The archetype of a cycle has played an essential role in explainingobservations of nature over thousands of years. At present, this perceptionsignificantly influences the worldview of modern societies, includingseveral areas of science. In the Earth sciences, the concept of cyclicity offers simple analytical solutions in the face of complex events and their respective products, in both time and space. Current stratigraphic research integrates several methods to identify repetitive patterns in thestratigraphic record and to interpret oscillatory geological processes. Thisessay proposes a historical review of the cyclic conceptions from theearliest phases in the Earth sciences to their subsequent evolution into current stratigraphic principles and practices, contributing to identifying opportunities in integrating methodologies and developing future researchmainly associated with quantitative approaches.

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The word “cycle” derives from the Greek term “κψκλoσ”, used to describe any circular body as well as any circular and perpetual movement of successive events or phenomena, whichkeep returning to their original position positions during their dynamics.Ancient Greeks described repetitive patterns to characterize theorganization of almost all known processes. This idea of uniformity andcontinuity has been influenced by empirical observations of naturalphenomena like day and night, changes in the moon phase, and seasons(Nelson, 1980).

From a historical perspective, the cycle archetype is found in severalancient traditions, attested, for instance, in lithic monuments such asStonehenge, built-in alignment with solar and lunar cycles (Hawkins, 1963),and religious practice regulated by the seasons and their astronomicalmarkers (Boutsikas and Ruggles, 2011). Nowadays, the cyclicity conception iswidespread in many areas of knowledge. The Italian philosopher GiambattistaVico (1668–1744), for example, introduced in the 18th century thecyclic idea of history (Vaughan, 1972). According to Vico, societies developin a similar and repetitive pattern, followed by phases of social andpolitical organizations, going from insurrection to inevitable decline. Anexciting aspect of Vico's vision is that the perpetual motion of historydoes not reproduce a perfectly circular pattern but a spiral: in each new cycle that begins, there is a remnant of the cycle that has ended. Inthe present century, Puetz (2009) proposed the “Unified Cycle Theory”, whichseeks to demonstrate how cycles dominate the universe's structure,influencing various aspects of life on Earth. Through the predictabilityaspect of the cyclical approach, this author pursues definition of future turning points for humanity.

Explanations of sound, tone, and harmonics were among the first elements ofmodern physical science. This early success in description and prediction ofperiodic astronomical events together with an understanding of periodicityrelated to vibration in the production of sounds led scientists to seekperiodicities elsewhere in the natural world. Today the list is extensivefor phenomena in which cycles have been studied. It includes sunspotactivity, tides and ocean waves, Earth tides, music, human speech, tree-ring growth, animal population changes, brain waves, heart rhythm, chemicalbonding forces, climatic activity, economic growth, light and otherelectromagnetic wave phenomena, and geological events (Preston andHenderson, 1964, p. 415).

Cycles, rhythms, oscillations, pulsations, repetitions, or periods areexamples of terms frequently used in the geological literature that reflecta profound influence of the conception of cyclicity in the Earth sciences. Whether through a historical heritage or from the various discoveries madeover time, examples are plentiful to demonstrate that the idea of cycles isused to describe geological processes and products containing somecharacteristic repetitive patterns in the geological record.

Considering the overuse of cyclicity concepts, Dott (1992) described them asa “powerful opiate” for geologists. The criticism of the cyclic approach isthat there is an innate psychological appeal to simplicity provided byrhythmically repetitive patterns that attempt to order randomness (e.g. Nagel, 1961; Zeller, 1964). It is a fact that, in many cases, cycle conceptsare vaguely used in the geological literature without the commitment todefining order and periodicity. This is the case of the rock cycle, apostulate that states that the rock record itself is a product of afundamental cycle in which igneous, sedimentary, and metamorphic rocks arecontinuously turned into one another (e.g. Gregor, 1992). It is understandable that, in cases like this, the concept of cyclicity is used asa device to didactically explain various complex and repetitive processesthat occur on the planet (e.g. Peloggia, 2018). However, the current understanding of the processes that integrate the Earth system theorizes theexistence of periodical processes, at different timescales, that emanatefrom the astronomical forces that make our planet interact with neighbouring celestial bodies (e.g. Hinnov, 2018) and from the complex dynamics of the Earth's interior (e.g. Mitchell et al., 2019). In this way, the occurrenceof “true cycles”, which correspond to an orderly, repetitive progression ofevents that is unlikely to occur by chance, is increasingly beingdemonstrated. Many of these cycles leave a recognizable mark in thegeological record, and their understanding is invaluable in the study ofstratigraphic organization.

Nature vibrates with rhythms, climatic and dystrophic, those finding stratigraphic expression ranging in period from the rapid oscillation of surface waters, recorded in ripple-marks, to those long-deferred stirrings of the deep imprisoned titans which have divided earth history into periods and eras. The flight of time is measured by the weaving of composite rhythms – day and night, calm and storm, summer and winter, birth and death – such as these are sensed in the brief life of man. But the career of the Earth recedes into a remoteness against which these lesser cycles are as unavailing for the measurement of that abyss of time as would be for human history the beating of an insect's wing. We must seek out, then, the nature of those longer rhythms whose very existence was unknown until man by the light of science sought to understand the Earth [...] Sedimentation is controlled by them, and the stratigraphic series constitutes a record, written on tablets of stone, of these lesser and greater waves which have pulsed through geologic time (Barrell, 1917, p. 746).

Henceforward, cycle concepts have been essential in promoting geologicalknowledge and constitute one of the pillars of stratigraphy (e.g. Schwarzacher, 2000). Current stratigraphic research integrates severalsystematic methods to identify and interpret repetitive units of thesedimentary record (e.g. sequence stratigraphy and cyclostratigraphy). In this context, comprehension of the origin and evolution of the cyclicity concepts in stratigraphy is quite relevant and opportune. Thefollowing synthesis reviews the main works that use these concepts tointerpret geological processes and their imprint in the stratigraphicrecord. It goes from a historical review to the current state of the art instratigraphic principles and practices.

Studies of cyclicity in geological processes commonly seek to findperiodicities in data series and explain them in terms of known naturalphenomena (Preston and Henderson, 1964). The current demonstration ofrecurring global processes, with regular periodicity, illustrates the searchfor “longer rhythms whose very existence was unknown until man by the lightof science sought to understand the Earth” (Barrell, 1917, p. 746). In arecent investigation into the recurrence and synchronicity of globalgeological events, Rampino et al. (2021) determined the existence of anEarth pulsation. The authors analysed 89 significant and well-dated geological events over the past 260 million years, including marine andnon-marine biological extinctions, major oceanic anoxic events, flood-basalteruptions, sea-level fluctuations, pulses of intraplate magmatism, and timesof changes in seafloor-spreading rates and plate reorganization.Moving-window analysis evidences the presence of 10 peaks or clusters in the number of events (Fig. 1a). Between these peaks, the number of eventsapproaches zero. Fourier analysis shows that the highest peak occurs at 27.5 Myr (99 % confidence), with a secondary signal at 8.9 Myr (Fig. 1b).Similar cycles have been determined in other studies analysing climate change (e.g. Shaviv et al., 2014), sea-level oscillations (e.g. Boulila et al., 2018), extinctions (e.g. Clube and Napier, 1996), and Earth's tectonicbehaviour (e.g. Müller and Dutkiewicz, 2018). The common finding of several authors is that these cyclical events are global, correlative, and tightly coupled. According to Rampino et al. (2021, p. 6), the correlationand cyclicity of these episodes point to an essentially periodic andcoordinated geological record, whose origin “may be entirely a function ofglobal internal Earth dynamics affecting global tectonics and climate, butsimilar cycles in the Earth's orbit in the Solar System and in the Galaxymight be pacing these events”.

Figure 1(a) Analysis of the ages of 89 geologic events using a 10 Myrmoving window centred every 0.5 Myr, with the number of occurrences that fall within the moving window computed at 1 Myr intervals. Ten clusters(peaks) are visible. In red is the Gaussian smoothing with a standard deviation of 5 Myr centred at every 0.1 Myr, with 10 peaks.(b) Fourier transform results show the highest peak in 27.5 Myr, and a strong secondary period occurs at 8.9 Myr (modified from Rampino et al., 2021).

2.1 The astronomical clock

Periodicity is one of the fundamental phenomena recorded by observant man.Cycles associated with astronomical events were among the first naturalphenomena described with sufficient precision and generality that suchevents could be predicted for the future. Even for primitive societies, onemeasure of their level of scientific understanding is the accuracy of theircalendars (Preston and Henderson, 1964, p. 415).

The roots of the geologists' appeal for the periodicity of natural processesmay be found in the Aristotelian worldview, which expanded the humanexperiences of the cyclic phenomena, such as day and night, tides, andseasons (Dott, 1992). In one of the first essays about the history ofgeology, the classic bookPrinciples of Geology by Charles Lyell (1797–1875) mentions thispossible relationship.

When we consider the acquaintance displayed by Aristotle, in his various works, with the destroying and renovating powers of nature, the introductory and concluding passages of the twelfth chapter of his “Meteorics” are certainly very remarkable. In the first sentence, he says, “the distribution of land and sea in particular regions does not endure throughout all time, but it becomes sea in those parts where it was land, and again it becomes land where it was sea; and there is a reason for thinking that these changes take place according to a certain system, and within a certain period.” The concluding observation is as follows: “As time never fails, and the Universe is eternal, neither the Tanais, nor the Nile, can have flowed forever. The places where they rise were once dry, and there is a limit to their operations, but there is none to time. So also of all other rivers; they spring up, and they perish; and the sea also continually deserts some lands and invades others. The same tracts, therefore, of the Earth are not, some always sea, and others always continents, but everything changes in the course of time.” It seems, then, that the Greeks [...] deduced, from their own observations, the theory of periodical revolutions in the inorganic world (Lyell, 1835, pp. 21–22).

Lyell (1835) discusses the intellectual advance of ancient civilizations,such as the Hindus and the Egyptians, and highlights mainly Greek philosophy that considered the course of events on the planet to be continually repeated in perpetual vicissitude, mainly influenced by the knowledge of astronomy. Thevarious Greek contributions to scientific knowledge reflect a strong senseof observation of astronomical cycles. Among the many examples, the studiesof celestial phenomena and their potential for temporal calibrations standout. Hipparchus of Nicaea (190–120 BC), considered by many to be thegreatest of Greek astronomers, used mathematical bases to determine thelength of the year and the recurrence of eclipses with relatively highprecision. Credit must be given to his conclusions about the motion of thestars, which Nicolaus Copernicus (1473–1543) later attributed to the “precession of the equinoxes” (Hockey et al., 2007). Twenty centuries later,these concepts would guide the research on orbital cyclicity used toconstruct paleoclimatic, cyclostratigraphic, and astrochronological models(e.g. Hinnov, 2018).

2.1.1 The beginning of glacial theories

The discovery of glacial cycles is among the greatest ever made in the Earth sciences. In 1837, Louis Agassiz (1807–1873), then president of the SwissSociety of Natural Sciences, presented ideas that shocked his peers (Imbrieand Imbrie, 1979). Agassiz (1840) argued that large fragments of rock, whichoccurred erratically in the region of the Jura mountains, far from theirareas of origin, were evidence of an ancient ice age. Although these ideaswere not necessarily original, having been put forward in the 18thcentury by James Hutton (1729–1797) and Bernard Friederich Kuhn (1762–1825), Agassiz brought “the glacial theory of scientific obscurity to thepublic eye” (Imbrie and Imbrie, 1979, p. 21).

Although the conception of an ice age was fundamentally as beingcatastrophic, its development took place on fertile ground for ideas of thecyclical nature of geological processes. Before Agassiz's work, one of thepioneers was Jens Esmark (1762–1839). Esmark (1824) showed that massiveglaciers covered different parts of Europe, sculpting the landscape, andproposed the eccentricity of the Earth's orbit as a hypothesis that causedclimate change. Influenced by William Whiston's (1667–1752) contributionsabout the elliptical orbit, which would periodically place Earth far fromthe Sun, Esmark combined these findings into a consistent theory (Hestmark, 2017). The dissemination of such ideas fostered the scientific debate that continues to the present day. Research into the relationshipbetween recurrent glaciations and orbital cycles advanced significantly with the contributions of Joseph Alphonse Adhémar (1797–1862) and James Croll (1821–1890).

Adhémar (1842) sought to explain glaciations by reinforcing thehypothesis of orbital controls, especially the precession of the equinoxes.In his bookLes Révolutions de la Mer, Déluges Périodiques, he argues that the glacial periods alternated between thehemispheres, with two glaciations – one to the north and one to the south– every 23 kyr. Anticipating what is now known as thermohaline circulation,he introduced the effects of large-scale ocean currents, which link theplanet's South Pole and North Pole, to explain the phenomenon of melting ice (Berger, 2012).

James Croll's works stood out for defending the astronomical theory ofglacial periods based on rigorous mathematical reasoning, significantlyinfluenced by the astronomer Urbain Leverrier (1811–1877) and his researchon orbital cyclicity. Croll sought to demonstrate that precession variation,modulated by eccentricity, drastically affects the intensity of radiationreceived by the Earth during each season of the year (Imbrie and Imbrie,1979). Thus, he defended the origin of glaciations based on this seasonaleffect. Furthermore, Croll considered the possibility of atmosphericamplification of orbital cycles through albedo effects as the snow caps growand of amplifying orbital effects through ocean circulation (Paillard,2001). In 1875, in the bookClimate and Time, Croll updated his theory considering thevariations in the inclination of the Earth's axis (obliquity cycle).Unfortunately, without further information on the timing of thesevariations, his study could not provide definitive answers (Imbrie andImbrie, 1979).

In the mid-19th century, the effects of glacial cycles were also studied, mainly on sea-level fluctuations. MacLaren (1842), for example,influenced mainly by the work of Agassiz, suggested that melting andreconstruction of the ice sheets that covered continents during glaciationshould cause significant variations in the volume of the ocean. He estimatedthat these variations would reach magnitudes of 100 to 200 m, closelyanticipating the current understanding of glacioeustasy (e.g. Sames et al., 2020). Jamieson (1865) proposed another glacial mechanism for the relativechange in sea level. From his investigations in Scotland, he suggested thatthe weight of the ice caps must have depressed part of the crust during theglaciation, which would return to its original position during the thaw(isostatic rebound).

2.1.2 Milankovitch and the definitive return of astronomical climate models

The legacy of Croll's work served as a foundation for the Serbian MilutinMilankovitch (1879–1958). Milankovitch is one of the most well-knownpioneers of planetary climatology, especially for finding a mathematicalsolution to correlate orbitally controlled insolation with the ice ages(Milankovitch, 1941; Paillard, 2001; Fig. 2).

Figure 2Orbital models for glacial cycles. Adhémar's model considersonly precession to explain cyclic glaciations alternating betweenhemispheres. Croll's model considers the interferences of eccentricity. Thelast is Milankovitch's model, a pioneer in determining the insolationcalculated from all orbital parameters (modified from Paillard, 2001).

Milankovitch (1941) calculated the glacial–interglacial climatic oscillations as a function of solar radiation incident at the top of theatmosphere (insolation) for the last 600 kyr. While his predecessors usedonly eccentricity and precession, Milankovitch also included obliquity inhis calculations. The triumph of Milankovitch's work was the precision,which could be tested with geological data for validation. The variations insolar radiation produce changes between colder (lower insolation rates) andwarmer global climatic periods (higher insolation rates), which theninfluence atmospheric, hydrological, oceanographic, biological, andsedimentological processes on the Earth's surface.

Some geologists accepted that the curves proposed by Milankovitch fit thegeological record. However, many others disagreed, discrediting astronomicalresearch, remaining skeptical until studies of deep-sea cores and isotopicresearch started (Imbrie and Imbrie, 1979). According to the Milankovitch model,Emiliani (1955, 1966, 1978) determined that ocean temperatures fluctuated,based on a record of oxygen isotope ratios in calcitic fossils. Later,Shackleton (1967) improved the interpretation of variations in oxygenisotope ratios, suggesting that they reflect oscillations in the totalvolume of ice sheets during glacial cycles. Nowadays, Milankovitch's work isan essential element of deductive analysis and has become the keystone ofcyclostratigraphy and astrochronology (e.g. Strasser et al., 2006). Astronomical solutions are calculated with ever-higher precision for thedeep geological past (e.g. Berger et al., 1989; Laskar et al., 2011; Hinnov, 2018), and Milankovitch cycles are used to improve the geologicaltimescale continually (e.g. Gradstein et al., 2021).

2.1.3 Astronomical forcings on the Earth system

Many astronomical cycles leave a recognizable imprint in the geologicalrecord (e.g. House, 1995, Fig. 3), ranging from twice-daily (such as tides; e.g. Kvale, 2006) to hundreds of millions of years (such as thevertical oscillation of the solar system across the galactic plane and its association with impact episodes and mass extinction events on Earth; e.g. Randall and Reece, 2014). The geochronological value of these astronomicalcycles has been recognized by many authors, which has led to the rise ofastrochronology (Hinnov, 2018). Astronomical dating helps reconstruct theglobal climate history (e.g. Westerhold et al., 2020) and is now a significant element of the geological timescale (e.g. Walker et al., 2013;Gradstein et al., 2021).

Figure 3Logarithmic table of the astronomical cycle frequencies (adaptedfrom House, 1995).

In addition to the build-up and melting of ice on the polar caps during icehouse conditions, astronomical cycles in the Milankovitch frequency bandalso force global processes during greenhouse times (e.g. Schulz and Schäfer-Neth, 1998; Boulila et al., 2018; Strasser, 2018; Wagreich et al., 2021). Geological records in different parts of the world suggest a strongcorrelation between orbital cycles and global sea-level fluctuations. Theeustasy associated with astronomical forcing on Earth's climate (Fig. 4a)includes the exchange of water between the ocean and terrestrial stores,either in the form of ice (glacioeustasy; Fig. 4a) or underground andsurface reservoirs (aquifereustasy and limnoeustasy; Fig. 4b), and also thermally induced volume changes in the oceans (thermoeustasy; Fig. 4c). During icehouse conditions, glacioeustasy predominates with high-amplitude sea-level fluctuations, while in a greenhouse world amplitudes are minor(e.g. Wilson, 1998; Séranne, 1999; Sames et al., 2016; Fig. 5).

Figure 4(a) Log-scale diagram of the timing and amplitudes of the mainmechanisms that control “short-term” sea-level variations. The valuesrepresented must be considered averages (modified from Sames et al., 2016);(b) schematic diagrams representing the processes that promotechanges in sea level (glacioeustasy, aquifer eustasy + limnoeustasy, and thermoeustasy) during climate changes induced by orbital cycles.

Figure 5Changing frequencies and amplitudes of eustasy. Sea-level curves,according to Vail et al. (1977) and Hallam (1977). In icehouse periods (inblue), these cycles have a high amplitude, mainly due to the effects ofglacioeustasy. Eustatic oscillations have lower amplitude in greenhouseperiods (in light red) since there is no significant glacial effect(modified from Wilson, 1998; Séranne, 1999; Montañez et al., 2011).

2.2 The internal gears of geodynamics

In the 18th century, during the Scottish Enlightenment, James Hutton (1726–1797) described the geological record observed in the landscape asa product of the continuous alternation of uplift, erosion, and depositionalprocesses. The emergence of geology as an individualized science iscurrently linked to James Hutton'sTheory of the Earth, which described the Earth as a body that acts cyclically over geological time (Chorley etal., 2009).

This uniformitarian conception has a cyclical approach, which considers apriori that geological processes present repetitive patterns (O'Hara, 2018).The most significant contributor to the spread of uniformitarian thinking,Charles Lyell, presented a fascinating tale of the Earth's internaloscillating processes. He visited the Macellum of Pozzuoli (also known as Serapis Temple – Fig. 6a) in the Italian region of Campania severaltimes, highlighting this Roman ruin in an illustration on the frontispieceof thePrinciples of Geology (Fig. 6b). In the middle portion of the three remaining marble pillars, there are borings left by marineLithophaga bivalves. According to Lyell, it is “unequivocal evidence that the relative level of land and sea has changed twice at Puzuolli, since the Cristian era, and each movement both of elevation and subsidence has exceeded twenty feet”(Lyell, 1835, p. 312). This variation of relative sea level identified byLyell is now understood as a product of bradyseism, which corresponds to vertical ground movements (Fig. 6c) caused by successive filling andemptying of magmatic chambers in volcanic areas (Parascandola, 1947;Bellucci et al., 2006; Lima et al., 2009; Cannatelli et al., 2020).

The search for processes in the Earth's internal dynamics, and theirrelationship with sea-level variations, continued for many years after Hutton and Lyell. However, such research focused on finding diastrophic rhythms atlarge temporal and spatial scales, as Barrell (1917) mentioned: “those long-deferred stirrings of the deep imprisoned titans which have dividedearth history into periods and eras”.

Figure 6Roman ruins of the Serapis Temple (Macellum of Pozzuoli), inPozzuoli, Italy.(a) Recent picture.(b) The illustration on the frontispiece of volume I ofPrinciples of Geology (Lyell, 1835). Both highlight the rough texture of theintermediate portion of the columns where bivalve wear is evident,indicating marine transgression after the temple's construction.(c) Vertical movements of the Serapis Temple show an alternating pattern of elevation and subsidence produced by bradyseism (modified from Bellucci et al., 2006).

2.2.1 Diastrophic theories and the birth of eustasy

The 18th and 19th centuries were the most scientifically activefor the nascent discipline of geology. During this period, Earth'scontraction was the leading theory for the origin and evolution of itsmorphology, such as mountain ranges. According to this conception, theEarth's radius diminished with time due to internal cooling, causing thecrust to wrinkle. The theory of the Earth's cooling and contraction has beendeveloped and modernized throughout history, with collaborations fromeminent scientists such as René Descartes (1596–1650), GottfriedWilhelm Leibniz (1646–1716), Henry De la Beche (1796–1855), Elie deBeaumont (1798–1874), William Thomson – Lord Kelvin (1824–1907), James Dana (1813–1895), and Eduard Suess (1831–1914).

In this context, Eduard Suess formulated one of the most critical conceptsin stratigraphy, which deals with the cyclicity of global sea level.According to Suess (1888), the contraction of the planet produced eustaticmovements. Such movements can be negative (decrease in global sea level) dueto the subsidence of ocean basins or positive (increase in global sea level) due to the continuous discharge of sediments that fill these basins.After Suess (1888), a tremendous scientific effort was initiated tounderstand the planet's internal dynamics, its relationships with thedevelopment of ocean basins and eustatic variations, and the potential touse the oscillations of the absolute sea level for global stratigraphiccorrelations.

In 1890, Grove Karl Gilbert (1834–1918) recommended using the term“diastrophism” to describe the vertical movements of the lithospheric crust.Gilbert (1890) proposed dividing dystrophic processes into orogenicprocesses, related to the relatively smaller scale that produced themountain ranges, and epirogenic processes, related to the broader movements that form the boundaries of continents and oceans.

For many years afterwards, the nature of diastrophism was up for debate in the scientific community. “Have diastrophic movements been in progressconstantly, or at intervals only, with quiescent periods between? Are theyperpetual or periodic?” (Chamberlin, 1909, p. 689). Defending the periodicconception of diastrophism, Thomas Chamberlin (1843–1928) proposed amodel for eustasy very similar to Suess (1888), in which the isostaticbalance would promote vertical adjustment cycles in the Earth's crust,leading to marine regressions and transgressions. The novelty offered byChamberlin (1898) was the linkage between diastrophism, sea-levelvariations, and climatic cycles. In his theory, the weathering of thesubaerially exposed continents during regression would promote substantialCO₂ consumption, causing global cooling. Conversely, duringtransgression, the excess of atmospheric CO₂ was supposed to improvewarming by the greenhouse effect. Chamberlin's primary motivation wasto establish a theoretical framework that could explain the global division of geological time and the stratigraphic correlations through base-levelchanges (Chamberlin, 1909). In his most famous work,Diastrophism as the Ultimate Basis of Correlation, Chamberlin (1909)reaffirms the global character of dystrophic movements and underlines theirimportance for correlations by base level. According to him, thesynchronicity of these events, associated with variations in sea level,allows for transoceanic correlations.

During this same period, William Morris Davis (1850–1934) developed ageomorphic cycle theory to explain landform evolution. According to Davis (1899, 1922), after an initial and rapid tectonic uplift, landforms undergoweathering and erosion processes, evolving through several intermediatestages until culminating in a general peneplanization. A change in the erosion level caused by a new tectonic uplift would cause landformrejuvenation, starting a new geomorphic cycle. Although later criticized fornot considering all the complexity of geomorphological processes, Davis'stheory became paradigmatic until the mid-20th century. Its cyclical conception influenced ideas about periodic variations in the generation,supply, and preservation of sedimentary deposits.

Barrell (1917) pioneered the understanding of the cyclic behaviour of erosion and accumulation processes. He was the first to propose a systematic link,at different orders, between base-level changes and the preservation of thestratigraphic record. A synthesis of his ideas is presented in the diagramin Fig. 7. With the alternation between deposition and erosion, producedby the harmonic of long-term (diastrophic) and short-term (climatic)base-level fluctuations, Barrell illustrated that most of the geologicaltime is contained in and represented by unconformity surfaces, which hecalled “diastems”. It is remarkable how many of the principles developed by this author are still in use. The sinusoidal representation of the base-level harmonic oscillations introduced a widespread way of illustratingthe logic of stratigraphic evolution (e.g. Van Wagoner, 1990).

Figure 7Cyclical variations of the base level and their control onpreserving the stratigraphic record through an alternation of deposition anderosion (modified from Barrell, 1917).

A year after the First World War, Alfred Wegener (1880–1930) publishedthe first edition ofThe Origin of the Continents and Oceans. Wegener (1915) was not the first to postulate thelateral movement of continents. However, he deserves the central role inthis theme above all for his persistence in defending continental driftagainst a scientific community hostile to these ideas. The exaggeratedreactions to Wegener's theory are due, in part, to the fact that he did nothave a satisfactory explanation for the mechanism controlling continentalmovements (Beckinsale and Chorley, 2003). Another understandable reason isresistance from the scientific community to some theoretical innovations.The continental drift proposal completely contradicted all formulations inforce at the time. Since the beginning of the 19th century, what had been advocated in force until the 1960s were the large vertical movements of theEarth's crust, which reached a final formulation in the geosyncline theory(Gnibidenko and Shashkin, 1970).

Hans Stille (1876–1966) was one of the great geologists of the geosyncline theory. Dedicated to describing the evolution of various geological terrains, Stille (1924) mapped successive unconformities inmarine deposits. He interpreted that orogenic processes occurred in globalsynchrony, producing regressions and transgressions of sea level. Thisproposal cannot be seen as fundamentally new, but Stille (1924) was apioneer by drawing up the first eustatic variation curve for the Phanerozoic(Fig. 8a).

Figure 8Global sea-level curves.(a) Modified from Stille (1926) and(b) modified from Grabau (1936). Both indicate the main orogenetic periods associated with rapid marine regressions. The red lines indicate the sameevents identified by Stille (1926) and Grabau (1936).(c) Paleozoic eustaticcycles of approximately 35 Myr (determined by bandpass filtering of datapresented by Haq and Schutter, 2008) and potential correlation (blue lines)with equivalent cycles of Grabau (1936) (modified from Boulila et al.,2021).

Amadeus William Grabau (1870–1946), through detailed stratigraphic dataand correlations in extensive areas of North America, Europe, and Asia,presented a proposal for sea-level fluctuations for long geological periods(Fig. 8b). Although Stille's and Grabau's cyclic conceptions of sea-levelvariations are similar, Grabau questioned the synchronicity of orogenies inthe entire world. He considered these processes to be of local importanceand believed that simultaneous sea-level fluctuations could be related tochanges in the volumes of ocean basins (Johnson, 1992). Grabau was inspiredby the work of Alfred Wegener (Mazur, 2006), and he citedThe Origin of the Continents and Oceans in his mostsignificant publication,The Rhythm of the Ages: Earth History in the Light of the Pulsation and Polar Control Theories, published in 1940 (Johnson, 1992).

2.2.2 Plate tectonics and Wilson cycles

Scientific progress and field evidence, particularly concerning the originof mountain belts, have resulted in the questioning of the contractiontheory (e.g. Dutton, 1874), which was finally abandoned. A crisis in the field of tectonics was triggered by the discovery of radiometric dating,which challenged the Earth's long-term cooling, and by the Alpine nappes andthrust sheets that demonstrated the mechanisms of large horizontaldisplacements of the crust. This crisis did not end until the definition ofplate tectonics in the 1960s (O'Hara, 2018).

During the 1960s, advances in post-World War II oceanographic researchprovided evidence for the evolution of the ocean floor. Such discoveriesexplained Alfred Wegener's theory of continental drift (Kearey et al., 2009),and the roots of the future plate tectonic paradigm were established (LePichon, 2019). The development of this theory can be considered the mostsignificant advance in understanding the Earth's dynamics and has even influenced the study of other planets (e.g. Hawkesworth and Brown, 2018; Karato and Barbot, 2018; Duarte et al., 2021).

John Tuzo Wilson (1908–1993) was one of the leading geoscientistsdeveloping the theory of plate tectonics. Wilson (1965) was the first tomention the existence of large rigid plates, describing specific limits ofthese, which the author called transform faults. However, Wilson's mostemblematic work was published the following year. Wilson (1966) presented aspecific aspect of the geotectonic process, showing the oceans' successiveopening and closing (Fig. 9). Today, the so-called Wilson cycle describesthe periodicity with which large continental masses separated and came backtogether. Over the past 50 years, this concept has proven to be crucial forthe theory and practice of geology (Wilson et al., 2019).

Figure 9Ocean closing and opening cycle (modified from Wilson,1966).(a) A closing ocean;(b) first contact between two opposite continental coasts;(c) ocean closure and final collision of oppositecontinental coasts;(d) a hypothetical line (dashed) along which a newcontinental rupture would engender a younger ocean to re-open;(e) a newocean opening after the break-up of an old continent.

It is notorious how the theory of plate tectonics followed the stubbornuniformitarianism of processes advocated by James Hutton and Charles Lyell.Stern and Scholl (2010) related the tectonic processes to cycles of creationand destruction of the continental crust, defining a particular equilibriumon Earth. They encapsulated this equilibrium in the traditional Chineseconcept of yin–yang, whereby dualities work together and in opposition. About this maintenance of geological systems defined by plate tectonics,Schwarzacher (2000, p. 51) wrote the following.

The environments of deposition from the Precambrian onwards have beensimilar and repeat themselves; apart from the fortunate exception of thebiosphere, there are very few indications of a progressive development ingeological processes during the last 1000 Ma. Indeed, based on our presentobservations, one could easily believe that most sedimentation and thereforestratigraphy should have ended long ago. All basins should have been filledand all mountains eroded. This is not the case and leads us to believe thattectonic events must interfere and revitalize the sedimentation systems.

The Wilson cycle was vital in defining the assembly and the breaking up of supercontinents. This self-organization in plate tectonics has been studiedfor decades, whose periodicity is in the range of 300–800 million years(Mitchell et al., 2021). Hence, new hypotheses for global cycles could alsobe formulated, and several questions about the impacts of tectonic events onsea-level and climatic variations were answered. For example, based on theWilson cycles, Fischer (1981, 1982) formulated the climatic oscillationproduced by Earth's icehouse and greenhouse states (Fig. 10).

2.2.3 Internal geodynamic forcings in the Earth system

Currently, the periodicity of several processes in the Earth's internaldynamics is well known (e.g. Matenco and Haq, 2020; Fig. 11). Mitchell et al. (2019) conducted time-series analyses of hafnium isotopes in zircon(Hf-zircon) to identify statistically significant periodicities of magmaticsystems throughout geological time. The Hf-zircon analysed by LA-ICP-MS (laser ablation inductively coupled plasma mass spectrometry) represents awell-dated proxy for the evolution of magmatism related to tectonic andmantle convection cycles. From time-series analysis of the global Hf-zircondatabase for the last∼ 2 Gyr, the authors defined a hierarchyof geodynamic cycles (Fig. 12), analogous to the orbital ones (Fig. 2).

Mitchell et al. (2019) recognized the periodicity of the superocean cycle (∼ 1.2 Gyr), the supercontinent cycle (∼ 600 Myr), the Wilson cycle (∼ 275 Myr), and an upper-mantle cycle(∼ 60–80 Myr). These cycles appear to be harmonics, implyinga coupling between the mantle and lithosphere convections. In addition tothese, magmatic cycles of∼ 20 and∼ 6 Myrare suggested by the high-resolution circum-Pacific records. According tothese authors, “the hierarchy of geodynamic cycles identified with Hfisotopes of zircon appears to represent, according to bandwidth, the lastfrontier of cyclicity in the Earth system to be identified and explored”(Mitchell et al., 2019, p. 247).

Climatic and eustatic oscillations may have interacted with internalgeodynamic processes as triggers or feedbacks (e.g. greenhouse–icehouse cycles; Fig. 10). Changes in ocean circulation related to theconfiguration of the continents and global volcanic pulses are an example ofa potential influence on Earth's climate (Rampino et al., 2021). The linkbetween Earth's internal dynamics and eustasy may come from changes in thevolume of marine waters (water exchange with a mantle) and in the volumeavailable in ocean basins (ocean ridge volume; dynamic topography; seafloorvolcanism; continental collision), which operate in the long term (greater than 1 Myr; e.g. Sames et al., 2016, 2020; Fig. 13).

Disagreements about the global synchronicity of tectonic cycles have beenraised since the beginning of the 20th century. According to Willis (1910, p. 247), “each region has experienced an individual history ofdiastrophism, in which the law of periodicity is expressed in cycles ofmovement and quiescence peculiar to that region”. This idea was encapsulatedin the concept of relative sea-level change (e.g. Wilgus et al., 1988). Relative sea-level change (as opposed to eustatic sea-level change) iscaused by tectonic deformation of the crust in marine and coastal areas,which results in uplift and subsidence of the land relative to the seasurface. Generally, these processes have a local to regional extent and occur at a higher frequency than global geodynamic processes (e.g. Matenco and Haq, 2020; Fig. 11). Thus, sea-level changes caused by geodynamicprocesses can be local when such processes are also localized (e.g. bradyseism; Fig. 4).

The cyclical behaviour of the mantle and the lithosphere, in association with astronomical cycles, completes the puzzle of cyclicity in the Earth system.The connection between the Earth's internal and external systems is notadequately investigated because tectonic and astronomical influences areoften considered independently. Boulila et al. (2021) suggest a potentialcoupling between Milankovitch forcing and Earth's internal processes for theeustatic sea-level record in the 35 Myr cycle range during the Phanerozoic.This is a cyclicity that is compatible with the one that was recognized along time ago, by several authors, such as Stille (1926) and Grabau (1936)(Fig. 8c). A challenge for stratigraphy is understanding how the Earthsystem's conduction mechanisms are imprinted in the geological record. AsBarrell (1917) concluded, “sedimentation is controlled by them, and thestratigraphic series constitutes a record, written on stone tablets, ofthese increasing waves of change that pulsed through geological time”. Such“waves” may correspond to the causal mechanism of biological extinctions,comet impacts, orogenic events, oceanic anoxic events, and sea-levelchanges, which support the division of geological time into intervals forglobal correlations (e.g. Rampino et al., 2021; Boulila et al., 2021).

Figure 10Cyclic outlines of Phanerozoic history (modified fromFischer, 1981, 1982). Climatic oscillations are composed of greenhouse andicehouse states, with minor internal climatic fluctuations. Sea-levelcurves, according to Vail et al. (1977) and Hallam (1977). Global graniteemplacement was deduced from data based on the American granite emplacements(after Engel and Engel, 1964).

Figure 11Temporal variability of the main periodic geodynamicmechanisms (based on Matenco and Haq, 2020).

The idea of a cycle involves repetition because a cycle can be recognized only if units are repeated in the same order. The question that inevitably arises is: How closely similar must the repetition be? An answer seems to depend on two requirements: (1) nearly complete transitions between variants must be observed, and (2) a generalization must be made reducing the cycle to its simplest form by excluding all unessential details. The cycles, then, must be closely similar with respect to this simple form (Weller, 1964, p. 613).

According to Goldhammer (1978), most, if not all, stratigraphic successionsexhibit repetitions of strata at different scales. Throughout the history ofstratigraphy, the concept of cyclicity played a crucial role in theinductive observations of the record and subsequent deductive reasoning.Several approaches have been used to describe this cyclicity. Among them,the following lines of description and interpretation will be brieflypresented: sedimentary facies cycles, cyclothems, clinoforms, stratigraphicsequences, and astrocycles.

Figure 12Global Hf database (black) and cycles determined by thetime-series analysis: superocean cycle (∼ 1.2 Gyr; red), thesupercontinent cycle (∼ 600 Myr; yellow), the Wilson cycle(∼ 275 Myr; green), and an upper mantle cycle (∼ 60–80 Myr; blue).

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Figure 13Log-scale diagram of the timing and amplitudes of themain mechanisms that control “long-term” sea-level variations related tointernal geodynamic processes. The values represented must be considered the average (modified from Sames et al., 2016).

3.1 Sedimentary facies cycles

Sedimentary cycles are recurrent sequences of strata each consisting of several similar lithologically distinctive members arranged in the same order. A great variety of cycles is possible ranging from simple to quite complex but only a comparatively few types actually have been recognized. Cycles may be either symmetrical or asymmetrical depending upon the pattern presented by their members. They record the occurrence of definite series of physical conditions, and resulting sedimentary environments, that were repeated in the same order with only minor variations (Weller, 1960, p. 367).

During the 15th and 16th centuries, observing the landscapeand the natural phenomena that modify it played a crucial role inconstructing modern science, especially in the Earth sciences (Puche-Riart, 2005). For example, through detailed observations of successive rock strata,Leonardo da Vinci (1452–1519) expressed nature in his paintings (Ferretti etal., 2020). He was probably one of the first to understand erosion,transport, deposition, and lithification processes from field observations.In theCodex Leicester, Leonardo da Vinci shows the vertical and lateral organization of rocky beds observed in the Alps that he interpreted as a record of river flood cycles (Ferretti et al., 2020).

In 1669, Nicolaus Steno (1638–1686) published one of the most crucial worksabout the genesis of rock layers and their fossil components. Based on aninterpretation of the geological evolution of Tuscany, he proposed threefundamental stratigraphic principles that continue to be used today(Kravitz, 2014). Through an evolutionary diagram (Fig. 14), Stenosuggested that the sedimentary beds are formed by successive floods,followed by reworking that erodes and deforms them. He noted that sediment layers were deposited in chronologic successions that display the oldestlayers on the bottom and the youngest ones on the top of the pile (principle of superposition). According to him, initially, the strata are organized in aset of horizontal layers (principle of original horizontality) that could belater eroded and deformed, and new horizontal layers are deposited overthem. Concerning the strata's geometry, Steno defined each sedimentary bed as extending laterally in all directions (principle of lateral continuity)until it reached an obstacle, such as the basin's border.

Figure 14Steno's evolutionary diagram describes six stages for thegeologic history of Tuscany, including flooding cycles and crustal collapse(modified from Kravitz, 2014).

Nicolaus Steno was responsible for introducing the term “facies” into thegeological literature. He used it to describe the fundamentalcharacteristics of a part of the Earth's surface during a specificgeological time (Teichert, 1958). Later, this concept evolved through thedescriptions of Amanz Gressly (1814–1865) in the Jura mountains at theFrench–Swiss border. Gressly (1838) defined the sedimentary facies as the different lithological features and fossil components of a sedimentarylayer, interpreted as a record of the original depositional processes. Heexplained the genesis of sedimentary facies as the product of processes thatoperated in depositional environments and demonstrated, throughstratigraphic correlations, the lateral facies transitions that compose amosaic of environments along a depositional profile (Cross, 1997).

In 1894, Johannes Walther (1860–1937) introduced an essential geologicalprinciple associated with the concept of facies (Middleton, 1973). Known asWalther's law of facies, this principle states that any vertical facies succession is a record of depositional environments that were laterallyadjacent to each other in the geological past. This vertical and lateralfacies correspondence is still used today for paleogeographic reconstructions, especially when associated with an actualistic approach (e.g. Fragoso et al., 2021).

Between the 19th and 20th centuries, several works presenteddetailed sections demonstrating repeated associations of different types ofrocks (Weller, 1964). The economic interest in carboniferous coal beds fueled some of the earliest observations. In 1912, Johan August Udden (1859–1932) was a pioneer in recognizing cycles in the stratigraphic record. Ina report about the geology of the US state of Illinois, he identified facies cycles in Pennsylvanian strata, composed, from bottom to top, bylayers of coal, limestone, and sandstone (Fig. 15). Udden (1912)interpreted such cycles as products of successive transgressions andregressions of the shoreline during the basin's subsidence. He establishedthat stratigraphic surfaces marked by paleosols correspond to the end of each cycle. According to him, these surfaces represent depositional gaps.

Laboratory simulations were introduced during the 1950s and 1960s,culminating in the flow regime concept (Simons and Richardson, 1966). Thisadvance improved the interpretation of sedimentary structures preserved inthe geological record (e.g. Allen, 1963; Middleton, 1965). Concomitantly, there was also much progress in facies models through studies of modernsedimentary environments (e.g. Fisk et al., 1954; Illing, 1954; Oomkens and Terwindt, 1960; Bernard and Major, 1963; Shearman, 1966; Glennie, 1970).

Figure 15Cycles in the Pennsylvanian of Illinois, United States (modifiedfrom Udden, 1912).

In the 1960s, the stratigraphic application of facies models evolvedconsiderably through the analysis of cyclicity seen in the outcrops (e.g. Weller, 1960). Recurrent sequences of sedimentary facies, arranged in aspecific order, have been interpreted as the record of similar depositionaland environmental processes, repeated at all scales, from millimetres to many hundreds of metres (Goldhammer, 1978; Schwarzacher, 2000). In this context, specific terms were created for describing sedimentary facies withregular alternation, such as “cyclites” or “rhythmites” (e.g. Kvale, 1978; Brodzikowski and Van Loon, 1991). Although generic, these terms have beenclosely associated with regular climate cycles (e.g. Chandler and Evans, 2021) or those produced in tidal environments (e.g. Kvale, 1978).

Researching cyclic depositional mechanisms in alluvial plains, Beerbower (1964) defined the concepts of autocyclic versus allocyclic. Autocyclic wasdefined as the sedimentation record generated purely within the givensedimentary system by the distribution of energy and sediments, such aslateral channel migration and meander abandonment. On the other hand,allocyclic was associated with the external processes that cause changes inthe alluvial channels' discharge, loading, and inclination. They differ fromautocyclic alternations in their wider lateral extension along the basin oreven to other depositional basins.

With some modernizations, the concepts of autocyclic and allocyclic controlscurrently encompass all geochemical, ecological, and physical sedimentaryprocesses (Cecil, 2003). Nowadays, autocyclic dynamics are understood as thespontaneous form of deposition within sedimentary systems, determiningspatial and temporal heterogeneities in the way sediments and water aredistributed in a landscape (Hajek and Straub, 2017; Fig. 16). Deltaswitching and lateral migration of channels, dunes, or ripples are examplesof autocyclic processes that produce cyclical deposits (e.g. Hajek and Straub, 2017; Miall, 2015). Other examples include episodic events, which,although recurrent, do not have periodicity, such as storms and sedimentgravity flows (e.g. Einsele, 2000). The autocyclic dynamics must be self-regulating and include feedback mechanisms to produce cyclicsedimentary records (Goldhammer, 1978). Since they do not always have aperiodic regularity, the preference is to use the term “autogenic” (Miall,2016).

Figure 16Schematic illustration with some autogenic controls onsedimentation in different environments.

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In turn, allocyclic (or allogenic) controls correspond to regional or globalprocesses fundamentally related to climate, eustasy, and tectonics. Theseprocesses influence, at different magnitudes and frequencies, theproduction, transport, accumulation, and preservation of sediments, be theyinorganic or organic, clastic, or chemical (e.g. Strasser et al., 2006; Holbrook and Miall, 2020; Matenco and Haq, 2020; Fig. 17). In contrast toautocycles, the allocyclic controls are regular and tend to have known frequencies (as seen in Sect. 2). They also define accommodation (defined by eustatic sea level and subsidence) and make the link to sequencestratigraphy (e.g. Holbrook and Miall, 2020; Fragoso et al., 2021). Hilgen et al. (2004) advised that even the record produced by sudden autocyclicevents (e.g. storms) may occur in clusters related to allocyclic controls (e.g. astronomical). Furthermore, the understanding of the organization offluvial systems, mainly controlled by the autogenic dynamics, was discussedby Abels et al. (2013). According to these authors, the regularities in suchsystems could be linked to allogeneic, astronomically forced climaticchanges.

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

Over the years, several authors raised the question of how sedimentarypreservation influences and possibly hampers the analysis and interpretationof facies and stratigraphic organization.

What does the stratigraphic record actually record? This rather fundamentalquestion spawns more questions, all of which are building blocks in thefoundations of geology. Are the processes and events recorded in the rockstruly representative of their time? At what resolution do rocks recordprocesses? What determines which examples of a repeated process are actuallypreserved? What is missing? What can be determined with certainty from whatremains? Geologists have mulled the answers to these questions at variousintensities since geology was in its infancy. The answers to these questionsultimately determine the legitimacy of every interpretation made of the pastfrom the stratigraphic record (Holbrook and Miall, 2020, p. 1).

Barrell's (1917) proposal for the alternation of deposition (base-levelrise) and erosion (base-level fall) processes at multiple amplitudes andfrequencies (Fig. 7), in which only one-sixth of the time is preserved inthe rock record, illustrates this question in a precise way. It is concludedthat much of geologic time is distributed across numerous gaps in the record(e.g. Dott, 1983; Udden, 1912; Ager, 1993; Sadler, 1999; Miall, 2015; Strasser, 2015; Holbrook and Miall, 2020), which limits the use ofWalther's law of facies in reconstructing laterally adjacent paleoenvironments (Fragoso et al., 2021).

In this respect, within what is considered “sedimentary geology” (sensu Middleton, 1978), there is a difference between sedimentological analysis,which is concerned with interpreting the processes at the origin ofsedimentary facies, to stratigraphic analysis, which is mainly related tothe organization of facies in geological time. With certain poetic freedom,it would be like considering that the harmonic amplitudes and frequencies ofthe base level oscillations compose the stratigraphic “music”, producingsedimentary “notes” spaced in time. Furthermore, as Wolfgang Amadeus Mozartsaid, “the music is not in the notes, but in the silence between”. For thisreason, stratigraphers must pay as much attention to surfaces that contain the gaps as they do to sedimentary facies, taking into account the effect ofpreservation.

Miall (2015), Holbrook and Miall (2020), and Miall et al. (2021)encapsulated this thought in a more objective and mechanistic way throughthe concept called a “preservation machine” or “stratigraphy machine” (Fig. 18a). These authors considered that the organization of the stratigraphic record occurs through multiple overlapping of autogenic and allogeneic processes, which generate and remove sedimentary deposits acrossthe whole range of geological timescales. Furthermore, the “cycles topreserve” (i.e. the number of sedimentary cycles needed to ensure some preservation at a given scale) constitutes a part of the rock record at each timescale, which can potentially be analysed hierarchically (Fig. 18b).

Figure 18Stratigraphy machine.(a) Playful representation of the “stratigraphy machine” concept that generates the stratigraphic record, organizing geological time into hierarchically preserved sedimentary unitsand hiatus surfaces from the bedform to the entire basin fill (based on Holbrook and Miall, 2020).(b) Table illustrating the stratigraphy machine's operation, which considers the simultaneous action of several accumulation,removal, and preservation processes, which interact at different timescales to generate the rock record. For convenience, the timescale is subdividedinto four broad intervals. The diagram should be read from left to right,where at each time interval the sediments are first generated by thedepositional processes, and what is not removed on the surface is preservedin the subsurface, creating the initial succession. Over time, long-termprocesses affect this succession, with preservation and/or removal. In thisway, long-term processes will affect short-term processes, as indicated bythe loops at the bottom of the figure. It is estimated that a period equalto or greater than 10⁷ years would be enough for all processes toperform a complete cycle. Due to the recurrent removal processes, numeroussedimentary gaps occur in the final product at all scales, and the rockrecord represents only a fraction of the elapsed time (modified fromHolbrook and Miall, 2020).

3.2 Cyclothems

Between the 1930s and 1960s, the sections presented by Udden (1912) becameemblematic. Initially called “suites” (Wanless, 1929) or “cyclicalformations” (Weller, 1930; Wanless, 1931), it was the term “cyclothems” (Wanless and Weller, 1932) that triumphed in the literature for describingsuch cyclic facies alternations.

The concept of cyclothems has become familiar to most geoscientists whodescribe sedimentary facies repetitions (e.g. Weller, 1943). The progress of the work in the Pennsylvanian of Illinois revealed that the recurrence ofindividual cyclothems not only corresponds to the unique rhythms to be observed in stratigraphic successions, but is also part of a larger order.

This repeated succession of cyclothems of different character indicates a rhythm of larger order than that shown in the individual cycles and suggests the desirability of a term to designate a combination of related cyclothems. The word “megacyclothem”” will be used in this sense to define a cycle of cyclothems (Moore et al., 1936, p. 29).

According to James Marvin Weller (1899–1976), “these larger rhythms maybe the long-sought key that will solve some of the perplexing problems ofinterbasin correlation” (Weller, 1943, p. 3). This author later proposed theexistence of even larger groups, called hypercyclothems (Weller, 1958). This marked characteristic of the cyclicity in the sedimentary record, in whichindividual cycles occur in clusters that make up larger cyclical units,remains in modern approaches of sequence stratigraphy (Catuneanu, 2019a,b; Magalhães et al., 2020; Fragoso et al., 2021; see item 3.3) andcyclostratigraphy (e.g. Hinnov, 2018; see item 3.4) The term “stacking pattern” is often used to describe a hierarchical order of cyclical units.

Raymond Cecil Moore (1892–1974) presented another feature of the cyclicalstratigraphic record quite pertinent in the modern context of sequencestratigraphy, concerning the definition of boundary surfaces. According toMoore (1964), both cyclothems and megacyclothems are limited by key surfaces, marked by disconformities or a change from continental to marinesedimentation (Fig. 19).

Figure 19Representative section of cyclothems indicating the alternationof continental and marine paleoenvironments (modified from Moore, 1964). Thealternatives of limits for cyclothems are (I) disconformities and (II) the transition from non-marine to marine conditions.

Concerning the origin of cyclothems, Klein and Willard (1989) argued thatsuch units are the product of the combined action of tectonic and eustaticprocesses. According to these authors, the integrated analysis of parametersrelated to geotectonic evolution, global paleoclimate (controlled byorbital, Milankovitch cycles), and laterally changing regional subsidenceallows understanding the paleogeographic variations that gave rise to marineand continental cyclothems, along with lateral correlations (Fig. 20).This approach presents many parallels to the analysis of systems tracts inthe context of sequence stratigraphy (e.g. Posamentier et al., 1988; Hunt and Tucker, 1992; Posamentier and Allen, 1999).

Figure 20The genesis of the different types of cyclothems in North America related to orbital parameters and lateral differences in the crust'sflexural intensity (modified from Klein and Willard, 1989).

3.3 Clinoforms

A broader analysis of the geometry of sedimentary deposits also revealedsedimentological alternations, which contributed to the definition of cyclicstratigraphic units. John Lyon Rich (1884–1956) was the first to describethe inclined geometry of marine deposition. Rich (1951) defined that, alonga transect from coast to basin, the sedimentary deposits can be subdividedinto three depositional forms: undaform, clinoform, and fondoform (Fig. 21). Among these terms, only “clinoform” is being used nowadays. However, the theoretical basis brought by such an approach remains similar,especially regarding the possibility of shifts between these environmentscaused by sea-level changes (Fig. 21b), resulting in characteristicsuccessions of the geometry of strata (Fig. 21c).

Figure 21Sketches and terminology for coastal marine deposits (modifiedfrom Rich, 1951):(a) undaform, clinoform, fondoform.(b) Area of thick sand on the outer edge produced by the slight reduction in sea level.(c) Alternations of coastal marine deposits produced by intermittent changes insea level.

DeWitt Clinton Van Siclen (1918–2001) considered the sloping geometriesof continental margin deposits to describe the lateral variations observedin the cyclothems. According to Van Siclen (1958), the alternation offluvial and coastal deposition with erosional disconformities predominateslandward, grading basin-ward to alternating marine and terrigenous deposition and finally reaching a totally marine domain, with an alternation of clastic and carbonate deposits. The author described cyclesin the deep sea composed of clastic sedimentation during stable or loweredsea level and non-deposition or thin black-shale layers deposited during higher sea stands. Considering different scenarios of changes in sea leveland sediment supply, Van Siclen (1958) proposed distinct types of clinoform successions (Fig. 22). This approach was handy for correlating well datawhen seismics did not support the oil and gas industry. It is interesting to realize how such a concept is similar to the current sequence-stratigraphicmodels.

Figure 22Different scenarios where sea-level changes and sediment supplycause different geometries and lithological compositions in continentalmargin deposition (modified from Van Siclen, 1958).

3.4 Stratigraphic sequences

Stratigraphic cyclicity can be observed at different scales. At each scale of observation (i.e., hierarchical level), the building blocks of the sequence stratigraphic framework are represented by sequences and their component systems tracts and depositional systems (Catuneanu, 2019b, p. 128).

Laurence Louis Sloss (1913–1996) is widely recognized as one of thepioneers of the concept of sequence stratigraphy, and many credit him withinstigating a revolution in stratigraphic thinking (Dott, 2014). Sloss etal. (1949) used for the first time the term “sequence” to refer tostratigraphic units that could be correlated over large areas throughgeological mapping and well data. Subsequently, this sequence model definedsuccessive stratigraphic units bounded by “interregional unconformities”that covered the North American craton (Sloss, 1963; Fig. 23).

Figure 23Sequences of the North American craton (modified from Sloss,1963). The black areas represent temporal gaps, and the light areasrepresent the depositional units.

In the late 1960s, under Sloss' guidance, Peter Vail, Robert Mitchum, andJohn Sangree studied North American Pennsylvanian cyclothems (Dott, 2014).Similarly to small-scale versions of Sloss sequences, bounded by numerous widespread unconformities, these cyclothems were interpreted by them as thestratigraphic record of glacioeustatic fluctuations. Subsequently, thesethree geologists collaborated with the Exxon research group to develop themethod of interpreting seismic data, refining their mentor's concept ofsequence (e.g. Mitchum, 1977).

During the 1960s and 1970s, the evolution of seismic interpretation wasresponsible for reuniting many stratigraphic concepts that underlie thecurrent sequence-stratigraphic methodology. The first reference to the term“seismic stratigraphy” was published at the 27th Brazilian Congress ofGeology (Fisher et al., 1973), and efforts in this area gained prominence inthe international community through AAPG Memoir 26 (Payton, 1977), where the main techniques developed by the Exxon research group were presented.The great innovation was to consider the continuous reflectors observed inseismic sections to be depositional timelines. In this way, it became possible to interpret that surfaces representing an unconformity pass laterally to acorrelative conformity, which was fundamental for the definition of asequence (e.g. Mitchum, 1977). The seismic interpretation, together with biostratigraphic constraints, made it possible to establishchronostratigraphic correlations within a basin and between different basins(e.g. Mitchum and Vail, 1977; Fig. 24). According to Vail (1992), this approach aimed at providing a unifying concept for sedimentary geology equalto what plate tectonics had done for structural geology.

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

Figure 25High-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 Magalhães et al., 2017). The sequences are composed of tidal channels and bars, bounded at the top by heterolithicintervals that configure cycles of retrogradational stacking patternsdefined by the recurrence of the same type of stratigraphic surface in thegeological record.

Different sequence-stratigraphic models were presented between the 1970s and1990s, resulting in a profusion of concepts and jargons. Catuneanu (2006)offered a complete review of these proposals. After the 2000s, a scientificeffort was made to standardize the nomenclature and the methodology ofsequence stratigraphy (Catuneanu et al., 2011), defining a simple andintegrating workflow appropriate for modern stratigraphic analysis (Miall,2016).

Over time, sequence characterization has proven helpful in academic andindustrial applications since such units constitute a natural structure forclassification and local to regional correlations (e.g. Fragoso et al., 2021). Catuneanu and Zecchin (2013; p. 27) defined sequences as a “cycle ofchange in stratal stacking patterns, dividable into systems tracts andbounded by sequence stratigraphic surfaces”. The currentsequence-stratigraphic methodology has a scale-independent approach, inwhich sequences can be defined from the basin (sensu Sloss et al., 1949; Sloss, 1963) to facies scale (e.g. Strasser et al., 1999; Magalhães et al., 2016, 2017; Fig. 25), ordered in a hierarchical framework(Magalhães et al., 2020).

According to Fragoso et al. (2021), the characterization of sequences withina cyclic and hierarchical framework should obey the following criteria(Fig. 26): transgressive–regressive (T–R) cycle anatomy; vertical recurrence of stacking patterns; vertical trends in the stacking patternscomposing subsequent hierarchies of cyclicity; recognizable mappability. Inthis sense, a stratigraphic sequence framework is composed of cyclesobserved at different hierarchies. A higher ranking comprises an organizedcluster of lower-ranking sequences (Catuneanu, 2019a, b; Magalhãeset al., 2020; Fragoso et al., 2021; Fig. 27). This cyclic approach of thestratigraphic analysis supports the objective results in predicting thevertical recurrence and the lateral correlation of genetic stratigraphicunits.

Figure 26Characteristics and criteria for defining stratigraphic sequenceswithin a cyclic and hierarchical framework (modified from Fragoso et al.,2021):(a) T–R cycle anatomy.(b) Vertical recurrence of individual cycles and trends in the cyclic stacking pattern (modulation of the smallest by the highest hierarchy).(c) Mappability of the stacking patterns and stratigraphic surfaces within a given framework, which is more significant the higher the hierarchy is. Abbreviations: MFS – maximum flooding surface; MRS – maximumregressive surface.

Figure 27Hierarchical stratigraphic sequence framework (modified fromMagalhães et al., 2020). High-frequency sequences (fourth or higherorders) are observed at outcrop and core scale. The vertical recurrence of high-frequency sequences composes the low-frequency sequences observed inseismic data (third order). First- and second-order low-frequency sequences occur at basin scale predominantly limited by unconformities, as proposed by Sloss et al. (1949).

3.5 Astrocycles

Gilbert (1895) was the first to consider that the sedimentary record mayexhibit repetitions controlled by orbital cycles. He correctly suggestedthat the Upper Cretaceous marl–limestone alternation in the US state of Colorado should correspond to an allocyclic record of climatic oscillation controlled by the orbital precession cycle of about 20 kyr. Althoughrudimentary, Gilbert's conclusions allowed the measurement of geologicaltime using the sedimentary record before the invention of radiometric dating(Strasser et al., 2006). After Gilbert, the studies of astronomically forcedclimatic cycles evolved considerably from Adhémar (1842), Croll (1875),and, especially, Milankovitch (1941). The application of this knowledge tosedimentary successions emerged gradually.

In the 1960s, some studies started identifying cycles in different depositional contexts related to orbital forcing. For example, Van Houten (1964) presented the cyclic character of the lacustrine record of the UpperTriassic Lockatong Formation in the United States. This work stands out bydetermining a stratigraphic ordering in three hierarchies and proposing atemporal definition based on orbital cycles (Fig. 28).

In 1976, one of the most influential articles in the study of Milankovitch'stheory was published. In their work entitled “Earth Orbit Variations: TheIce Age Pacemaker”, James Hays, John Imbrie, and Nick Shackleton establishedthe effects of orbital parameters on the long-term climate record obtainedfrom the analysis of marine sediments. Thus, Hays et al. (1976) “legitimizedwhat was to become one of the most powerful tools in stratigraphy” (Maslin,2016, p. 208).

In the 1980s, the studies about the geological record of astronomical cyclesintegrated a subdiscipline of stratigraphy named “cyclostratigraphy”(Strasser et al., 2006). According to Hilgen et al. (2004),cyclostratigraphy identifies, characterizes, correlates, and interpretscyclical variations (periodic or quasi-periodic) in the stratigraphicrecord. In cyclostratigraphic studies, temporal calibrations can be done byeither correlating sedimentary cycles – identified through variations inpaleoenvironmental or paleoclimatic proxies sampled along a section or core(e.g. Li et al., 2019) – or by astronomical target curves of precession, obliquity and eccentricity, or by related insolation curves (Strasser etal., 2006). Weedon (2003) and Kodama and Hinnov (2015) present mathematicaltechniques for processing signals obtained by these proxies. Once theperiodicity of a sedimentary cycle has been demonstrated, a very detailedanalysis of sedimentological, paleoecological, or geochemical processes canbe evaluated in a high-resolution time-stratigraphic framework (Strasser etal., 2006).

Figure 28Cyclic lacustrine sedimentation of the Upper Triassic LockatongFormation (modified from Van Houten, 1964).(a) Model of detrital and chemical short cycles;(b) generalized stratigraphic section of LockatongFormation and adjacent units. The columns show the alternating geographicenvironments and the long climatic cycles of wetter and drier phases. An agemodel is presented based on two long climatic cycles, with intermediate andshort cycles associated.

The term “sedimentary cycle” in cyclostratigraphy has a specific meaning,which differs from more generic applications (e.g. Weller, 1960). The sedimentary cycle as used in cyclostratigraphy corresponds to “onesuccession of lithofacies that repeats itself many times in the sedimentaryrecord and that is, or is inferred to be, causally linked to an oscillatingsystem and, as a consequence, is (nearly) periodic and has timesignificance” (Hilgen et al., 2004, p. 305; Fig. 29). Thus, Strasser etal. (2006) proposed the term “astrocycle” to define specific cycles whose periodicity can be demonstrated by the cyclostratigraphic analysis.

Figure 29Outcrop examples of sedimentary cycles determined bycyclostratigraphic analysis.(a) Long eccentricity, short eccentricity, and precession cycles in hemipelagic limestone and marl alternations of theSopelana section (Maastrichtian), Spain (modified from Batenburg et al.,2014);(b) long eccentricity cycles in hemipelagic limestone and marlalternations of the La Marcouline section (Middle Aptian), France (modifiedfrom Kuhnt and Moullade, 2007);(c) long and short eccentricity cycles inshallow-marine deposits of the Kope Formation (Ordovician), United States(modified from Ellwood et al., 2013).

At this time, cyclostratigraphic analysis is part of integrated stratigraphy, which combines several stratigraphic subdisciplines (e.g. biostratigraphy, magnetostratigraphy, chemostratigraphy, geochronology) tosolve problems related to geological time (Hilgen et al., 2015). Thisintegration aids paleoenvironmental interpretation, focusing on multi-proxyanalyses, and provides accurate geochronological information forastronomical tuning of stratigraphic records into target curves of orbitalcycles and the related insolation curves. Thus, the integrated stratigraphysupports the construction of a high-resolution astronomical timescale that is currently decisive to determine a Global Stratotype Section and Point(GSSP – e.g. Lirer and Laccarino, 2011) and to refine the Geological Time Scale (Gradstein et al., 2021).

Since the beginning of their existence, humans have dealt with cycles. Fromthe simple day–night, hungry–satisfied, and sleeping–awake to the passing of the seasons and the coming and going of migratory animals, cycles are omnipresent and contribute to shaping the human way of thinking. This aspecthas had an epistemological influence on observing and interpreting the mostdiverse natural phenomena that control the Earth system. In Earth sciences, cycle concepts improved geological knowledge, offering simple analyticalsolutions to describe rock records and interpret geological processes. Thereis a primordial function in the practice of geology within what isconsidered a hermeneutic circle (e.g. Frodeman, 1995; Miall, 2004; Frodeman, 2014). This point of view establishes that geology is developed bythe processes of induction and deduction, where the set of detaileddescriptions supports general theories, while deductive reasoning enhancesand refines the descriptive methodologies and techniques (Fig. 30).

Figure 30The hermeneutic circle (based on Miall, 2004).

Geology is a prominent example of a synthetic science, combining a varietyof logical techniques to solve its problems. The geologist exemplifiesLévi-Strauss's bricoleur, the thinker whose intellectual toolbox contains a variety of tools that he or she selects as appropriate to the jobat hand (Frodeman, 2014, p. 77).

In the Earth sciences, understanding the entire geological record starts with a primordial rock cycle, in which sedimentary processes are a fundamentalpart. The cyclic nature of the sedimentary processes is evidenced bymultiple steps of erosion–transport–sedimentation experienced by any sedimentary particle from its source rock to its destination in asedimentary basin. Many organisms also produce sediment, and their lifecycles are controlled by cyclically changing environmental conditions. Aharmonic produced by oscillations from different sources, frequencies, andamplitudes throughout this long sedimentation process modulates the finalsedimentary product. Thus, the cyclical conception has an importantimplication for understanding the sedimentary record over geological time.In the big picture, the analysis of cyclicity is a crucial tool to correctlydecode the sedimentary record (e.g. Barrell, 1917).

However, according to Miall (2004), contrary to the hermeneutic circle, the practice of stratigraphy throughout history has separated the empirical descriptive (inductive) and theoretical (deductive) approaches. Despite the advances and contributions of different research groups working alongeach of these lines, this author warns of the danger in the use ofstratigraphic models that specifically seek evidence of regularity orcyclicity of processes on Earth, which may lead to a bias.

There is no place for superimposed, inadequately grounded theoreticalassumptions in the construction of the geologic timescale. The hermeneutic circle is, after all, a circle. We need to be as adept at climbing theupward-directed arrow of theory based on rigorous observation as we areskilled at avoiding the downward slide of making our observations fit ourdeductions (Miall and Miall, 2004, p. 44).

On the opposite side, but in a complementary way, stratigraphic analysiscannot be reduced to a mere collection of sedimentological descriptions, asgaps span an equivalent or even longer time than the sedimentary rock record(e.g. Dott, 1983; Ager, 1993; Miall, 2004, 2017). Given the lack of tools or parameters for measuring these time gaps in the stratigraphicalrecord, Fragoso et al. (2021) warn that conceptual models are traditionallyconstructed from a mistaken perspective that assumes the completepreservation of three-dimensional depositional systems based on anoversimplification of continuous sedimentation processes. To guaranteerealistic representations, these authors propose that conceptual modelsincorporate knowledge of the processes that control the generation, destruction, and preservation of sedimentary units to define, at any timescales, predictable and ordered stratigraphic patterns for both the gaps andthe preserved record.

Historical perspective is essential for identifying unsolved problems and developing future research programmes. As can be seen throughout this briefreview, the identification and interpretation of cycles correspond to akeystone in the history of stratigraphy. However, the use of the term“cycle” has changed through time. Stratigraphic cycles have been describedas physical units with characteristic repetitive patterns but not always with a strict periodicity. Facies cycles, cyclothems, clinoforms, andstratigraphic sequences are examples where what is called a “cycle” is asedimentary unit that repeats itself in the stratigraphic record, with orwithout inference of the processes responsible for this repetition. In thesecases, the concept of cyclicity has a cognitive and didactic purpose,functioning as an association of general ideas that support the descriptionand characterization of the repetitive stratigraphic record. What isinteresting to note is that despite the different approaches andnomenclatures, stratigraphic cycles have been described with very similarcharacteristics, such as stacking patterns, bounding surfaces, andhierarchical frameworks. This common thread of the different approachespaves the way for integrating efforts and the consequent methodologicalimprovement.

For many years, efforts have been made to develop mathematical andstatistical tools to characterize stratigraphic cycles. Statisticaldistribution fitting (e.g. Pantopoulos et al., 2013), Markov chains (e.g. Krumbein and Dacey, 1969; Carr, 1982; Purkis et al., 2012), Fischer plots(e.g. Fischer, 1964; Read and Goldhammer, 1988; Husinec et al., 2008), time-series analysis (e.g. Schwarzacher, 1975; Hinnov and Park, 1998;Weedon, 2003; Martinez et al., 2016), and automatic stratigraphiccorrelations (e.g. Nio et al., 2005; Behdad, 2019; Shi et al., 2021) are examples of techniques used in stratigraphic research for quantifying cycles. With the so-called digital transformation currently in force in manyareas of knowledge, such quantitative approaches tend to be expanded. Thus,the knowledge acquired about the main cyclic characteristics observed in thesedimentary record over the past few years should be the plumb line towards a digital revolution within stratigraphy.

The effort to obtain mathematical solutions is legitimate and perhaps the only way to resolve which cycles (physical observation) are candidates forbeing periodic (with a predictive time value) or merely episodic. However, the mathematical solutions must be combined with a rigorous analysis of the rockrecord that independently characterizes the sedimentological,palaeontological, and geochronological aspects. In this sense, integrated stratigraphy is undoubtedly the appropriate way to reinforce the linksbetween different methodologies. Astronomical calibration of thestratigraphic record is appropriate for reducing uncertainties regarding interpretations of changes in sea-level, hydrodynamics, climate, physical, chemical, and biological processes (Schwarzacher, 2000; Hilgen et al., 2004;Strasser et al., 2006; Fragoso et al., 2021).

The recognition of multi-scale stratigraphic cycles, associated withtemporal calibrations that better define the relationship – simple orcomplex – of cause (geological process) and effect (observablestratigraphic entity), will undoubtedly boost the current three-dimensionalsimulations of depositional systems. In this stratigraphic forward modelling, such parameters have already been used to simulate the genesis of low- tohigh-frequency sequences in three-dimensional models applied to oil and natural gas exploration and production projects (e.g. Huang et al., 2015; Faria et al., 2017).

In order to deeply understand the cyclicity in geological process, it isnecessary to consider its ultimate root: thermodynamics (e.g. Richet et al., 2010). The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyedbut can change from one form to another. In this sense, everything in theUniverse can be classified as a form of energy, regardless of its physicalnature. Thus, it is possible to convert energy into any different form, beit a rock, a tree, or a human being. When we consider the Law ofConservation of Energy applied to deep time, it becomes possible to defineseveral and constant cycles of energy transformation, such as the rockcycle. However, in thermodynamics, the reversibility of natural processesonly occurs when they do not lead to an increase in entropy. In this way,the cyclicity of geological processes does not show absolute stability, andtransformations must be considered at an appropriate timescale. That is, both the planet's internal geodynamics and the complex astronomical systemcan be visualized as spiral cycles that constantly change at different timescales (e.g. Schwarzacher, 1993). This logical construction is similar to the one of perpetual movement of history proposed by Giambattista Vico, inwhich a new cycle always begins with a remnant of the cycle that ended(Vaughan, 1972).

It is challenging to think that the Earth itself is a specific product, intime and space, of the cyclic process of formation and destruction of stars,which has been repeated since the beginning of the Universe. Differentchemical elements are formed at each new cycle and subtly change the starnebula composition resulting from the great supernova explosions. If it were not for the existence of one of these nebulae, with a particularchemical composition inherited from these past cycles, hovering in aspecific corner of our galaxy 4.6 Ga ago, we would not have the Earth system as we know it today. Carl Sagan famously stated that “the cosmos is within us. We are made of star-stuff.” We are all, then, star-stuff on a deep journey of cyclic transformation.

No data sets were used in this article.

DGCF conceived the presented idea, wrote the manuscript draft, prepared thefigures, and made changes to the manuscript according to the reviewers' suggestions. MK, AJCM, CMDSS, GPRG, and AS reviewed and improved themanuscript through corrections and suggestions.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank Petrobras and the Petrobras School ofHigh-Resolution Stratigraphy members. Special thanks to Dora Atman and Romeu Rossi Júnior for valuable discussions and suggestions. The authors aregrateful to Andrew D. Miall and Annalisa Ferretti for detailedand constructive feedback as well as to editors Roman Leonhardt and Kristian Schlegel for their support during the review process. Daniel Galvão Carnier Fragosoand Matheus Kuchenbecker would like to make an honourable mention of theirAlma Mater (Universidade Federal de Minas Gerais), especially Luiz Guilherme Knauer, Lúcia Maria Fantinel, and Ricardo Diniz da Costa.

This paper was edited by Roman Leonhardt and reviewed by Andrew Miall and Annalisa Ferretti.

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• Article(24264 KB)
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• Abstract
• Introduction
• Cyclicity of geological processes
• Cyclicity of the stratigraphic record
• Discussion
• Data availability
• Author contributions
• Competing interests
• Disclaimer
• Acknowledgements
• Review statement
• References