Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Hist Geo Space Sci 13 39ndash69 2022httpsdoiorg105194hgss-13-39-2022copy Author(s) 2022 This work is distributed underthe Creative Commons Attribution 40 License

Cyclicity in Earth sciences quo vadis Essay on cycleconcepts in geological thinking and their historical

influence on stratigraphic practices

Daniel Galvatildeo Carnier Fragoso12 Matheus Kuchenbecker34 Antonio Jorge Campos Magalhatildees567Claiton Marlon Dos Santos Scherer2 Guilherme Pederneiras Raja Gabaglia1 and Andreacute Strasser8

1Petrobras Rio de Janeiro Brazil2Universidade Federal do Rio Grande do Sul Instituto de Geociecircncias Porto Alegre Brazil

3Universidade Federal dos Vales do Jequitinhonha e Mucuri Instituto de Ciecircncia e Tecnologia Centro deEstudos em Geociecircncias Laboratoacuterio de Estudos Tectocircnicos Diamantina Brazil

4Centro de Pesquisas Professor Manoel Teixeira da Costa Instituto de Geociecircncias Universidade Federal deMinas Gerais Belo Horizonte Brazil

5Instituto Dom Luiz (IDL) Faculdade de Ciecircncias Universidade de Lisboa Lisbon Portugal6Universidade Federal do Rio Grande do Norte Departamento de Geologia Programa de Poacutes-Graduaccedilatildeo em

Geodinacircmica e Geofiacutesica (PPGG-LAE) Natal Brazil7China-Brazil Joint Geoscience Research Center IGGCAS Beijing 100029 China

8Department of Geosciences Geology-Paleontology University of Fribourg Fribourg Switzerland

Correspondence Daniel Galvatildeo Carnier Fragoso (galgeogmailcom)

Received 22 November 2021 ndash Discussion started 17 December 2021Revised 25 February 2022 ndash Accepted 10 March 2022 ndash Published 1 April 2022

Abstract The archetype of a cycle has played an essential role in explaining observations of nature over thou-sands of years At present this perception significantly influences the worldview of modern societies includingseveral areas of science In the Earth sciences the concept of cyclicity offers simple analytical solutions in theface of complex events and their respective products in both time and space Current stratigraphic researchintegrates several methods to identify repetitive patterns in the stratigraphic record and to interpret oscillatorygeological processes This essay proposes a historical review of the cyclic conceptions from the earliest phases inthe Earth sciences to their subsequent evolution into current stratigraphic principles and practices contributingto identifying opportunities in integrating methodologies and developing future research mainly associated withquantitative approaches

1 Introduction

The word ldquocyclerdquo derives from the Greek term ldquoκψκλoσrdquoused to describe any circular body as well as any circularand perpetual movement of successive events or phenom-ena which keep returning to their original position positionsduring their dynamics Ancient Greeks described repetitivepatterns to characterize the organization of almost all knownprocesses This idea of uniformity and continuity has beeninfluenced by empirical observations of natural phenomena

like day and night changes in the moon phase and seasons(Nelson 1980)

From a historical perspective the cycle archetype is foundin several ancient traditions attested for instance in lithicmonuments such as Stonehenge built-in alignment with so-lar and lunar cycles (Hawkins 1963) and religious prac-tice regulated by the seasons and their astronomical mark-ers (Boutsikas and Ruggles 2011) Nowadays the cyclicityconception is widespread in many areas of knowledge TheItalian philosopher Giambattista Vico (1668ndash1744) for ex-ample introduced in the 18th century the cyclic idea of his-

Published by Copernicus Publications

40 D G C Fragoso et al Cyclicity in Earth sciences quo vadis

tory (Vaughan 1972) According to Vico societies developin a similar and repetitive pattern followed by phases of so-cial and political organizations going from insurrection toinevitable decline An exciting aspect of Vicorsquos vision is thatthe perpetual motion of history does not reproduce a per-fectly circular pattern but a spiral in each new cycle thatbegins there is a remnant of the cycle that has ended In thepresent century Puetz (2009) proposed the ldquoUnified CycleTheoryrdquo which seeks to demonstrate how cycles dominatethe universersquos structure influencing various aspects of lifeon Earth Through the predictability aspect of the cyclical ap-proach this author pursues definition of future turning pointsfor humanity

Explanations of sound tone and harmonics wereamong the first elements of modern physical sci-ence This early success in description and predic-tion of periodic astronomical events together withan understanding of periodicity related to vibra-tion in the production of sounds led scientists toseek periodicities elsewhere in the natural worldToday the list is extensive for phenomena in whichcycles have been studied It includes sunspot ac-tivity tides and ocean waves Earth tides musichuman speech tree-ring growth animal popula-tion changes brain waves heart rhythm chem-ical bonding forces climatic activity economicgrowth light and other electromagnetic wave phe-nomena and geological events (Preston and Hen-derson 1964 p 415)

Cycles rhythms oscillations pulsations repetitions orperiods are examples of terms frequently used in the geo-logical literature that reflect a profound influence of the con-ception of cyclicity in the Earth sciences Whether through ahistorical heritage or from the various discoveries made overtime examples are plentiful to demonstrate that the idea ofcycles is used to describe geological processes and productscontaining some characteristic repetitive patterns in the geo-logical record

Considering the overuse of cyclicity concepts Dott (1992)described them as a ldquopowerful opiaterdquo for geologists Thecriticism of the cyclic approach is that there is an innatepsychological appeal to simplicity provided by rhythmicallyrepetitive patterns that attempt to order randomness (egNagel 1961 Zeller 1964) It is a fact that in many casescycle concepts are vaguely used in the geological literaturewithout the commitment to defining order and periodicityThis is the case of the rock cycle a postulate that states thatthe rock record itself is a product of a fundamental cycle inwhich igneous sedimentary and metamorphic rocks are con-tinuously turned into one another (eg Gregor 1992) It is un-derstandable that in cases like this the concept of cyclicity isused as a device to didactically explain various complex andrepetitive processes that occur on the planet (eg Peloggia2018) However the current understanding of the processes

that integrate the Earth system theorizes the existence of pe-riodical processes at different timescales that emanate fromthe astronomical forces that make our planet interact withneighbouring celestial bodies (eg Hinnov 2018) and fromthe complex dynamics of the Earthrsquos interior (eg Mitchell etal 2019) In this way the occurrence of ldquotrue cyclesrdquo whichcorrespond to an orderly repetitive progression of events thatis unlikely to occur by chance is increasingly being demon-strated Many of these cycles leave a recognizable mark inthe geological record and their understanding is invaluablein the study of stratigraphic organization

Nature vibrates with rhythms climatic and dys-trophic those finding stratigraphic expressionranging in period from the rapid oscillation ofsurface waters recorded in ripple-marks to thoselong-deferred stirrings of the deep imprisoned ti-tans which have divided earth history into periodsand eras The flight of time is measured by theweaving of composite rhythms ndash day and nightcalm and storm summer and winter birth anddeath ndash such as these are sensed in the brief lifeof man But the career of the Earth recedes intoa remoteness against which these lesser cycles areas unavailing for the measurement of that abyss oftime as would be for human history the beating ofan insectrsquos wing We must seek out then the na-ture of those longer rhythms whose very existencewas unknown until man by the light of sciencesought to understand the Earth [] Sedimentationis controlled by them and the stratigraphic seriesconstitutes a record written on tablets of stone ofthese lesser and greater waves which have pulsedthrough geologic time (Barrell 1917 p 746)

Henceforward cycle concepts have been essential in pro-moting geological knowledge and constitute one of the pil-lars of stratigraphy (eg Schwarzacher 2000) Current strati-graphic research integrates several systematic methods toidentify and interpret repetitive units of the sedimentaryrecord (eg sequence stratigraphy and cyclostratigraphy) Inthis context comprehension of the origin and evolution of thecyclicity concepts in stratigraphy is quite relevant and oppor-tune The following synthesis reviews the main works thatuse these concepts to interpret geological processes and theirimprint in the stratigraphic record It goes from a historicalreview to the current state of the art in stratigraphic principlesand practices

2 Cyclicity of geological processes

Studies of cyclicity in geological processes commonly seekto find periodicities in data series and explain them interms of known natural phenomena (Preston and Hender-son 1964) The current demonstration of recurring global

Hist Geo Space Sci 13 39ndash69 2022 httpsdoiorg105194hgss-13-39-2022

D G C Fragoso et al Cyclicity in Earth sciences quo vadis 41

processes with regular periodicity illustrates the search forldquolonger rhythms whose very existence was unknown untilman by the light of science sought to understand the Earthrdquo(Barrell 1917 p 746) In a recent investigation into therecurrence and synchronicity of global geological eventsRampino et al (2021) determined the existence of an Earthpulsation The authors analysed 89 significant and well-dated geological events over the past 260 million years in-cluding marine and non-marine biological extinctions ma-jor oceanic anoxic events flood-basalt eruptions sea-levelfluctuations pulses of intraplate magmatism and times ofchanges in seafloor-spreading rates and plate reorganizationMoving-window analysis evidences the presence of 10 peaksor clusters in the number of events (Fig 1a) Between thesepeaks the number of events approaches zero Fourier analy-sis shows that the highest peak occurs at 275 Myr (99 con-fidence) with a secondary signal at 89 Myr (Fig 1b) Sim-ilar cycles have been determined in other studies analysingclimate change (eg Shaviv et al 2014) sea-level oscilla-tions (eg Boulila et al 2018) extinctions (eg Clube andNapier 1996) and Earthrsquos tectonic behaviour (eg Muumlllerand Dutkiewicz 2018) The common finding of several au-thors is that these cyclical events are global correlative andtightly coupled According to Rampino et al (2021 p 6)the correlation and cyclicity of these episodes point to an es-sentially periodic and coordinated geological record whoseorigin ldquomay be entirely a function of global internal Earth dy-namics affecting global tectonics and climate but similar cy-cles in the Earthrsquos orbit in the Solar System and in the Galaxymight be pacing these eventsrdquo

21 The astronomical clock

Periodicity is one of the fundamental phenomenarecorded by observant man Cycles associated withastronomical events were among the first naturalphenomena described with sufficient precision andgenerality that such events could be predicted forthe future Even for primitive societies one mea-sure of their level of scientific understanding is theaccuracy of their calendars (Preston and Hender-son 1964 p 415)

The roots of the geologistsrsquo appeal for the periodicity ofnatural processes may be found in the Aristotelian world-view which expanded the human experiences of the cyclicphenomena such as day and night tides and seasons (Dott1992) In one of the first essays about the history of geol-ogy the classic book Principles of Geology by Charles Lyell(1797ndash1875) mentions this possible relationship

When we consider the acquaintance displayed byAristotle in his various works with the destroy-ing and renovating powers of nature the introduc-tory and concluding passages of the twelfth chap-ter of his ldquoMeteoricsrdquo are certainly very remark-

able In the first sentence he says ldquothe distribu-tion of land and sea in particular regions does notendure throughout all time but it becomes sea inthose parts where it was land and again it becomesland where it was sea and there is a reason forthinking that these changes take place accordingto a certain system and within a certain periodrdquoThe concluding observation is as follows ldquoAs timenever fails and the Universe is eternal neither theTanais nor the Nile can have flowed forever Theplaces where they rise were once dry and there is alimit to their operations but there is none to timeSo also of all other rivers they spring up and theyperish and the sea also continually deserts somelands and invades others The same tracts there-fore of the Earth are not some always sea and oth-ers always continents but everything changes inthe course of timerdquo It seems then that the Greeks[] deduced from their own observations the the-ory of periodical revolutions in the inorganic world(Lyell 1835 pp 21ndash22)

Lyell (1835) discusses the intellectual advance of ancientcivilizations such as the Hindus and the Egyptians and high-lights mainly Greek philosophy that considered the course ofevents on the planet to be continually repeated in perpetualvicissitude mainly influenced by the knowledge of astron-omy The various Greek contributions to scientific knowl-edge reflect a strong sense of observation of astronomi-cal cycles Among the many examples the studies of ce-lestial phenomena and their potential for temporal calibra-tions stand out Hipparchus of Nicaea (190ndash120 BC) con-sidered by many to be the greatest of Greek astronomersused mathematical bases to determine the length of the yearand the recurrence of eclipses with relatively high precisionCredit must be given to his conclusions about the motion ofthe stars which Nicolaus Copernicus (1473ndash1543) later at-tributed to the ldquoprecession of the equinoxesrdquo (Hockey et al2007) Twenty centuries later these concepts would guide theresearch on orbital cyclicity used to construct paleoclimaticcyclostratigraphic and astrochronological models (eg Hin-nov 2018)

211 The beginning of glacial theories

The discovery of glacial cycles is among the greatest evermade in the Earth sciences In 1837 Louis Agassiz (1807ndash1873) then president of the Swiss Society of Natural Sci-ences presented ideas that shocked his peers (Imbrie andImbrie 1979) Agassiz (1840) argued that large fragmentsof rock which occurred erratically in the region of the Juramountains far from their areas of origin were evidence ofan ancient ice age Although these ideas were not neces-sarily original having been put forward in the 18th centuryby James Hutton (1729ndash1797) and Bernard Friederich Kuhn

httpsdoiorg105194hgss-13-39-2022 Hist Geo Space Sci 13 39ndash69 2022

Figure 1 (a) Analysis of the ages of 89 geologic events using a 10 Myr moving window centred every 05 Myr with the number of occur-rences that fall within the moving window computed at 1 Myr intervals Ten clusters (peaks) are visible In red is the Gaussian smoothingwith a standard deviation of 5 Myr centred at every 01 Myr with 10 peaks (b) Fourier transform results show the highest peak in 275 Myrand a strong secondary period occurs at 89 Myr (modified from Rampino et al 2021)

(1762ndash1825) Agassiz brought ldquothe glacial theory of scien-tific obscurity to the public eyerdquo (Imbrie and Imbrie 1979p 21)

Although the conception of an ice age was fundamen-tally as being catastrophic its development took place onfertile ground for ideas of the cyclical nature of geologicalprocesses Before Agassizrsquos work one of the pioneers wasJens Esmark (1762ndash1839) Esmark (1824) showed that mas-sive glaciers covered different parts of Europe sculpting thelandscape and proposed the eccentricity of the Earthrsquos or-bit as a hypothesis that caused climate change Influenced byWilliam Whistonrsquos (1667ndash1752) contributions about the el-liptical orbit which would periodically place Earth far fromthe Sun Esmark combined these findings into a consistenttheory (Hestmark 2017) The dissemination of such ideasfostered the scientific debate that continues to the presentday Research into the relationship between recurrent glacia-tions and orbital cycles advanced significantly with the con-tributions of Joseph Alphonse Adheacutemar (1797ndash1862) andJames Croll (1821ndash1890)

Adheacutemar (1842) sought to explain glaciations by reinforc-ing the hypothesis of orbital controls especially the preces-sion of the equinoxes In his book Les Reacutevolutions de la MerDeacuteluges Peacuteriodiques he argues that the glacial periods alter-nated between the hemispheres with two glaciations ndash oneto the north and one to the south ndash every 23 kyr Anticipat-ing what is now known as thermohaline circulation he in-troduced the effects of large-scale ocean currents which linkthe planetrsquos South Pole and North Pole to explain the phe-nomenon of melting ice (Berger 2012)

James Crollrsquos works stood out for defending the astronom-ical theory of glacial periods based on rigorous mathematicalreasoning significantly influenced by the astronomer UrbainLeverrier (1811ndash1877) and his research on orbital cyclicityCroll sought to demonstrate that precession variation mod-ulated by eccentricity drastically affects the intensity of ra-

diation received by the Earth during each season of the year(Imbrie and Imbrie 1979) Thus he defended the origin ofglaciations based on this seasonal effect Furthermore Crollconsidered the possibility of atmospheric amplification of or-bital cycles through albedo effects as the snow caps grow andof amplifying orbital effects through ocean circulation (Pail-lard 2001) In 1875 in the book Climate and Time Crollupdated his theory considering the variations in the inclina-tion of the Earthrsquos axis (obliquity cycle) Unfortunately with-out further information on the timing of these variations hisstudy could not provide definitive answers (Imbrie and Im-brie 1979)

In the mid-19th century the effects of glacial cycleswere also studied mainly on sea-level fluctuations Ma-cLaren (1842) for example influenced mainly by the workof Agassiz suggested that melting and reconstruction of theice sheets that covered continents during glaciation shouldcause significant variations in the volume of the ocean Heestimated that these variations would reach magnitudes of100 to 200 m closely anticipating the current understandingof glacioeustasy (eg Sames et al 2020) Jamieson (1865)proposed another glacial mechanism for the relative changein sea level From his investigations in Scotland he suggestedthat the weight of the ice caps must have depressed part of thecrust during the glaciation which would return to its originalposition during the thaw (isostatic rebound)

212 Milankovitch and the definitive return ofastronomical climate models

The legacy of Crollrsquos work served as a foundation for the Ser-bian Milutin Milankovitch (1879ndash1958) Milankovitch is oneof the most well-known pioneers of planetary climatologyespecially for finding a mathematical solution to correlate or-bitally controlled insolation with the ice ages (Milankovitch1941 Paillard 2001 Fig 2)

Figure 2 Orbital models for glacial cycles Adheacutemarrsquos model con-siders only precession to explain cyclic glaciations alternating be-tween hemispheres Crollrsquos model considers the interferences of ec-centricity The last is Milankovitchrsquos model a pioneer in determin-ing the insolation calculated from all orbital parameters (modifiedfrom Paillard 2001)

Milankovitch (1941) calculated the glacialndashinterglacialclimatic oscillations as a function of solar radiation inci-dent at the top of the atmosphere (insolation) for the last600 kyr While his predecessors used only eccentricity andprecession Milankovitch also included obliquity in his cal-culations The triumph of Milankovitchrsquos work was the pre-cision which could be tested with geological data for val-idation The variations in solar radiation produce changesbetween colder (lower insolation rates) and warmer globalclimatic periods (higher insolation rates) which then influ-

ence atmospheric hydrological oceanographic biologicaland sedimentological processes on the Earthrsquos surface

Some geologists accepted that the curves proposed by Mi-lankovitch fit the geological record However many oth-ers disagreed discrediting astronomical research remainingskeptical until studies of deep-sea cores and isotopic researchstarted (Imbrie and Imbrie 1979) According to the Mi-lankovitch model Emiliani (1955 1966 1978) determinedthat ocean temperatures fluctuated based on a record of oxy-gen isotope ratios in calcitic fossils Later Shackleton (1967)improved the interpretation of variations in oxygen isotoperatios suggesting that they reflect oscillations in the totalvolume of ice sheets during glacial cycles Nowadays Mi-lankovitchrsquos work is an essential element of deductive anal-ysis and has become the keystone of cyclostratigraphy andastrochronology (eg Strasser et al 2006) Astronomical so-lutions are calculated with ever-higher precision for the deepgeological past (eg Berger et al 1989 Laskar et al 2011Hinnov 2018) and Milankovitch cycles are used to improvethe geological timescale continually (eg Gradstein et al2021)

213 Astronomical forcings on the Earth system

Many astronomical cycles leave a recognizable imprint in thegeological record (eg House 1995 Fig 3) ranging fromtwice-daily (such as tides eg Kvale 2006) to hundreds ofmillions of years (such as the vertical oscillation of the solarsystem across the galactic plane and its association with im-pact episodes and mass extinction events on Earth eg Ran-dall and Reece 2014) The geochronological value of theseastronomical cycles has been recognized by many authorswhich has led to the rise of astrochronology (Hinnov 2018)Astronomical dating helps reconstruct the global climate his-tory (eg Westerhold et al 2020) and is now a significantelement of the geological timescale (eg Walker et al 2013Gradstein et al 2021)

In addition to the build-up and melting of ice on thepolar caps during icehouse conditions astronomical cyclesin the Milankovitch frequency band also force global pro-cesses during greenhouse times (eg Schulz and Schaumlfer-Neth 1998 Boulila et al 2018 Strasser 2018 Wagre-ich et al 2021) Geological records in different parts ofthe world suggest a strong correlation between orbital cy-cles and global sea-level fluctuations The eustasy associatedwith astronomical forcing on Earthrsquos climate (Fig 4a) in-cludes the exchange of water between the ocean and terres-trial stores either in the form of ice (glacioeustasy Fig 4a)or underground and surface reservoirs (aquifereustasy andlimnoeustasy Fig 4b) and also thermally induced vol-ume changes in the oceans (thermoeustasy Fig 4c) Duringicehouse conditions glacioeustasy predominates with high-amplitude sea-level fluctuations while in a greenhouse worldamplitudes are minor (eg Wilson 1998 Seacuteranne 1999Sames et al 2016 Fig 5)

Figure 3 Logarithmic table of the astronomical cycle frequencies (adapted from House 1995)

Figure 4 (a) Log-scale diagram of the timing and amplitudes of the main mechanisms that control ldquoshort-termrdquo sea-level variations Thevalues represented must be considered averages (modified from Sames et al 2016) (b) schematic diagrams representing the processes thatpromote changes in sea level (glacioeustasy aquifer eustasy+ limnoeustasy and thermoeustasy) during climate changes induced by orbitalcycles

22 The internal gears of geodynamics

In the 18th century during the Scottish Enlightenment JamesHutton (1726ndash1797) described the geological record ob-served in the landscape as a product of the continuous al-ternation of uplift erosion and depositional processes Theemergence of geology as an individualized science is cur-rently linked to James Huttonrsquos Theory of the Earth whichdescribed the Earth as a body that acts cyclically over geo-logical time (Chorley et al 2009)

This uniformitarian conception has a cyclical approachwhich considers a priori that geological processes presentrepetitive patterns (OrsquoHara 2018) The most significant con-tributor to the spread of uniformitarian thinking CharlesLyell presented a fascinating tale of the Earthrsquos internaloscillating processes He visited the Macellum of Pozzuoli(also known as Serapis Temple ndash Fig 6a) in the Italian regionof Campania several times highlighting this Roman ruin inan illustration on the frontispiece of the Principles of Geol-ogy (Fig 6b) In the middle portion of the three remainingmarble pillars there are borings left by marine Lithophagabivalves According to Lyell it is ldquounequivocal evidence

that the relative level of land and sea has changed twice atPuzuolli since the Cristian era and each movement both ofelevation and subsidence has exceeded twenty feetrdquo (Lyell1835 p 312) This variation of relative sea level identified byLyell is now understood as a product of bradyseism whichcorresponds to vertical ground movements (Fig 6c) causedby successive filling and emptying of magmatic chambersin volcanic areas (Parascandola 1947 Bellucci et al 2006Lima et al 2009 Cannatelli et al 2020)

The search for processes in the Earthrsquos internal dynam-ics and their relationship with sea-level variations contin-ued for many years after Hutton and Lyell However suchresearch focused on finding diastrophic rhythms at large tem-poral and spatial scales as Barrell (1917) mentioned ldquothoselong-deferred stirrings of the deep imprisoned titans whichhave divided earth history into periods and erasrdquo

221 Diastrophic theories and the birth of eustasy

The 18th and 19th centuries were the most scientificallyactive for the nascent discipline of geology During thisperiod Earthrsquos contraction was the leading theory for the

Figure 5 Changing frequencies and amplitudes of eustasy Sea-level curves according to Vail et al (1977) and Hallam (1977) In icehouseperiods (in blue) these cycles have a high amplitude mainly due to the effects of glacioeustasy Eustatic oscillations have lower amplitudein greenhouse periods (in light red) since there is no significant glacial effect (modified from Wilson 1998 Seacuteranne 1999 Montantildeez et al2011)

origin and evolution of its morphology such as mountainranges According to this conception the Earthrsquos radius di-minished with time due to internal cooling causing the crustto wrinkle The theory of the Earthrsquos cooling and contrac-tion has been developed and modernized throughout historywith collaborations from eminent scientists such as ReneacuteDescartes (1596ndash1650) Gottfried Wilhelm Leibniz (1646ndash1716) Henry De la Beche (1796ndash1855) Elie de Beaumont(1798ndash1874) William Thomson ndash Lord Kelvin (1824ndash1907)James Dana (1813ndash1895) and Eduard Suess (1831ndash1914)

In this context Eduard Suess formulated one of the mostcritical concepts in stratigraphy which deals with the cyclic-ity of global sea level According to Suess (1888) the con-traction of the planet produced eustatic movements Suchmovements can be negative (decrease in global sea level)due to the subsidence of ocean basins or positive (increasein global sea level) due to the continuous discharge of sedi-ments that fill these basins After Suess (1888) a tremendousscientific effort was initiated to understand the planetrsquos inter-nal dynamics its relationships with the development of oceanbasins and eustatic variations and the potential to use theoscillations of the absolute sea level for global stratigraphiccorrelations

In 1890 Grove Karl Gilbert (1834ndash1918) recommendedusing the term ldquodiastrophismrdquo to describe the vertical move-ments of the lithospheric crust Gilbert (1890) proposeddividing dystrophic processes into orogenic processes re-

lated to the relatively smaller scale that produced the moun-tain ranges and epirogenic processes related to the broadermovements that form the boundaries of continents andoceans

For many years afterwards the nature of diastrophismwas up for debate in the scientific community ldquoHave di-astrophic movements been in progress constantly or at in-tervals only with quiescent periods between Are they per-petual or periodicrdquo (Chamberlin 1909 p 689) Defendingthe periodic conception of diastrophism Thomas Chamber-lin (1843ndash1928) proposed a model for eustasy very similar toSuess (1888) in which the isostatic balance would promotevertical adjustment cycles in the Earthrsquos crust leading to ma-rine regressions and transgressions The novelty offered byChamberlin (1898) was the linkage between diastrophismsea-level variations and climatic cycles In his theory theweathering of the subaerially exposed continents during re-gression would promote substantial CO2 consumption caus-ing global cooling Conversely during transgression the ex-cess of atmospheric CO2 was supposed to improve warmingby the greenhouse effect Chamberlinrsquos primary motivationwas to establish a theoretical framework that could explainthe global division of geological time and the stratigraphiccorrelations through base-level changes (Chamberlin 1909)In his most famous work Diastrophism as the Ultimate Ba-sis of Correlation Chamberlin (1909) reaffirms the globalcharacter of dystrophic movements and underlines their im-

Figure 6 Roman ruins of the Serapis Temple (Macellum of Poz-zuoli) in Pozzuoli Italy (a) Recent picture (b) The illustration onthe frontispiece of volume I of Principles of Geology (Lyell 1835)Both highlight the rough texture of the intermediate portion of thecolumns where bivalve wear is evident indicating marine transgres-sion after the templersquos construction (c) Vertical movements of theSerapis Temple show an alternating pattern of elevation and sub-sidence produced by bradyseism (modified from Bellucci et al2006)

portance for correlations by base level According to himthe synchronicity of these events associated with variationsin sea level allows for transoceanic correlations

During this same period William Morris Davis (1850ndash1934) developed a geomorphic cycle theory to explain land-form evolution According to Davis (1899 1922) after aninitial and rapid tectonic uplift landforms undergo weather-ing and erosion processes evolving through several interme-diate stages until culminating in a general peneplanizationA change in the erosion level caused by a new tectonic up-lift would cause landform rejuvenation starting a new geo-morphic cycle Although later criticized for not consideringall the complexity of geomorphological processes Davisrsquostheory became paradigmatic until the mid-20th century Itscyclical conception influenced ideas about periodic varia-tions in the generation supply and preservation of sedimen-tary deposits

Barrell (1917) pioneered the understanding of the cyclicbehaviour of erosion and accumulation processes He was thefirst to propose a systematic link at different orders betweenbase-level changes and the preservation of the stratigraphicrecord A synthesis of his ideas is presented in the diagramin Fig 7 With the alternation between deposition and ero-

sion produced by the harmonic of long-term (diastrophic)and short-term (climatic) base-level fluctuations Barrell il-lustrated that most of the geological time is contained in andrepresented by unconformity surfaces which he called ldquodi-astemsrdquo It is remarkable how many of the principles devel-oped by this author are still in use The sinusoidal represen-tation of the base-level harmonic oscillations introduced awidespread way of illustrating the logic of stratigraphic evo-lution (eg Van Wagoner 1990)

A year after the First World War Alfred Wegener (1880ndash1930) published the first edition of The Origin of the Conti-nents and Oceans Wegener (1915) was not the first to pos-tulate the lateral movement of continents However he de-serves the central role in this theme above all for his per-sistence in defending continental drift against a scientificcommunity hostile to these ideas The exaggerated reactionsto Wegenerrsquos theory are due in part to the fact that hedid not have a satisfactory explanation for the mechanismcontrolling continental movements (Beckinsale and Chorley2003) Another understandable reason is resistance from thescientific community to some theoretical innovations Thecontinental drift proposal completely contradicted all for-mulations in force at the time Since the beginning of the19th century what had been advocated in force until the1960s were the large vertical movements of the Earthrsquos crustwhich reached a final formulation in the geosyncline theory(Gnibidenko and Shashkin 1970)

Hans Stille (1876ndash1966) was one of the great geologistsof the geosyncline theory Dedicated to describing the evo-lution of various geological terrains Stille (1924) mappedsuccessive unconformities in marine deposits He interpretedthat orogenic processes occurred in global synchrony pro-ducing regressions and transgressions of sea level This pro-posal cannot be seen as fundamentally new but Stille (1924)was a pioneer by drawing up the first eustatic variation curvefor the Phanerozoic (Fig 8a)

Amadeus William Grabau (1870ndash1946) through detailedstratigraphic data and correlations in extensive areas of NorthAmerica Europe and Asia presented a proposal for sea-level fluctuations for long geological periods (Fig 8b) Al-though Stillersquos and Grabaursquos cyclic conceptions of sea-levelvariations are similar Grabau questioned the synchronicityof orogenies in the entire world He considered these pro-cesses to be of local importance and believed that simulta-neous sea-level fluctuations could be related to changes inthe volumes of ocean basins (Johnson 1992) Grabau wasinspired by the work of Alfred Wegener (Mazur 2006) andhe cited The Origin of the Continents and Oceans in his mostsignificant publication The Rhythm of the Ages Earth His-tory in the Light of the Pulsation and Polar Control Theoriespublished in 1940 (Johnson 1992)

Figure 7 Cyclical variations of the base level and their control on preserving the stratigraphic record through an alternation of depositionand erosion (modified from Barrell 1917)

222 Plate tectonics and Wilson cycles

Scientific progress and field evidence particularly concern-ing the origin of mountain belts have resulted in the ques-tioning of the contraction theory (eg Dutton 1874) whichwas finally abandoned A crisis in the field of tectonics wastriggered by the discovery of radiometric dating which chal-lenged the Earthrsquos long-term cooling and by the Alpinenappes and thrust sheets that demonstrated the mechanismsof large horizontal displacements of the crust This crisis didnot end until the definition of plate tectonics in the 1960s(OrsquoHara 2018)

During the 1960s advances in post-World War II oceano-graphic research provided evidence for the evolution of theocean floor Such discoveries explained Alfred Wegenerrsquostheory of continental drift (Kearey et al 2009) and the rootsof the future plate tectonic paradigm were established (LePichon 2019) The development of this theory can be con-sidered the most significant advance in understanding theEarthrsquos dynamics and has even influenced the study of otherplanets (eg Hawkesworth and Brown 2018 Karato andBarbot 2018 Duarte et al 2021)

John Tuzo Wilson (1908ndash1993) was one of the leadinggeoscientists developing the theory of plate tectonics Wil-son (1965) was the first to mention the existence of large rigidplates describing specific limits of these which the authorcalled transform faults However Wilsonrsquos most emblem-atic work was published the following year Wilson (1966)presented a specific aspect of the geotectonic process show-ing the oceansrsquo successive opening and closing (Fig 9) To-day the so-called Wilson cycle describes the periodicity with

which large continental masses separated and came back to-gether Over the past 50 years this concept has proven to becrucial for the theory and practice of geology (Wilson et al2019)

It is notorious how the theory of plate tectonics followedthe stubborn uniformitarianism of processes advocated byJames Hutton and Charles Lyell Stern and Scholl (2010)related the tectonic processes to cycles of creation and de-struction of the continental crust defining a particular equi-librium on Earth They encapsulated this equilibrium inthe traditional Chinese concept of yinndashyang whereby du-alities work together and in opposition About this main-tenance of geological systems defined by plate tectonicsSchwarzacher (2000 p 51) wrote the following

The environments of deposition from the Precam-brian onwards have been similar and repeat them-selves apart from the fortunate exception of thebiosphere there are very few indications of a pro-gressive development in geological processes dur-ing the last 1000 Ma Indeed based on our presentobservations one could easily believe that mostsedimentation and therefore stratigraphy shouldhave ended long ago All basins should have beenfilled and all mountains eroded This is not the caseand leads us to believe that tectonic events must in-terfere and revitalize the sedimentation systems

The Wilson cycle was vital in defining the assembly andthe breaking up of supercontinents This self-organization inplate tectonics has been studied for decades whose period-

Figure 8 Global sea-level curves (a) Modified from Stille (1926) and (b) modified from Grabau (1936) Both indicate the main orogeneticperiods associated with rapid marine regressions The red lines indicate the same events identified by Stille (1926) and Grabau (1936)(c) Paleozoic eustatic cycles of approximately 35 Myr (determined by bandpass filtering of data presented by Haq and Schutter 2008) andpotential correlation (blue lines) with equivalent cycles of Grabau (1936) (modified from Boulila et al 2021)

icity is in the range of 300ndash800 million years (Mitchell etal 2021) Hence new hypotheses for global cycles couldalso be formulated and several questions about the impactsof tectonic events on sea-level and climatic variations wereanswered For example based on the Wilson cycles Fis-cher (1981 1982) formulated the climatic oscillation pro-duced by Earthrsquos icehouse and greenhouse states (Fig 10)

223 Internal geodynamic forcings in the Earth system

Currently the periodicity of several processes in the Earthrsquosinternal dynamics is well known (eg Matenco and Haq2020 Fig 11) Mitchell et al (2019) conducted time-seriesanalyses of hafnium isotopes in zircon (Hf-zircon) to iden-tify statistically significant periodicities of magmatic sys-tems throughout geological time The Hf-zircon analysed byLA-ICP-MS (laser ablation inductively coupled plasma massspectrometry) represents a well-dated proxy for the evolu-tion of magmatism related to tectonic and mantle convec-tion cycles From time-series analysis of the global Hf-zircondatabase for the last sim 2 Gyr the authors defined a hierarchy

of geodynamic cycles (Fig 12) analogous to the orbital ones(Fig 2)

Mitchell et al (2019) recognized the periodicity ofthe superocean cycle (sim 12 Gyr) the supercontinent cycle(sim 600 Myr) the Wilson cycle (sim 275 Myr) and an upper-mantle cycle (sim 60ndash80 Myr) These cycles appear to be har-monics implying a coupling between the mantle and litho-sphere convections In addition to these magmatic cyclesof sim 20 and sim 6 Myr are suggested by the high-resolutioncircum-Pacific records According to these authors ldquothe hi-erarchy of geodynamic cycles identified with Hf isotopes ofzircon appears to represent according to bandwidth the lastfrontier of cyclicity in the Earth system to be identified andexploredrdquo (Mitchell et al 2019 p 247)

Climatic and eustatic oscillations may have interacted withinternal geodynamic processes as triggers or feedbacks (eggreenhousendashicehouse cycles Fig 10) Changes in ocean cir-culation related to the configuration of the continents andglobal volcanic pulses are an example of a potential influ-ence on Earthrsquos climate (Rampino et al 2021) The link be-

Figure 9 Ocean closing and opening cycle (modified from Wil-son 1966) (a) A closing ocean (b) first contact between two op-posite continental coasts (c) ocean closure and final collision ofopposite continental coasts (d) a hypothetical line (dashed) alongwhich a new continental rupture would engender a younger oceanto re-open (e) a new ocean opening after the break-up of an oldcontinent

tween Earthrsquos internal dynamics and eustasy may come fromchanges in the volume of marine waters (water exchangewith a mantle) and in the volume available in ocean basins(ocean ridge volume dynamic topography seafloor volcan-ism continental collision) which operate in the long term(greater than 1 Myr eg Sames et al 2016 2020 Fig 13)

Disagreements about the global synchronicity of tectoniccycles have been raised since the beginning of the 20th cen-tury According to Willis (1910 p 247) ldquoeach region hasexperienced an individual history of diastrophism in whichthe law of periodicity is expressed in cycles of movement andquiescence peculiar to that regionrdquo This idea was encapsu-lated in the concept of relative sea-level change (eg Wilguset al 1988) Relative sea-level change (as opposed to eu-static sea-level change) is caused by tectonic deformation ofthe crust in marine and coastal areas which results in upliftand subsidence of the land relative to the sea surface Gener-ally these processes have a local to regional extent and occurat a higher frequency than global geodynamic processes (egMatenco and Haq 2020 Fig 11) Thus sea-level changescaused by geodynamic processes can be local when such pro-cesses are also localized (eg bradyseism Fig 4)

The cyclical behaviour of the mantle and the lithospherein association with astronomical cycles completes the puz-zle of cyclicity in the Earth system The connection betweenthe Earthrsquos internal and external systems is not adequately in-vestigated because tectonic and astronomical influences areoften considered independently Boulila et al (2021) sug-

Figure 10 Cyclic outlines of Phanerozoic history (modified fromFischer 1981 1982) Climatic oscillations are composed of green-house and icehouse states with minor internal climatic fluctuationsSea-level curves according to Vail et al (1977) and Hallam (1977)Global granite emplacement was deduced from data based on theAmerican granite emplacements (after Engel and Engel 1964)

gest a potential coupling between Milankovitch forcing andEarthrsquos internal processes for the eustatic sea-level recordin the 35 Myr cycle range during the Phanerozoic This is acyclicity that is compatible with the one that was recognizeda long time ago by several authors such as Stille (1926) andGrabau (1936) (Fig 8c) A challenge for stratigraphy is un-derstanding how the Earth systemrsquos conduction mechanismsare imprinted in the geological record As Barrell (1917) con-cluded ldquosedimentation is controlled by them and the strati-graphic series constitutes a record written on stone tabletsof these increasing waves of change that pulsed through geo-logical timerdquo Such ldquowavesrdquo may correspond to the causalmechanism of biological extinctions comet impacts oro-genic events oceanic anoxic events and sea-level changeswhich support the division of geological time into intervalsfor global correlations (eg Rampino et al 2021 Boulila etal 2021)

3 Cyclicity of the stratigraphic record

The idea of a cycle involves repetition becausea cycle can be recognized only if units are re-peated in the same order The question that in-evitably arises is How closely similar must therepetition be An answer seems to depend on tworequirements (1) nearly complete transitions be-tween variants must be observed and (2) a gen-eralization must be made reducing the cycle to itssimplest form by excluding all unessential detailsThe cycles then must be closely similar with re-spect to this simple form (Weller 1964 p 613)

Figure 11 Temporal variability of the main periodic geodynamic mechanisms (based on Matenco and Haq 2020)

According to Goldhammer (1978) most if not all strati-graphic successions exhibit repetitions of strata at differentscales Throughout the history of stratigraphy the conceptof cyclicity played a crucial role in the inductive observa-tions of the record and subsequent deductive reasoning Sev-eral approaches have been used to describe this cyclicityAmong them the following lines of description and interpre-tation will be briefly presented sedimentary facies cyclescyclothems clinoforms stratigraphic sequences and astro-cycles

31 Sedimentary facies cycles

Sedimentary cycles are recurrent sequences ofstrata each consisting of several similar lithologi-cally distinctive members arranged in the same or-der A great variety of cycles is possible rangingfrom simple to quite complex but only a compar-atively few types actually have been recognizedCycles may be either symmetrical or asymmetri-cal depending upon the pattern presented by theirmembers They record the occurrence of definiteseries of physical conditions and resulting sedi-mentary environments that were repeated in thesame order with only minor variations (Weller1960 p 367)

During the 15th and 16th centuries observing the land-scape and the natural phenomena that modify it played acrucial role in constructing modern science especially in theEarth sciences (Puche-Riart 2005) For example through de-tailed observations of successive rock strata Leonardo daVinci (1452ndash1519) expressed nature in his paintings (Fer-retti et al 2020) He was probably one of the first tounderstand erosion transport deposition and lithificationprocesses from field observations In the Codex LeicesterLeonardo da Vinci shows the vertical and lateral organiza-

Figure 12 Global Hf database (black) and cycles determined by thetime-series analysis superocean cycle (sim 12 Gyr red) the super-continent cycle (sim 600 Myr yellow) the Wilson cycle (sim 275 Myrgreen) and an upper mantle cycle (sim 60ndash80 Myr blue)

tion of rocky beds observed in the Alps that he interpreted asa record of river flood cycles (Ferretti et al 2020)

In 1669 Nicolaus Steno (1638ndash1686) published one ofthe most crucial works about the genesis of rock layers andtheir fossil components Based on an interpretation of thegeological evolution of Tuscany he proposed three funda-mental stratigraphic principles that continue to be used today(Kravitz 2014) Through an evolutionary diagram (Fig 14)Steno suggested that the sedimentary beds are formed by

Figure 13 Log-scale diagram of the timing and amplitudes ofthe main mechanisms that control ldquolong-termrdquo sea-level variationsrelated to internal geodynamic processes The values representedmust be considered the average (modified from Sames et al 2016)

successive floods followed by reworking that erodes and de-forms them He noted that sediment layers were deposited inchronologic successions that display the oldest layers on thebottom and the youngest ones on the top of the pile (principleof superposition) According to him initially the strata areorganized in a set of horizontal layers (principle of originalhorizontality) that could be later eroded and deformed andnew horizontal layers are deposited over them Concerningthe stratarsquos geometry Steno defined each sedimentary bed asextending laterally in all directions (principle of lateral conti-nuity) until it reached an obstacle such as the basinrsquos border

Nicolaus Steno was responsible for introducing the termldquofaciesrdquo into the geological literature He used it to describethe fundamental characteristics of a part of the Earthrsquos sur-face during a specific geological time (Teichert 1958) Laterthis concept evolved through the descriptions of AmanzGressly (1814ndash1865) in the Jura mountains at the FrenchndashSwiss border Gressly (1838) defined the sedimentary faciesas the different lithological features and fossil componentsof a sedimentary layer interpreted as a record of the origi-nal depositional processes He explained the genesis of sed-imentary facies as the product of processes that operated indepositional environments and demonstrated through strati-graphic correlations the lateral facies transitions that com-pose a mosaic of environments along a depositional profile(Cross 1997)

In 1894 Johannes Walther (1860ndash1937) introduced an es-sential geological principle associated with the concept of fa-cies (Middleton 1973) Known as Waltherrsquos law of faciesthis principle states that any vertical facies succession is a

record of depositional environments that were laterally ad-jacent to each other in the geological past This vertical andlateral facies correspondence is still used today for paleogeo-graphic reconstructions especially when associated with anactualistic approach (eg Fragoso et al 2021)

Between the 19th and 20th centuries several works pre-sented detailed sections demonstrating repeated associationsof different types of rocks (Weller 1964) The economicinterest in carboniferous coal beds fueled some of the ear-liest observations In 1912 Johan August Udden (1859ndash1932) was a pioneer in recognizing cycles in the stratigraphicrecord In a report about the geology of the US state of Illi-nois he identified facies cycles in Pennsylvanian strata com-posed from bottom to top by layers of coal limestone andsandstone (Fig 15) Udden (1912) interpreted such cycles asproducts of successive transgressions and regressions of theshoreline during the basinrsquos subsidence He established thatstratigraphic surfaces marked by paleosols correspond to theend of each cycle According to him these surfaces representdepositional gaps

Laboratory simulations were introduced during the 1950sand 1960s culminating in the flow regime concept (Simonsand Richardson 1966) This advance improved the interpre-tation of sedimentary structures preserved in the geologicalrecord (eg Allen 1963 Middleton 1965) Concomitantlythere was also much progress in facies models through stud-ies of modern sedimentary environments (eg Fisk et al1954 Illing 1954 Oomkens and Terwindt 1960 Bernardand Major 1963 Shearman 1966 Glennie 1970)

In the 1960s the stratigraphic application of facies mod-els evolved considerably through the analysis of cyclicityseen in the outcrops (eg Weller 1960) Recurrent sequencesof sedimentary facies arranged in a specific order havebeen interpreted as the record of similar depositional andenvironmental processes repeated at all scales from mil-limetres to many hundreds of metres (Goldhammer 1978Schwarzacher 2000) In this context specific terms were cre-ated for describing sedimentary facies with regular alterna-tion such as ldquocyclitesrdquo or ldquorhythmitesrdquo (eg Kvale 1978Brodzikowski and Van Loon 1991) Although generic theseterms have been closely associated with regular climate cy-cles (eg Chandler and Evans 2021) or those produced intidal environments (eg Kvale 1978)

Researching cyclic depositional mechanisms in alluvialplains Beerbower (1964) defined the concepts of autocyclicversus allocyclic Autocyclic was defined as the sedimenta-tion record generated purely within the given sedimentarysystem by the distribution of energy and sediments such aslateral channel migration and meander abandonment On theother hand allocyclic was associated with the external pro-cesses that cause changes in the alluvial channelsrsquo dischargeloading and inclination They differ from autocyclic alterna-tions in their wider lateral extension along the basin or evento other depositional basins

Figure 14 Stenorsquos evolutionary diagram describes six stages for the geologic history of Tuscany including flooding cycles and crustalcollapse (modified from Kravitz 2014)

With some modernizations the concepts of autocyclicand allocyclic controls currently encompass all geochemi-cal ecological and physical sedimentary processes (Cecil2003) Nowadays autocyclic dynamics are understood as thespontaneous form of deposition within sedimentary systemsdetermining spatial and temporal heterogeneities in the waysediments and water are distributed in a landscape (Hajekand Straub 2017 Fig 16) Delta switching and lateral mi-gration of channels dunes or ripples are examples of au-tocyclic processes that produce cyclical deposits (eg Ha-jek and Straub 2017 Miall 2015) Other examples includeepisodic events which although recurrent do not have peri-odicity such as storms and sediment gravity flows (eg Ein-sele 2000) The autocyclic dynamics must be self-regulatingand include feedback mechanisms to produce cyclic sedi-mentary records (Goldhammer 1978) Since they do not al-ways have a periodic regularity the preference is to use theterm ldquoautogenicrdquo (Miall 2016)

In turn allocyclic (or allogenic) controls correspond to re-gional or global processes fundamentally related to climateeustasy and tectonics These processes influence at differ-ent magnitudes and frequencies the production transportaccumulation and preservation of sediments be they inor-ganic or organic clastic or chemical (eg Strasser et al2006 Holbrook and Miall 2020 Matenco and Haq 2020Fig 17) In contrast to autocycles the allocyclic controlsare regular and tend to have known frequencies (as seen inSect 2) They also define accommodation (defined by eu-static sea level and subsidence) and make the link to sequencestratigraphy (eg Holbrook and Miall 2020 Fragoso et al2021) Hilgen et al (2004) advised that even the record pro-duced by sudden autocyclic events (eg storms) may occurin clusters related to allocyclic controls (eg astronomical)Furthermore the understanding of the organization of fluvialsystems mainly controlled by the autogenic dynamics wasdiscussed by Abels et al (2013) According to these authors

the regularities in such systems could be linked to allogeneicastronomically forced climatic changes

Over the years several authors raised the question of howsedimentary preservation influences and possibly hampersthe analysis and interpretation of facies and stratigraphic or-ganization

What does the stratigraphic record actually recordThis rather fundamental question spawns morequestions all of which are building blocks in thefoundations of geology Are the processes andevents recorded in the rocks truly representativeof their time At what resolution do rocks recordprocesses What determines which examples ofa repeated process are actually preserved Whatis missing What can be determined with cer-tainty from what remains Geologists have mulledthe answers to these questions at various inten-sities since geology was in its infancy The an-swers to these questions ultimately determine thelegitimacy of every interpretation made of the pastfrom the stratigraphic record (Holbrook and Miall2020 p 1)

Barrellrsquos (1917) proposal for the alternation of deposi-tion (base-level rise) and erosion (base-level fall) processesat multiple amplitudes and frequencies (Fig 7) in whichonly one-sixth of the time is preserved in the rock recordillustrates this question in a precise way It is concludedthat much of geologic time is distributed across numerousgaps in the record (eg Dott 1983 Udden 1912 Ager1993 Sadler 1999 Miall 2015 Strasser 2015 Holbrookand Miall 2020) which limits the use of Waltherrsquos law offacies in reconstructing laterally adjacent paleoenvironments(Fragoso et al 2021)

In this respect within what is considered ldquosedimentarygeologyrdquo (sensu Middleton 1978) there is a difference be-

Figure 15 Cycles in the Pennsylvanian of Illinois United States(modified from Udden 1912)

tween sedimentological analysis which is concerned withinterpreting the processes at the origin of sedimentary fa-cies to stratigraphic analysis which is mainly related tothe organization of facies in geological time With certainpoetic freedom it would be like considering that the har-monic amplitudes and frequencies of the base level oscil-lations compose the stratigraphic ldquomusicrdquo producing sedi-mentary ldquonotesrdquo spaced in time Furthermore as WolfgangAmadeus Mozart said ldquothe music is not in the notes but inthe silence betweenrdquo For this reason stratigraphers must payas much attention to surfaces that contain the gaps as they doto sedimentary facies taking into account the effect of preser-vation

Miall (2015) Holbrook and Miall (2020) and Miall etal (2021) encapsulated this thought in a more objective andmechanistic way through the concept called a ldquopreservationmachinerdquo or ldquostratigraphy machinerdquo (Fig 18a) These au-thors considered that the organization of the stratigraphic

record occurs through multiple overlapping of autogenic andallogeneic processes which generate and remove sedimen-tary deposits across the whole range of geological timescalesFurthermore the ldquocycles to preserverdquo (ie the number ofsedimentary cycles needed to ensure some preservation ata given scale) constitutes a part of the rock record at eachtimescale which can potentially be analysed hierarchically(Fig 18b)

32 Cyclothems

Between the 1930s and 1960s the sections presented byUdden (1912) became emblematic Initially called ldquosuitesrdquo(Wanless 1929) or ldquocyclical formationsrdquo (Weller 1930Wanless 1931) it was the term ldquocyclothemsrdquo (Wanless andWeller 1932) that triumphed in the literature for describingsuch cyclic facies alternations

The concept of cyclothems has become familiar to mostgeoscientists who describe sedimentary facies repetitions(eg Weller 1943) The progress of the work in the Pennsyl-vanian of Illinois revealed that the recurrence of individualcyclothems not only corresponds to the unique rhythms tobe observed in stratigraphic successions but is also part of alarger order

This repeated succession of cyclothems of differ-ent character indicates a rhythm of larger orderthan that shown in the individual cycles and sug-gests the desirability of a term to designate a com-bination of related cyclothems The word ldquomega-cyclothemrdquordquo will be used in this sense to define acycle of cyclothems (Moore et al 1936 p 29)

According to James Marvin Weller (1899ndash1976) ldquotheselarger rhythms may be the long-sought key that will solvesome of the perplexing problems of interbasin correlationrdquo(Weller 1943 p 3) This author later proposed the exis-tence of even larger groups called hypercyclothems (Weller1958) This marked characteristic of the cyclicity in the sed-imentary record in which individual cycles occur in clus-ters that make up larger cyclical units remains in modernapproaches of sequence stratigraphy (Catuneanu 2019a bMagalhatildees et al 2020 Fragoso et al 2021 see item 33)and cyclostratigraphy (eg Hinnov 2018 see item 34) Theterm ldquostacking patternrdquo is often used to describe a hierarchi-cal order of cyclical units

Raymond Cecil Moore (1892ndash1974) presented anotherfeature of the cyclical stratigraphic record quite pertinent inthe modern context of sequence stratigraphy concerning thedefinition of boundary surfaces According to Moore (1964)both cyclothems and megacyclothems are limited by key sur-faces marked by disconformities or a change from continen-tal to marine sedimentation (Fig 19)

Concerning the origin of cyclothems Klein andWillard (1989) argued that such units are the productof the combined action of tectonic and eustatic processes

Figure 16 Schematic illustration with some autogenic controls on sedimentation in different environments

Figure 17 Schematic diagram illustrating the main allocyclic controls on sedimentation (modified from Strasser et al 2006)

According to these authors the integrated analysis of param-eters related to geotectonic evolution global paleoclimate(controlled by orbital Milankovitch cycles) and laterallychanging regional subsidence allows understanding thepaleogeographic variations that gave rise to marine andcontinental cyclothems along with lateral correlations(Fig 20) This approach presents many parallels to theanalysis of systems tracts in the context of sequence stratig-raphy (eg Posamentier et al 1988 Hunt and Tucker 1992Posamentier and Allen 1999)

33 Clinoforms

A broader analysis of the geometry of sedimentary de-posits also revealed sedimentological alternations whichcontributed to the definition of cyclic stratigraphic units John

Lyon Rich (1884ndash1956) was the first to describe the inclinedgeometry of marine deposition Rich (1951) defined thatalong a transect from coast to basin the sedimentary depositscan be subdivided into three depositional forms undaformclinoform and fondoform (Fig 21) Among these termsonly ldquoclinoformrdquo is being used nowadays However the the-oretical basis brought by such an approach remains similarespecially regarding the possibility of shifts between theseenvironments caused by sea-level changes (Fig 21b) result-ing in characteristic successions of the geometry of strata(Fig 21c)

DeWitt Clinton Van Siclen (1918ndash2001) considered thesloping geometries of continental margin deposits to describethe lateral variations observed in the cyclothems Accordingto Van Siclen (1958) the alternation of fluvial and coastal de-position with erosional disconformities predominates land-

Figure 18 Stratigraphy machine (a) Playful representation of the ldquostratigraphy machinerdquo concept that generates the stratigraphic recordorganizing geological time into hierarchically preserved sedimentary units and hiatus surfaces from the bedform to the entire basin fill (basedon Holbrook and Miall 2020) (b) Table illustrating the stratigraphy machinersquos operation which considers the simultaneous action of severalaccumulation removal and preservation processes which interact at different timescales to generate the rock record For convenience thetimescale is subdivided into four broad intervals The diagram should be read from left to right where at each time interval the sedimentsare first generated by the depositional processes and what is not removed on the surface is preserved in the subsurface creating the initialsuccession Over time long-term processes affect this succession with preservation andor removal In this way long-term processes willaffect short-term processes as indicated by the loops at the bottom of the figure It is estimated that a period equal to or greater than 107 yearswould be enough for all processes to perform a complete cycle Due to the recurrent removal processes numerous sedimentary gaps occur inthe final product at all scales and the rock record represents only a fraction of the elapsed time (modified from Holbrook and Miall 2020)

ward grading basin-ward to alternating marine and terrige-nous deposition and finally reaching a totally marine domainwith an alternation of clastic and carbonate deposits The au-thor described cycles in the deep sea composed of clasticsedimentation during stable or lowered sea level and non-deposition or thin black-shale layers deposited during highersea stands Considering different scenarios of changes in sealevel and sediment supply Van Siclen (1958) proposed dis-tinct types of clinoform successions (Fig 22) This approachwas handy for correlating well data when seismics did notsupport the oil and gas industry It is interesting to real-

ize how such a concept is similar to the current sequence-stratigraphic models

34 Stratigraphic sequences

Stratigraphic cyclicity can be observed at differ-ent scales At each scale of observation (ie hi-erarchical level) the building blocks of the se-quence stratigraphic framework are represented bysequences and their component systems tracts anddepositional systems (Catuneanu 2019b p 128)

Figure 19 Representative section of cyclothems indicating the al-ternation of continental and marine paleoenvironments (modifiedfrom Moore 1964) The alternatives of limits for cyclothems are (I)disconformities and (II) the transition from non-marine to marineconditions

Figure 20 The genesis of the different types of cyclothems inNorth America related to orbital parameters and lateral differencesin the crustrsquos flexural intensity (modified from Klein and Willard1989)

Laurence Louis Sloss (1913ndash1996) is widely recognizedas one of the pioneers of the concept of sequence stratig-raphy and many credit him with instigating a revolution instratigraphic thinking (Dott 2014) Sloss et al (1949) usedfor the first time the term ldquosequencerdquo to refer to stratigraphicunits that could be correlated over large areas through geo-logical mapping and well data Subsequently this sequencemodel defined successive stratigraphic units bounded by ldquoin-

Figure 21 Sketches and terminology for coastal marine deposits(modified from Rich 1951) (a) undaform clinoform fondoform(b) Area of thick sand on the outer edge produced by the slightreduction in sea level (c) Alternations of coastal marine depositsproduced by intermittent changes in sea level

terregional unconformitiesrdquo that covered the North Americancraton (Sloss 1963 Fig 23)

In the late 1960s under Slossrsquo guidance Peter VailRobert Mitchum and John Sangree studied North Amer-ican Pennsylvanian cyclothems (Dott 2014) Similarly tosmall-scale versions of Sloss sequences bounded by numer-ous widespread unconformities these cyclothems were inter-preted by them as the stratigraphic record of glacioeustaticfluctuations Subsequently these three geologists collabo-rated with the Exxon research group to develop the methodof interpreting seismic data refining their mentorrsquos conceptof sequence (eg Mitchum 1977)

During the 1960s and 1970s the evolution of seismic in-terpretation was responsible for reuniting many stratigraphicconcepts that underlie the current sequence-stratigraphicmethodology The first reference to the term ldquoseismic stratig-raphyrdquo was published at the 27th Brazilian Congress of Ge-ology (Fisher et al 1973) and efforts in this area gainedprominence in the international community through AAPGMemoir 26 (Payton 1977) where the main techniques de-veloped by the Exxon research group were presented Thegreat innovation was to consider the continuous reflectorsobserved in seismic sections to be depositional timelinesIn this way it became possible to interpret that surfacesrepresenting an unconformity pass laterally to a correlativeconformity which was fundamental for the definition of asequence (eg Mitchum 1977) The seismic interpretationtogether with biostratigraphic constraints made it possibleto establish chronostratigraphic correlations within a basinand between different basins (eg Mitchum and Vail 1977Fig 24) According to Vail (1992) this approach aimed atproviding a unifying concept for sedimentary geology equalto what plate tectonics had done for structural geology

Different sequence-stratigraphic models were presentedbetween the 1970s and 1990s resulting in a profusion ofconcepts and jargons Catuneanu (2006) offered a completereview of these proposals After the 2000s a scientific effortwas made to standardize the nomenclature and the methodol-ogy of sequence stratigraphy (Catuneanu et al 2011) defin-

Figure 22 Different scenarios where sea-level changes and sediment supply cause different geometries and lithological compositions incontinental margin deposition (modified from Van Siclen 1958)

ing a simple and integrating workflow appropriate for mod-ern stratigraphic analysis (Miall 2016)

Over time sequence characterization has proven helpfulin academic and industrial applications since such units con-stitute a natural structure for classification and local to re-gional correlations (eg Fragoso et al 2021) Catuneanuand Zecchin (2013 p 27) defined sequences as a ldquocycleof change in stratal stacking patterns dividable into sys-tems tracts and bounded by sequence stratigraphic surfacesrdquoThe current sequence-stratigraphic methodology has a scale-independent approach in which sequences can be definedfrom the basin (sensu Sloss et al 1949 Sloss 1963) to faciesscale (eg Strasser et al 1999 Magalhatildees et al 2016 2017Fig 25) ordered in a hierarchical framework (Magalhatildees etal 2020)

According to Fragoso et al (2021) the characterizationof sequences within a cyclic and hierarchical frameworkshould obey the following criteria (Fig 26) transgressivendashregressive (T ndashR) cycle anatomy vertical recurrence ofstacking patterns vertical trends in the stacking patterns

composing subsequent hierarchies of cyclicity recognizablemappability In this sense a stratigraphic sequence frame-work is composed of cycles observed at different hierarchiesA higher ranking comprises an organized cluster of lower-ranking sequences (Catuneanu 2019a b Magalhatildees et al2020 Fragoso et al 2021 Fig 27) This cyclic approachof the stratigraphic analysis supports the objective results inpredicting the vertical recurrence and the lateral correlationof genetic stratigraphic units

35 Astrocycles

Gilbert (1895) was the first to consider that the sedimen-tary record may exhibit repetitions controlled by orbital cy-cles He correctly suggested that the Upper Cretaceous marlndashlimestone alternation in the US state of Colorado should cor-respond to an allocyclic record of climatic oscillation con-trolled by the orbital precession cycle of about 20 kyr Al-though rudimentary Gilbertrsquos conclusions allowed the mea-surement of geological time using the sedimentary record

Figure 23 Sequences of the North American craton (modified fromSloss 1963) The black areas represent temporal gaps and the lightareas represent the depositional units

before the invention of radiometric dating (Strasser et al2006) After Gilbert the studies of astronomically forcedclimatic cycles evolved considerably from Adheacutemar (1842)Croll (1875) and especially Milankovitch (1941) Theapplication of this knowledge to sedimentary successionsemerged gradually

In the 1960s some studies started identifying cycles in dif-ferent depositional contexts related to orbital forcing For ex-ample Van Houten (1964) presented the cyclic character ofthe lacustrine record of the Upper Triassic Lockatong Forma-tion in the United States This work stands out by determin-ing a stratigraphic ordering in three hierarchies and propos-ing a temporal definition based on orbital cycles (Fig 28)

In 1976 one of the most influential articles in the studyof Milankovitchrsquos theory was published In their work enti-tled ldquoEarth Orbit Variations The Ice Age Pacemakerrdquo JamesHays John Imbrie and Nick Shackleton established the ef-fects of orbital parameters on the long-term climate recordobtained from the analysis of marine sediments Thus Hayset al (1976) ldquolegitimized what was to become one of themost powerful tools in stratigraphyrdquo (Maslin 2016 p 208)

In the 1980s the studies about the geological record of as-tronomical cycles integrated a subdiscipline of stratigraphynamed ldquocyclostratigraphyrdquo (Strasser et al 2006) Accordingto Hilgen et al (2004) cyclostratigraphy identifies charac-terizes correlates and interprets cyclical variations (periodicor quasi-periodic) in the stratigraphic record In cyclostrati-graphic studies temporal calibrations can be done by ei-ther correlating sedimentary cycles ndash identified through vari-ations in paleoenvironmental or paleoclimatic proxies sam-pled along a section or core (eg Li et al 2019) ndash or by as-tronomical target curves of precession obliquity and eccen-

tricity or by related insolation curves (Strasser et al 2006)Weedon (2003) and Kodama and Hinnov (2015) presentmathematical techniques for processing signals obtained bythese proxies Once the periodicity of a sedimentary cyclehas been demonstrated a very detailed analysis of sedimen-tological paleoecological or geochemical processes can beevaluated in a high-resolution time-stratigraphic framework(Strasser et al 2006)

The term ldquosedimentary cyclerdquo in cyclostratigraphy has aspecific meaning which differs from more generic applica-tions (eg Weller 1960) The sedimentary cycle as used incyclostratigraphy corresponds to ldquoone succession of lithofa-cies that repeats itself many times in the sedimentary recordand that is or is inferred to be causally linked to an oscil-lating system and as a consequence is (nearly) periodic andhas time significancerdquo (Hilgen et al 2004 p 305 Fig 29)Thus Strasser et al (2006) proposed the term ldquoastrocyclerdquo todefine specific cycles whose periodicity can be demonstratedby the cyclostratigraphic analysis

At this time cyclostratigraphic analysis is part of in-tegrated stratigraphy which combines several stratigraphicsubdisciplines (eg biostratigraphy magnetostratigraphychemostratigraphy geochronology) to solve problems re-lated to geological time (Hilgen et al 2015) This integrationaids paleoenvironmental interpretation focusing on multi-proxy analyses and provides accurate geochronological in-formation for astronomical tuning of stratigraphic recordsinto target curves of orbital cycles and the related insolationcurves Thus the integrated stratigraphy supports the con-struction of a high-resolution astronomical timescale that iscurrently decisive to determine a Global Stratotype Sectionand Point (GSSP ndash eg Lirer and Laccarino 2011) and torefine the Geological Time Scale (Gradstein et al 2021)

4 Discussion

Since the beginning of their existence humans have dealtwith cycles From the simple dayndashnight hungryndashsatisfiedand sleepingndashawake to the passing of the seasons and thecoming and going of migratory animals cycles are om-nipresent and contribute to shaping the human way of think-ing This aspect has had an epistemological influence on ob-serving and interpreting the most diverse natural phenomenathat control the Earth system In Earth sciences cycle con-cepts improved geological knowledge offering simple ana-lytical solutions to describe rock records and interpret geo-logical processes There is a primordial function in the prac-tice of geology within what is considered a hermeneutic cir-cle (eg Frodeman 1995 Miall 2004 Frodeman 2014)This point of view establishes that geology is developed bythe processes of induction and deduction where the set ofdetailed descriptions supports general theories while deduc-tive reasoning enhances and refines the descriptive method-ologies and techniques (Fig 30)

Figure 24 Seismic section from offshore north-western Africa showing sequences defined by seismic reflectors Black lines show thesequence boundaries (modified from Mitchum and Vial 1977)

Figure 25 High-frequency sequences identified in an outcrop and in a ground-penetrating radar (GPR) profile of the Tombador Formation(Mesoproterozoic) Chapada Diamantina region Brazil (modified from Magalhatildees et al 2017) The sequences are composed of tidal chan-nels and bars bounded at the top by heterolithic intervals that configure cycles of retrogradational stacking patterns defined by the recurrenceof the same type of stratigraphic surface in the geological record

Geology is a prominent example of a synthetic sci-ence combining a variety of logical techniques tosolve its problems The geologist exemplifies Leacutevi-Straussrsquos bricoleur the thinker whose intellectualtoolbox contains a variety of tools that he or she se-lects as appropriate to the job at hand (Frodeman2014 p 77)

In the Earth sciences understanding the entire geologicalrecord starts with a primordial rock cycle in which sedi-mentary processes are a fundamental part The cyclic natureof the sedimentary processes is evidenced by multiple stepsof erosionndashtransportndashsedimentation experienced by any sed-imentary particle from its source rock to its destination in asedimentary basin Many organisms also produce sedimentand their life cycles are controlled by cyclically changing

Figure 26 Characteristics and criteria for defining stratigraphic sequences within a cyclic and hierarchical framework (modified fromFragoso et al 2021) (a) T ndashR cycle anatomy (b) Vertical recurrence of individual cycles and trends in the cyclic stacking pattern (modulationof the smallest by the highest hierarchy) (c) Mappability of the stacking patterns and stratigraphic surfaces within a given framework whichis more significant the higher the hierarchy is Abbreviations MFS ndash maximum flooding surface MRS ndash maximum regressive surface

Figure 27 Hierarchical stratigraphic sequence framework (modified from Magalhatildees et al 2020) High-frequency sequences (fourth orhigher orders) are observed at outcrop and core scale The vertical recurrence of high-frequency sequences composes the low-frequencysequences observed in seismic data (third order) First- and second-order low-frequency sequences occur at basin scale predominantlylimited by unconformities as proposed by Sloss et al (1949)

environmental conditions A harmonic produced by oscil-lations from different sources frequencies and amplitudesthroughout this long sedimentation process modulates the fi-nal sedimentary product Thus the cyclical conception hasan important implication for understanding the sedimentaryrecord over geological time In the big picture the analysis ofcyclicity is a crucial tool to correctly decode the sedimentaryrecord (eg Barrell 1917)

However according to Miall (2004) contrary to thehermeneutic circle the practice of stratigraphy throughouthistory has separated the empirical descriptive (inductive)and theoretical (deductive) approaches Despite the advancesand contributions of different research groups working alongeach of these lines this author warns of the danger in the useof stratigraphic models that specifically seek evidence of reg-ularity or cyclicity of processes on Earth which may lead toa bias

Figure 28 Cyclic lacustrine sedimentation of the Upper Triassic Lockatong Formation (modified from Van Houten 1964) (a) Model ofdetrital and chemical short cycles (b) generalized stratigraphic section of Lockatong Formation and adjacent units The columns show thealternating geographic environments and the long climatic cycles of wetter and drier phases An age model is presented based on two longclimatic cycles with intermediate and short cycles associated

There is no place for superimposed inadequatelygrounded theoretical assumptions in the construc-tion of the geologic timescale The hermeneuticcircle is after all a circle We need to be as adeptat climbing the upward-directed arrow of theorybased on rigorous observation as we are skilled atavoiding the downward slide of making our obser-vations fit our deductions (Miall and Miall 2004p 44)

On the opposite side but in a complementary way strati-graphic analysis cannot be reduced to a mere collection ofsedimentological descriptions as gaps span an equivalentor even longer time than the sedimentary rock record (egDott 1983 Ager 1993 Miall 2004 2017) Given the lackof tools or parameters for measuring these time gaps in thestratigraphical record Fragoso et al (2021) warn that con-ceptual models are traditionally constructed from a mistakenperspective that assumes the complete preservation of three-dimensional depositional systems based on an oversimpli-fication of continuous sedimentation processes To guaran-tee realistic representations these authors propose that con-ceptual models incorporate knowledge of the processes thatcontrol the generation destruction and preservation of sed-imentary units to define at any timescales predictable andordered stratigraphic patterns for both the gaps and the pre-served record

Historical perspective is essential for identifying unsolvedproblems and developing future research programmes Ascan be seen throughout this brief review the identificationand interpretation of cycles correspond to a keystone in thehistory of stratigraphy However the use of the term ldquocyclerdquohas changed through time Stratigraphic cycles have been de-scribed as physical units with characteristic repetitive pat-terns but not always with a strict periodicity Facies cyclescyclothems clinoforms and stratigraphic sequences are ex-amples where what is called a ldquocyclerdquo is a sedimentary unitthat repeats itself in the stratigraphic record with or withoutinference of the processes responsible for this repetition Inthese cases the concept of cyclicity has a cognitive and di-dactic purpose functioning as an association of general ideasthat support the description and characterization of the repet-itive stratigraphic record What is interesting to note is thatdespite the different approaches and nomenclatures strati-graphic cycles have been described with very similar char-acteristics such as stacking patterns bounding surfaces andhierarchical frameworks This common thread of the differ-ent approaches paves the way for integrating efforts and theconsequent methodological improvement

For many years efforts have been made to develop math-ematical and statistical tools to characterize stratigraphic cy-cles Statistical distribution fitting (eg Pantopoulos et al2013) Markov chains (eg Krumbein and Dacey 1969

Figure 29 Outcrop examples of sedimentary cycles determined by cyclostratigraphic analysis (a) Long eccentricity short eccentricity andprecession cycles in hemipelagic limestone and marl alternations of the Sopelana section (Maastrichtian) Spain (modified from Batenburget al 2014) (b) long eccentricity cycles in hemipelagic limestone and marl alternations of the La Marcouline section (Middle Aptian)France (modified from Kuhnt and Moullade 2007) (c) long and short eccentricity cycles in shallow-marine deposits of the Kope Formation(Ordovician) United States (modified from Ellwood et al 2013)

Carr 1982 Purkis et al 2012) Fischer plots (eg Fischer1964 Read and Goldhammer 1988 Husinec et al 2008)time-series analysis (eg Schwarzacher 1975 Hinnov andPark 1998 Weedon 2003 Martinez et al 2016) and au-tomatic stratigraphic correlations (eg Nio et al 2005 Be-hdad 2019 Shi et al 2021) are examples of techniques usedin stratigraphic research for quantifying cycles With the so-called digital transformation currently in force in many areasof knowledge such quantitative approaches tend to be ex-panded Thus the knowledge acquired about the main cycliccharacteristics observed in the sedimentary record over thepast few years should be the plumb line towards a digitalrevolution within stratigraphy

The effort to obtain mathematical solutions is legitimateand perhaps the only way to resolve which cycles (physicalobservation) are candidates for being periodic (with a predic-

tive time value) or merely episodic However the mathemat-ical solutions must be combined with a rigorous analysis ofthe rock record that independently characterizes the sedimen-tological palaeontological and geochronological aspects Inthis sense integrated stratigraphy is undoubtedly the appro-priate way to reinforce the links between different method-ologies Astronomical calibration of the stratigraphic recordis appropriate for reducing uncertainties regarding interpreta-tions of changes in sea-level hydrodynamics climate physi-cal chemical and biological processes (Schwarzacher 2000Hilgen et al 2004 Strasser et al 2006 Fragoso et al 2021)

The recognition of multi-scale stratigraphic cycles asso-ciated with temporal calibrations that better define the rela-tionship ndash simple or complex ndash of cause (geological process)and effect (observable stratigraphic entity) will undoubtedlyboost the current three-dimensional simulations of deposi-

Figure 30 The hermeneutic circle (based on Miall 2004)

tional systems In this stratigraphic forward modelling suchparameters have already been used to simulate the genesis oflow- to high-frequency sequences in three-dimensional mod-els applied to oil and natural gas exploration and productionprojects (eg Huang et al 2015 Faria et al 2017)

In order to deeply understand the cyclicity in geologicalprocess it is necessary to consider its ultimate root ther-modynamics (eg Richet et al 2010) The first law of ther-modynamics also known as the law of conservation of en-ergy states that energy cannot be created or destroyed butcan change from one form to another In this sense every-thing in the Universe can be classified as a form of energyregardless of its physical nature Thus it is possible to con-vert energy into any different form be it a rock a tree or ahuman being When we consider the Law of Conservation ofEnergy applied to deep time it becomes possible to defineseveral and constant cycles of energy transformation such asthe rock cycle However in thermodynamics the reversibil-ity of natural processes only occurs when they do not lead toan increase in entropy In this way the cyclicity of geologicalprocesses does not show absolute stability and transforma-tions must be considered at an appropriate timescale Thatis both the planetrsquos internal geodynamics and the complexastronomical system can be visualized as spiral cycles thatconstantly change at different timescales (eg Schwarzacher1993) This logical construction is similar to the one of per-petual movement of history proposed by Giambattista Vicoin which a new cycle always begins with a remnant of thecycle that ended (Vaughan 1972)

It is challenging to think that the Earth itself is a specificproduct in time and space of the cyclic process of formationand destruction of stars which has been repeated since thebeginning of the Universe Different chemical elements areformed at each new cycle and subtly change the star nebulacomposition resulting from the great supernova explosionsIf it were not for the existence of one of these nebulae with

a particular chemical composition inherited from these pastcycles hovering in a specific corner of our galaxy 46 Ga agowe would not have the Earth system as we know it todayCarl Sagan famously stated that ldquothe cosmos is within usWe are made of star-stuffrdquo We are all then star-stuff on adeep journey of cyclic transformation

Data availability No data sets were used in this article

Author contributions DGCF conceived the presented ideawrote the manuscript draft prepared the figures and made changesto the manuscript according to the reviewersrsquo suggestions MKAJCM CMDSS GPRG and AS reviewed and improved themanuscript through corrections and suggestions

Competing interests The contact author has declared that nei-ther they nor their co-authors have any competing interests

Disclaimer Publisherrsquos note Copernicus Publications remainsneutral with regard to jurisdictional claims in published maps andinstitutional affiliations

Acknowledgements The authors would like to thank Petrobrasand the Petrobras School of High-Resolution Stratigraphy mem-bers Special thanks to Dora Atman and Romeu Rossi Juacuteniorfor valuable discussions and suggestions The authors are grate-ful to Andrew D Miall and Annalisa Ferretti for detailed andconstructive feedback as well as to editors Roman Leonhardt andKristian Schlegel for their support during the review processDaniel Galvatildeo Carnier Fragoso and Matheus Kuchenbecker wouldlike to make an honourable mention of their Alma Mater (Universi-dade Federal de Minas Gerais) especially Luiz Guilherme KnauerLuacutecia Maria Fantinel and Ricardo Diniz da Costa

Review statement This paper was edited by Roman Leonhardtand reviewed by Andrew Miall and Annalisa Ferretti

References

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Fischer A G Climatic oscillations in the bioshere in BioticCrises in Ecological and Evolutionary Time edited by NiteckiM H Academic Press 103ndash131 httpsdoiorg101016B978-0-12-519640-650012-0 1981

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Fisher W L Gama Jr E and Ojeda H A O Estratigrafia siacutes-mica e sistemas deposicionais da Formaccedilatildeo Piaccedilabuccedilu XXVIICongresso Brasileiro de Geologia Aracaju 123ndash134 1973

Fisk H N Kolb C R McFarlan E and Wilbert L J Sedi-mentary framework of the modern Mississippi delta [Louisiana]J Sediment Res 24 76ndash99 httpsdoiorg101306D4269661-2B26-11D7-8648000102C1865D 1954

Fragoso D G C Gabaglia G P R Magalhatildees AJ C and Scherer C M dos S Cyclicity and hi-erarchy in sequence stratigraphy an integrated approachBraz J Geol 51 e20200106 httpsdoiorg1015902317-4889202120200106 2021

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Gilbert G K Lake Bonneville Lake Bonneville US GovernmentPrinting Office Washington DC httpsdoiorg103133m11890

Gilbert G K Sedimentary Measurement of Cretaceous Time JGeol 3 121ndash127 httpsdoiorg101086607150 1895

Glennie K W Desert sedimentary environments ElsevierISBN 9780080869254 2010

Gnibidenko H S and Shashkin K S Basic principlesof the geosynclinal theory Tectonophysics 9 5ndash13httpsdoiorg1010160040-1951(70)90025-9 1970

Goldhammer R K Cyclic sedimentation in SedimentologySpringer Berlin Heidelberg Berlin Heidelberg 271ndash293httpsdoiorg1010073-540-31079-7_57 1978

Grabau A Oscillation or pulsation 16th International GeologicalCongress Washington Report 539ndash552 1936

Gradstein F M Ogg J G Schmitz M D and Ogg G M Geo-logic Time Scale 2020 Elsevier ISBN 9780128243619 2020

Gregor B Some ideas on the rock cycle 1788ndash1988 GeochimCosmochim Ac 56 2993ndash3000 httpsdoiorg1010160016-7037(92)90285-Q 1992

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Hajek E A and Straub K M Autogenic Sedimentation in Clas-tic Stratigraphy Annu Rev Earth Planet Sc 45 681ndash709httpsdoiorg101146annurev-earth-063016-015935 2017

Hallam A Secular changes in marine inundation of USSR andNorth America through the Phanerozoic Nature 269 769ndash772httpsdoiorg101038269769a0 1977

Haq B U and Schutter S R A chronology of Pa-leozoic sea-level changes Science 322 64ndash68httpsdoiorg101126science1161648 2008

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Hays J D Imbrie J and Shackleton N J Variationsin the Earthrsquos Orbit Pacemaker of the Ice Ages For500000 years major climatic changes have followed varia-tions in obliquity and precession Science 194 1121ndash1132httpsdoiorg101126science19442701121 1976

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Hinnov L A Cyclostratigraphy and astrochronology in 2018in Stratigraphy amp Timescales Vol 3 Elsevier 1ndash80httpsdoiorg101016bssats201808004 2018

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Hockey T Trimble V Williams T R Bracher K Jarrell R AMarcheacute J D Palmeri J and Green D W E (Eds) Biograph-ical Encyclopedia of Astronomers Springer New York NewYork NY httpsdoiorg101007978-1-4419-9917-7 2014

Holbrook J M and Miall A D Time in the RockA field guide to interpreting past events and processesfrom siliciclastic stratigraphy Earth-Sci Rev 203 103121httpsdoiorg101016jearscirev2020103121 2020

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Hunt D and Tucker M E Stranded parasequences and the forcedregressive wedge systems tract deposition during base-levelrsquofallSediment Geol 81 1ndash9 httpsdoiorg1010160037-0738(92)90052-S 1992

Husinec A Basch D Rose B and Read J F FISCHER-PLOTS An Excel spreadsheet for computing Fischer plots ofaccommodation change in cyclic carbonate successions in boththe time and depth domains Comput Geosci 34 269ndash277httpsdoiorg101016jcageo200702004 2008

Illing L V Bahaman calcareous sands AAPG Bull 381ndash95 httpsdoiorg1013065CEADEB4-16BB-11D7-8645000102C1865D 1954

Imbrie J and Imbrie K P Ice ages solving the mystery HarvardUniversity Press ISBN 0674440757 1986

Jamieson T F On the History of the Last GeologicalChanges in Scotland Q J Geol Soc 21 161ndash204httpsdoiorg101144GSLJGS186502101-0224 1865

Johnson M E Chap 5 A W Grabaursquos embryonic sequencestratigraphy and eustatic curve in Geological Society of Amer-ica Memoirs Vol 180 Geological Society of America 43ndash54httpsdoiorg101130MEM180-p43 1992

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Kearey P Klepeis K A and Vine F J Global tectonics JohnWiley amp Sons ISBN 978-1-405-10777-8 2009

Klein G deV and Willard D A Origin of the Penn-sylvanian coal-bearing cyclothems of North AmericaGeology 17 152ndash155 httpsdoiorg1011300091-7613(1989)017lt0152OOTPCBgt23CO2 1989

Kodama K P and Hinnov L A Rock magnetic cyclostratigra-phy Wiley-Blackwell Chichester West Sussex UK ISBN 978-1-118-56128-7 2015

Kravitz G The Geohistorical Time Arrow From Stenorsquos Strati-graphic Principles to Boltzmannrsquos Past Hypothesis J GeosciEduc 62 691ndash700 httpsdoiorg10540813-1071 2014

Krumbein W C and Dacey M F Markov chains and embed-ded Markov chains in geology Mathemat Geol 1 79ndash96httpsdoiorg101007BF02047072 1969

Kvale E P Tides and tidal rhytmites in SedimentologySpringer Berlin Heidelberg Berlin Heidelberg 1224ndash1228httpsdoiorg1010073-540-31079-7_238 1978

Laskar J Fienga A Gastineau M and Manche H La2010a new orbital solution for the long-term motion of the Earth

Astron Astrophys 532 A89 httpsdoiorg1010510004-6361201116836 2011

Le Pichon X Fifty years of plate tectonics Af-terthoughts of a witness Tectonics 38 2919ndash2933httpsdoiorg1010292018TC005350 2019

Li M Huang C Ogg J Zhang Y Hinnov L Wu HChen Z-Q and Zou Z Paleoclimate proxies for cyclostratig-raphy Comparative analysis using a Lower Triassic ma-rine section in South China Earth-Sci Rev 189 125ndash146httpsdoiorg101016jearscirev201901011 2019

Lima A De Vivo B Spera F J Bodnar R J MiliaA Nunziata C Belkin H E and Cannatelli C Ther-modynamic model for uplift and deflation episodes (brady-seism) associated with magmaticndashhydrothermal activity atthe Campi Flegrei (Italy) Earth-Sci Rev 97 44ndash58httpsdoiorg101016jearscirev200910001 2009

Lirer F and Iaccarino S Mediterranean Neogene historical stra-totype sections and Global Stratotype Section and Point (GSSP)state of the art Ann Naturhist Mus Wien Ser A 113 67ndash1442011

Lyell C Principles of geology John Murray 1835Maclaren C The glacial Theory of Prof Agassiz Am J Sci Art

42 346ndash365 1842Magalhatildees A J C Raja Gabaglia G P Scherer C M S Baacutel-

lico M B Guadagnin F Bento Freire E Silva Born L Rand Catuneanu O Sequence hierarchy in a Mesoproterozoic in-terior sag basin from basin fill to reservoir scale the TombadorFormation Chapada Diamantina Basin Brazil Basin Res 28393ndash432 httpsdoiorg101111bre12117 2016

Magalhatildees A J C Lima-Filho F P Guadagnin F SilvaV A Teixeira W L E Souza A M Raja GabagliaG P and Catuneanu O Ground penetrating radar forfacies architecture and high-resolution stratigraphy Ex-amples from the Mesoproterozoic in the Chapada Dia-mantina Basin Brazil Mar Petrol Geol 86 1191ndash1206httpsdoiorg101016jmarpetgeo201707027 2017

Magalhatildees A J C Raja Gabaglia G P Fragoso D G CBento Freire E Lykawka R Arregui C D Silveira M ML Carpio K M T De Gasperi A Pedrinha S ArtagatildeoV M Terra G J S Bunevich R B Roemers-OliveiraE Gomes J P Hernaacutendez J I Hernaacutendez R M andBruhn C H L High-resolution sequence stratigraphy appliedto reservoir zonation and characterisation and its impact onproduction performance ndash shallow marine fluvial downstreamand lacustrine carbonate settings Earth-Sci Rev 210 103325httpsdoiorg101016jearscirev2020103325 2020

Martinez M Kotov S De Vleeschouwer D Pas D and Pauml-like H Testing the impact of stratigraphic uncertainty on spec-tral analyses of sedimentary series Clim Past 12 1765ndash1783httpsdoiorg105194cp-12-1765-2016 2016

Maslin M Forty years of linking orbits to ice ages Nature 540208ndash209 httpsdoiorg101038540208a 2016

Matenco L C and Haq B U Multi-scale depositional suc-cessions in tectonic settings Earth-Sci Rev 200 102991httpsdoiorg101016jearscirev2019102991 2020

Mazur A Amadeus Grabau in China 1920ndash1946 Carbon-ate Evaporite 21 51ndash93 httpsdoiorg101007BF031754682006

Miall A D Empiricism and model building in stratigraphy thehistorical roots of present-day practices Stratigraphy 1 3ndash252004

Miall AD Updating uniformitarianism stratigraphy as just a setof ldquofrozen accidentsrdquo Geological Society of London SpecialPublications 404 11ndash36 httpsdoiorg101144SP4044 2015

Miall A D Stratigraphy A Modern Synthesis Springer Inter-national Publishing Cham httpsdoiorg101007978-3-319-24304-7 2016

Miall A D Holbrook J M Bhattacharya J P TheStratigraphy Machine J Sediment Res 91 595ndash610httpsdoiorg102110jsr2020143 2021

Miall A D and Miall C E Empiricism and model-buildingin stratigraphy around the hermeneutic circle in the pursuit ofstratigraphic correlation Stratigraphy 1 27ndash46 2004

Middleton G V (Ed) Primary Sedimentary Structures and theirHydrodynamic Interpretation SEPM Spec Publ12 265 pp1965

Middleton G V Johannes Waltherrsquos Law of the Correlation ofFacies GSA Bull 84 979ndash988 httpsdoiorg1011300016-7606(1973)84lt979JWLOTCgt20CO2 1973

Middleton G V Sedimentary geology in SedimentologySpringer Netherlands Dordrecht httpsdoiorg1010073-540-31079-7_184 1978

Milankovitch M Kanon der Erdbestrahlung und seine Anwendungauf das Eiszeitenproblem Mihaila Curcica Belgrade 633 pp1941

Mitchell R N Spencer C J Kirscher U He X-F MurphyJ B Li Z-X and Collins W J Harmonic hierarchy ofmantle and lithospheric convective cycles Time series analysisof hafnium isotopes of zircon Gondwana Res 75 239ndash248httpsdoiorg101016jgr201906003 2019

Mitchum Jr R M Seismic stratigraphy and global changes ofsea level Part 11 Glossary of terms used in seismic stratigra-phy Section 2 Application of seismic reflection configurationto stratigraphic interpretation in Seismic Stratigraphy Appli-cations to Hydrocarbon Exploration edited by Payton C EAAPG Memoir 26 51ndash52 1977

Mitchum Jr R M and Vail P R Seismic stratigraphy and globalchanges of sea level Part 7 Seismic stratigraphic interpretationprocedure Section 2 Application of seismic reflection config-uration to stratigraphic interpretation in Seismic StratigraphyApplications to Hydrocarbon Exploration edited by Payton CE AAPG Memoir 26 135ndash143 1977

Moore R C Stratigraphic classification of the Pennsylvanianrocks of Kansas Kansas Geological Survey Bulletin Tulsa 22256 pp 1936

Moore R C Paleoecological aspects of Kansas Pennsylvanianand Permian cyclothems in Symposium on cyclic sedimenta-tion 169 edited by Merriam D F Kansas Geological SurveyUnited States of America 287ndash380 1964

Muumlller R D and Dutkiewicz A Oceanic crustal carbon cycledrives 26-million-year atmospheric carbon dioxide periodicitiesSci Adv 6 eaaq0500 httpsdoiorg101126sciadvabd09532018

Montantildeez I Norris R MA C Johnson K MJ K Kiehl JKump L Ravelo A and KK T Understanding Earthrsquos DeepPast Lessons for our Climate Future The National AcademiesPress Washington DC ISBN 978-0-309-20919-9 2011

Nelson H Kykloi cyclic theories in ancient Greece MSPortland State University United States of Americahttpsdoiorg1015760etd3256 1980

Nagel E The Structure of Science Problems in the Logic of Sci-entific Explanation Harcourt Brace amp World United States ofAmerica ISBN 0710018827 1961

Nio S D Brouwer J H Smith D de Jong M and BoumlhmA R Spectral trend attribute analysis applications in thestratigraphic analysis of wireline logs First Break 23 71ndash75httpsdoiorg1039971365-239723426503 2005

OrsquoHara K D A Brief History of Geology Cam-bridge University Press Cambridge United Kingdomhttpsdoiorg1010179781316809990 2018

Oomkens E and Terwindt J H J Inshore estuarine sedi-ments in the Haringvliet (Netherlands) Geologie en mijnbouw orgaan voor officieele mededelingen van het Geologisch-Mijnbouwkundig Genootschap voor Nederland en Kolonien 39701ndash710 1960

Paillard D Glacial cycles toward a new paradigm Rev Geophys39 325ndash346 httpsdoiorg1010292000RG000091 2001

Pantopoulos G Vakalas I Maravelis A and ZelilidisA Statistical analysis of turbidite bed thickness pat-terns from the Alpine fold and thrust belt of westernand southeastern Greece Sediment Geol 294 37ndash57httpsdoiorg101016jsedgeo201305007 2013

Parascandola A (Ed) I fenomeni bradisismici del Serapeo di Poz-zuoli Stabilmento tipografico G Genovese 117 pp 1947

Payton C E (Ed) Seismic Stratigraphy mdash Applications to Hydro-carbon Exploration American Association of Petroleum Geolo-gists 516 pp httpsdoiorg101306M26490 1977

Posarnentier H W and Allen G P (Eds) Siliciclastic SequenceStratigraphy SEPM (Society for Sedimentary Geology) SEPM(Society for Sedimentary Geology) United States of Americahttpsdoiorg102110csp9907 1999

Peloggia A U G The Rock Cycle of the Anthropocene insertinghuman agency into the Earth System Revista do Instituto Ge-oloacutegico 39 1ndash13 httpsdoiorg1059350100-929x201800012018

Posamentier H W and Allen G P Siliciclastic sequencestratigraphy Concepts and Applications SEPM Con-cepts in Sedimentology and Paleontology 7 210 pphttpsdoiorg102110csp9907 1999

Posamentier H W Jervey M T and Vail P R Eustatic Controlson Clastic Deposition ImdashConceptual Framework in Sea-LevelChanges An Integrated Approach vol 42 edited by Wilgus CK Hastings B S Posamentier H Wagoner J V Ross C Aand Kendall C G St C SEPM Society for Sedimentary Geol-ogy 109-124 httpsdoiorg102110pec88010109 1988

Preston F W and Henderson J Fourier series characterization ofcyclic sediments for stratigraphic correlation in Symposium oncyclic sedimentation 169 edited by Merriam D F Kansas Ge-ological Survey United States of America 415ndash425 1964

Puche-Riart O History of Geology up to 1780 in Encyclope-dia of Geology Elsevier 167ndash172 httpsdoiorg101016B0-12-369396-900367-1 2005

Puetz S J The Unified Cycle Theory How Cycles Dominate theStructure of the Universe and Influence Life on Earth OutskirtsPress United States of America 489 pp ISBN 97814327121672009

Purkis S Vlaswinkel B and Gracias N Vertical-To-LateralTransitions Among Cretaceous Carbonate FaciesndashA Means To3-D Framework Construction Via Markov Analysis J SedimentRes 82 232ndash243 httpsdoiorg102110jsr201223 2012

Rampino M R Caldeira K and Zhu Y A pulse of theEarth A 275-Myr underlying cycle in coordinated geologi-cal events over the last 260 Myr Geosci Front 12 101245httpsdoiorg101016jgsf2021101245 2021

Randall L and Reece M Dark Matter as a Trigger forPeriodic Comet Impacts Phys Rev Lett 112 1ndash5httpsdoiorg101103PhysRevLett112161301 2014

Read J F and Goldhammer R K Use of Fischerplots to define third-order sea-level curves in Or-dovician peritidal cyclic carbonates AppalachiansGeology 16 895ndash899 httpsdoiorg1011300091-7613(1988)016lt0895UOFPTDgt23CO2 1988

Rich J L Three critical environments of deposition and cri-teria for recognition of rocks deposited in each of themGeol Soc Am Bull 62 1ndash20 httpsdoiorg1011300016-7606(1951)62[1TCEODA]20CO2 1951

Richet P Henderson G and Neuville D ThermodynamicsThe Oldest Branch of Earth Science Element 6 287ndash292httpsdoiorg102113gselements65287 2010

Sadler P The influence of hiatuses on sediment accumulation ratesin on the determination of sediment accumulation rates GeoRe-search Forum 5 5ndash40 1999

Sames B Wagreich M Conrad C P and Iqbal S Aquifer-eustasy as the main driver of short-term sea-level fluc-tuations during Cretaceous hothouse climate phases Geo-logical Society London Special Publications 498 9ndash38httpsdoiorg101144SP498-2019-105 2020

Schulz M and Schaumlfer-Neth C Translating Milankovitch cli-mate forcing into eustatic fluctuations via thermal deep wa-ter expansion a conceptual link Terra Nova 9 228-231httpsdoiorg101111j1365-31211997tb00018x 1998

Schwarzacher W Sedimentation models and quantitative stratigra-phy Elsevier the Netherlands 381 pp ISBN 97800808693151975

Schwarzacher W Cyclostratigraphy and the Milankovitch Theo-rym Elsevier the Netherlands 226 pp ISBN 97800808696671993

Schwarzacher W Repetitions and cycles in stratigraphy Earth-SciRev 50 51ndash75 httpsdoiorg101016S0012-8252(99)00070-7 2000

Seranne M Early Oligocene stratigraphic turnover on thewest Africa continental margin a signature of the Tertiarygreenhouse-to-icehouse transition Terra Nova 11 135ndash140httpsdoiorg101046j1365-3121199900246x 1999

Shackleton N Oxygen isotope analyses and Pleis-tocene temperatures re-assessed Nature 215 15ndash17httpsdoiorg101038215015a0 1967

Shaviv N J Prokoph A and Veizer J Is the solar systemrsquos galac-tic motion imprinted in the Phanerozoic climate Sci Rep 41ndash6 httpsdoiorg101038srep06150 2014

Shearman D J Origin of marine evaporites by diagenesis Trans-actions of the Institute of Mining and Metallurgy Section B 75208ndash215 1966

Shi B Chang X Liu Z Pang Y Xu Y Mao L Zhang Pand Chen G Intelligent identification of sequence stratigraphy

constrained by multipopulation genetic algorithm and dynamictime warping technique A case study of Lower Cretaceous Qing-shuihe Formation in hinterland of Junggar Basin (NW China)Basin Res 33 2517ndash2544 httpsdoiorg101111bre125672021

Simons D B and Richardson E V Resistance to flow in allu-vial channels Professional Paper U S Govt Print Off 70 pphttpsdoiorg103133pp422J 1966

Sloss L L Sequences in the Cratonic Interior of NorthAmerica GSA Bull 74 93ndash114 httpsdoiorg1011300016-7606(1963)74[93SITCIO]20CO2 1963

Sloss L L Krumbein W C and Dapples E C Integrated Fa-cies Analysis in Geological Society of America Memoirs 39Geol Soc Am 39 91ndash124 httpsdoiorg101130MEM39-p91 1949

Stern R J and Scholl D W Yin and yang of continental crust cre-ation and destruction by plate tectonic processes Int Geol Rev52 1ndash31 httpsdoiorg10108000206810903332322 2010

Stille H Grundfragen der vergleichenden Tektonik Nature 117192ndash192 httpsdoiorg101038117192b0 1926

Strasser A Hiatuses and condensation an estimation of time loston a shallow carbonate platform Depositional Record 1 91ndash117 httpsdoiorg101002dep29 2015

Strasser A Cyclostratigraphy of shallow-marinecarbonatesndashlimitations and opportunities in Cy-clostratigraphy and Astrochronology 3 edited byMichael Montenari Elsevier the Netherlands 151ndash187httpsdoiorg101016bssats201807001 2018

Strasser A Pittet B Hillgaumlrtner H and Pasquier J-BDepositional sequences in shallow carbonate-dominated sed-imentary systems concepts for a high-resolution analysisSediment Geol 128 201ndash221 httpsdoiorg101016S0037-0738(99)00070-6 1999

Strasser A Hilgen F J and Heckel P H Cyclostratigraphy-concepts definitions and applications Newsl Stratigr 42 75ndash114 httpsdoiorg1011270078-042120060042-0075 2006

Suess E Das antlitz der erde F Tempsky 1888Teichert C Concepts of Facies AAPG Bull 42 2718ndash

2744 httpsdoiorg1013060BDA5C0C-16BD-11D7-8645000102C1865D 1958

Timothy R C Log-Linear Models Markov Chainsand Cyclic Sedimentation SEPM JSR 52 905ndash912 httpsdoiorg101306212F808A-2B24-11D7-8648000102C1865D 1982

Udden J A Geology and mineral resources of the Peoriaquadrangle Illinois Bull Govt Print Off 506 103 pphttpsdoiorg103133b506 1912

Vail P R Chap 8 The evolution of seismic stratigraphyand the global sea-level curve in Eustasy The HistoricalUps and Downs of a Major Geological Concept edited byDott Jr R H Geological Society of America 180 83ndash92httpsdoiorg101130MEM180-p83 1992

Vail P R Mitchum R M and Thompson S Seismic Stratig-raphy and Global Changes of Sea Level Part 4 Global Cyclesof Relative Changes of Sea Level in Seismic Stratigraphy Ap-plications to Hydrocarbon Exploration edited by Payton C EAAPG Memoir 26 83ndash97 httpsdoiorg101306M26490C61977

Van Houten F B Cyclic lacustrine sedimentation upper Trias-sic Lockatong formation central New Jersey and adjacent Penn-sylvania in Symposium on cyclic sedimentation 169 editedby Merriam D F Kansas Geological Survey United States ofAmerica 497ndash531 1964

Van Siclen D C Depositional topography ndash ex-amples and theory AAPG Bull 42 1897ndash1913httpsdoiorg1013060BDA5B88-16BD-11D7-8645000102C1865D 1958

Van Wagoner J C Mitchum R M Campion K M and Rah-manian V D Siliciclastic sequence stratigraphy in well logscores and outcrops concepts for high-resolution correlation oftime and facies American Association of Petroleum GeologistsUnited States of America httpsdoiorg101306Mth75101990

Vaughan F The Political Philosophy of Giambattista Vico AnIntroduction to La Scienza Nuova Springer the Netherlandshttpsdoiorg101007978-94-010-2781-6 1972

Wagreich M Sames B Hart M and Yilmaz I O An in-troduction to causes and consequences of Cretaceous sea-levelchanges (IGCP 609) Geol Soc Lond Sp Publ 498 1ndash8httpsdoiorg101144SP498-2019-156 2020

Walker J D Geissman J W Bowring S A and Babcock L EThe Geological Society of America geologic time scale GSABull 125 259ndash272 httpsdoiorg101130B307121 2013

Wanless H R Geology and Mineral Resources of the AlexisQuadrangle Illinois State Geological Survey Bulletin 57 UnitedStates of America 268 pp ISBN 10 0265850355 1929

Wanless H R Pennsylvanian Section in Western Illinois GSABull 42 801ndash812 httpsdoiorg101130GSAB-42-801 1931

Wanless H R and Weller J M Correlation and Extentof Pennsylvanian Cyclothems GSA Bull 43 1003ndash1016httpsdoiorg101130GSAB-43-1003 1932

Weedon G P Time-Series Analysis and Cyclostratig-raphy Examining Stratigraphic Records of Environ-mental Cycles 1st edn Cambridge University Presshttpsdoiorg101017CBO9780511535482 2003

Wegener A Die Entstehung der Kontinente und Ozeane Braun-schweig 94 ISBN 9783443010560 1915

Weller J M Cyclical Sedimentation of the Pennsylva-nian Period and Its Significance J Geol 38 97ndash135httpsdoiorg101086623695 1930

Weller J M Rhythms in upper Pennsylvanian cyclothems IllinoisState Geological Survey Bulletin 92 United States of America1943

Weller J M Cyclothems and larger sedimentary cy-cles of the Pennsylvanian J Geol 66 195ndash207httpsdoiorg101086626494 1958

Weller J M Stratigraphic principles and practice Harper UnitedStates of America 725 pp 1960

Weller J M Development of the concept and interpretation ofcyclic sedimentation in Symposium on cyclic sedimentation169 edited by DF Merriam Kansas Geological Survey UnitedStates of America 607ndash621 1964

Westerhold T Marwan N Drury A J Liebrand D Agnini CAnagnostou E Barnet J S Bohaty S M De VleeschouwerD and Florindo F An astronomically dated record of Earthrsquosclimate and its predictability over the last 66 million years Sci-ence 369 1383ndash1387 httpsdoiorg101126scienceaba68532020

Wilgus C K Hastings B S Posamentier H Wagoner J VRoss C A and Kendall C G St C (Eds) Sea-Level ChangesAn Integrated Approach SEPM Society for Sedimentary Geol-ogy 407 pp 1988

Willis B Principles of paleogeography Science 31 241ndash260httpsdoiorg101126science31790241 1910

Wilson J T A new class of faults and their bearing on continentaldrift Nature 207 343ndash347 httpsdoiorg101038207343a01965

Wilson J T Did the Atlantic close and then re-open Nature 211676ndash681 httpsdoiorg101038211676a0 1966

Wilson R C L Sequence stratigraphy a revolution with-out a cause Geol Soc Lond Sp Publ 143 303ndash314httpsdoiorg101144GSLSP19981430120 1998

Wilson R W Houseman G A Buiter S J H McCaffrey K Jand Doreacute A G Fifty years of the Wilson Cycle concept in platetectonics an overview Geol Soc Lond Sp Publ 470 1ndash17httpsdoiorg101144SP470-2019-58 2019

Zeller EJ Cycles and psychology in Symposium on cyclic sed-imentation 169 edited by Merriam D F Kansas GeologicalSurvey United States of America 631ndash636 1964

Abstract
Introduction
Cyclicity of geological processes
- The astronomical clock
- - The beginning of glacial theories
  - Milankovitch and the definitive return of astronomical climate models
  - Astronomical forcings on the Earth system
  - - The internal gears of geodynamics
    - - Diastrophic theories and the birth of eustasy
      - Plate tectonics and Wilson cycles
      - Internal geodynamic forcings in the Earth system
      - Cyclicity of the stratigraphic record
        
        Sedimentary facies cycles
        
        Cyclothems
        
        Clinoforms
        
        Stratigraphic sequences
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        Author contributions
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 2: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

tory (Vaughan 1972) According to Vico societies developin a similar and repetitive pattern followed by phases of so-cial and political organizations going from insurrection toinevitable decline An exciting aspect of Vicorsquos vision is thatthe perpetual motion of history does not reproduce a per-fectly circular pattern but a spiral in each new cycle thatbegins there is a remnant of the cycle that has ended In thepresent century Puetz (2009) proposed the ldquoUnified CycleTheoryrdquo which seeks to demonstrate how cycles dominatethe universersquos structure influencing various aspects of lifeon Earth Through the predictability aspect of the cyclical ap-proach this author pursues definition of future turning pointsfor humanity

Explanations of sound tone and harmonics wereamong the first elements of modern physical sci-ence This early success in description and predic-tion of periodic astronomical events together withan understanding of periodicity related to vibra-tion in the production of sounds led scientists toseek periodicities elsewhere in the natural worldToday the list is extensive for phenomena in whichcycles have been studied It includes sunspot ac-tivity tides and ocean waves Earth tides musichuman speech tree-ring growth animal popula-tion changes brain waves heart rhythm chem-ical bonding forces climatic activity economicgrowth light and other electromagnetic wave phe-nomena and geological events (Preston and Hen-derson 1964 p 415)

Cycles rhythms oscillations pulsations repetitions orperiods are examples of terms frequently used in the geo-logical literature that reflect a profound influence of the con-ception of cyclicity in the Earth sciences Whether through ahistorical heritage or from the various discoveries made overtime examples are plentiful to demonstrate that the idea ofcycles is used to describe geological processes and productscontaining some characteristic repetitive patterns in the geo-logical record

Considering the overuse of cyclicity concepts Dott (1992)described them as a ldquopowerful opiaterdquo for geologists Thecriticism of the cyclic approach is that there is an innatepsychological appeal to simplicity provided by rhythmicallyrepetitive patterns that attempt to order randomness (egNagel 1961 Zeller 1964) It is a fact that in many casescycle concepts are vaguely used in the geological literaturewithout the commitment to defining order and periodicityThis is the case of the rock cycle a postulate that states thatthe rock record itself is a product of a fundamental cycle inwhich igneous sedimentary and metamorphic rocks are con-tinuously turned into one another (eg Gregor 1992) It is un-derstandable that in cases like this the concept of cyclicity isused as a device to didactically explain various complex andrepetitive processes that occur on the planet (eg Peloggia2018) However the current understanding of the processes

that integrate the Earth system theorizes the existence of pe-riodical processes at different timescales that emanate fromthe astronomical forces that make our planet interact withneighbouring celestial bodies (eg Hinnov 2018) and fromthe complex dynamics of the Earthrsquos interior (eg Mitchell etal 2019) In this way the occurrence of ldquotrue cyclesrdquo whichcorrespond to an orderly repetitive progression of events thatis unlikely to occur by chance is increasingly being demon-strated Many of these cycles leave a recognizable mark inthe geological record and their understanding is invaluablein the study of stratigraphic organization

Nature vibrates with rhythms climatic and dys-trophic those finding stratigraphic expressionranging in period from the rapid oscillation ofsurface waters recorded in ripple-marks to thoselong-deferred stirrings of the deep imprisoned ti-tans which have divided earth history into periodsand eras The flight of time is measured by theweaving of composite rhythms ndash day and nightcalm and storm summer and winter birth anddeath ndash such as these are sensed in the brief lifeof man But the career of the Earth recedes intoa remoteness against which these lesser cycles areas unavailing for the measurement of that abyss oftime as would be for human history the beating ofan insectrsquos wing We must seek out then the na-ture of those longer rhythms whose very existencewas unknown until man by the light of sciencesought to understand the Earth [] Sedimentationis controlled by them and the stratigraphic seriesconstitutes a record written on tablets of stone ofthese lesser and greater waves which have pulsedthrough geologic time (Barrell 1917 p 746)

Henceforward cycle concepts have been essential in pro-moting geological knowledge and constitute one of the pil-lars of stratigraphy (eg Schwarzacher 2000) Current strati-graphic research integrates several systematic methods toidentify and interpret repetitive units of the sedimentaryrecord (eg sequence stratigraphy and cyclostratigraphy) Inthis context comprehension of the origin and evolution of thecyclicity concepts in stratigraphy is quite relevant and oppor-tune The following synthesis reviews the main works thatuse these concepts to interpret geological processes and theirimprint in the stratigraphic record It goes from a historicalreview to the current state of the art in stratigraphic principlesand practices

2 Cyclicity of geological processes

Studies of cyclicity in geological processes commonly seekto find periodicities in data series and explain them interms of known natural phenomena (Preston and Hender-son 1964) The current demonstration of recurring global

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 3: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 4: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 5: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 6: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 7: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 8: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 9: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 10: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 11: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 12: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 13: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 14: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 15: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

32 Cyclothems

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 16: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

33 Clinoforms

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 17: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 18: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 19: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

35 Astrocycles

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 20: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

4 Discussion

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 21: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 22: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 23: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 24: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 25: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

References

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 26: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 27: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 28: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 29: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 30: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

Page 31: Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

Abstract
Introduction
        
        
        Cyclothems
        
        Clinoforms
        
        
        Astrocycles
        
        Discussion
        
        Data availability
        
        
        Competing interests
        
        Disclaimer
        
        Acknowledgements
        
        Review statement
        
        References

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Cyclicity in Earth sciences, quo vadis? Essay on cycle ... - HGSS

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