the global third-order sea-level changes; In contrast, during the Changhsingian, which had a cooling event, a about 1.2myr obliquity cycle was probably strong.

3) The coevolution trends in the orbital power, global and local sea-level changes, and sedimentation rate have significant implications for identifying the sequence boundaries and reconstructing the temporal depositional history at a regional scale.

Acknowledgements

This work was supported by a National Natural Science Foundation of China (Grant No. 91958210), the Government Finance Level II Project (No. DD20190083) and ‘the 13th Five-Year Plan’ National Science and Tech- nology Major Project (No. 2016ZX05034001-003). We thank Drs. Mingsong Li, Guo Chen, and Qiang Fang for their assistance with the experiments and the writing of the manuscript.

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. E-mail: xunhuazh611102@sina.com

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(Edited by Ji Dechun)