He Huang

Hanting Zhong
email: zhonghanting@cdut.edu.cn

Chao Ma

Matthias Sinnesael

Yuan Gao

Yuyin Li

Mingcai Hou

Chengshan Wang

A new method to evaluate the power ratio distributions of astronomical signals: a case study from Upper Cretaceous terrestrial sediments

Keywords: Orbital cycles, paleoclimate proxies, depositional processes, RAOPR, Songliao Basin 1

Astronomical cycles reliably identified in the sedimentary record are useful for their paleoclimatic interpretations and construction of astrochronology. However, the depositional response and burial-diagenesis processes play a crucial role in distorting the time scales of geological records and introducing noise to orbital signals. How to evaluate the response of varied depositional environments to astronomical forcing remains a challenge. We developed the random-length average orbital power ratio calculation (RAOPR) method to evaluate average orbital power ratio distributions within a specific time interval and applied this new method to the theoretical eccentricity-tilt-precession (ETP) plus noise series and an astronomically tuned Cretaceous terrestrial stratigraphic record spanning ∼24 m.y. (92-65 Ma, except for an ∼3.8 m.y. gap from ca. 79.9 Ma to 76.1 Ma). Using the merged ETP plus noise series, we observed different orbital power ratio distributions for different background noise intervals. For the Cretaceous terrestrial Songliao Basin, we retrieved long-term orbital variations and used the RAOPR method to calculate the average orbital power ratios in different depositional environment intervals. Our results suggest that unusually high precession power in the Yaojia Formation resulted, in part, from autogenic processes, and unusually low precession power in the Nenjiang Formation can be attributed to marine incursion events. The eccentricity power of the meandering river facies was much higher than observed in other facies intervals. Conversely, the lowest precession power in the meandering facies may be attributed, in part, to the erosion "clipping" effect, which decreases the high-frequency precession band power and increases low-frequency eccentricity band power.

INTRODUCTION

Sedimentary archives contain complex signals produced by multiple climatic and depositional processes. These signals can include cyclical astronomical signals (i.e., Milankovitch cycles), irregular oscillations and abrupt events [START_REF] Hinnov | Cyclostratigraphy and its revolutionizing applications in the earth and planetary sciences[END_REF]Li et al., 2019b;[START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF]. The astronomical cycles have been widely identified in stratigraphic time series by state-of-art spectral analysis tools [START_REF] Meyers | Astrochron: An R package for astrochronology[END_REF]Li et al., 2019a), which greatly improved the fidelity of cyclostratigraphy. Therefore, in recent year, multiple indirect proxies with climate-induced signatures in sediments have been proposed for reconstructing paleoclimate and establishing astronomical time scales (ATS) (e.g., [START_REF] Hays | Variations in the Earth's orbit: pacemaker of the ice ages[END_REF][START_REF] Hinnov | Cyclostratigraphy and its revolutionizing applications in the earth and planetary sciences[END_REF][START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF]. However, these orbital signals are often affected by heterogeneous depositional processes, burial-diagenesis processes and stochastic noise [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF][START_REF] Sinnesael | Spectral Moments in Cyclostratigraphy: Advantages and Disadvantages Compared to more Classic Approaches: Paleoceanography and Paleoclimatology[END_REF]Li et al., 2019b;[START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF][START_REF] Wouters | A decomposition approach to cyclostratigraphic signal processing[END_REF], and all of these depositional factors make the interpretation of sedimentary signals sometimes challenging.

Among them, the depositional response and burial-diagenesis processes are particularly significant as they contribute to the distortion of geological record time scales and introduce noise into orbital signals [START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF]. However, there remains a lack of research in this specific area.

Terrestrial sedimentary environments present a unique challenge compared to marine depositional settings due to the superimposition of local climatic information and distinct depositional processes that vary from place to place. Some simulation works have emphasized the terrestrial depositional processes could transform the orbital signals before they preserved (e.g., [START_REF] Sadler | Estimation of completeness of stratigraphical sections using empirical data and theoretical models[END_REF][START_REF] Bazykin | Autocycles vs. allocycles in shallow marine carbonate platform deposits: insights from 2-dimensional computer modelling experiments[END_REF][START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF][START_REF] Wang | Lateral and vertical characteristics of floodplain aggradation cycles in the lower Eocene Willwood Formation[END_REF]. Therefore, it seems that the changing climate backgrounds and/or depositional processes may have different impacts on recording consistent external orbital signals. For instance, in an alluvial river system, channel avulsion is a typical autogenic phenomenon, and the stratigraphic record of this process may exhibit periodic-like variations (e.g., Willwood Formation, [START_REF] Abels | Precession-scale cyclicity in the fluvial lower Eocene Willwood Formation of the Bighorn Basin[END_REF]. Therefore, caution must be exercised in interpreting cyclic environmental signals in alluvial sedimentary successions, and various methods should be utilized (for instance the average spectral misfit (ASM, [START_REF] Meyers | Quantification of Deep-Time Orbital Forcing by Average Spectral Misfit[END_REF], time scale optimization (TimeOpt, [START_REF] Meyers | The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization[END_REF], evolutionary time scale optimization (eTimeOpt, [START_REF] Meyers | The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization[END_REF][START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF], correlation coefficient (COCO & eCOCO, Li et al., 2018)), where necessary, to ascertain the reliability of such periodic signals. In addition to the fluvial system, delta and shallow lake depositional settings may also be affected by the dynamics of the source-to-sink network [START_REF] Carroll | Stratigraphic classification of ancient lakes: Balancing tectonic and climatic controls[END_REF][START_REF] Allen | From landscapes into geological history[END_REF]. Variations in the sediment transport system can give rise to episodes of sediment storage and release, which have the potential to impart rhythmic features to the stratigraphic record. These autogenic depositional processes (e.g., delta growth, shoreline progradation) can generate not only periodic signals (noise) but also obscure some genuine climate signals prior to their incorporation into the sedimentary archive (Kim et al., 2010).

Moreover, variations in accommodation are associated with the dynamics of the equilibrium profile and all allogenic processes (tectonics of source area, basin subsidence, climate, and lake level fluctuation) (e.g., Huang et al., 2021a), which are intrinsically combined with autogenic processes and impact the preservation of orbital signals in the stratigraphic record [START_REF] Hinnov | New perspectives on orbitally forced stratigraphy[END_REF].

To some extent, recent studies have examined the impact of depositional processes on the preservation of orbital signals within strata, with investigations conducted in both marine environments (Li et al., 2019a;[START_REF] Levy | Antarctic ice-sheet sensitivity to obliquity forcing enhanced through ocean connections[END_REF] and terrestrial lake settings [START_REF] Wang | Distinct responses of late Miocene eolian and lacustrine systems to astronomical forcing in NE Tibet[END_REF][START_REF] Walters | Influence of lake-basin morphology on climate-sediment transfer functions: Early Eocene Wilkins Peak Member, Green River Formation[END_REF][START_REF] Wang | Lateral and vertical characteristics of floodplain aggradation cycles in the lower Eocene Willwood Formation[END_REF]. However, comprehending the complete picture behind this scene, particularly within complex terrestrial sedimentary systems, remains challenging. The evaluation of astronomical signal features in different depositional backgrounds poses two fundamental challenges: the need for a proper evaluation method to decipher these coded messages and a long, continuous geological record that covers different depositional environments. Therefore, the main objectives of this study are to: 1) develop a new evaluation method (i.e., Random-length average orbital power ratio calculation, RAOPR) for assessing different depositional settings response to astronomical forcing; 2) evaluate the orbital power distributions in diverse depositional backgrounds within the astronomically-tuned terrestrial record obtained from the SK-1 core in the SLB; 3) ascertain the influences of depositional processes on preserving the orbital signals in the Late Cretaceous SLB.

GEOLOGICAL SETTING

Geological background of the Songliao Basin and the SK-1 drilling core

The SLB covers roughly 260,000 km 2 in Heilongjiang, Jilin, and Liaoning provinces of NE China (Fig. 1A). During the Cretaceous, the SLB was a large rift basin and preserved as much as 10,000 m of sediments with volcaniclastic, alluvial fan, fluvial and lacustrine facies (Wang C et al., 2013). The first phase of the International Continental Scientific Drilling Project (SK-1) obtained a total of 2486 m of composite core, combining the south core (SK-1s) and the north core (SK-1n) (Fig. 1B). In the ascending order, the SK-1 core contains the Quantou (K 2 q), Qingshankou (K 2 qn), Yaojia (K 2 y), Nenjiang (K 2 n), Sifangtai (K 2 s) and Mingshui (K 2 m) Formations (Fig. 2). Due to the relative short duration of the Quantou Formation in the SK-1s core, this formation was excluded for performing the RAOPR analysis in this study.

In the SK-1 core, the Qingshankou Formation consists of dark gray and black mudstone interbedded with oil shale, indicating a deep lacustrine (DL) depositional environment [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The Yaojia Formation comprises red, gray, grayish green mudstone, siltstone and sandstone, which deposited in a shallow lake (SL) setting [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The first and second members of Nenjiang Formation (K 2 n 1 -K 2 n 2 ) are dominated by gray to black mudstone, marl, shelly limestone, and oil shale interbedded with gray siltstone and fine sandstone, which deposited in a deep lake (DL) environment [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The third to fifth members of Nenjiang Formation consist of grey, red, grayish mudstone, siltstone and sandstone, reflecting a delta to meandering river facies (DEL-MR) [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The Sifangtai Formation consists of brick-red pebbly sandstone and shale interbedded with brown, gray and gray-green sandstone and muddy siltstone [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The Mingshui Formation is composed of gray-green, gray, black and brown-red shale and gray-green sandstone [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The lithological associations in the Sifangtai and Mingshui formations indicate a meandering river (MR) facies [START_REF] Feng | Tectonostratigraphic units and stratigraphic sequences of the nonmarine Songliao basin, northeast China[END_REF][START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. We also noticed that in the Sifangtai and Mingshui Formations, four episodes of shallow lake facies were identified (Table. S2) [START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF], while these four short duration (~1 Myr) SL facies intervals would not have a significant impact on subsequent average power ratios calculations.

Age framework of the SK-1 drilling core

The chronostratigraphic framework of the SK-I composited core is constrained by biostratigraphy [START_REF] Wan | Late Cretaceous stratigraphy, Songliao Basin, NE China: SK1 cores: Paleogeogr[END_REF], magnetostratigraphy [START_REF] Deng | Chronology of the terrestrial Upper Cretaceous in the Songliao Basin[END_REF] and high-quality CA-ID-TIMS U-Pb zircon radiometric ages [START_REF] Ramezani | High-precision U-Pb geochronologic constraints on the Late Cretaceous terrestrial cyclostratigraphy and geomagnetic polarity from the Songliao Basin[END_REF]. Four 206 Pb/ 238 U ages of 91.886 ± 0.11 Ma, 90.974 ± 0.12 Ma, 90.536 ± 0.12 Ma, and 83.269 ± 0.11 Ma were determined (Fig. 3) [START_REF] Ramezani | High-precision U-Pb geochronologic constraints on the Late Cretaceous terrestrial cyclostratigraphy and geomagnetic polarity from the Songliao Basin[END_REF]. Eleven local magnetozones have been identified as Chrons C34n to C28n (Fig. 3) [START_REF] Deng | Chronology of the terrestrial Upper Cretaceous in the Songliao Basin[END_REF]. Meanwhile, an astronomical time scale was established by tuning the 405 kyr eccentricity cycles extracted from Th logging data to the La2010d target curve based on the magnetostratigraphic time framework of the SK-1n borehole [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]. The initial anchor points for tuning to La2010d were selected from C30n/C29r and C34n/C33r reversal boundary, which respectively located in the K 2 m and K 2 n (Fig. 3) [START_REF] Deng | Chronology of the terrestrial Upper Cretaceous in the Songliao Basin[END_REF][START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]. Recently, chronostratigraphic framework of the SK-1s core has been revised by cyclostratigraphic analysis of the Th series, which provides a continuous geological time framework from 92.531 Ma to 82.358 Ma [START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF]. In this study, we adopt the new high-precision radio-isotopically constrained ATS for the SK-1s core, because this new age model has greatly improved the time framework of the Nenjiang Formation, while the SK-1n core age model is still adopted from Th-calibrated ATS in [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]. Therefore, the ATS-calibrated boundary ages for various layers in the SK-1n and SK-1s cores were determined (Table. S2), revealing an ~3.8 Myr-long hiatus between the K 2 n and K 2 s in the SK-1n core from 79.9 to 76.1 million years ago.

Paleoclimate proxy

Milankovitch signals can be recorded in the strata through periodic climatic shifts and associated depositional feedbacks, such as changes in precipitation and temperature, monsoon intensity, weathering and runoff rates. Multiple paleoclimate proxies, including gamma ray (GR), thorium (Th), density (Den), XRF, total organic carbon content (TOC) and organic carbon isotope (δ 13 C org ) have been used to recognize the Milankovitch cycles through objective statistical analysis (e.g., average spectral misfit (ASM, [START_REF] Meyers | Quantification of Deep-Time Orbital Forcing by Average Spectral Misfit[END_REF], time scale optimization (TimeOpt, [START_REF] Meyers | The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization[END_REF], evolutionary time scale optimization (eTimeOpt, [START_REF] Meyers | The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization[END_REF][START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF], correlation coefficient (COCO & eCOCO, Li et al., 2018)) in the SLB [START_REF] Wu | Astrochronology of the Early Turonian-Early Campanian terrestrial succession in the Songliao Basin, northeastern China and its implication for long-period behavior of the solar system: Palaeogeogr[END_REF][START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]Huang et al., 2021a;Zhang et al., 2022;[START_REF] Li | Chemical weathering characteristics of the Late Cretaceous Nenjiang Formation from the Songliao Basin (Northeastern China) reveal prominent Milankovitch band variations[END_REF]. However, only the thorium (Th) logging data has been tuned for establishing the ATS of the SK-1 composite core, obviating the necessity for reconducted astronomical tuning by ourselves. Therefore, the astronomically-tuned Th time series has covered different types of depositional environment intervals [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]2022). Moreover, the Th values are closely associated with the lithological changes and can reflect the paleoclimate features, such as precipitation, weathering and terrestrial inputs [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]2022;Li et al., 2019b;Zhang et al., 2022). In this study, the Th well logging data was used as the paleoclimatic and paleoenvironmental proxy for evaluation of the orbital signal distributions in different depositional environment intervals in the Songliao Basin.

METHODOLOGY

Spectral analysis

The multi-taper method (MTM; [START_REF] Thomson | Spectrum estimation and harmonic analysis[END_REF] with a red noise null hypothesis model [START_REF] Mann | Robust estimation of background noise and signal detection in climatic time series[END_REF] and the wavelet spectral analysis [START_REF] Torrence | A practical guide to wavelet analysis[END_REF] were applied for seeking the orbital signals in the detrended Th time series (data from [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF][START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF] (Fig. 4). Prior to spectral analysis, the astronomically-tuned Th series was firstly linear interpolated to the medium sampling rate (~1.43 kyr) to obtain an even time series. The long eccentricity signals were extracted from the stratigraphic series using a Gaussian bandpass filter with a bandwidth at 0.002-0.003 kyr -1 (Fig. 4). All of these spectral analysis were performed in the Acycle software (Li et al., 2019a).

Calculation of the orbital power variations

To date, there have been only a limited number of studies that have utilized statistical methods to compute the power and band power ratios of climate proxy data in the time domain (e.g., [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF]Li et al., 2016;[START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF][START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF][START_REF] Huang | Astronomical forcing of Middle Permian terrestrial climate recorded in a large paleolake in northwestern China[END_REF]. The integratePower algorithm determines the total power within a given bandwidth, and also the ratio of this power to the total power in the spectrum [START_REF] Meyers | Astrochron: An R package for astrochronology[END_REF]. Similarly, Li et al (2019b) introduced a power decomposition analysis (PDA) method to calculate and compare dynamic target orbital power to total power ratio of multiple proxies from the same time and locality, so as to test their sensitivities to external climate forcing. Recently, a sedimentary noise model (DYNOT) was proposed to reconstruct past sea-level changes based on the ratio of signal variance unrelated to orbital forcing in paleoclimate proxies (i.e., noise) to the total variance in proxies (Li et al., 2018a). Afterwards, many studies have demonstrated that this model can be applied to also infer paleolake level changes (e.g., [START_REF] Wang | Astronomical forcing and sedimentary noise modeling of lake-level changes in the Paleogene Dongpu Depression of North China[END_REF][START_REF] Huang | Astronomical forcing of Middle Permian terrestrial climate recorded in a large paleolake in northwestern China[END_REF]Zhang et al., 2022;[START_REF] Wei | Obliquity forcing of continental aquifers during the late Paleozoic ice age: Earth and Planetary Science Letters[END_REF], finding that the DYNOT ratio was lower during lake level high-stands than during intervals of low lake level. Hence, these statistical methods can be employed in the evaluation of orbital/noise power variations in astronomical-tuned time series (Fig. 5).

Here, we employ the PDA, integratePower and DYNOT methods to assess the orbital signal power variations in both the theoretical eccentricity-tilt-precession (ETP) [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF] and the synthetic ETP-plus-noise time series (with a length of 10000 kyr and temporal resolution of 1 kyr) (Fig. 5). We only investigate the frequencies and their power lower than 0.08 kyr -1 (12.5 kyr/cycle), because all of the astronomical signal frequencies (precession, obliquity and eccentricity) are located at this range. Four intervals with different types of noise have been incorporated into the theoretical ETP series (Fig. 5d) (modified from [START_REF] Li | Sedimentary noise and sea levels linked to land-ocean water exchange and obliquity forcing[END_REF]. All of these ETP+noise series are generated from Acycle software (Li et al., 2019a).

Random-length Average Orbital Power Ratio calculation (RAOPR)

Motivation for developing the RAOPR method

Although the PDA, integratePower, and DYNOT methods offer a semi-quantitative approach to assessing the orbital signals power variations, the inherent long-term orbital signal power variations still exist (Fig. 5). Therefore, distinguishing between the inherent long-term cycles and changes in orbital signal strength resulting from different climatic backgrounds or depositional processes remains challenging. The inherent long-term orbital signals mainly include the ~2.4-Myr eccentricity and ~1.2-Myr obliquity cycles during the Cretaceous period [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF][START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF][START_REF] Ma | Testing Late Cretaceous astronomical solutions in a 15 million year astrochronologic record from North America[END_REF][START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF]. Nonetheless, in the Triassic period, the eccentricity amplitude modulation (AM) cycle appears to be shorter [START_REF] Olsen | Mapping Solar System chaos with the Geological Orrery[END_REF]. [START_REF] Levy | Antarctic ice-sheet sensitivity to obliquity forcing enhanced through ocean connections[END_REF] applied the integratePower algorithm to compute the obliquity sensitivity by dividing obliquity variance (i.e., 1.2-Myr amplitude modulation cycle) in a compiled δ 18 O mega-splice (from ~5-34 Ma) by the variance of the theoretical obliquity solution, which effectively eliminating the inherent 1.2-Myr long-term obliquity variation. However, due to the inherent limitation of the astronomical solutions and the age precision of the sedimentary successions, this process is only viable within the last 55 Ma [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF]. Thus, to address these shortages, we develop a new method (RAOPR) for assessing orbital power variations in regarding to compare the orbital signal patterns in different climate and/or depositional backgrounds.

The RAOPR method

The integratePower algorithm, in its original form, employs power ratios to quantify the contribution of the isolated orbital power to the total power, which equals to the isolated band power in a defined frequency range divided to the total power of the power spectrum. This process can partly reduce the long-term amplitude modulation signal variation components of the orbital signal (e.g., [START_REF] Levy | Antarctic ice-sheet sensitivity to obliquity forcing enhanced through ocean connections[END_REF]. Thus, the power ratios may have a potential usage for evaluating the orbital response sensitivity in diverse sedimentary environments, if we can remove the inherent long-term cycle imprints originated from the theoretical astronomical solutions. However, the direct subtraction of long-term cycles (i.e., ~1.2 Myr and ~2.4 Myr in the Cretaceous period) from geological records is not feasible, given the phase distortion of the orbital signal (which arises from age uncertainty, stratigraphic warping, and the lag time of depositional response) and the precision limitations of the orbital solutions (as noted by [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF]. Therefore, to compare the orbital power ratios and deviations at different intervals, one can average the long-term variation for a given stratigraphic succession. By repeatedly calculating the average power ratios for varying lengths of the dataset, it is possible to obtain the most probable distribution patterns of the orbital signals in a specific stratigraphic unit. This method is so-called random-length average orbital power ratio calculation (RAOPR) method, and is in its current form designed to be used in the time domain.

To evaluate the possible usage of the RAOPR method to reflect the orbital response sensitivity, we generated sixteen time series (with a length of 20000 kyr and temporal resolution of 1 kyr, the data length is roughly equal to the geological data that we will test in the following work), including the theoretical eccentricity-tilt-precession (ETP weight: 1:1:-1) curve [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF]) and fifteen ETP with noise series (i.e., five ETP+red noise: std=0, mean=0.5, ρ=0.8;

five ETP+white noise: std=1, mean=0; five ETP+red+white noise) in the Acycle software (Li et al., 2019a).

We conducted two additional sensitivity analyses on these generated time series: (1) we evaluated the fraction of the eccentricity (E+e), obliquity (~40 kyr) and precession (~20 kyr) variance, retrieved from the ETP and ETP plus noise series by using the integratePower algorithm in astrochron package [START_REF] Meyers | Astrochron: An R package for astrochronology[END_REF]. The spectrum integration was conducted from 0.001 to 0.012 kyr -1 (1000 to 83 kyr) for eccentricity, 0.018-0.036 kyr -1 (~55 to 27 kyr) for obliquity and 0.038-0.058 kyr -1 (~26 to 17 kyr) for precession. All the time-frequency analyses employed three 2π prolate data tapers, with a 500 kyr window and a 5 kyr time step. The frequency band widths of obliquity and precession were adjusted to account for the shorter cycles resulting from tidal friction effects [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF]. ( 2) We extracted random length of the power ratio data and calculated the average ratio value distributions. Because of the amplitude modulation cycles imposed on the precession (100 kyr and 400 kyr), obliquity (173 kyr and 1200 kyr) and eccentricity (2400 kyr), the minimum random length (duration) was assigned at 500 kyr for precession, 1500 kyr for obliquity, 2500 kyr for eccentricity. The maximum random length is equal to the data series length (20000 kyr) subtract the maximum duration. Then we selected the random length of the time slice from each isolated power ratio curve for 5000 times, and finally we obtained 5000 average power ratio values for each orbital signal band (Fig. S1,S2,S3). The same procedure was applied to the astronomically-tuned Th time series in the SK-1 core (Fig. S4). Moreover, we also analyzed another paleoclimatic proxy (K%) from the same drilling core to test the broader applicability of this new method (see supplemental file, Fig. S5,S6).

RESULTS

Orbital power variations in the synthetic ETP+noise series

As expected from the theory and previous case studies (e.g., [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF]Li et al., 2019b), the orbital signal strength would decrease when the noise increases (Fig. 5). The merged ETP+noise series analyzed using the PDA and integratePower methods exhibit low orbital signal power values due to strong noise, as shown in Figure 5. Furthermore, the DYNOT modeling results also show coeval changes with PDA and integratePower results but in an anti-phase manner (Fig. 5). Hence, the PDA, integratePower, and DYNOT methods offer a semi-quantitative approach to assessing the orbital signals power variations.

Orbital power ratio distributions in the synthetic ETP+noise series

We have observed that the signal of the power ratios decrease especially between the ETP+1 and the ETP+5 noise simulations (Fig. 6; Fig. S1, S2, S3), although different types of synthetic ETP+noise series displayed different reduction patterns in their orbital signal components (Fig. 6). From the ETP+red noise results, the precession power ratios decrease faster than obliquity power ratios, and the eccentricity power ratios have the same decrease rate as the precession signal (Fig. 6, S1), a phenomenon that may originate from the eccentricity-precession modulate effects. However, in the synthetic ETP+white noise series, the eccentricity power ratios decrease faster than obliquity and precession power ratios. Especially in the precession band, their power ratios are relative stable (Fig. 6, S2), the reason was that the white noise has been included in the precession bands, which increased the precession band power. Especially in the ETP+red+white noise series, when the noise increased the obliquity and precession band power ratio values were became stable (Fig. 6, S3), and compared to the ETP+red noise series, we can find the obliquity and precession signals have been greatly influenced by the white noise component.

Orbital power variations of tuned Th time series

The total power of the astronomical signal in the Th sequence of SK-1 core is greatly enhanced during the Solar system chaotic event (and the OAE3) of the Qingshankou Formation, whereas the total energy in the marine transgressive interval of the Nenjiang Formation experiences a sharp decline (Fig. 7g). In the Mingshui Formation, the total power also rises rapidly during the two humid periods (Fig. 7g). The change of the eccentricity signal energy is basically consistent with the total power energy. The possible reason is that the data itself is based on the long eccentricity tuning, and therefore the eccentricity should be the strongest periodic signal, and its proportion is the highest in most layers (Fig. 7f); moreover, according to the spectral characteristics with red noise effect [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF], the energy integral of the eccentricity period at low frequencies accounts for most of the total energy integral.

The obliquity band power and power ratio demonstrate relative stability across the entire formations and display periodic variations (Fig. 7c,d). Notably, within the Qingshankou Formation, the obliquity band power and power ratio exhibit synchronous changes, whereas the Nenjiang Formation reveals discrepancies in both amplitude and phase for the obliquity band power and power ratio.

The precession band power and power ratio show a coeval variation pattern throughout the whole formations (Fig. 7a,b). However, there are variations in the amplitude of the band power and power ratio between the deep lake facies of the Qingshankou and Nenjiang formations.

Notably, the Yaojia Formation has an exceptionally high amplitude (Fig. 7a,b). Additionally, in the SK-1n core, the Mingshui Formation displays two intervals of high amplitude for the precession band power and power ratio (Fig. 7a,b). Generally, from lake facies to river delta facies, precession power and power ratio decreases (Fig. 7a,b) while the eccentricity power and power ratio increases (Fig. 7e,f), the obliquity band power and power ratio are relative stable (Fig. 7c,d).

Orbital power ratio distributions in different Formations of SK-1 core

Based on the orbital power ratios results, we have performed the RAOPR method to extract the power ratio distribution from each depositional facies intervals and calculate the average power ratio with its standard deviation (2σ) (Table . 1). For the deep lake facies, the orbital signal proportions of the Qingshankou Formation are different from the lower part of the Nenjiang Formation (Fig. 8,S4). As we noticed, the eccentricity power ratio in Qingshankou Formation (0.289±0.004) is lower than that in the first and second members of the Nenjiang Formation (0.41±0.0092). The obliquity power ratios have similar values in Qingshankou (0.345±0.0052) and lower part of the Nenjiang formation (0.331±0.0102), while the precession power ratios of Qingshankou Formation (0.152±0.0042) is higher than those in the first and second members of the Nenjiang Formation (0.053±0.0024) (Fig. 8; Fig. S4).

The shallow lake facies of the Yaojia Formation has higher eccentricity (0.315±0.0094) and precession (0.226±0.0072) power ratios than those in the Qingshankou Formation, while the obliquity band power ratio (0151±0.0032) was much lower compared to the Qingshankou Formation (Fig. 8; Table . 1).

The delta to meandering river facies of the Nenjiang Formation has a higher precession power ratio (0.143±0.018) than that observed in the deep lake facies of Nenjiang Formation, while the eccentricity power ratios are comparable within these two different facies in the whole Nenjiang Formation (Fig. 8; Table . 1). However, the obliquity power ratio in the delta to meandering facies interval (0.187±0.006) was much lower than that found in the deep lake facies interval (0.331±0.0102) of the Nenjiang Formation (Fig. 8; Table . 1). The meandering river facies of the Sifangtai and Mingshui formations have the highest eccentricity power ratios (0.427±0.0092, 0.591±0.0074) and relative low precession power ratios (0.095±0.0018, 0.046±0.002), the obliquity power ratio (0.271±0.0078) in the Sifangtai Formation higher than that in the Mingshui Formation (0.173±0.006) (Fig. 8; Table . 1).

DISCUSSION

Comments on the RAOPR approach

In this study, we have tested different kinds synthetic ETP+noise series. The red noise exhibits more significant intensity at lower frequencies, which roughly corresponds to the primary response of the climate system [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF][START_REF] Sinnesael | Spectral Moments in Cyclostratigraphy: Advantages and Disadvantages Compared to more Classic Approaches: Paleoceanography and Paleoclimatology[END_REF]. White noise, on the other hand, is a random signal with uniform intensity at all frequencies, signifying that it has a relative influence on high frequency bands than low frequency bands [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF][START_REF] Sinnesael | Spectral Moments in Cyclostratigraphy: Advantages and Disadvantages Compared to more Classic Approaches: Paleoceanography and Paleoclimatology[END_REF] (Fig. 2). From a geological perspective, the ETP+red noise models represent a straightforward stochastic process motivated by climate and depositional system dynamics [START_REF] Hasselmann | Stochastic climate models: Part I[END_REF][START_REF] Sadler | Estimation of completeness of stratigraphical sections using empirical data and theoretical models[END_REF][START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF], while the white noise source may reflect the slower response time in Earth climatic and depositional systems [START_REF] Meyers | Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2[END_REF].

Besides, in the ETP+red noise models, the high-frequency orbital signal (e.g., precession) seems easier influenced by the sedimentary noise (Fig. 6), and this phenomenon has been observed from the geological records [START_REF] Ripepe | Stratigraphic rhythms synthesized from orbital variations[END_REF][START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF][START_REF] Huang | Astronomical forcing of Middle Permian terrestrial climate recorded in a large paleolake in northwestern China[END_REF]. These modeling results confirm that our assessment of the isolated average power ratios is robust for calculating the orbital response variabilities in geological records. Furthermore, this method also can normalize the secular changes in the sensitivity of sedimentation to Milankovitch-forced climate change.

However, the current form of this new method also exhibits certain limitations. To illustrate, firstly, it is exclusively applicable to astronomically-tuned records. Secondly, due to the presence of long-term amplitude modulation signals (e. g., 2.4 Ma eccentricity AM cycle), this method imposes stringent prerequisites on the data length. Thus, we recommend a minimum data length of 3 m.y., considering the edge effect of the integratePower approach.

Orbital signal power variations from 92 Ma to 66 Ma in the SK-1 core

Geological records provide an avenue for exploring the dynamics of theoretical celestial motion and the chaotic behavior of the Solar system (e.g., [START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF][START_REF] Ma | Testing Late Cretaceous astronomical solutions in a 15 million year astrochronologic record from North America[END_REF][START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF][START_REF] Olsen | Mapping Solar System chaos with the Geological Orrery[END_REF][START_REF] Zeebe | Solar System chaos and the Paleocene-Eocene boundary age constrained by geology and astronomy[END_REF]. Recent studies have shown that integrated orbital power variations, specifically in the short eccentricity and obliquity band power curves, can reveal the secular resonance transition during the Late Cretaceous [START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF][START_REF] Ma | Testing Late Cretaceous astronomical solutions in a 15 million year astrochronologic record from North America[END_REF]. In the Songliao Basin, the short eccentricity and obliquity band power curves in the SK-1s core were retrieved from the astronomically-tuned Th time series and Ostracode shell abundance dataset to reveal the secular resonance transition during the Late Cretaceous [START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF].

The relative wide eccentricity (1/1000 kyr to 1/83 kyr frequencies bands) band power curve is generally comparable with the sole short eccentricity (~83-127 kyr) integrated band power from [START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF], in terms of both the amplitude and the pattern of secular variations from 91.97 Ma to 82.35 Ma. The 2.4 Myr to 1.2 Myr and back to 2.4 Myr secular resonance transition was also recognized in the eccentricity band power curve and the total power curve (Fig. 7f,g).

These observed eccentricity AM shifts are coincident in timing with La2004 astronomical solution during this period [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF], and might show some potential linkages between the unique celestial configuration and the geological events, such as OAE3 [START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF][START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF]. In contrast, the eccentricity band power curve in the SK-1n core (76-65

Ma) appears noisier, with no obvious ~2.4 Myr eccentricity AM cycles observed (Fig. 7f), the reasons might be ascribed to the different astronomical response at different stages of Basin's evolution and the uncertainties in the temporal calibration. However, two high eccentricity power intervals have been identified in the Mingshui Formation (Fig. 7f), which roughly corresponding to the paleo-lake transgressive stage [START_REF] Gao | Mid-latitude terrestrial climate of East Asia linked to global climate in the late Cretaceous[END_REF]. In addition, a significant global cooling event at approximately 70 Ma, reflected by a pronounced positive oxygen isotope excursion in benthic foraminifera [START_REF] Miller | Visions of ice sheets in a greenhouse world[END_REF][START_REF] Friedrich | Evolution of middle to late Cretaceous oceans-a 55 m.y. record of Earth's temperature and carbon cycle[END_REF], was also recognized by the pedogenic carbonate oxygen isotope in the Songliao Basin [START_REF] Gao | Mid-latitude terrestrial climate of East Asia linked to global climate in the late Cretaceous[END_REF][START_REF] Gao | Terrestrial climate in mid-latitude East Asia from the latest Cretaceous to the earliest Paleogene: A multiproxy record from the Songliao Basin in northeastern China[END_REF]. A typical lake shrink interval was also inferred from the DYNOT result, which roughly corresponding to the low eccentricity power and high obliquity power interval (Fig. 7h). Afterward, this cooling interval was terminated by a transient climatic warming in the middle Maastrichtian (ca.

69.5-68.5 Ma), which marked by the increased marine bottom water temperature [START_REF] Jung | Campanian-Maastrichtian Ocean circulation in the tropical Pacific[END_REF][START_REF] Mateo | Early to late Maastrichtian environmental changes in the Indian Ocean compared with Tethys and South Atlantic: Paleogeogr[END_REF]. Interestingly, this warming period was timely associated with the high eccentricity power interval (Fig. 7), indicating the high sensitivity of eccentricity to the warm climatic and depositional processes [START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF].

The obliquity band power in the SK-1 core (91.97-65.06 Ma) and obliquity/total power both reveal ~1.2 Myr cycle, although it is not persistent throughout the entire study interval (Fig. 7c,d). The lower part of the Qingshankou Formation (ca. 91.9-88.5 Ma) displays a high obliquity signal and a distinct ~1.2 Myr obliquity AM cycle (Fig. 7c,d). Huang et al. (2021a) have proposed a threshold clipping amplified model to interpret the low-amplitude AM signals in geological records, which also hints that the strong obliquity signal is favorable for preserving low frequency AM cycles (e.g., [START_REF] Levy | Antarctic ice-sheet sensitivity to obliquity forcing enhanced through ocean connections[END_REF][START_REF] Huang | Astronomical forcing of Middle Permian terrestrial climate recorded in a large paleolake in northwestern China[END_REF]Huang et al., , 2021a)). Additionally, the integrate obliquity band power suggests the absence of a strong 1.2 Myr obliquity cycle at around 84 Ma which timely associated with the resonance transition (Fig. 7d). This phenomenon was firstly documented in the Libsack FMI record in North America, which means the resonance state may suggest a transient change in the sensitivity of the climate or sedimentary system to obliquity forcing at a global scale [START_REF] Ma | Theory of chaotic orbital variations confirmed by Cretaceous geological evidence[END_REF]. In the Songliao Basin, this transition corresponds to a rapid shift from shallow (Yaojia Fm.) to deep lake (Nenjiang Fm.) condition and associated with increased organic carbon burial and marine incursion events (Fig. 7).

To our knowledge, no previous studies employed integrated precession band power derived from astronomical tuned time series to examine paleoclimatic changes. The main reason for this might be ascribed to the fact that the amplitude of the precession has been modulated by eccentricity, and thus it is difficult to separate the variation of the precession caused by the different depositional settings from the eccentricity itself. Besides, in high frequency bands, the sedimentary noise tends to superimpose on astronomical signals [START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF]. Here, we have attempted to retrieve the precession band power from the Th time series (Fig. 7b).

According to the integrate precession band power curve, we have not observed any discernible periodical orbital signals (Fig. 7b), but the precession band signal exhibited relatively high power during the deposition of the Yaojia and Mingshui Formations compared to other periods (Fig. 7b).

However, during the high precession band power intervals, the corresponding eccentricity band power is relatively low (Fig. 7f), which does not conform with the eccentricity-precession modulation effect. This may suggest these high precession band power intervals were not only included the orbital precession signals, but also existed regular sedimentary relative small-scale autocyclicities [START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF]. As we noticed, these high precession band power intervals are corresponded to the shallow lake and meandering river facies, these sedimentary environments indicate a shallow water condition, which is also confirmed by the DYNOT result (Fig. 7h). Therefore, we posit that the high precession band power intervals are partly influenced by the autogenic sedimentation processes, and this will be discussed in the following section.

Different orbital power ratio distributions in varied sedimentary environments

Within the context of sedimentary facies division, we have calculated the average orbital power ratio distributions for different facies intervals by applying the RAOPR method (Fig. 8, S4; Table . 1). For the deep lake facies, we have found that the eccentricity and precession power ratios were different between Qingshankou and Nenjiang formations. To interpret these discrepancies, we consider the local geological events have played a major role in recording and preserving the orbital signals. According to the depositional background, the lower part of Nenjiang Formation has been disturbed by the intermittent marine incursion events [START_REF] Hu | Seawater Incursion Events in a Cretaceous Paleo-lake Revealed by Specific[END_REF], which could change the equilibrium of the lake biogeochemistry [START_REF] Wang | Compound-specific carbon isotope study on the hydrocarbon biomarkers in lacustrine source rocks from Songliao Basin[END_REF].

Recently, Huang et al (2021a) have proposed a biogeochemical threshold clipping response model to explain the ~40 kyr obliquity transformed to ~173 kyr obliquity AM cycle, and considered the disturbance of lake biogeochemical conditions can change the orbital signal components. In addition, model simulation results confirmed that the non-linear accumulation or bioturbation effects also can transform the precession-forced carbonate cycle into eccentricity band [START_REF] Ripepe | Stratigraphic rhythms synthesized from orbital variations[END_REF]. Therefore, the low precession and high eccentricity bands signal in the first and second member of Nenjiang Formation may indicate the marine incursion events have altered the original orbital signal components. Besides, we also noticed that, the two deep lake facies intervals have the highest obliquity power ratio in this ~24 Myr-long sedimentary record. Considering the paleogeographic location of the Songliao Basin, the obliquity may play a major role in modulating the hydrological cycle through controlling meridional insolation circulation and enhancing poleward moisture transport [START_REF] Raymo | The 41 kyr world: Milankovitch's other unsolved mystery: Paleoceanogr[END_REF]. The ~173 kyr obliquity AM cycle has been both detected in the Qingshankou TOC series (Huang et al., 2021a) and Nenjiang chemical weathering proxies (Li et al., 2022), which further confirmed that the obliquity forced the Songliao paleo-lake hydrological variations and controlling the organic carbon burial (Huang et al., 2021a).

From the Qingshankou to Yaojia formations, the Songliao paleo-lake water depth was decreased, which is demonstrated both by the sedimentary facies analysis and DYNOT lake-level modelling (Fig. 7h). Theoretically, the shallow lake environment should have relative lower orbital signals than the deep lake depositional environment, because the sedimentary noise was higher in shallow water than deep water [START_REF] Li | Sedimentary noise and sea levels linked to land-ocean water exchange and obliquity forcing[END_REF][START_REF] Wang | Astronomical forcing and sedimentary noise modeling of lake-level changes in the Paleogene Dongpu Depression of North China[END_REF]. So, it would be abnormal for shallow lake facies owning high precession power ratio, as well as its modulation signal in eccentricity band. This abnormal feature indicates that the high precession power in the Yaojia formation was not only originated from the Earth's orbital precession forcing. In contrast, there are some specific sedimentary processes to generate the precession-like signals. Previous studies demonstrated that autogenic processes could destroy orbital-scale signals in some specific sedimentary environments and some periodicities produced by autogenic variability might be confused with orbital forcing [START_REF] Jerolmack | Shredding of environmental signals by sediment transport[END_REF]Li et al., 2016;[START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF]. Especially, the simulation experiment of lake formation and infilling in the maximum subsidence zone indicated about 10 4 -10 5 years autogenic variability [START_REF] Kim | Long-period cyclic sedimentation with constant tectonic forcing in an experimental relay ramp[END_REF]. Therefore, the autogenic process might reasonably explain the high precession power ratio in the Yaojia Formation.

As the Songliao paleo-lake shranked, the upper part of the Nenjiang Formation and the whole Sifangtai and Mingshui formations were deposited from delta to meandering river environments [START_REF] Wang | Cretaceous paleogeography and paleoclimate and the setting of SKI borehole sites in Songliao Basin[END_REF]. The average eccentricity power ratio was increased and precession power ratio was reduced from the Nenjiang Formation to Mingshui Formation (Fig. 8). From the MTM spectrum results, we also found that the precession band signals do not reach to the autoregressive lag-1 stochastic noise model testing (Fig. 4). This orbital signal component is prevalent in the progradational and retrogradational trends of the alluvial-delta-lacustrine systems. For example, the Late Eocene to Middle Miocene delta sequence in the Ebro Basin [START_REF] Valero | 20 Myr of eccentricity paced lacustrine cycles in the Cenozoic Ebro Basin[END_REF] and the Middle Miocene Madrid Basin (Abels et al., 2009) both show a significant power at eccentricity bands but no obvious precession signals existed. Moreover, in the coal-bearing terrestrial successions, the occurrence of coal intervals is often linked to the eccentricity driven forcing, while the precession index can barely be identified (e.g., review by Oplustil et al., 2022). All of these features indicated the high frequency orbital signals can hardly preserve in continental shallow water environments. Suppose that there is a regularly sedimentary process (e.g., the balance between sediment supply and subsidence) to erase the high-frequency orbital signals before they preserved in the stratigraphic succession, this "depositional clipping function" would impose a rectification effect on the original signal [START_REF] Ripepe | Stratigraphic rhythms synthesized from orbital variations[END_REF][START_REF] Hinnov | Cyclostratigraphy and Astrochronology in 2018: Stratigraphy & Timescales[END_REF]Huang et al., 2021a). In addition, the non-linear sedimentary response (e.g., bioturbation and/or lake geochemistry equilibrium) will further amplify the low frequency signals and eradicate the high frequency index [START_REF] Ripepe | Stratigraphic rhythms synthesized from orbital variations[END_REF][START_REF] Hinnov | Cyclostratigraphy and Astrochronology in 2018: Stratigraphy & Timescales[END_REF]Huang et al., 2021a). Therefore, in the terrestrial delta and/or meandering river facies, the low frequency orbital signals (e.g., ~400 kyr and 100 kyr eccentricity) could be preserved but the high frequency signals (e.g., ~20 kyr precession) might often be erased.

In general, from the orbital signal components of different sedimentary facies intervals, we considered that the Yaojia, Nenjiang (3-5 members), Sifangtai and Mingshui formations might be disturbed by autogenic processes, such as river migration, delta growth, lake transgressive and Formation has disturbed by the marine incursion events, which greatly changed the orbital signal components through the intrabasinal processes. The Qingshankou Formation represented the most stable lake depositional environment, its orbital signal component might reflect the original climatic information, although some orbital amplitude modulation cycle associated with allogenic processes have been found in other paleoclimatic proxies (e.g., Huang et al., 2021a).

Astronomical climate-deposition transfer processes in terrestrial depositional systems.

Resolving astronomical signals from stratigraphic records is always challenging, because there are many complex factors that influence the orbital signal propagating into geological archives [START_REF] Strasser | Cyclostratigraphyconcepts, definitions, and applications[END_REF]Meyers et al., 2008;[START_REF] Hinnov | Cyclostratigraphy and its revolutionizing applications in the earth and planetary sciences[END_REF]. Thus, a thorough astrochronological evaluation necessitates careful consideration of astronomical, geological, climatic, and statistical aspects [START_REF] Meyers | Cyclostratigraphy and the problem of astrochronologic testing[END_REF][START_REF] Sinnesael | The Cyclostratigraphy Intercomparison Project (CIP): consistency, merits and pitfalls[END_REF][START_REF] Wouters | A decomposition approach to cyclostratigraphic signal processing[END_REF][START_REF] Wang | Lateral and vertical characteristics of floodplain aggradation cycles in the lower Eocene Willwood Formation[END_REF].

In light of the aforementioned considerations, we have reconsidered some fundamental issues in the realm of cyclostratigraphy, especially the interpretation of the environmental periodic signals from continental sedimentary settings. Generally, a complete terrestrial sedimentary system mainly includes three elements: sediment supply, sediments transport and accommodation space (Fig. 9) (Carroll and Bohacs,1999;[START_REF] Allen | From landscapes into geological history[END_REF]. The topographic gradient resulting from tectonic dynamics represents the first-order control on the spatial distribution of uplift and subsidence on the Earth's surface, while the rate and mass of material transport is contingent upon climate [START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF]. Therefore, the tectonic processes in the source area and climatic variations can affect the sediment and water supply. In the vicinity of the source region, we usually cannot detect any periodic environmental signals (Fig. 9).

Terrestrial sediment transport networks mainly comprise the fluvial and aeolian systems, and for sedimentary archives deposited under aeolian conditions, environmental signals are typically associated with the orbital-monsoon system (e.g., [START_REF] An | Magnetic susceptibility evidence of monsoon variation on the Loess Plateau of central China during the last 130,000 years[END_REF]. As for fluvial systems, that usually move and reconfigure themselves at the orbital temporal scales (Kim et al., 2010).

In natural systems, an important endeavor is to decipher which types and scales of rhythmic stratal patterns are reflective of internal dynamics of terrestrial environments, and how to effectively differentiate between internal periodic variations and orbital signals. Fortunately, the natural autogenic cyclicities would not produce strong enough power signals in the spectrum periodogram [START_REF] Hajek | Autogenic sedimentation in clastic stratigraphy[END_REF][START_REF] Huang | Astronomical forcing of Middle Permian terrestrial climate recorded in a large paleolake in northwestern China[END_REF], and the improved understanding of the autogenic dynamics (e.g., [START_REF] Wang | Lateral and vertical characteristics of floodplain aggradation cycles in the lower Eocene Willwood Formation[END_REF]) could help constrain the potential autogenic signals and build improved or new statistical tests to detecting astronomical climate cycles. To this end, we present a flexible guideline for identifying orbital signals from terrestrial strata that have formed in varying sedimentary contexts. In practice, the power spectrum of proxies should be examined, and null-hypothesis statistical models and confidence tests that are better-suited should be constructed (e.g., ASM, MTM, FFT, COCO and eCOCO). Additionally, the amplitude modulation effect between eccentricity and precession provides a robust solution for discriminating orbital signals from autogenic cyclicity (TimeOpt and eTimeOpt, testPrecession).

Moreover, combining the integrate power and RAOPR methods enables the tracking of orbital power variations and identification of the orbital signal distributions from strata. And finally, by utilizing the distinctive features of abnormal signal alteration and taking into account the relevant sedimentary conditions, we can proficiently discern whether the periodical signal in the geological record has been subject to modification through sedimentation processes.

CONCLUSION

In this study, we present a new method called the Random-length Average Orbital Power Ratio calculation (RAOPR). This method expands the more established power integration method that investigates changes in astronomical frequencies by integrating their respective frequency ranges over a stratigraphic signal by repeating the calculation over many different window lengths, and thus reducing the sensitivity to the theoretical inherent long-term signals.

Through an investigation of the distributions of orbital power ratios across various levels of synthetic Eccentricity-Tilt-Precession (ETP) series with the inclusion of noise, we have been able to unambiguously identify distinct distributions of orbital power ratios within these merged ETP+noise series. As such, it could be a powerful tool for identifying the orbital signals that have been modified by depositional environment changes.

By analyzing astronomically-tuned Th logging data from the terrestrial Songliao Basin, we uncovered distinctive orbital power ratio distributions that are associated with different depositional environments. By integrating these findings with geological information, we were able to infer the types of depositional processes that impacted the recording and preservation of the orbital signals. For example, we found that the marine incursion events in the lower part of the Nenjiang Formation led to a decrease in precession signal power. The unexpectedly high precession band power observed in the Yaojia Formation may imply that autogenic processes played a substantial role in generating precession-like autocyclicity. Furthermore, the high power in eccentricity bands and very low power in precession bands observed in the Sifangtai and Mingshui formations suggested that high-frequency orbital signals can be challenging to preserve in shallow water environments. Taken together, these findings underscore the complex interactions between orbital forcing and climatic/depositional feedbacks, and highlight the importance of geological factors such as depositional environments, sediment transport processes, and local geological events when assessing orbital signals from stratigraphic successions. Ma) was used as anchored point for astronomical tuning for SK-1s core [START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF], while the C34n/C33r and C30n/C29r boundary [START_REF] Deng | Chronology of the terrestrial Upper Cretaceous in the Songliao Basin[END_REF] were used as anchored points for orbital tuning in the SK-1n core [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]. The black line represents the SK-1s core logging Th series while the blue line is the SK-1n core logging Th series.

FIGURE CAPTURES

Fig. 4. The multi-taper method (MTM; [START_REF] Thomson | Spectrum estimation and harmonic analysis[END_REF] with a red noise null model [START_REF] Mann | Robust estimation of background noise and signal detection in climatic time series[END_REF] and the wavelet spectral analysis [START_REF] Torrence | A practical guide to wavelet analysis[END_REF] were applied for seeking the orbital signals in Th time series (data from [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF][START_REF] Wu | Continental geological evidence for Solar System chaotic behavior in the Late Cretaceous[END_REF]. The long eccentricity signals were extracted from the stratigraphic series using a Gaussian bandpass filter with a bandwidth at 0.002-0.003 kyr -1 . Note: for the MTM analysis, the discrete prolate spheroidal sequences (DPSS) is set to (2*tbw)-1, where tbw=2, tbw: time-bandwidth. The long-term evolution of the orbital signal power and power ratio retrieved from the SK-1 borehole astronomically-tuned Th time series [START_REF] Wu | Cyclostratigraphy and orbital tuning of the terrestrial upper Santonian-lower Danian in Songliao Basin. northeastern China[END_REF]2022). The eccentricity, obliquity and precession band power (b, d, f), power ratios (a, c, e) and total orbital power (g)

were calculated by the PDA method in Acycle free software (Li et al., 2019a). The simulated lake-level was obtained by using the DYNOT methods (h). The purple areas indicate high lake level associated with high orbital power, while the yellow area represents the high lake level corresponding to the low orbital signal power interval. DL: deep lake facies; MR: meandering river facies; SL: shallow lake facies; Del: delta facies. the average precession power ratios.

  regressive phases. The Nenjiang (3-5), Sifangtai and Mingshui formations displayed high power in eccentricity bands and low power in precession bands, suggesting that meandering river environments may not record precession signals or that post-depositional processes have erased them. While the Yaojia Formation has shown the highest precession band power among the five stratigraphic intervals (Fig.8c), which means the local depositional processes has generated regular periodic signals at about ten-thousands time scale. The lower part of the Nenjiang

Fig. 1 .

 1 Fig. 1. The geological setting of the Songliao Basin and SK-1 core. (A) The Songliao Basin of

Fig. 2 .

 2 Fig. 2. The strata information, sedimentary facies and typical core photos of the SK-1 composite

Fig. 3 .

 3 Fig. 3. The chronostratigraphic framework and astronomical tuning anchored points of SK-1

Fig. 5 .

 5 Fig. 5. Evaluation of the total orbital power variations from the synthetic stratigraphic noise

Fig. 6 .

 6 Fig. 6. The average orbital power ratios in different ETP plus noise modeling time series. (A)

Fig. 8 .

 8 Fig. 8. The average orbital power ratios in different formations (or different sedimentary facies

Fig. 9 .

 9 Fig. 9. The conceptual pictures showing the interaction of orbital forcing and terrestrial

Table . 1

 . . The average orbital power ratios and their standard deviation values calculated from the SK-1 tuned Th time series.

		Sediment	eccentricity	Standard	obliquity	Standard	precession	Standard
	Formations						power
		ary facies	power ratio	(2δ)	power ratio	(2δ)		(2δ)
							ratio
	Qingshankou	DL	0.289	0.004	0.345	0.0052	0.152	0.0042
	Yaojia	SL	0.315	0.0094	0.151	0.0032	0.226	0.0072
	Nenjiang(1+2)	DL	0.41	0.0092	0.331	0.0102	0.053	0.0024
	Nenjiang(3-5)	DEL-MR 0.401	0.0042	0.187	0.006	0.143	0.0018
	Sifangtai	MR	0.427	0.0092	0.271	0.0078	0.095	0.0018
	Mingshui	MR	0.591	0.0074	0.173	0.006	0.046	0.002

ACKNOWLEDGMENTS

We thank Brad Singer and M. Smith for carefully handled our manuscript. We also thank two anonymous reviewers for helpful and constructive comments, which have greatly improved our work. This study was financially supported by the National Natural Science Foundation of China (Grant Nos. 41888101, 42302122, 42172137, 41972096, 42050102 and 42050104), Sichuan Provincial Youth Science & Technology Innovative Research Group Fund (No. 2022JDTD0004), Deep-time Digital Earth (DDE) Big Science Program and Everest Scientific Research Program of Chengdu University of Technology (Grant No. 10912-KYQD202209480). He Huang Thanks Chengdu University of Technology (CDUT) provides the financial support (Grant No. 21700-000504) for visiting the IMCCE, CNRS, Observatoire de Paris, France. Matthias Sinnesael thanks European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program (Advanced Grant AstroGeo-885250) for funding.


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L Griffon

Genetic parameters of maturing rate index and asymptotic adult weight in French beef cattle

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Genetic parameters of maturing rate index and asymptotic adult weight in French beef cattle

CONCLUSION

Maturing rate index is …  Measurable from commercial data, although it is highly dependent on weighing at weaning and post-weaning.  Heritable and genetically variable, so direct selection is possible.  Genetically correlated with other traits, allowing indirect selection in particular via reduction in adult weight.

RESULTS

MATERIALS AND METHODS

 Not enough data for the Aubrac breed  Standard deviation of error between 0.01 and 0.03  Average genetic variation coefficient equal to 6.16% for adult weight and 9.09% for maturing rate index

Average female performance in each of the five considered breeds:

Funding :

Genetic correlation of maturing rate index with bodyweight at different ages (average of the 4 breeds):

The maturing rate index seems to be a good phenotype for early development. It would be possible to genetically select the maturing rate index (due to its heritability and genetic variance) without increasing birth weight (average genetic correlation of -0.12). The maturing rate index seems to be positively correlated with adjusted weights between 7 and 24 months. However, the lack of animals with adjusted weights at 18 and 24 months limits the accuracy of the associated correlations and therefore their possible interpretation. The highly negative genetic correlation between maturing rate index and adult weight shows that selecting for heavier adult animals reduces their maturing speed. The disadvantage of the maturing rate index are that the phenotype arrives at the end of the animals' lives and is very dependent on the weaning and post-weaning weights. To obtain breeding values for young animals, a genomic prediction needs to be developed.

Research program (co)funded by APIS-GENE Many thanks to the 6 breed societies who participated.

1

  Institut de l'Elevage, UMR 1313 GABI, F78350 Jouy-en-Josas, 2 ELIANCE, UMR 1313 GABI, F78350 Jouy-en-Josas, 3 INRAE, UMR 1313 GABI, F78350 Jouy-en-Josas, 4 Institut de l'Elevage, F75595 Paris Can early development be estimated from on-farm weighing? Is genetic selection for early development possible? Phenotypes (5 beef breeds): Use of Brody equation from birth weight declared by breeders, performance control weights and NORMABEV carcass weights of adult females.

  Genetic parameters: Estimated adult weight and maturing rate index: data corrected for fixed effects related to birth and slaughter.  Birth weight and adjusted weights (AW) at 7m, 12m, 18m and 24m: corrected performances with a correction of genetic progress.

  𝑊𝑒𝑖𝑔ℎ𝑡 𝑡𝑖𝑚𝑒 = 𝑊𝑒𝑖𝑔ℎ𝑡 𝑎𝑑𝑢𝑙𝑡 -𝑊𝑒𝑖𝑔ℎ𝑡 𝑎𝑑𝑢𝑙𝑡 -𝑊𝑒𝑖𝑔ℎ𝑡 𝑏𝑖𝑟𝑡ℎ 𝑒 -maturing rate index * time ? INTRODUCTION Working on the early development of French beef cows is interesting to:  Reduce fattening time and added concentrates  Reduce the environmental impact of finished products  Facilitate 2-year-old calving through early development