Long Period Astronomical Cycles from the Triassic to Jurassic Bedded Chert Sequence (Inuyama, Japan); Geologic Evidences for the Chaotic Behavior of Solar Planets

Earth Planets Space, 65, 351–360, 2013

Long period astronomical cycles from the Triassic to Jurassic bedded chert sequence (Inuyama, Japan); Geologic evidences for the chaotic behavior of solar planets

Masayuki Ikeda1 and Ryuji Tada2

1Department of Earth Sciences, Graduate School of Science and Engineering, Ehime University, Ehime 790-8577, Japan 2Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

(Received July 11, 2012; Revised August 31, 2012; Accepted September 10, 2012; Online published May 7, 2013)

Astronomical theory predicts that ∼2 Myr eccentricity cycle have changed its periodicity and amplitude through time because of the chaotic behavior of solar planets, especially Earth-Mars secular resonance. Although the ∼2 Myr eccentricity cycle has been occasionally recognized in geological records, their frequency transitions have never been reported. To explore the frequency evolution of ∼2 Myr eccentricity cycle, we used the bedded chert sequence in Inuyama, Japan, of which rhythms were proven to be of astronomical origin, covering the ∼30 Myr long spanning from the Triassic to Jurassic. The frequency modulation of ∼2 Myr cycle between ∼1.6 and ∼1.8 Myr periodicity detected from wavelet analysis of chert bed thickness variation are the ﬁrst geologic record of chaotic transition of Earth-Mars secular resonance. The frequency modulation of ∼2 Myr cycle will provide new constraints for the orbital models. Additionally, ∼8 Myr cycle detected as chert bed thickness variation and its amplitude modulation of ∼2 Myr cycle may be related to the amplitude modulation of ∼2 Myr eccentricity cycle through non-linear process(es) of Earth system dynamics, suggesting possible impact of the chaotic behavior of Solar planets on climate change. Key words: Astronomical cycle, bedded chert, chaos, eccentricity, Earth-Mars secular resonance, Triassic- Jurassic.

1. Introduction ical cycles could have occurred before Neogene, and that It has been widely demonstrated that Earth’s astronomi- their solution before Neogene may not be accurate enough cal parameters (precession, obliquity, and eccentricity) con- for orbital tuning due to the uncertainty on the frequency trol Earth’s climate through changes in temporal and spa- of the long period astronomical cycles. If so, geological tial distribution of insolation on the Earth’s surface (e.g., records of astronomically paced rhythms are the only evi- Milankovitch, 1941; Hays et al., 1976; Berger et al., 1989). dence on actual frequency changes of these long period as- With the increase in the lengths of high-resolution sedimen- tronomical cycles in the past, and will be able to provide tary and paleoclimatic records, long period amplitude mod- new constraints on orbital models with respect to the fre- ulations of the obliquity and eccentricity cycles with period- quency modulation of the long period astronomical cycles. icities of ∼1 and ∼2 Myr have been increasingly recognized The eccentricity cycle related to the Earth-Mars secular res- (e.g. Beaufort, 1994; Olsen and Kent, 1999; Zachos et al., onance with the periodicity different from ∼2.4 Myr were 2001; Lourens et al., 2005; Palike¨ et al., 2006; van Dam et reported from the older part of the geological records such al., 2006; Ikeda et al., 2010a, b; Boulila et al., 2011). This as ∼1.6 Myr cycle in Early Cretaceous (Grippo et al., 2004; fact suggests the significant influence of these astronomical Huang et al., 2010b), and ∼2.0 Myr cycle in Late Juras- cycles on the global climate. sic (Huang et al., 2010a), ∼1.8 Myr cycle in Late Triassic The long period astronomical cycles (>0.5 Myr periodic- (Olsen and Kent, 1999; Husing¨ et al., 2011) and Middle ity) are predicted to have changed their frequencies through Triassic (Ikeda et al., 2010a), and ∼1.5 Myr cycle in Late time due to the “chaotic” behavior of the inner planets, es- Permian to Early Triassic (Huang et al., 2011). However, so pecially Earth-Mars secular resonance (e.g. Laskar, 1990; far no study has identified frequency transition of these long Laskar et al., 2004, 2011a, b). The sensitivity tests on period cycles. To identify frequency transition of long pe- the solar oblateness, tidal dissipation factor, and integration riod cycles, determine their precise timing, and describe the step-size by Laskar et al. (2004, 2011a, b) suggest that a nature of frequency transition, long and continuous geolog- significant frequency change of the long period astronomical records of astronomically driven rhythms are needed. In this study, we adopted method of Ikeda et al. (2010a) Copyright c The Society of Geomagnetism and Earth, Planetary and Space Sci- to an Upper Triassic to Lower Jurassic bedded chert se- ences (SGEPSS); The Seismological Society of Japan; The Volcanological Society ∼ of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sci- quence that covers 30 Myr interval, in order to identify ences; TERRAPUB. orbital cycles and explore the evolution of long period astronomical cycles. Bedded chert consists of centimeter- doi:10.5047/eps.2012.09.004

351 352 M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT

Fig. 1. (a) A Location map showing the locations of the Inuyama section, Mino-Tanba Terrane, Japan. (b) A geologic map of the Inuyama area showing the location of the Katsuyama section (modified from Matsuda and Isozaki, 1991). (c) A paleogeographic map during Triassic-Jurassic showing the localities of the Inuyama section. Base map is after Oda and Suzuki (2000). (d) A geologic sketch map with location of measurement transects in this study (modified after Kimura and Hori, 1993). scale rhythmical alternations of chert and shale beds whose is located in the Inuyama area, southwestern part of the rhythms are paced by precession and eccentricity cycles Mino Terrane, Central Japan (Fig. 1). The Mino Terrane (e.g. Fischer, 1976; Hori et al., 1993; Ikeda et al., 2010a). is a Paleozoic-Mesozoic accretionary complex consisting The sedimentary rhythms of bedded chert formed as a re- of greenstone, limestone, bedded chert, and clastic rocks sult of cyclic changes in the accumulation rate of biogenic (Wakita, 1988). The accretionary complex exposed in the SiO2 within a background of extremely slow accumulation Inuyama area comprises Middle Triassic to Lower Juras- of pelagic clay (e.g. Hori et al., 1993). Additionally, bedded sic bedded chert and Middle Jurassic clastic rocks, which chert accumulated continuously on pelagic deep seafloor so are repeated as tectonic slices (Fig. 1; Yao et al., 1980; that it covers a long time interval over hundreds of millions Matsuda and Isozaki, 1991). The bedded chert sequence of years. Consequently, a bedded chert sequence has a po- was deposited on pelagic deep seafloor of superocean Pan- tential to record the evolution of the long period astronom- thalassa below the carbonate compensation depth (CCD), ical cycles. We measured thickness of individual chert bed whereas the clastic rocks are considered to have been de- throughout the sequence, and confirmed ∼20 kyr preces- posited within a trench in a subduction zone (Matsuda and sion cycle origin of chert-shale couplet based on biostrati- Isozaki, 1991). Paleomagnetic studies of the bedded chert graphic ages. We then constructed the astronomical time sequence in the study area suggest that the site of deposition scale of the bedded chert sequence by tuning ∼20 beds cy- moved from low latitudes during Middle Triassic to middle cle to 405 kyr eccentricity cycle of constant duration, and latitudes during Lower Jurassic as a course of plate motion conducted spectral analyses on the chert bed thickness time (Fig. 1(c); Shibuya and Sasajima, 1986; Oda and Suzuki, series to reconstruct temporal changes in the frequency and 2000; Ando et al., 2001). amplitude of ∼2 Myr eccentricity cycle. Additionally, we We constructed a continuous columnar section of ∼30 m examined amplitude modulation of ∼2 Myr cycle and its re- thick spanning from Norian (middle Late Triassic) to Toar- lation to the origin of ∼8 Myr cycle of chert bed thickness cian (late Early Jurassic) based on bed by bed thick- variations detected in this study. ness measurements of 1563 chert and 1563 shale beds at the upper part of the Katsuyama Section of Matsuoka et 2. Geologic Setting al. (1994), (Fig. 2). This section includes the Section The studied section is the Katsuyama section (e.g. Hori, Katsuyama (UF: Rhaetian to Toarcian) of Nakaseko and 1990; Matsuoka et al., 1994; Carter and Hori, 2005), which Nishimura (1979), Hori (1990), and Carter and Hori (2005), M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT 353

Fig. 2. Estimated average duration of individual chert-shale couplet based on the relationship between bed number and age for the Rhaetian, Hettangian to Pliensbachian, and Rhaetian to Pliensbachian bedded chert in the Inuyama area, central Japan. The average durations of the couplet were estimated from the intervals of interest divided by the number of beds (see text for details). The ranges of the estimated durations are based on errors in the ages of geological stage boundaries (Ogg, 2012; Ogg and Hinnov, 2012) and uncertainties in the stratigraphic positions of the geological boundaries described by Hori (1990), Sugiyama (1997), Carter and Hori (2005), and Grocke¨ et al. (2011). Radiolarian zones and stratigraphic distribution of selected taxa are from Hori (1990, 1997), Sugiyama (1997), Carter and Hori (2005), and Grocke¨ et al. (2011). Tethyan ammonite zone is after Ogg (2012), Ogg and Hinnov (2012). and the Sections H1, H2, and H3 (Norian to Rhaetian) of on radiolarian-conodont-ammonoid biostratigraphic corre- Sugiyama (1997), respectively. The columnar section con- lation with reference sections, where numerical ages have sists mostly of chert and shale beds which are red, green- been estimated. The Norian/Rhaetian boundary in the stud- ish gray, purple, and black in color. The lower and middle ied section is correlated to the horizon of the last occurrence parts of the columnar section contain two red shale beds of of the radiolarian Betracclum deweveri within the interval ∼30 mm thick each, which are correlated to the shale bed between the bed number 400 and 450 based on the radi- named CS-2 and CS-3 (Sugiyama, 1997), in ascending or- olarian biostratigraphic correlation with the Queen Char- der. The lower limit of our section consists of a white chert lotte Island, Canada (Sugiyama, 1997). In the Queen Char- bed of ∼200 mm thick, which is ∼0.5 m below the CS-2. lotte Island, the Norian/Rhaetian boundary is also identi- The upper limit of the columnar section consists of a white fiedastheGnomohalorites cordileranus/Paracochloceras chert bed of ca. 500 mm thick, which is correlated to the amoenum ammonoid zone boundary (Carter, 1993; Carter Toarcian massive white chert of Hori (1990). We selected and Orchard, 2007). This ammonoid zone boundary is a measurement transect with minimal lateral change in bed correlated with the Metasibirites spinescens/Cochlocearas thickness. The bed number is defined such that the red chert suesssi ammonoid zone boundary in European sections, bed just above the white chert bed, which is the lower limit which is assigned as the Norian/Rhaetian boundary (Ogg, of our columnar section, is assigned as number 1, and the 2012). The age of the Norian/Rhaetian boundary is esti- bed number increases upsection. mated as 209.5±1.0 Ma by magnetstratigraphic correlation with the astronomically tuned geomagnetic polarity time 3. Average Duration of Individual Chert-Shale scale in the Newark Supergroup (Husing¨ et al., 2011; Olsen Couplets et al., 2011; Ogg, 2012). The end-Triassic mass extinc- To estimate the average duration of individual chert- tion interval in the studied section is well constrained within shale couplets, we constructed an age model for the Up- the interval of a chert bed number 796 based on the radio- per Triassic to Lower Jurassic bedded chert sequence based larian faunal turnover from the Globolaxtorum tozeri zone 354 M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT to Pantanellium tanuense zone with the last occurrence of bachian/Toarcian boundary (Ogg and Hinnov, 2012). The conodont Misikella posthernsteini (Hori, 1992; Carter and age of the Pliensbachian/Toarcian boundary was assigned Hori, 2005). Across the end-Triassic mass extinction in- as 182.7 ± 0.5 Ma (Ogg and Hinnov, 2012). This correla- terval, radiolarian fauna shows a similar turnover pattern tion is supported by a negative excursion of organic carbon between the pelagic bedded chert sequence in the Inuyama isotope (Grocke¨ et al., 2011). area and the shallow marine sequence in the Queen Char- Based on the above age model, the average durations for lotte Islands, Canada (Carter and Hori, 2005). In the Queen a chert-shale couplet were calculated for the intervals cor- Charlotte Islands, the radiolarian turnover is also followed responding to Rhaetian, Hettangian to Pliensbachian, and by the last occurrence of conodont Norigondolella sp. and Rhaetian to Pliensbachian by dividing the duration by the Triassic ammonoid Choristoceras rhaeticum, and predated number of beds in each interval. The average duration of an by the first occurrence of Jurassic ammonoid Psiloceras individual chert-shale couplet ranges between 17 and 28 kyr aff. primocostatum (Tipper et al., 1994; Williford et al., (median value, 22 kyr) for Rhaetian, between 18 and 27 kyr 2007). The similar ammonoid turnover across the end- (median value, 21 kyr) for Hettangian to Pliensbachian, and Triassic mass extinction is widely found in shallow marine between 19 and 25 kyr (median value, 21 kyr) for Rhaetian sequences, such as the New York Canyon section in U.S.A., to Pliensbachian, respectively (Fig. 2). These estimated du- Pucara section in Peru and the St. Audrie’s Bay section in rations for an individual chert–shale couplet are consistent UK (e.g. Warrington et al., 2008; Schoene et al., 2010). with the 17 to 21 kyr duration of the precession cycle during The correlation among these areas is supported by a posi- Late Triassic to Early Jurassic (Berger et al., 1989). tive excursion of organic carbon isotope after a sharp negative excursion (Ward et al., 2001, 2004, 2007; Hesselbo et al., 2002; Guex et al., 2004; Williford et al., 2007). U- 4. Spectral Analysis of a Bed Number Series of Pb age of 201.36 ± 0.13 Ma was measured at the horizon Chert Bed Thickness between the end-Triassic mass extinction interval and the To examine sedimentary rhythms of the bedded chert, Triassic/Jurassic boundary in the Pucara section (Schoene thickness of individual chert bed and shale bed was mea- et al., 2010). Additionally, the duration of the interval sured at the outcrops with the precision of one mm. Fig- between the end-Triassic mass extinction interval and the ure 3(a) shows the stratigraphic variation in chert bed thick- Triassic/Jurassic boundary, which is characterized by the ness and its 50 point moving average over the entire stud- last occurrences of the Triassic fauna and flora, including ied sequence. The chert bed thickness ranges from 5 to 92 conodont Misikella posthernsteini, and the first occurrence mm with an average of 24 mm and standard deviation of of Jurassic ammonoid Psiloceras planorbis, respectively, 10 mm. The smoothed stratigraphic variations in chert bed was equivalent to 6 precession cycles (∼120 kyr), accord- thickness show ∼100 bed cyclicity with the amplitude of ing to the cyclostratigraphy at the St. Audrie’s Bay section, ∼10 mm (Fig. 3(a)). (Ruhl et al., 2010). Based on these chronostratigraphic con- To assess the cyclicity of stratigraphic variations in the straints, the end-Triassic mass extinction interval in the In- chert bed thickness, we performed wavelet analyses on the uyama bedded chert can be estimated as 201.36 ± 0.20 Ma. bed number series of chert bed thickness using a series This age uncertainties arose from the U-Pb age error and the of Matlab algorithms modified from those developed by duration of the end-Triassic mass extinction interval of the Torrence and Compo (1998). This software can identify shallow marine section in UK, as described above (Schoene whether peaks in the spectrum of time series are signifi- et al., 2010; Ruhl et al., 2010; Ogg and Hinnov, 2012). cant against the red-noise (autoregressive lag1) background The Hettangian/Sinemurian and Sinemurian/Pliensbachian spectrum. The analysis was conducted in the bed number boundaries are not well constrained in this section (Hori, domain rather than in the depth domain because the sedi- 1990, 1997). Thus, we treated an interval between Het- mentation rates are considered to have changed significantly tangian and Pliensbachian as “Hettangian to Pliensbachian” between chert beds and intercalated shale beds (Hori et al., interval. The Pliensbachian/Toarcian boundary is correlated 1993). with a horizon within an interval between bed number 1540 Figure 3(a) shows the results of wavelet analyses of the and 1563 based on the uppermost part of P. simplum IV bed number series of chert bed thickness. The global Subzone of Hori (1990, 1997; Trillus elkhornensis Assem- wavelet power spectrum (Torrence and Compo, 1998) of the blagezone) and the lower part of the H. hexagonus (Hh) bed number series of chert bed thickness variations shows Zone (Hori, 1990, 1997; Grocke¨ et al., 2011). These radi- cyclicities of ∼3 to 5 beds, ∼100 beds, and ∼500 beds olarian zones correspond to the radiolarian zones of Eucyr- above the 90% confidence level (Fig. 3(a)). The wavelet tidiellum nagaiae—Praeparvicingula tlellensis to Elodium spectrum of the bed number series of chert bed thickness pessagnoi—H. hexagonus (Carter et al., 2010). The ages of variations revealed occurrences of a ∼100 bed cycle within these radiolarian zones are constrained as the upper Pliens- the intervals between bed number 0 and 400, 700 and 900, bachian and lower Toarcian, respectively, by ammonite 1200 and 1300, and 1500 and 1563 and a ∼20 bed cycle biostratigraphy of Queen Charlotte Islands and other areas in intervals between bed number 0 and 120, 200 and 270, from North America (Carter et al., 2010). Thus, the hori- 1000 and 1040, 1100 and 1140, and 1520 and 1563 above zon of the uppermost part of P. simplum IV Subzone of Hori the 10% significant level (Fig. 3(a)). (1990, 1997) is correlated with the Emaciaticeras emacia- tum/Dactylioceras tenuicostatum ammonite Zone boundary of European sections, which corresponds to the Pliens- M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT 355

Fig. 3. (a) Stratigraphic variations in the chert bed thickness and 50 point moving average of the chert bed thickness, and (b) Wavelet power spectrum and bandpass filter of a bed number series of chert bed thickness variations in upper Triassic to lower Jurassic bedded chert, and (c) a 405 kyr tuned chert bed thickness time series in upper Triassic to lower Jurassic chert beds in the Inuyama area, Central Japan. The cross-hatched region is the cone of influence, where zero padding has reduced the variance. Black contour is the 90% confidence level, using a red-noise (autoregressive lag1) background spectrum (Torrence and Compo, 1998). Radiolarian zones are based on Hori (1990, 1997), Sugiyama (1997) and Carter and Hori (2005).

5. Conversion of Bed Number Series to Time Se- 2010a). This is the reason the spectral peak of 20 bed cycle ries is not a dominant cycle, but split between ∼18 bed and ∼25 To convert a bed number series of chert bed thickness bed cycle. variations to a time series, we used the 405 kyr eccentricity To test the idea of changes in thickness of one chert- cycle as a tuning target for the time series (e.g. Olsen and shale couplet, we converted the ∼20 bed cycle in the bed Kent, 1999; Ikeda et al., 2010a). Laskar et al. (2004) number domain to a cycle with a constant duration of 405 proposed the use of the 405 kyr eccentricity cycle for the kyr in the time domain, assuming ∼20 bed cycle as 405 kyr absolute time calibration for Mesozoic, because this cycle eccentricity cycle. We then conducted spectral analyses of is originated from gravitational interaction between Jupiter the tuned time series of chert bed thickness variations. As and Venus, and is highly stable and constant in duration, is shown in Fig. 3(c), the wavelet spectra of the chert bed as well as showing a dominant spectral peak due to the thickness time series revealed distinct peaks at periodicities great mass of Jupiter (Laskar et al., 1993). On the contrary, of ∼0.1, ∼2 and ∼8 Myr above the 90% conﬁdence levels, the ∼20 bed cycle, which is correlated with the 405 kyr in addition to the 405 kyr periodicity. Additionally, we cycle assuming each chert-shale couplet as the ∼20 kyr found frequency modulation of ∼2 Myr eccentricity cycle precession cycle, is modulated its frequency between ∼18 with ∼8 Myr periodicity and the amplitude modulation with beds and ∼25 beds due to the frequency modulation of ∼4 Myr and ∼8 Myr periodicities (Fig. 3(c)), respectively. the precession cycle between 17 kyr and 21 kyr cycle (the wavelet spectra in Fig. 3(a); see also ﬁgure 6 of Ikeda et al., 356 M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT

Fig. 4. (a) Bandpass ﬁltered data of ∼2 Myr and ∼8 Myr cycles and (b) S-transform spectrum of a 405 kyr tuned chert bed thickness time series in upper Triassic to lower Jurassic in the Inuyama area, Central Japan. (c) S-transform spectrum of eccentricity of orbital solutions of La2004 (Laskar et al., 2004) and La2010d (Laskar et al., 2011a) from 220 Ma to 185 Ma. The vertical lines in (b) and (c) correspond to period of 2 Myr, and 8 Myr, respectively.

6. Comparison of the Long Period Cycles between Vesta, Pallas, Iris, and Bamberga (Laskar et al., 2011a), al- Geological Record and Orbital Solution though La2010a, La2010b and La2010c are fit to INPOP08 To further examine the long period cycles in the sedimen- over only the last 580 kyr for the La2010a and La2010b, tary rhythms of bedded chert and confirm their astronomical and over the last 1 Myr for La2010c, but La2010c does cycle origin, we compare the nature of the frequency mod- not include the five major asteroids. Thus, the La2010d ulation of ∼2 Myr cycle between our geological data and version could be considered as the most constrained ver- the orbital solutions of Laskar et al. (2004, 2011a) during sion in the La2010 models (Laskar et al., 2011a, b). Nev- the period from Late Triassic to Early Jurassic. To com- ertheless, the orbital solutions for pre-Neogene time can- pare the long period astronomical cycles in the geologic not be solved precisely due to the uncertainty in the fre- data with that of orbital solution with high frequency reso- quency of the long period astronomical cycles that reflects lution, we conducted S-transform on the chert bed thickness the “chaotic” behavior of the inner planets, especially the time series and orbital solution of Laskar et al. (2004). The ∼2 Myr cycle of Earth-Mars secular resonance (Laskar et S-transform is a sophisticated wavelet analysis customized al., 2004, 2011a, b). Here we examine the general trend and to better visualize the frequency modulation of low fre- nature of frequency modulation and amplitude modulation quency cycles using a moving and scalable localizing Gaus- of the ∼2 Myr eccentricity cycle computed by the orbital sian window (Stockwell et al., 1996). The orbital models of models. La2004 and La2010 were demonstrated as precise for the The S-transform spectrum for the chert bed thickness last 40 Myr and 50 Myr, respectively (Laskar et al., 2004, time series shows a dominant cycle at ∼2 Myr periodicity 2011a, b). The main difference between the La2004 and and a secondary cycle at ∼8 Myr periodicity (Fig. 4). The La2010 models is that the initial conditions of La2004 are local maxima in the amplitude of the ∼2 Myr cyclicity on adjusted to the JPL numerical ephemeris DE406 (Standish, the S-transform spectrum for the chert bed thickness time 1998) over −5000 yr to +1000 yr from the present date, series occur with ∼1.8 Myr periodicity around 212 Ma with while La2010 is fit to the most precise planetary ephemeris an amplitude of 7.5 mm, ∼1.6 Myr periodicity around 206 INPOP06 and INPOP08 (Fienga et al., 2008, 2009). In par- Ma with an amplitude of 4 mm and around 201 Ma with ticular, the La2010d version is adjusted to INPOP06 over an amplitude of 7 mm, ∼1.8 Myr periodicity around 192 the last 1 Myr that includes the five major asteroids, Ceres, Ma with an amplitude of 5 mm, and ∼1.7 Myr periodicity M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT 357 around 185 Ma with an amplitude of 5 mm (Fig. 4). In other limestone sequence in the Fucoid Marls, Italy (Grippo et words, the frequency transition of the ∼2 Myr cyclicity of al., 2004; Huang et al., 2010b), ∼2.0 Myr cycle is reported the chert bed thickness time series occurred around 212 to from the TOC record of the Upper Jurassic limestone se- 206 Ma, and 201 to 192 Ma with amplitude modulation with quence in the Kimmeridge Clay, England (Huang et al., ∼4 Myr and ∼8 Myr periodicities (Fig. 4). Additionally, the 2010a), ∼1.8 Myr cycles are reported from the depth rank ∼8 Myr periodicities observed in the amplitude modulation and color records of the Upper Triassic lacustrine sequence of the ∼2 Myr cycle of the chert bed thickness time series in the Newark Supergroup in North America (Olsen and is nearly in-phase with the ∼8 Myr cycle of the chert bed Kent, 1999), magnetic suscepitability records of the Upper thickness time series (Fig. 4). Triassic limestone sequence in Italy (Husing¨ et al., 2011) The S-transform spectra for the orbital solutions of and from the chert bed thickness record of the Middle Tri- Laskar et al. (2004, 2011a) also show the frequency mod- assic bedded chert sequence in Japan (Ikeda et al., 2010a), ulation and amplitude modulation of ∼2 Myr periodicities, and ∼1.5 Myr cycles are reported from the magnetic sus- but their timing and frequency of the local maxima in am- ceptibility record of the Upper Permian to Lower Triassic plitude are different with each other (Fig. 4(c)). Namely, hemi-pelagic sequence in China (Huang et al., 2011), re- the local maxima in amplitude of the ∼2 Myr eccentricity spectively. However, no geological evidence has been pre- cycle in the orbital solution of La2004 occur as ∼2.6 Myr sented on the timings and nature of frequency transitions of periodicity around 217 Ma, ∼2.1 Myr periodicity around the ∼2 Myr long eccentricity cycle. 212 Ma and 201 Ma, and ∼2.3 Myr periodicity around 192 In this study, ∼2 Myr cycle changed its dominant fre- Ma, respectively. Those of La2010d occur as ∼1.8 Myr pe- quency between ∼1.6 and ∼1.8 Myr at least twice during riodicity around 218 Ma, ∼2.5 Myr periodicity around 212 the Late Triassic to Early Jurassic (Fig. 4). Namely, the Ma, ∼1.8 Myr periodicity around 205 Ma, ∼1.6 Myr peri- frequency transition of the ∼2 Myr cyclicity of the chert odicity around 200 Ma, and ∼2.8 Myr periodicity around bed thickness time series occurred around 212 to 206 Ma, 188 Ma, respectively. In other words, the frequency transi- and 201 to 192 Ma (Fig. 4). These frequency changes tion of the ∼2 Myr eccentricity cycle in the orbital solution of ∼2 Myr cycle indicate that the Earth-Mars secular res- of La2004 occurred around 215 Ma and 198 Ma, and that of onance have undergone the chaotic transitions during the La2010d occurs at 215 Ma, 207 Ma, 203 Ma, and 195 Ma Late Triassic to Early Jurassic. The ∼1.8 Myr cycle dur- (Fig. 4(c)). Additionally, the ∼2 Myr eccentricity cycles ing Rhaetian is consistent with the previous reports from in the orbital solutions of La2004 and La2010d show am- lake level records of Newark Supergroup and magnetic plitude modulation with ∼5to∼10 Myr periodicities, but suscepitability records of the limestone sequence in Italy the ∼8 Myr cycle detected in the chert bed thickness time (Husing¨ et al., 2011). series is not dominant in the wavelet spectral results of the Worthy of note is the fact that the timings and nature eccentricity in the orbital solutions of Laskar et al. (2004, of frequency changes of the ∼2 Myr cycle are different 2011a) (Fig. 4). between the chert bed thickness time series and the orbital solutions of Laskar et al. (2004, 2011a), although 7. Discussion La2010d and chert bed thickness time series are similar in 7.1 Evolution of long period astronomical cycles dur- the ∼1.6 Myr cycle at 200 Ma (Fig. 4). Additionally, the ing Late Triassic to Early Jurassic ∼2 Myr cycle detected in the S-transform spectra of the The Upper Triassic to Lower Jurassic bedded chert se- chert bed thickness time series shows the amplitude mod- quence, a ∼30 Myr long sedimentary record, is useful for ulation with ∼4 Myr and ∼8 Myr periodicities, which is examining the frequency transitions of long period astro- different from the orbital solutions in which the ∼2 Myr ec- nomical cycles (Figs. 3 and 4). The ∼2 Myr (100 bed) cycle centricity cycle shows the amplitude modulation with ∼5 observed in the chert bed thickness variations shows one of to 10 Myr periodicity (Fig. 4). As described by Laskar et the strongest peaks on the wavelet and S-transform spectra. al. (2004, 2011a, b), their orbital solutions before Neogene This could be correspond to the ∼2.4 Myr eccentricity cy- have large degree of uncertainty due to the chaotic behav- cle observed today, because the ∼2.4 Myr eccentricity cycle ior of Earth-Mars secular resonance. The timings and na- shows the strongest peaks among long period astronomical ture of frequency transition of the ∼2 Myr cycle detected cycles (e.g. Laskar et al., 2004, 2011a). This ∼2.4 Myr in the geological record should have potential to constrain eccentricity cycle is considered as having undergone fre- the “chaotic” evolution of the Solar system by adjusting the quency transitions before Neogene due to the “chaotic” be- timings and nature of frequency modulation of the ∼2 Myr havior of Earth-Mars secular resonance (figure 23 in Laskar eccentricity cycle in the orbital solutions to those of our ge- et al., 2004). Frequency transitions of the ∼2 Myr eccen- ologic record. tricity cycle can be used as constraints for orbital models, 7.2 Origin of the ∼8 Myr cycle and its possible relation if they are detected in geological records (Olsen and Kent, with the chaotic behavior of Solar planets 1999; Laskar et al., 2004). The present state of Earth-Mars Although a spectral peak at the ∼8 Myr (400 bed) cycle secular resonance characterized by the presence of ∼2.4 of the chert bed thickness variation has the strongest power, Myr cycle in geological records can be traced back to 40 this periodicity is not known as the dominant periodicity of Ma (e.g. Palike¨ et al., 2004). On the other hand, in addition astronomical cycles (Laskar et al., 2004) (Fig. 4). Similar to the ∼2.4 Myr periodicity caused by the eccentricity cycle ∼9 Myr cycle has recently been reported from the Cenozoic related to Earth-Mars secular resonance, ∼1.6 Myr cycle is carbon isotope records of Zachos et al. (2001, 2008), which reported from the gray scale record of the Lower Cretaceous has been interpreted as the result of the amplitude modula- 358 M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT tion of the ∼2 Myr eccentricity cycle (Boulila et al., 2012). 405 kyr periodicity above 10% significant level. Among This study also record the ∼8 Myr periodicity as the ampli- these, the ∼2 Myr cycle, which is interpreted as the long tude modulation cycle of the ∼2 Myr cycle of the chert bed period eccentricity cycle caused by Earth-Mars secular res- thickness time series with nearly in-phase with the ∼8 Myr onance, changes its frequency between ∼1.6 and ∼1.8 Myr. cycle (Fig. 4(a)). Therefore, the amplitude modulation of The frequency transitions of the ∼2 Myr cycle in the chert the ∼2 Myr eccentricity cycle is probably related to the ∼8 bed thickness time series are the first geologic evidence of Myr cycle in the chert bed thickness time series. chaotic transitions of Earth-Mars secular resonance. Such Orbital solutions suggested that the eccentricity cycles modulation patterns of the ∼2 Myr cycle in the geologi- have negligible power in annual and seasonal insolation cal records will provide an important constraint on orbital time series, although it does modulate the amplitude of the models. Furthermore, the ∼8 Myr (400 beds) cycle is de- climatic precession, and the amplitude of seasonal insola- tected from the spectral analyses of the chert bed thickness tion. According to the researches on astronomical cycles variation. Our results suggest that the ∼8 Myr cycle in our during Quaternary, it is generally thought that the ∼100 record may reflect the amplitude modulation of the ∼2Myr kyr glacial-interglacial cycles are paced by the ∼100 kyr eccentricity cycle associated with Earth-Mars secular reso- eccentricity, which is amplified and/or rectified through nance through non-linear amplification and/or rectification non-linear internal climate feedback processes influenced process(es) within the global climate system, probably sim- through the amplitude modulation of the seasonal insola- ilar to the origin of ∼9 Myr cycle of the carbon isotope tion by the eccentricity (e.g. Hays et al., 1976; Imbrie et al., variation during Cenozoic (Boulila et al., 2012). 1993; Huybers and Wunsch, 2003). The signal of astronomical cycles detected in this study would also be amplified Acknowledgments. We thank Prof. Paul E. Olsen (Lamont- and/or rectified by similar internal non-linear processes(es). Doherty Earth Observatory, Columbia University) for his con- ∼ structive comments for cyclostratigraphy and astronomical theory, Similarly, we suggest that the 8 Myr cycle in the chert bed Dr. T. Ito (National Astronomical Observatory of Japan) for his thickness time series results from amplitude modulation of advice concerning the astronomical theory and orbital calculation the ∼2 Myr eccentricity cycle through non-linear amplifi- model, Dr. H. Miyahara (The University of Tokyo) for her advice cation process(es). Boulila et al. (2012) suggested that the regarding spectral analysis, and Drs. A. Karasuda, H. Sakuma, S. amplitude modulation of the ∼2 Myr eccentricity cycle may Yamamoto, S. Takahashi (The University of Tokyo), and R. S. Hori (Ehime University) for their fruitful discussion. We also wish play an important role in carbon cycling, controlling a chain to thank Mr. S. Robbins of the University of Tokyo’s GCOE pro- of astro-climatically sensitive processes such as terrestrial gram for the English proofreading and editing of this paper. We weathering, biosphere productivity, carbonate sedimenta- are grateful for editor T. Yamazaki. The manuscript was greatly tion and dissolution, burial and oxidation of organic carbon, improved by careful reviews from Prof. J. Ogg (Purdue Univer- etc. (e.g., Palike¨ et al., 2006; Li et al., 2009). Although sity) and an anonymous referee. This research was partly supported by grants from the Japan Society for the Promotion of Sci- their potential link with the chert bed thickness variation is ence (20098755 and 20127776), Overseas Internship Program for highly speculative, productivity is most likely related with Outstanding Young Earth and Planetary Researchers, and Fujiwara the chert bed thickness variation (e.g. Hori et al., 1993). In Natural History Foundation awarded to M. Ikeda. addition, terrestrial weathering is also potentially a controlling factor of the chert bed thickness variation, because the References extreme source of biogenic silica burial in the ocean is the Ando, A., K. Kodama, and S. Kojima, Low-latitude and Southern Hemi- dissolved silica from continents (e.g. Treguer´ et al., 1995; sphere origin of Anisian (Triassic) bedded chert in the Inuyama area, Treguer,´ 2002). The formation mechanism of bedded chert Mino terrene, central Japan, J. Geophys. Res., 106, 1973–1986, 2001. rhythms and their genetic relation to long period astronom- Beaufort, L., Climatic importance of the modulation of the 100 kyr cycle inferred from 16 m.y. long Miocene records, Paleoceanography, 9, 821– ical cycles would be a key for understanding this non-linear 834, 1994. amplification process(es), which should be clarified in the Berger, A., M.-F. Loutre, and V. Dehant, Influence of the changing lunar future. The ∼30 Myr orbitally-paced lake level records in orbit on the astronomical frequencies of pre-Quaternary insolation pat- the Newark Supergroup during Late Triassic will also pro- terns, Paleoceanography, 4, 555–564, 1989. Boulila, S., B. Galbrun, K. G. Miller, S. F. Pekar, J. V. Browning, J. Laskar, vide additional constraints for this topic. These issues must and J. D. Wright, On the origin of Cenozoic and Mesozoic “third-order” be addressed for complete understanding of the impact of eustatic sequences, Earth-Sci. Rev., 109, 94–112, 2011. long period astronomical cycles on global surface environ- Boulila, S., B. Galbrun, J. Laskar, and H. Palike,¨ A ∼9 myr cycle in Cenozoic δ13C record and long-term orbital eccentricity modulation: ments. Is there a link?, Earth Planet. Sci. Lett., 317, 273–281, 2012. Carter, E. S., Biochronology and paleontology of uppermost Triassic 8. Conclusions (Rhaetian) radiolarians, Queen Charlotte Islands, British Columbia, Canada, Memoires´ de Geologie´ (Lausanne), 11, 175 pp., 1993. The nature of long-term astronomical cycles preserved in Carter, E. S. and R. S. Hori, Global correlation of the radiolarian faunal the Late Triassic to Early Jurassic bedded chert sequence change across the Triassic-Jurassic boundary, Can. J. Earth Sci., 42, in the Inuyama area, Japan, covering ∼30 Myr has been 777–790, 2005. examined. The average duration of a chert-shale couplet Carter, E. S. and M. J. Orchard, Radiolarian-conodont-ammonoid inter- ∼ calibration around the Norian-Rhaetian Boundary and implications for during Late Triassic to Early Jurassic is 20 kyr, support- trans-Panthalassan correlation, Albertiana, 36, 149–163, 2007. ing its precession cycle origin. Spectral analyses of the Carter, E. S., S.ˇ Gorican,ˇ J. Guex, L. O’Dogherty, P. De Wever, P. Du- chert bed thickness time series, which is fine-tuned based mitrica, R. S. Hori, A. Matsuoka, and P. A. Whalen, Global radiolar- on the assumption that ∼20 bed cycle is the 405 kyr ec- ian zonation for the Pliensbachian, Toarcian and Aalenian, Palaeogeogr. Palaeoclim. Palaeoecol., 297, 401–419, 2010. centricity cycle of constant duration, revealed the presence Fienga, A., H. Manche, J. Laskar, and M. Gastineau, INPOP06. A new of ∼0.1, ∼2 and ∼8 Myr periodicities in addition to the numerical planetary ephemeris, Astron. Astrophys., 477, 315–327, 2008. M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT 359

Fienga, A., J. Laskar, T. Morley, H. Manche, P. Kuchynka, C. Le Poncin- chaos induced by close encounters with Ceres and Vesta, Astron. Astro- Lafitte, F. Budnik, M. Gastineau, and L. Somenzi, INPOP08, a 4-D phys., 532, L4, doi:10.1051/0004-6361/201117504, 2011b. planetary ephemeris: from asteroid and time-scale computations to ESA Li, G., J. Ji, J. Chen, and D. B. Kemp, Evolution of the Cenozoic carbon Mars Express and Venus Express contributions, Astron. Astrophys., 507, cycle: the roles of tectonics and CO2 fertilization, Glob. Biogeochem. 1675–1686, 2009. Cycles, 23, GB1009, doi:10.1029/2008GB003220, 2009. Fischer, A. G., Pelagic sediments as clues to Earth behavior, Memorie Lourens, L. J., A. Sluijs, D. Kroon, J. C. Zachos, E. Thomas, U. Rohl,¨ J. Della Societa Geologica Italianna, 15, 1–18, 1976. Bowles, and I. Raffi, Astronomical pacing of late Palaeocene to early Grippo, A., A. G. Fischer, L. A. Hinnov, T. D. Herbert, and I. Premoli Silva, Eocene global warming events, Nature, 435, 1083–1108, 2005. Cyclostratigraphy and chronology of the Albian stage (Piobbico core, Matsuda, T. and Y. Isozaki, Well-documented travel history of Mesozoic Italy), in Cyclostratigraphy: Approaches and Case Histories, edited pelagic chert in Japan: From remote ocean to subduction zone, Tecton- by B. D’Argenio, A. G. Fischer, I. Premoli Silva, H. Weissert, and V. ics, 10, 475–499, 1991. Ferreri, 57–81, Tulsa, SEPM Special Publication No. 81, 2004. Matsuoka, A., R. Hori, K. Kuwahara, M. Hiraishi, A. Yao, and Y. Ezaki, Grocke,¨ D. R., R. S. Hori, J. Trabucho-Alexandre, D. B. Kemp, and L. Triassic–Jurassic radiolarian-bearing sequences in the Mino Terrane, Schwark, An open marine record of the Toarcian oceanic anoxic event, Central Japan, Guide Book for Interrad VII Field Excursion, 19–61, Solid Earth, 2, 245–257, 2011. 1994. Guex, J., A. Bartolini, V. Atudorei, and D. Taylor, High-resolution am- Milankovitch, M., Canon of Insolation and the Ice-Age Problem. Belgrade: monite and carbon isotope stratigraphy across the Triassic–Jurassic Serbian Academy of Sciences and Arts, Special Publication 132, Sec- boundary at New York Canyon (Nevada), Earth Planet. Sci. Lett., 225, tion of Mathematical and Natural Sciences, 39 3/4, YU, 634 p., (1998 29–41, 2004. English Translation), 1941. Hays, J. D., J. Imbrie, and N. J. Shackleton, Variations in the Earth’s orbit: Nakaseko, K. and A. Nishimura, Upper Triassic Radiolaria from South- Pacemaker of the ice ages, Science, 194, 1121–1132, 1976. west Japan, Rep. Col. Gen. Educ. Osaka Univ., 28, 61–109, 1979. Hesselbo, S. P., S. A. Robinson, F. Surlyk, and S. Piasecki, Terrestrial Oda, H. and H. Suzuki, Paleomagnetism of Triassic and Jurassic red bed- and marine extinction at the Triassic–Jurassic boundary synchronized ded chert of the Inuyama area, central Japan, J. Geophys. Res., 105, with major carbon-cycle perturbation: A link to initiation of massive 743–767, 2000. volcanism?, Geology, 30, 251–254, 2002. Ogg, J. G., The Triassic period, in A Geologic Time Scale 2012, edited Hori, R., Lower Jurassic radiolarian zones of SW Japan, Trans. Proc. by F. M. Gradstein et al., p. 681–730, Cambridge University Press, Palaeont. Soc. Jpn., N.S., 159, 562–586, 1990. Cambridge, UK, 2012. Hori, R., Radiolarian biostratigraphy at the Triassic-Jurassic Period bound- Ogg, J. G. and L. A. Hinnov, Jurassic, in A Geologic Time Scale 2012, ary in bedded cherts from the Inuyama area, central Japan, J. Geosci. edited by F. M. Gradstein et al., p. 731–791, Cambridge University Osaka City Univ., 35, 53–65, 1992. Press, Cambridge, UK, 2012. Hori, S. R., The Toarcian radiolarian event in bedded cherts from south- Olsen, P. E. and D. V. Kent, Long period Milankovitch cycles from the western Japan, Mar. Micropaleontol., 30, 159–169, 1997. Late Triassic and Early Jurassic of eastern North America and their Hori, S. R., C. Cho, and H. Umeda, Origin of cyclicity in Triassic-Jurassic implications for the calibration of the early Mesozoic timescale and the radiolarian bedded cherts of the Mino accretionary complex from Japan, long-term behavior of the planets, Phil. Trans. R. Soc. London Ser. A, The Island Arc, 3, 170–180, 1993. 357, 1761–1786, 1999. Huang, C., S. P. Hesselbo, and L. A. Hinnov, Astrochronology of the Late Olsen, P. E., D. V. Kent, and H. Whiteside, Implications of the Newark Jurassic Kimmeridge Clay (Dorset, England) and implications for Earth Supergroup-based astrochronology and geomagnetic polarity time scale system processes, Earth Planet. Sci. Lett., 289, 242–255, 2010a. (Newark-APTS) for the tempo and mode of the early diversification of Huang, C., L. Hinnov, A. G. Fischer, A. Grippo, and T. Herbert, Astronom- the Dinosauria, Earth Environ. Sci. Trans. R. Soc. Edinburgh, 101, 201– ical tuning of the Aptian Stage from Italian reference sections, Geology, 229, 2011. 38, 899–902, 2010b. Palike,¨ H., J. Laskar, and N. J. Shackleton, Geologic constraints on the Huang, C., J. Tong, L. Hinnov, and Z. Chen, Did the great dying of life take chaotic diffusion of the Solar System, Geology, 32, 929–932, 2004. 700 k.y.? Evidence from global astronomical correlation of the Permian- Palike,¨ H., R. D. Norris, J. O. Herrle, P. A. Wilson, H. K. Coxall, C. H. Triassic boundary interval, Geology, 39, 779–782, 2011. Lear, N. J. Shackleton, A. K. Tripati, and B. S. Wade, The heartbeat of Husing,¨ S. K., M. H. Deenen, J. G. Koopmans, and W. Krijgsman, Magne- the Oligocene climate system, Science, 314, 1894–1898, 2006. tostratigraphic dating of the proposed Rhaetian GSSP at Steinbergkogel Ruhl, M., M. L. Deenen, H. A. Abels, N. R. Bonis, W. Krijgsman, and (Upper Triassic, Austria): Implications for the Late Triassic time scale, W. M. Kurschner,¨ Astronomical constraints on the duration of the early Earth Planet. Sci. Lett., 302, 203–216, 2011. Jurassic Hettangian stage and recovery rates following the end-Triassic Huybers, P. and T. Wunsch, Rectification and precession-period mass extinction (St Audrie’s Bay/East Quantoxhead, UK), Earth Planet. signals in the climate system, Geophys. Res. Lett., 30, 19, Sci. Lett., 295, 262–276, 2010. doi:10.1029/2003GL017875, 2003. Schoene, B., J. Guex, A. Bartolini, U. Schaltegger, and T. Blackburn, Ikeda, M., R. Tada, and H. Sakuma, Astronomical cycle origin of bedded Correlating the end-Triassic mass extinction and flood basalt volcanism chert; middle Triassic bedded chert sequence, Inuyama, Japan, Earth at the 100000-year level, Geology, 38, 387–390, 2010. Planet. Sci. Lett., 297, 369–378, 2010a. Shibuya, H. and S. Sasajima, Paleomagnetism of red cherts: A case study Ikeda, M., R. Tada, A. Karasuda, and H. Sakuma, Long period Astronom- in the Inuyama area, central Japan, J. Geophys. Res., 91, 105–116, 1986. ical Cycles from the Upper Triassic to Lower Jurassic Bedded Chert se- Standish, E. M., JPL Planetary and Lunar Ephemerides, DE405/LE405. Jet quence: Implications for Jurassic Cyclostratigraphy, Earth Sci. Front., Propulsion Laboratory, Interoffice Memorandum, IOM, 312, F–98–048, 17, 112–113, 2010b. 1998. Imbrie, J., A. Berger, E. A. Boyle, S. C. Clemens, and A. Duffy, On the Stockwell, R. G., L. Mansinha, and R. P. Lowem, Localization of the structure and origin of major glaciation cycles: 2. The 100,000-year Complex Spectrum: The S Transform, IEEE Transactions on Signal cycle, Paleoceanography, 8, 699–735, 1993. Processing, 44, 998–1001, 1996. Kimura, K. and R. Hori, Offscraping accretion of Jurassic chert-clastic Sugiyama, K., Triassic and Lower Jurassic radiolarian biostratigraphy in complexes in the Mino-Tamba Belt, cental Japan, J. Struct. Geo1., 15, the siliceous claystone and bedded chert units of the southeastern Mino 145–161, 1993. Terrane, Central Japan, Bull. Mizunami Fossil Mus., 24, 79–193, 1997. Laskar, J., The chaotic motion of the solar-system—A numerical estimate Tipper, H. W. and J. Guex, Preliminary Remarks on the Hettangian Am- of the size of the chaotic zone, Icarus, 88, 266–291, 1990. monite Succession in Queen Charlotte Islands, British Columbia, in Laskar, J., F. Joutel, and F. Boudin, Orbital, precessional and insolation 3rd International Symposium on Jurassic Stratigraphy, Poitiers, France, quantities for the Earth from −20 Myr to 10 Myr, Astron. Astrophys., 1991, edited by E. Cariou and P. Hantzperque, Geobios, Memoire´ 270, 522–533, 1993. Special,´ 17, 477–483, 1994. Laskar, J., P. Robutel, F. Joutel, M. Gastineau, A. C. M. Correia, and B. Torrence, C. and G. P. Compo, A practical guide to wavelet analysis, Bull. Levrard, A long term numerical solution for the insolation quantities of Am. Meteor. Soc., 79, 61–78, 1998. the Earth, Astron. Astrophys., 428, 261–285, 2004. Treguer,´ P., Silica and the cycle of carbon in the ocean, C. R. Geosci., 334, Laskar, J., A. Fienga, M. Gastineau, and H. Manche, La2010: A new or- 3–11, 2002. bital solution for the long term motion of the Earth, Astron. Astrophys., Treguer,´ P., D. M. Nelson, A. J. Vanbennekom, D. J. DeMaster, A. Ley- 532, A89, doi:10.1051/0004-6361/201116836, 2011a. naert, and B. Queguiner, The silica balance in the world ocean: A rees- Laskar, J., M. Gastineau, J.-B. Delisle, A. Farres,´ and A. Fienga, Strong timate, Science, 268, 375–379, 1995. 360 M. IKEDA AND R. TADA: CHAOTIC EVOLUTION OF ASTRONOMICAL CYCLE FROM TRIASSIC-JURASSIC BEDDED CHERT van Dam, J. A., A. H. Abdul, A. S. Angeles, F. J. Hilgen, H. O. van Den, L. Doniford Bay section, Somerset, England: Updated proposal for a can- J. Louren, P. Mein, A. J. van Der Meulen, and P. Pelaez-Campomanes, didate Global Stratotype Section and Point for the base of the Hettan- Long-period astronomical forcing of mammal turnover, Nature, 443, gian Stage, and of the Jurassic System, International Subcommission on 687–691, 2006. Jurassic Stratigraphy Newsletter, 35, 2–66, 2008. Wakita, K., Origin of chaotically mixed rock bodies in the Early Jurassic Williford, K. H., P. D. Ward, G. H. Garrison, and R. Buick, An extended to Early Cretaceous sedimentary complex of the Mino Terrane, central organic carbon-isotope record across the Triassic–Jurassic boundary in Japan, Bull. Geol. Surv. Jpn., 39, 675–757, 1988. the Queen Charlotte Islands, British Columbia, Canada, Palaeogeogr. Ward, P. D., J. W. Haggart, E. S. Carter, D. Wilbur, H. W. Tipper, and Palaeoclim. Palaeoecol., 244, 290–296, 2007. T. Evans, Sudden productivity collapse associated with the Triassic– Yao, A., T. Matsuda, and Y. Isozaki, Triassic and Jurassic radiolarians from Jurassic boundary mass extinction, Science, 292, 1148–1151, 2001. the Inuyma area, central Japan, J. Geosci. Osaka City Univ., 23, 135– Ward, P. D., G. H. Garrison, J. W. Haggart, D. A. Kring, and M. J. Beattie, 154, 1980. Isotopic evidence bearing on Late Triassic extinction events, Queen Zachos, J. C., M. Pagani, L. Sloan, E. Thomas, and K. Billups, Trends, Charlotte Islands, British Columbia, and implications for the duration rhythms, aberrations in global climate 65Ma to present, Science, 292, and cause of the Triassic/Jurassic mass extinction, Earth Planet. Sci. 686–693, 2001. Lett., 224, 589–600, 2004. Zachos, J. C., G. R. Dickens, and R. E. Zeebe, An early Cenozoic perspec- Ward, P. D., G. H. Garrison, K. H. Williford, D. Kring, D. Goodwin, M. tive on greenhouse warming and carbon-cycle dynamics, Nature, 451, Beattie, and C. McRoberts, The organic carbon isotopic and paleon- 279–283, 2008. tological record across the Triassic–Jurassic boundary at the candidate GSSP section at Ferguson Hill, Muller Canyon, Nevada, USA, Palaeo- geogr. Palaeoclim. Palaeoecol., 244, 279–287, 2007. M. Ikeda (e-mail: [email protected]) and R. Tada Warrington, G., C. W. Cope, and H. C. Ivimey-Cook, The St Audrie’s Bay-