Article

Volume 12, Number 9

8 September 2011

Q09003, doi:10.1029/2011GC003602

ISSN: 1525‐2027

Spectral analysis and modeling of microcyclostratigraphyin late Paleozoic glaciogenic rhythmites, Paraná Basin,Brazil

Daniel R. FrancoDepartment of Geophysics, National Observatory, R. Gal. José Cristino, 77, 20921‐400 Rio deJaneiro, Brazil (drfranco@on.br)

Linda A. HinnovDepartment of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, Maryland 21218,USA

Marcia ErnestoDepartment of Geophysics, University of São Paulo, 05508‐900 São Paulo, Brazil

[1] We investigate the depositional time scale of lithological couplets (fine sandstone/siltstone–siltstone/mudstone) from two distinctive outcrops of Permo‐Carboniferous glacial rhythmites in the Itararé Group(Paraná Basin, Brazil). Resolving the fundamental issue of time scale for these rhythmites is importantin light of recent evidence for paleosecular variation measured in these sequences. Spectral analysis andtuning of high‐resolution gray scale scans of sediment core microstratigraphy, which comprises pervasivelaminations, reveal a comparable spectral content at both localities, with a frequency suite interpreted asthat of short‐term climate variability of Recent and modern times. This evidence for decadal‐ to centennial‐scale deposition of these lithological couplets is discussed in light of the ‘varvic’ character, i.e., annual timescale that was previously assumed for the rhythmites.

Components: 8600 words, 5 figures.

Keywords: Itararé Group; Paraná Basin; Brazil; Permo‐Carboniferous; glacial rhythmites; laminated sediment.

Index Terms: 1861 Hydrology: Sedimentation (4863); 3255 Mathematical Geophysics: Spectral analysis (3205, 3280,4319); 9614 Information Related to Geologic Time: Paleozoic.

Received 2 March 2011; Revised 8 July 2011; Accepted 12 July 2011; Published 8 September 2011.

Franco, D. R., L. A. Hinnov, and M. Ernesto (2011), Spectral analysis and modeling of microcyclostratigraphy in latePaleozoic glaciogenic rhythmites, Paraná Basin, Brazil, Geochem. Geophys. Geosyst., 12, Q09003,doi:10.1029/2011GC003602.

1. Introduction

[2] Climate changes during the Late Quaternaryicehouse appear to have been episodic and evenabrupt, reflecting a highly nonlinear interplayamong different climate system components [e.g.,Alley et al., 1999; Broecker, 2000; Alley et al., 2003;

Rial, 2004]. Multiple environmental proxies haveindicated millennial‐scale variability as major con-tributors for these changes [e.g., Alley et al., 1999,2003;Marchant and Hooghiemstra, 2004;Clemens,2005; Flückiger et al., 2006]. Is it possible thatsimilar millennial‐scale harmonic patterns occurredthroughout geological time as a prevalent feature of

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the climate system? To address this question, itis necessary to carry out investigations on high‐resolution paleoclimatic data sets with broad spatialand time scale coverage from representative timeslices throughout Earth history.

[3] In this context, the occurrence of undisturbedlate Paleozoic laminated rocks, which crop out in theItararé Group (IG, Paraná Basin, Brazil; Figure 1),have been targeted as an important archive ofGondwanan glacial climate. These laminated rocks,

Figure 1. (a) Location and distribution of stratigraphic supersequences in the Paraná Basin, southeastern Brazil. TheItararé Group is classified as a Gondwana I Supersequence. Locations of the Itu and Rio do Sul quarries are also indi-cated; the S‐SE to N‐NW line refers to the cross section depicted in Figure 1b. Modified after Souza et al. [2006],Milani [1997], and Souza and Marques‐Toigo [2003]. (b) Stratigraphy of the Paraná Basin Gondwana I Super-sequence. Period boundary ages are as follows: Mississippian‐Pennsylvanian, 322.8 Ma [Davydov et al., 2010];Pennsylvanian‐Permian, 298.7 Ma [Ramezani et al., 2007], and Permian‐Triassic, 252.16 Ma [Shen et al., 2010;Huang et al., 2011]. The cross section (see map in Figure 1a) is redrawn from Souza et al. [2006] and Souza [2006](copyright 2006, with permission from Elsevier) shows the time‐space distribution of basinal formations; theapproximate stratigraphic positions of the Itu and Rio do Sul study sites are indicated, based on palynostratigraphy[Souza et al., 2010]. The depositional environment interpretation is from Eyles et al. [1993] and Souza et al. [2006].

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or “rhythmites,” consist of, from fine to coarse,stratified mudstone, siltstone and sandstones, [Settiand Rocha‐Campos, 1999] with centimeter‐scalesandstone/siltstone and siltstone/mudstone alterna-tions forming lithological pairs or couplets withsome regularity (Figure 2). Early sedimentologicaland palynological interpretations [Leinz, 1937;Rocha‐Campos, 1967;Rocha‐Campos and Sundaram, 1981;Rocha‐Campos et al., 1981] noted a similarity of thesuccessions with Pleistocene varvic clays, althoughthe unusual thickness of the couplets (up to 500 mm)requiring extraordinarily fast deposition rates, alwayscaused some skepticism in the geological community[e.g., Eyles, 1993].

[4] In their detailed study of the Itu exposure basedon petrography andmacroscopic features of the lightlayers Caetano‐Chang and Ferreira [2006] rejectedthe varve designation for the Itu rhythmic sequence.They argued that the rhythmites constitute relativelydistal portions of subaquatic fans influenced byunderflow during periods of great ice melting, anddecantation during winter. The shale laminae thatcover the silt layers formed sporadically when moresevere winters occurred or when the glacier wascloser, in nonannually paced variable time intervals.These authors counted up to tens of massive orgraded (coarse or fine silt) laminae within centi-metric or decimetric layers. Normally the laminationis parallel, but in thicker layers cross lamination ispresent, indicating flow energy variations.

Figure 2. Stratigraphy and sedimentology of the target Permo‐Carboniferous rhythmites. (top left) On‐location fieldphoto at Itu Quarry of the Itu rhythmites (Late Carboniferous) showing lithologic couplet stratification. Note pro-nounced cross stratified bedding at bottom left. (top right) Stratigraphic progression and sedimentary structures. Addi-tional photos are available from Eyles et al. [1993, Figures 16 and 17], in photos 14–17 of Gama et al. [1992b], andfrom Rocha‐Campos [2002]. (bottom left) On‐location field photo at Itau Quarry of the Rio dol Sul rhythmites (earlyPermian). The first author, D. Franco (height: 180 cm), is pictured for scale. (bottom right) Stratigraphic progressionand sedimentary structures.

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[5] Based on the old assumption that each coupletcorresponded to one year of sedimentation Ernestoand Pacca [1981] performed spectral analysis of thecouplet thickness sequence and found periodicities of∼11 and ∼22 units (interpreted in terms of years by theauthors), as well as longer cycles. D. R. Franco et al.(Magnetostratigraphy and mid‐paleolatitude VGPdispersion during the Permo‐Carboniferous Super-chron: Results from late Paleozoic rhythmites (ParanáBasin, Brazil), submitted to Geophysical JournalInternational, 2011) have investigated the paleomag-netic variation within each couplet (sliced into speci-mens of ∼2 cm thickness) in the same IG rhythmitesequences investigated here. The results indicatehomogenous magnetic declination/inclination withincouplets but large variations (∼20°–50° in declination)between adjacent lithological couplets suggestive ofsignificant missing time between couplets. In moderntimes, this magnitude of change is associated withcentennial time scales [e.g., Courtillot and Le Mouël,1988]. Additionally, the paleomagnetic data have adistribution indicative of a well‐sampled, full secularvariation pattern, which implies that elapsed timesbetween couplets might be of the order of somethousands of years. The calculated paleomagnetic poleis in good agreement with the established Paleozoicapparent polar wander path. Therefore, the paleo-magnetic data corroborate the recent reinterpretationfor a nonvarvic character for the IG rhythmites.

[6] Using cyclostratigraphic techniques Silva andAzambuja Filho [2005] investigated glacial sedi-ments of the Itararé Group from a borehole nearAnitápolis, Santa Catarina state, about 100 kmsoutheast fromRio do Sul (Figure 1). The Anitápolissection (Core 7‐RL‐04‐SC) exhibits 0.1–1.1 mthick silt beds alternating with 0.1–0.2 m thick shalelayers with abrupt contacts. The authors concludedthat the cyclic sedimentation was influenced byastronomical forcing and other, millennial‐scalephenomena, indicating accumulation rates of 7.5 to8.4 cm/kyr for the section. Silva and Azambuja Filho[2005] also investigated two smaller intervals withinthe section at ultrahigh resolution using gray scalescans: (1) 526.70–525.89 m; (2) 525.87–525.47 m.They documented variations interpreted as decadalsolar cycles (Schwabe and Hale cycles) and otherquasiperiodicities related to solar activity, includingGleissberg and King Hele/Seuss cycles. They alsoreported other centennial to millennial periodicitiesat 280 yr and 650–1000 yr.

[7] These studies support a much slower sedimenta-tion rate than those assumed for decadal scale phe-nomena interpreted in earlier studies of Itararé

rhythmites [Ernesto andPacca, 1981;Rocha‐Camposet al., 1981]. If this is true it is possible that short‐period cyclic processes compatible with well‐knownenvironmental mechanisms are embedded within thelithological couplets. To investigate this we per-formed high‐resolution analysis of the laminationswithin individual rhythmite couplets using gray scalescans in a manner similar to the procedures of Archer[1994] and Silva and Azambuja Filho [2005]. Weconsider two hypotheses to explain the laminationsand their stratigraphic patterns, in an attempt to decideon the precise timing of the couplets (annual or cen-tennial‐millennial), and to identify the periodicities ofthe couplet variations.

2. Geological Setting and StratigraphicFramework

[8] The studied successions of glaciogenic rhyth-mites are from the eastern outcropping belt andsouthern portion of the Permo‐Carboniferous ItararéGroup (IG), Paraná Basin, Brazil (Figure 1a). Thesediments occur within the Gondwana I Super-sequence recorded in Gondwanaland during the latePaleozoic [Rocha‐Campos et al., 1997;Ferreira, 1997;Milani and Zalán, 1999;Weinschütz and Castro, 2004;Souza, 2006; Vesely and Assine, 2006]. The IGformed in glaciolacustrine and/or brackish waterpaleoenvironmental settings, within an upwardlyincreasing marine influence and increasing faciesdiversity [Gama et al., 1992a, 1992b; Eyles et al.,1993]. Facies indicate subaqueous gravity flows,resulting in high sedimentation rates and proximity tosteep, fault‐bounded basinmargins [Eyles et al., 1993].These aspects, as well as another glaciotectonic fea-tures, e.g., roche moutonnée, striated surfaces, dia-mictites, and regular rhythmites with dropstones,support the hypothesis for an record of ice masses,provided by a large south African ice sheet, advancingfrom SE to NW into the Paraná Basin [Rocha‐Campos, 1967; França and Potter, 1991; Eyleset al., 1993; Santos et al., 1996; Rocha‐Camposet al., 2000; Vesely and Assine, 2002; Gesicki et al.,2002; Archanjo et al., 2006].

[9] Setti and Rocha‐Campos [1999] undertook adetailed facies description of the rhythmites, sug-gesting that they were deposited in a glacialregime, and were seasonally controlled. Decliningthicknesses of the couplets up section, along withdecreasing grain size, was suggestive of glacierretreat. Santos et al. [1996] concluded that the IGdeposits formed in a restricted marine environment,strongly influenced by meltwater sources.

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[10] The ages of these rhythmites have historicallypresented a challenge. Souza et al. [2010] providethe most recent chronostratigraphy from detailedpalynostratigraphic analysis of drill cores and quarryrocks (Figure 1b). The Itu rhythmites have palyno-floras from the Crucisaccites monoletus IntervalZone, which correlates to the Late PennsylvanianKasimovian‐Gzhelian stages. The Rio do Sulrhythmites are younger, with palynofloras from theVittatina costabilis Interval Zone, corresponding tothe Early Permian Asselian‐Sakmarian stages.

[11] Rocha‐Campos et al. [2006] reported a U‐PbSHRIMP age of 298.5 ± 2.6 Ma in the Rio BonitoFormation (above the IG), which is very close to themost recent Carboniferous‐Permian boundary ageof 298.9 + 0.3/ −0.15 Ma [Ramezani et al., 2007],and in good agreement with U‐Pb SHRIMP dating(302.0 ± 3.0 and 299.2 ± 3.2 Ma) for the KarooSupergroup, southern Africa [Bangert et al., 1999].In the lower IG, a U‐Pb SHRIMP age of 323.0 ±15.0 Ma has been measured for the youngest detritalzircon ever found in the IG, indicating that the IGcannot be older than Late Mississippian (A. Rocha‐Campos, personal communication, 2010).

3. Sedimentology of the Study Sites

3.1. Itu Rhythmites

[12] Itu (IT) Quarry (23° 16′S; 47° 19′W), in thecity of Itu (state of São Paulo), is preserved as ageological park (“Varvite Park”), and is the bestknown glacial rhythmite exposure inBrazil (Figure 2,top). Here the rhythmites occur in a ∼15 m thicksuccession, with approximately 260 lithologicalpairs or couplets [Sinito et al., 1981; Ernesto andPacca, 1981], each one consisting of a basal,thicker (cm‐dm), light‐colored layer of fine sand-stone/siltstone, coupled with an overlying dark thinlayer/lamina (mm) of siltstone/mudstone. There isan upward trend of declining thickness and granu-lometry in the couplets, mainly due to changes in thelight layers (from ∼20 cm to 50 cm at the bottom to∼1.5 cm at the top); the thickness of the dark layers/laminae is almost constant along the entire sequence(∼5mm). There are sharp contacts between couplets,and abrupt but transitional contacts between lightand dark layers within couplets [Rocha‐Camposet al., 1981; Setti and Rocha‐Campos, 1999].

[13] Sedimentary structures in light layers includeboth flat and cross lamination, climbing ripple crosslamination, and an abundance of normally gradedsubmillimeter‐scale laminae. Clasts (mm‐dm) com-

posed of granite or quartzite occur as dropstoneswithin the sequence [Rocha‐Campos and Sundaram,1981; Gama et al., 1992a, 1992b; Ferreira, 1997;Setti and Rocha‐Campos, 1999]. The light layersconsist of quartz silt (80–100%), mica (<10%), andtrace amounts of feldspar and rock fragments, and arecemented mainly by quartz; the dark shale layerscontain chlorite, illite and orthoclase [Caetano‐Chang and Ferreira, 2006].

[14] Noteworthy is the presence of ichnofossils,produced by benthonic invertebrates on beddingplanes, especially on the tops of dark layers. At IT,Fernandes et al. [1987] identified two ichnogenera(Isopodichus and Diplichnites, representing arthro-pod tracks), closely related to ichnofossils found inthe Permo‐Carboniferous Karoo Basin (DwykaGroup, South Africa) [Carvalho and Fernandes,1989].

[15] Setti and Rocha‐Campos [1999] proposed aseasonally controlled glacial depositional model forthe Itu rhythmites, based on the observed facies andother associated rocks close to the IT exposure. Intheir model, the eastern margin of the original basinhad a sizable water body, in a bay or indentation‐like setting, open toward the NW direction. Sedi-mentary structures indicate paleocurrents indicatingflow to from SSE to NNW [e.g., Vesely and Assine,2004, 2006; Gesicki et al., 2002]. Detailed studiesof other areas [Santos et al., 1996] report thatdeposition of rhythmites along the eastern edge ofthe basin occurred in a restrictive marine environ-ment, in response to thawing and glacier removalas the supercontinent drifted away from the polarregion. The distribution of sediments in the basinwas influenced by current activity under seasonalcontrol, and eventually and secondarily, by tur-bidity flows. Progressive glacier retreat from the Itudepocenter is suggested by thinning‐upward bed-ding thicknesses and granulometry reductiontoward the top of the sequence [Rocha‐Campos,2002] (see also Figure 2).

3.2. Rio do Sul Rhythmites

[16] The Rio do Sul (RS) rhythmites (27° 10′S;49° 35′W) are well exposed at Itaú Quarry nearthe city of Trombudo Central (state of Santa Catar-ina) (Figure 2, bottom). The outcrop is approxi-mately 9 m thick, with 127 lithological couplets[Rocha‐Campos et al., 1981], each composed of alight lamina/layer of siltstone overlain by a darklamina/layer (mudstone). The couplets range from1.2 cm–32.0 cm in thickness, mainly in the lightlamina/layers. As observed at Itu, the dark laminae

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have thicknesses around 2–9 mm along the entiresequence [Rocha‐Campos et al., 1981; Rocha‐Campos and Sundaram, 1981; Canuto, 1993]; thereare sharp contacts between couplets, and transi-tional contacts between light and dark layers withincouplets.

[17] There are two patterns of thickness variation inthe RS succession. In the lower two thirds of thesequence, there is an alternation of thicker strata(thickness greater than 9.5 cm) with the thinnestones (∼2 cm); there is an upward thickening trendin the top third of the succession. Rocha‐Camposand Sundaram [1981] and Rocha‐Campos et al.[1981] report sedimentary features related to thebed/laminae, including both normal and reverse‐graded laminae, cross lamination, clay partingswithin light bed/laminae, and normal grading andinclusions of fine sand partings in the dark laminae.There are also numerous lenses of chips or pelletsassociated with shallow furrows on bedding planes,and clasts (cm‐dm), ichnofossils and a diversepalynoflora [Canuto, 1993]. Recently, discoverieshave been made of arthropod tracks (Diplichnites,Umfolozia), trails (Cruziana, Diplopodichnus), rest-ing traces (Gluckstadtella,Rusophycus), and grazingtrails (Helminthoidichnites), interpreted as a brack-ish water assemblage [Buatois et al., 2006; Nettoet al., 2009]; the presence of marine plankton hasalso been reported [Buatois et al., 2010].

[18] Canuto [1993] suggested that the Rio do Sulrhythmites represent a proximal glaciomarine sys-tem with laterally connected fluviodeltaic fans.Eyles et al. [1993] interpreted a low‐energy depo-sitional setting, at some distance from major sedi-ment input points. Santos et al. [1992] pointed toclasts and spill deposits as evidence for a largemeltwater input. Buatois et al. [2006] report evolu-tion from a marine Glossifungites to brackish waterCruziana‐Skolithos ichnofacies in the Rio do Sulformation, thought to represent a deglaciation signal.

4. Data and Methods

[19] The absence of conclusive, high‐precisiongeochronology for these successions is a basicchallenge in this study. Previous work on theserhythmites was premised on a constraints‐freeassumption for the depositional time scale of thecouplets [e.g., Ernesto and Pacca, 1981; Rocha‐Campos et al., 1981]. Our strategy is also con-straints free, but is based the investigation of theharmonic features of fine‐scale laminations withinthe couplets through spectral analysis of gray scale

scanning data sets carried out from selected coresof representative couplets of both successions.

[20] We consider the following hypotheses: 1) thelithologic couplets are annual [e.g., Ernesto andPacca, 1981]; and 2) the laminations within cou-plets are annual (recently implied by new paleo-magnetic data (Franco et al., submitted manuscript,2011)). If Hypothesis 1 applies, it is reasonable tosuppose that the microlaminations within the cou-plets might express tidal cycles. For Hypothesis 2,patterns in intracouplet laminations could indicatedecadal‐ to centennial‐scale harmonic features anda climatic origin. There are other hypotheses, ofcourse, including the possibility that there are onlyrandom variations in lamination succession pattern.

[21] The procedures for assessment of ‘within‐couplet’ harmonic features are as follows. High‐resolution images of core cylinders were taken ofrepresentative lithological couplets (Figure 3a).This resulted, for the selected couplets, IT‐82 andRS‐89 (4.2 and 7.8 cm thick, respectively), strati-graphic resolutions of 95.26 and 17.71 pixels/mm,respectively. Software ImageJ version 1.41o forWindows (NIH, USA) was used for a pixel‐to‐grayscale conversion (values from 0 (white) to 255(black)), through a single‐pixel transect close to thecenter of each image. The “raw” gray scale dataseries (Figure 3b) were detrended by subtracting a30%weighted average (Lowess method [Cleveland,1979]).

[22] Individual laminae within the scan wereassumed to represent equal units of time, either 1 dayunits (Hypothesis 1), or 1 year units (Hypothesis 2).Thus, the greyscale scans were “tuned” to laminathicknesses (Figure 3c). The tuned series wereinterpolated (Figure 3d), and after a 30% weightedaverage estimation and removal (Figure 3e), 2pprolate multitaper spectral analysis was performed.The multitaper method is suitable for analysis ofshort, quasiperiodic time series typical in geology,providing robust power spectra by application oforthogonal tapers. Summed together, the orthogonaltapers provide a rectangular observation windowthat is proportional to the data length [Thomson,1982].

5. Results

[23] The tuned power spectra (Figure 3f) exhibit arich spectral content in couplet microstratigraphy,with elevated power at periods (in ‘units’) of 83.3,15.8, 22.4, 10.8, 6.9, 4.3, 3.8, and 1.0 (IT‐82;Figure 3f, left), and 97.1, 41.7, 23.3, 17.4, 9.7, 4.6,

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Figure 3. Schematic representation of technical procedures, to assess harmonic features through spectral analysis ofhigh‐resolution gray scale scans of core laminations. (a) High‐resolution (∼2000 dpi) gray scale images of cores fromrepresentative lithological couplets of (left) Itu and (right) Rio do Sul quarries. Orange lines are single‐pixel transectsfor the pixel‐to‐gray‐scale conversions (values between 0 (white) and 255 (black)). (b) Raw gray scale data series(blue lines) and associated smoothed curves (in red; 30% weighted average). (c) Tuning curves, unit to pixel no. alongthe series. (d) Tuned series after interpolation (blue lines) and associated smoothed curves (in red; 30% weighted aver-age). (e) Tuned series after removal of the weighted average. (f) Power spectra (2p multitapered) of the tuned series inFigure 3e.

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4.1, and 1.0 (RS‐89; Figure 3f, right). The clearlydefined unit peak at f = 1.0 cycles/unit is theconsequence of tuning each lamination to the(dimensionless) time increment of unity. Thisallows consideration of different hypothetical timescales for the laminations, and periodicitiesobserved in the spectra. For example, if unit =1 year, then all of the periods listed above corre-spond to years; if unit = 1 day, then the periodscorrespond to days.

[24] A notable aspect of these spectra is, besides thesharp peak at 1.00, the general absence of compa-rably sharp lines at frequencies that would indicatetidal forcing. For example, if the laminations reflectdiurnal tidal forcing (unit = 1 day), ideally spectralpeaks should occur at periods of 14.8 to 13.6 days(fortnightly) and 27.3 days (monthly); during theCarboniferous Period, these are predicted to beonly very slightly shorter than the present day[Archer and Johnson, 1997]. The stronger tideswould be represented by lighter, i.e., coarser lam-inae, and weaker tides by darker, finer‐grainedlaminae. If some (weaker) tides are systematicallynot recorded, both spectral peaks should migrate toshorter apparent periods. The IT spectrum hasspectral peaks at 15.8 (too long) and 22.4 (tooshort); likewise, the RS spectrum has spectral peaksat 17.2 (too long) and 23.3 (too short), and are notconsistent with expected tidal periods.

[25] In the tuned RS sequence from Units 1–185,i.e., above the distinctive “discontinuity” at Unit

186 (Figure 3d, right), there is a strong spectralcomponent with a period of 10 that is the solecomponent in the sequence over this interval(Figure 4). The significance of this as a possibletidal feature is discussed further below.

[26] In the tuned IT sequence, there is no compa-rable grouping of laminae. If the laminations areassumed to be semidiurnal (unit = 1/2 day), none ofthe spectral peaks in either rhythmite sequencewould qualify as tidal components.

[27] Alternatively, if the laminations reflect annual(seasonal) cycles (unit = 1 year), then the peaks inthe tuned IT and RS spectra have periods that arerecognizable as high‐frequency climate variations(see section 6 below).

6. Discussion

[28] The lack of an adequately resolved geochro-nology in these ∼300 Ma rhythmite sequencesrequires that we analyze other criteria, includingsedimentology, facies, paleontology and strati-graphic patterns, to infer rhythmite time scale.Below, we discuss the evidence supporting twoproposed hypotheses for rhythmite deposition.

6.1. Hypothesis 1: Diurnal‐ScaleLaminations and Annual‐Scale Couplets

[29] If the centimeter‐scale rhythmite couplets arevarves they represent annual (seasonal) cycles. This

Figure 4. Unusual nonrandom patterns in RS‐89 microcyclostratigraphy. (a) Original gray scale scan. (b) The 2pmultitaper power spectrum of the gray scale scan, following removal of a 30% weighted average. Labeled peaks indi-cate wavelength in pixel units. (c) Tuned gray‐scale scan (see Figure 3). Vertical gray lines indicate points of cor-relation; also highlighted are bundles of 10 laminae along the scan. (d) The 2p multitaper power spectrum of the tunedgray‐scale scan, following removal of a 30% weighted average. Labels are in ‘units’ (see text for further details).

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suggests that the laminations within the coupletsmay represent tidal cycles, i.e., diurnal (or evensemidiurnal) cycles. A tidal origin for the lamina-tions is a real possibility, since both rhythmitesequences were deposited in a marine environment.

[30] Tidewater glacial estuaries have been shown tohave tidally paced sediment deposition. Here wediscuss a modern example in coastal Alaska fromCowan et al. [1998], and a Miocene example incoastal Antarctica from Krissek et al. [2007]. InMuir Inlet, Alaska, deep water (241 m) depositionoccurs in a semidiurnal tidal regime with individual‘cyclopels’ of silt laminae draped by very thin mudlaminae. Upward, the mud laminae progressivelythicken and the intervening silt laminae becomeless noticeable over groups of 3 to 18, the groupsaveraging 3 cm in thickness, i.e., the fortnightlycycle. Deposition occurs as the result of suspensionsettling from shallow glacial meltwater plumesinfluenced by surface tidal currents [Cowan andPowell, 1990]. There is no deposition during thewinter season; only 8 fortnightly cycles are recor-ded each year during the meltwater season (May toAugust). There is no evidence for bioturbation orsignificant bottom currents. Similarly, depositedunder the ancestral Ross Ice Shelf, Antarctica,Miocene ‘cyclopsams’ recovered by the AntarcticDrilling Project consist of sharp‐based, very finesand laminae grading into silt laminae, in 2–5 cmthick groups of 6–10 laminae, marked by pro-gressively finer grained, thicker cyclopsams withingroups [Krissek et al., 2007]. There are isolatedlenses or thin beds of sand and granules, as well assmall dropstones, but no bioturbation.

[31] There are some similarities but many markeddifferences between these two tidalites and the IGrhythmites. In general, energy levels were muchhigher at IT compared to RS. The IT rhythmitesshow abundant evidence of current activity and bedload transport, with cross lamination and ripple driftcross lamination at numerous stratigraphic levels,especially in the lower half of the sequence, andeven slumping and large cross bedding (Figure 2)[Eyles et al., 1993]. At IT, laminae consist of quartzsiltites that grade normally upward and are drapedby thin clays [Caetano‐Chang and Ferreira, 2006];arthropod tracks are preserved on couplet beddingsurfaces. RS rhythmites with their arthropod tracks,trails resting traces, and grazing trials, are inter-preted as a brackish water assemblage [Netto et al.,2009; Buatois et al., 2010]. The presence of epi-fauna suggests relatively slow sedimentation rates,although not slow enough to rule out tidal deposi-tion. At RS, laminae grade normally, and there are

also instances of reverse grading [Rocha‐Camposet al., 1981]. This could indicate the presence ofunstable turbidity or bottom currents that redis-tributed sediment; however, in general, the RSenvironment was relatively quiet.

[32] The spectral analysis (Figure 3e) of IT and RSdoes not show pervasive, deterministic harmonicfeatures that would be expected from tidal forcing.However, RS‐89 has an unusual interval with asingle harmonic component with a period of 10 unitsin the upper part of the couplet (Figure 4). This couldbe evidence for a fortnightly tidal record (cf. themodern and Miocene tidalites with groupings of 3–18 and 6–10 discussed above). This laminationpattern develops a slightly “sawtoothed” aspectmarked by gradual increases toward lighter laminaethat are followed by sudden drops to darker laminae.The pattern is short lived, however, and cannot betraced to the older portion of the couplet below the“discontinuity” at Unit 186.

[33] An annual seasonal modulation should presentas a ∼380 day cycle, assuming a 23 h long Car-boniferous day [Wells et al., 2005]. If there isseasonal ice cover, there may not be depositionduring the winter season. The IT‐82 couplet con-tains 250 laminations; there are 460 laminations inRS‐89. Neither couplet appears to have a lamina-tion pattern indicating a seasonal component.Possibly the laminations are products of multiplemeltwater pulses that occur throughout the summerseason, delivering sediment up to several times aday. (In this case, the assumption that the lamina-tions represent equal units of time breaks down.) InRS‐89, near the end of the meltwater season, themeltwater pulses abate, revealing an underlyingtidal forcing (upper segment of RS‐89).

6.2. Hypothesis 2: Annual‐ScaleLaminations and Centennial‐Scale Couplets

[34] Assuming that laminations within couplets areannual, then the spectra in Figure 3f become recog-nizable as those reported for the modern instrumentalrecord [e.g., Mann and Park, 1999] and for paleo-climate proxies for the Holocene and Quaternary[e.g., Burns et al., 2002; Frisia et al., 2003]. Varia-tions in these records include 3–6 year cycles,ascribed to ENSO forcing, a quasi‐decadal (∼10 year)cycle phased with the Schwabe cycle [e.g., Keelingand Whorf, 1997]. (These climate records also havea strong red noise continuum [Pelletier, 1998;Huybers andCurry, 2006].) There are also 20–25 yearcycles, possibly the Hale cycle, and 80–90 yearcycles – the so‐called Gleissberg cycle.

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[35] It has been reported by some authors [e.g.,Braun et al., 2005] that the Gleissberg cycle isassociated with the ∼1.5 kyr Dansgaard‐Oeschger(DO) cycle, which has been responsible for abruptclimatic oscillations at a global scale during LateQuaternary times [Schulz et al., 1999; Bard, 2002;Hinnov et al., 2002; Schulz et al., 2004; Witt andSchumann, 2005; Ditlevsen et al., 2007]. Braunet al. [2005] suggested that the DO cycle could bea response from the superposition of the decadal‐ tocentennial‐scale 80–90 yr Gleissberg and ∼210 yrSuess solar cycles, approximately equal to primefactors of the DO cycle. Similarly, the ∼2.3–2.4 kyrHallstatt cycle, related to the long‐period modula-tion of heliomagnetic activity [e.g., Clilverd et al.,2003] has been discussed as possibly generated byamplitude modulation of the Gleissberg solar cycle[Usoskin and Mursula, 2003].

[36] The work of Silva and Azambuja Filho [2005]on an IG rhythmite sequence southwest of RS atAnitapolis (state of Santa Catarina) is consistentwith our results. A core from the 7‐RL‐04‐SCborehole samples 32 m of rhythmites. Two consec-utive portions (depths 526.70–525.89 m and525.87–525.47 m) were gray scale–scanned at0.2538 mm resolution. The complete scannedinterval (1.23 m) of 413 pairs of light gray silt/darkgray shale laminae was assigned a time scale of9108 years. This was based on an initial time cali-bration of meter‐scale cyclicity to the precessionindex, indicating that the 1.23 m interval representsapproximately 12,000 years. This time scale wasfurther adjusted upon high‐resolution analysis sug-gesting an apparent Hale cycle period (22 years) forthe individual laminations. This result accords withthe interpretation of the IT sequence by Caetano‐Chang and Ferreira [2006], but differs from aninterpretation of laminations as annual.

6.3. Paleomagnetic Constraintson Time Scale

[37] Franco et al. (submitted manuscript, 2011)present declination/inclination data sets from ChRMmeasurements on the IT and RS sequences; theseshow distinct “jumps” in declination of ∼20–50°between adjacent lithological couplets (Figure 5).This suggests that there is significant missing timebetween couplets. Within couplets, declinationvaries (smoothly) up to ±10°. Although changes ingeomagnetic declination are highly dependent onthe geographic location, present models (IGRF) ofthe geomagnetic field predict mean annual changesin declination of the order of only 0.5° per year

[Gubbins andHerrero‐Bervera, 2007]. The observedchanges of more than an order of magnitude largerthan 0.5° suggests that individual couplets mustrepresent substantial time, much longer than theannual scale that was originally envisioned (i.e., byHypothesis 1). Consequently, we assigned 0.5° as an“alarm level” in the evaluation of DD (Figure 5).

[38] The so‐called secular variation of the geomag-netic field covers a broad time scale, from years toseveral millennia, and affects both direction andintensity of the field. The drift of the Earth’s mag-netic poles is one of the characteristics of secularvariation, and may be described by the generalwestward drift plus a northward (southward) driftcomponent. The mean drift velocity is calculated tobe around 0.2° per year, reflecting in a declinationvariation of the order of few minutes per year,although velocities and directions are quite variable.Kuznetsov [2006] noticed an acceleration of northmagnetic pole toward the geographic pole in the lastfew decades. However, velocity of the south mag-netic pole decreased from 8 to 4 km/yr (∼0.04–0.08°/yr) during the time of instrumental observa-tions, illustrating the slow variation in declination.

7. Conclusions

[39] The Permo‐Carboniferous glacial rhythmitesequences of the Itararé Group (Paraná Basin, Brazil)consist of centimeter‐scale fine sandstone/siltstone tosiltstone/argillite couplets with pervasive internallaminations. These sequences have been targeted asexcellent candidates for providing information on thePermo‐Carboniferous paleopole, and for its record ofpaleoclimatic change (warming and glacial retreat)within theGondwana I Supersequence. The relativelystable depositional environments represented in therhythmites – especially for the RS outcrop – alsosuggest preservation of the paleosecular variationnear the start of the Kiaman Reversed Superchron.Understanding all of these elements in this remark-able sedimentary archive, however, requires knowl-edge of the time scale of the rhythmites, which thusfar has been impossible to resolve. The traditionalview has been that the centimeter‐scale coupletsrepresent annual varves, but recent work on thepaleosecular variation of the geomagnetic field(Franco et al., submitted manuscript, 2011), petrog-raphy and sedimententology [Caetano‐Chang andFerreira, 2006] and independent cyclostratigraphicanalysis of other IG rhythmites [Silva and AzambujaFilho, 2005] suggests that the couplets representmuch longer time scales.

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[40] We approached the time scale problem from theperspective of the highest frequencies recorded in therhythmites – the pervasive microcyclostratigraphywithin couplets. We considered two hypotheses:1) the couplets are annual; laminations are intraannual(diurnal); and 2) the laminations are annual; coupletsare interannual (decadal‐centennial). Building onsedimentologic considerations from previous work,we performed time series analysis on gray scale scansof lamination sequences within individual coupletsfrom Itu (IT; latest Carboniferous) and Rio do Sul(RS; earliest Permian). Both localities have paleon-tological evidence indicating brackish marine depo-sitional environments, i.e., a coastal glaciomarinesetting, possibly proglacial estuarine, with significantmeltwater sources. We also evaluate recent paleo-

magnetic measurements from both rhythmite sequen-ces. Results are as follows:

[41] 1. Tuning the laminations to “unity” distributesspectral power into similar frequency bands in IT‐82and RS‐89, corresponding to periods (in time“units”) of 3–4, 9.7–10.8, 15.8–17.2, and 22.4–23.3.Other longer periodicities are also present but notshared (41.7 and 97.1 in RS versus 83.3 in IT)(Figure 3). IT shows higher ambient noise in the lowfrequencies compared with RS. This may be due tothe higher energy depositional environment repre-sented by IT, compared with the relatively quietenvironment of RS.

[42] 2. Evidence in favor of Hypothesis 1 (coupletsare annual scale; laminations are diurnal scale) is

Figure 5. Variation in declination from ChRM data sets for Itu and Rio do Sul rhythmites. (a) Schematic represen-tation of the three approaches (for each approach, the top and bottom graphs are related to Itu and Rio do Sul data sets,respectively): (b) DD boundary, (c) DD “within‐site dispersion,” and (d) all DD values. The “alarm level” of 0.5°/yr(red lines) and average DD values (dashed lines) are also displayed. Red and black circles indicate DD values asso-ciated with estimated uncertainties (SDD ≈ 5°) which are above and at/below the 0.5°/yr alarm level, respectively.

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found in the upper portion of RS‐89, where lami-nations are strongly organized into upward light-ening groups of 10 (Figure 4). This pattern isreminiscent of tidally influenced sedimentation inmodern tidewater glacial estuaries, that recorddiurnal tidal “cyclopels” (or coarser “cyclospams”)bundled by the fortnightly tidal cycle. Ideally, thereshould be 14 diurnal cyclopels in these bundles, buttypically the weakest tidal cycles do not register intidalite sequences, and so there are often fewer than14. A similar 10:1 bundling pattern was recognizedin IG rhythmite laminations in the 7‐RL‐04‐SCborehole near Anitapolis (Santa Catarina) [Silvaand Azambuja Filho, 2005], but were interpretedmuch differently, as evidence for King Hele/Seusscycles.

[43] 3. Evidence in favor of Hypothesis 2 (lamina-tions are annual scale; couplets are centennial scale)is supported by recent magnetostratigraphic researchon both rhythmite sequences (Figure 5). Withincouplets, as well as for all DD values for the entiresuccessions, declination varies (smoothly) up to±10°. Today, annual declination changes are onthe order of 0.5°; if this applies to the Permo‐Carboniferous, then these observations imply a cou-plet time scale that is significantly longer than oneyear. If the laminations within couplets are annual,the couplets would be centennial scale. Additionally,large jumps in declination of ∼20–50° occur betweenadjacent couplets, suggesting significant missing (orcompressed) time between couplets. Finally, there isa lack of a sustained, strict periodicity in the lami-nations that would be required for a tidal origin(Hypothesis 1).

[44] 4. A third hypothesis should also be considered,namely, that the laminations within couplets are nei-ther diurnal nor annual, but represent randomly timedunits of deposition derived from glacial meltwaterpulses. There is some suggestion of this in RS‐89,where in the lower half of the couplet, the laminationpattern is quite complicated and therefore possiblyrandom in time, whereas in the upper half, a dominant10:1 bundling takes precedence to the exclusion of allother variation. Our interpretation of this change inpattern is that in the lower part of RS‐89, the lamina-tions could be products of randommeltwater events—possibly several per day –whereas in the upper part ofRS‐89, meltwater activity has diminished, and isinfluenced by underlying diurnal (tidal) forcing.

[45] The problem of time scales in rhythmites is notnew having arisen previously with regard to Pre-cambrian rhythmites [Williams and Gerard, 1990].The same issue applies here: do the rhythmite lami-

nations reflect solar climate or tidal forcing? In viewof all the results presented above, Hypothesis 2, i.e.,solar climate forcing, is favored, but not fullyresolved. In future work, the analysis presented herewill be integrated with studies of low frequency pat-terns presented in these rhythmites in a continuedeffort to understand the broadest frequency bandpossible of rhythmite variability, which may in turnhelp lead to the correct time calibration.

Acknowledgments

[46] The authors are grateful to Ricardo I. F. Trindade (Instituteof Astronomy, Geophysics and Atmospheric Sciences, Univer-sity of São Paulo, Brazil), Rob Coe and Xixi Zhao (Departmentof Earth and Planetary Sciences, University of California at SantaCruz), and Antônio Rocha‐Campos (Institute of Geosciences,University of São Paulo, Brazil) for valuable discussions andBruceMarsh (Department of Earth and Planetary Sciences, JohnsHopkins University, USA) for use of photographic equipment.This work was supported by Brazilian agencies FAPESP (grant02/06480‐0) and CAPES (grant 2603‐07‐1). Careful reviewsby Christopher Fielding (University of Nebraska) and AllenArcher (Kansas StateUniversity) greatly improved the readabilityand accuracy of the concepts presented in this paper.

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