Abrupt global events in the Earth's history: a physics perspective

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Rep. Prog. Phys. 73 (2010) 122801 (12pp) doi:10.1088/0034-4885/73/12/122801

Abrupt global events in the Earth’shistory: a physics perspectiveGregory Ryskin

Robert R McCormick School of Engineering and Applied Science, Northwestern University, Evanston,IL 60208, USA

E-mail: ryskin@northwestern.edu

Received 4 January 2010, in final form 8 July 2010Published 8 November 2010Online at stacks.iop.org/RoPP/73/122801

AbstractThe timeline of the Earth’s history reveals quasi-periodicity of the geological record over thelast 542 Myr, on timescales close, in the order of magnitude, to 1 Myr. What is the origin ofthis quasi-periodicity? What is the nature of the global events that define the boundaries of thegeological time scale? I propose that a single mechanism is responsible for all three types ofsuch events: mass extinctions, geomagnetic polarity reversals, and sea-level fluctuations. Themechanism is fast, and involves a significant energy release. The mechanism is unlikely tohave astronomical causes, both because of the energies involved and because it actsquasi-periodically. It must then be sought within the Earth itself. And it must be capable ofreversing the Earth’s magnetic field. The last requirement makes it incompatible with theconsensus model of the origin of the geomagnetic field—the hydromagnetic dynamo operatingin the Earth’s fluid core. In the second part of the paper, I show that a vast amount ofseemingly unconnected geophysical and geological data can be understood in a unified way ifthe source of the Earth’s main magnetic field is a ∼200 km thick lithosphere, repeatedlymagnetized as a result of methane-driven oceanic eruptions, which produce ocean flow capableof dynamo action. The eruptions are driven by the interplay of buoyancy forces and exsolutionof dissolved gas, which accumulates in the oceanic water masses prone to stagnation andanoxia. Polarity reversals, mass extinctions and sequence boundaries are consequences ofthese eruptions. Unlike the consensus model of geomagnetism, this scenario is consistent withthe paleomagnetic data showing that ‘directional changes during a reversal can beastonishingly fast, possibly occurring as a nearly instantaneous jump from one inclineddipolar state to another in the opposite hemisphere’.

(Some figures in this article are in colour only in the electronic version)

This article was invited by A Kostinski.

Contents

1. Framing the questions 21.1. Introduction 21.2. Quasi-periodicity of the geological record 21.3. Mass extinctions and biostratigraphy 31.4. Magnetostratigraphy and sequence

stratigraphy 41.5. A single mechanism? 51.6. The problem of accurate dating 61.7. Playing with time 61.8. Summary of part 1 7

2. A common origin for the Earth’s magnetic field andstratigraphic boundaries 72.1. Geomagnetism as a problem of physics 72.2. The magnetizable lithosphere 82.3. Methane-driven oceanic eruption as dynamo 82.4. Dynamo field and the lithosphere 92.5. Geomagnetic and geological implications 92.6. Conclusion 10

References 10

0034-4885/10/122801+12$90.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA

Rep. Prog. Phys. 73 (2010) 122801 G Ryskin

1. Framing the questions

1.1. Introduction

What makes physics different? Steven Weinberg put it well:‘One of the primary goals of physics is to understand thewonderful variety of nature in a unified way’ (Weinberg1999). By contrast, historical sciences such as biology orgeology focus on the particular, and deal with an overwhelmingamount of detail, most of it contingent on the actual path ofdevelopment (the history) of their subject matter. An attemptto find a unifying theme in a maze of historical detail mayencounter strong resistance. But on those rare occasionswhen such an attempt succeeds, the result is a transformationof revolutionary proportions. Examples are the molecularbiology revolution, and the plate tectonics revolution in Earthscience.

With few exceptions, the Earth science community wasfirmly opposed to Alfred Wegener’s proposal of continentaldrift for 50 years, until in 1963 Lawrence Morley andindependently Vine and Matthews (1963) combined theseafloor-spreading hypothesis of Hess (1962) with thegeomagnetic polarity reversals (whose reality was denied foreven longer time). The Vine–Matthews–Morley hypothesisstarted the plate tectonics revolution; the conversion of theEarth science community was complete in a few years (Hallam1989, Oreskes 2001). Prior to these developments, Wegener’sproposal was deemed unacceptable because ‘It was too large,too unifying, too ambitious. Features that were later viewed asvirtues of plate tectonics were attacked as flaws of continentaldrift.’ (Oreskes 2001, p 11).

Some of the processes that were initially inferred on thebasis of geological record are now directly measurable. Forexample, the theory of plate tectonics implied that continentswere moving with velocities of the order of a few centimetersper year; such movements can now be tracked using theglobal positioning system. Nevertheless, the most interestingquestions in Earth science, and the answers to them, must besought in the geological record. As in cosmology (anotherhistorical science), that record is unique, and the system isnot subject to experimentation. In the case of cosmology, theassumptions of symmetry (homogeneity and isotropy) on thelarge scale reduce the complexity of the problem enormously;for geology, nothing comparable is possible. It is hardlysurprising that, with the exception of plate tectonics, noprogress has been made toward a ‘unified theory’ of geology.

1.2. Quasi-periodicity of the geological record

One feature of the Earth’s history may present an opportunityfor theoretical analysis. The geological time scale (Gradsteinet al 2004; see figure 1) reveals quasi-periodicity of thegeological record over the last 542 Myr, on timescales close,in the order of magnitude, to 1 Myr. For example, the intervalsbetween geomagnetic polarity reversals typically range from0.2 to 2 Myr; between geological stage boundaries—from 1 to10 Myr, etc. Exceptions do exist, e.g. there were no polarityreversals between 84 and 124 Myr ago.

The geological time scale is the final result of assimilationand interpretation of a staggering amount of geologicaland geophysical data. This is done within the conceptualframework of stratigraphy, the study of sedimentary rockstrata, their temporal correlation and ordering (ICS 2009). Thevery existence of stratigraphy is predicated on the presence inthe geological record of clearly identifiable markers, reflectingsome global events. Given the imperfection of the geologicalrecord, it is obvious that abrupt, geologically instantaneousglobal events would leave the best possible markers. Butit is far from obvious why the Earth should produce suchevents. The fact that it has, at least for the last 542 Myr, isremarkable; it is telling us something very important, but inorder to understand the message, the right questions must beasked first. My purpose in this paper is to frame the questions(part 1), and also to describe my own attempts to provideanswers (part 2).

Among the most important branches of stratigraphyare biostratigraphy (based on the fossil content of therock), magnetostraigraphy (based on the geomagnetic polarityrecorded in the rock), and sequence stratigraphy (based onsequences of strata deposited on continental margins bythe cycles of sea-level rise and fall). Biostratigraphy wasdeveloped in the first half of the 19th century (Hancock 1977,Hallam 1989), magnetostratigraphy—in 1960s (Glen 1982),and sequence stratigraphy—in 1970s. All three have beenspectacularly successful in practical terms. Biostratigraphy, inparticular, provides relative ages of the strata; after absoluteages of a number of tie points were determined usingthe radiometric dating, it became possible to establish thegeological time scale for the last 542 Myr (the Phanerozoiceon). The rocks older than 542 Myr contain hardly any fossils,and biostratigraphy cannot be used.

Yet, there is still no understanding of what caused theglobal events on which these powerful methodologies arebased. This is not unusual: astronomy was put to practicaluses such as the calendar and navigation long before terrestrialand celestial mechanics were unified by Isaac Newton.Some attempts at explanation have been made in the past.Georges Cuvier suggested that discontinuities in the fossilrecord reflected mass extinctions produced by environmentalcatastrophes, such as inundations by the sea; he did not discusspossible causes of the catastrophes per se. His influential essayof 1812 was entitled ‘Discours sur les revolutions de la surfacedu globe’; an English translation came out the following year(Cuvier 1813) and went through several editions. At thattime, catastrophism had eloquent supporters in Britain, butthey were soon outnumbered by the uniformitarians, whosemotto was ‘the present is the key to the past’, and who tookthis to mean that only the processes observable now mayhave operated in the past (Hallam 1989). Charles Darwin,in particular, denied the reality of mass extinctions altogether,and ascribed any evidence for them to gaps in the geologicalrecord (Raup 1994). This is not surprising: even thoughDarwin used the fossil succession as evidence of evolution, thetheory of evolution offers no explanation for mass extinctions(Raup 1994).

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Figure 1. The geological time scale. (In this version, the smallest unit of the time scale is called ‘age’, normally, the term ‘stage’ is usedinstead; see Gradstein et al (2004, p 20).) Note the quasi-periodicity of the geological record over the last 542 Myr, on timescales close, inthe order of magnitude, to 1 Myr. (The Precambrian part of the time scale, subdivided formally by absolute age, is not useful for presentpurposes.) For example, the intervals between geomagnetic polarity reversals typically range from 0.2 to 2 Myr; the intervals betweengeological stage boundaries—from 1 to 10 Myr, etc. Exceptions do exist, e.g. there were no polarity reversals between 84 and 124 Myr ago.The origin of this quasi-periodicity and the nature of the abrupt global events that define the boundaries of the geological time scale are thefocus of the present paper.Copyright 2009 Geological Society of America, reprinted with permission from http://www.geosociety.org/science/timescale/

1.3. Mass extinctions and biostratigraphy

In most of the geological literature, the designation ‘massextinction’ is reserved for the most severe extinctions in theEarth’s history, such as the Permian–Triassic ca 251 Myr ago,the Cretaceous–Tertiary (Cretaceous–Paleogene) ca 65 Myrago, and a few others. Each of these extinctions eliminated∼70% to 90% of the total number of species; consequently,these extinctions define the most significant boundaries ofthe geological time scale. In particular, the two extinctionsmentioned above define the boundaries between the geologicaleras, Paleozoic, Mesozoic and Cenozoic, which togethercomprise the Phanerozoic eon. However, as emphasizedby Raup (1994), other extinctions—e.g. the ones markingstage boundaries—were not qualitatively different from the‘Big Five’, and should be included in the same category.Hallam and Wignall (1997, p 1) define mass extinction as‘an extinction of a significant proportion of the world’s biotain a geologically insignificant period of time’. Generally

speaking, a biostratigraphic boundary is marked by a massextinction:

‘Five percent [of the total number of species] isroughly the extinction level that normally defines[the boundary of] the “biostratigraphic zone”—thesmallest unit in geologic time recognizable by fossilson a global or near-global basis. In many parts of thegeologic column, paleontologists have estimated theaverage duration of a stratigraphic zone to be aboutone million years.’ (Raup 1991, p 170)

Stage boundaries are defined by mass extinctions of greaterseverity (typically, a few tens of percent), followed, in therough order of severity, by the boundaries between epochs,periods and eras. (The time units ‘age’, ‘epoch’ and ‘period’correspond to the stratigraphic units ‘stage’, ‘series’ and‘system’.)

It may seem that the extinction level of 5% is relatively low,and does not qualify as a mass extinction when compared withextinctions of 70%. This view is common in the geologicalliterature, but is incorrect (Raup 1991, 1994). The percentageof species lost is not the right statistic to consider when trying

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to weigh the severity of the environmental perturbation (anabrupt global event) that caused mass mortality in the biota,and resulted in the disappearance of a number of species.Instead, one should compare the mortality statistics at the levelof individuals; this paints a completely different picture. It is,of course, the individuals that are actually affected; on thetimescale of the extinction-causing event, the species is anabstract entity.

The following analysis is based on the statistical approachoriginated by Raup (1979, 1991, pp 70–5); the final result (1)appears to be new. Assume for simplicity’s sake that the extinc-tion of a species requires the death of all its individual members(organisms). Let the total number of organisms in a speciesbeN . If killing is completely random, the probability of extinc-tion is Pext = (1−Psi)

N , where Psi is the probability of survivalfor an individual. Hence ln(1 − Psi) = N−1 ln Pext; here N

is a large number, while ln(1 − Psi) is small because Psi � 1.Then ln(1 − Psi) = −Psi, and so Psi = −N−1 ln Pext.

Consider now the expected number of surviving individualsin a species, nsi = NPsi. This number is very simplyrelated to Pext, and the relation does not include N , namely,nsi = −ln Pext. Or, equivalently,

Pext = e−nsi . (1)

In an extinction where 5% of species are lost, only about threeindividuals in a species are expected to survive, on average.The expected number of survivors drops to 1 for the extinctionlevel of 37%, as could occur, e.g., at a stage or a seriesboundary. It drops to 0.1 for the extinction level of 90%,possibly reached in the greatest extinction in the Earth’s history,the Permian–Triassic boundary.

On the other hand, a catastrophic event slightly less fatal,such that 10 individuals in a species were expected to survive,would leave no evidence of extinction in the fossil record:given the imperfection of the latter, the extinction level of0.005% is unobservable.

These examples may be counter-intuitive, but they expressa simple truth: for a species with a large number of members,to become extinct is highly improbable, as survival of evena single member is enough to prevent that from happening.And only species extinction is relevant for the fossil record;mortality at the level of individuals is not. A catastrophicevent may cause nearly complete mortality in the biota, butstill fail to cause mass extinction; such an event would leavehardly any trace in the fossil record.

The above simple analysis cannot be true in detail; itassumes random killing and ignores the fact that some of thespecies are more resilient than others (Raup 1979, 1991, pp 70–75). But its main message is valid: a sudden environmentalevent capable of causing even a ‘minor’ mass extinction mustbe utterly catastrophic at the level of individuals. This messageis essentially contained, even if never stated explicitly, in theworks of Raup (1991, 1994).

I conclude: the occurrence, over the last 542 Myr,of hundreds of mass extinctions at the biostratigraphicboundaries, suggests the existence of some unknownmechanism, acting quasi-periodically on timescales of order1 Myr, and causing some terrifying global catastrophes.

1.4. Magnetostratigraphy and sequence stratigraphy

Similarly to mass extinctions, the reality of geomagneticpolarity reversals was denied for nearly 60 years, until theVine–Matthews–Morley hypothesis connected the polarityreversals with the seafloor spreading, and ushered in theplate tectonics revolution (Hallam 1989, Oreskes 2001).Magnetostratigraphy has since become an indispensable toolof stratigraphic correlation, even though the mechanism ofreversals remains as mysterious as ever. I discuss in part 2 whythe ‘standard model’ of geomagnetism—the hydromagneticdynamo operating in the Earth’s fluid core, and occasionallyself-reversing—is unlikely to be true.

As far as sequence stratigraphy is concerned, the denialstage is not over yet, though this has not prevented sequencestratigraphy from becoming a tool of choice in oil and gasexploration. Here by denial I mean the refusal to accept themain tenet of sequence stratigraphy, namely, that depositionalsequences reflect cycles of sea-level rise and fall (Vail et al1977a, 1977b). Indeed, some geologists maintain that thecentral ideas of sequence stratigraphy are nothing but a myth(Dickinson 2003). The conceptual problem is real: globalsea-level changes ∼100 m on timescales ∼1 Myr cannot beexplained in the absence of continental ice sheets. Thus Deweyand Pitman (1998) write:

‘We can discern no mechanism that can causethe necessary short-wavelength [∼1 Myr], large-amplitude sea-level changes implicit in globallysynchronous eustatic third-order cycles’ of sequencestratigraphy.

Miller et al (2004) concur:

‘Either continental ice sheets paced sea-level changesduring the Late Cretaceous [an ice-free epoch byall other indications], or our understanding ofcausal mechanisms for global sea-level change isfundamentally flawed.’

The sequence stratigraphy community has ignored thisobjection (Miall and Miall 2001), and the paradox remainsunresolved.

They have not been able, however, to ignore anotherobjection: their original sea-level curve, based directly on theseismic reflection record, showed the sea-level falls (but notrises) as geologically instantaneous (Vail et al 1977a, 1977b).This caused such a storm of criticism that in subsequentpublications they invoked factors invisible in the seismicrecord, such as tectonic subsidence, and produced a ‘moresinusoidal’ sea-level curve (Haq et al 1987, Jervey 1988,Hallam 1992, p 25). (Uniformitarianism is alive and well—any suggestion of abrupt change is strongly resisted. Cf Weart2003.) The original saw-tooth sea-level curve was not entirelyabandoned; it survives under the name ‘coastal onlap’ (Haqet al 1987), or simply ‘onlap’ (Haq and Schutter 2008), seefigure 2.

The pattern is becoming clear now: every new branch ofstratigraphy utilizes a new type of marker in the geologicalrecord. The reality of the abrupt global events that left thesemarkers is invariably denied by the majority of experts; this,

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Figure 2. The sea-level curves of sequence stratigraphy. Theoriginal saw-tooth sea-level curve (Vail et al 1977a, 1977b) has beenrenamed ‘onlap’. (It proved impossible to explain the abruptsea-level falls of the original saw-tooth curve.) The smooth version(called ‘sea-level changes’ in the figure) is justified by invokingfactors invisible in the seismic record, such as tectonic subsidence(Jervey 1988, Haq et al 1987). Now consider the following thoughtexperiment: if the assumption of constant sedimentation rate isdropped, the time axis can be locally stretched or compressed atwill, with the sea-level curve being deformed as a result. Imaginenow the sea-level curve transformed into a comb-like series ofinstantaneous peaks, coinciding in time with the abrupt sea-levelfalls of the original saw-tooth curve. In other words, could an entirecycle of sea-level rise and fall be geologically instantaneous? Theanswer proposed here is in the affirmative. See section 1.7 fordetails. (Reprinted with permission from Haq and Schutter (2008).Copyright 2008 American Association for the Advancement ofScience.)

however, does not stop the practitioners of the new stratigraphyfrom achieving great practical success. As a result, the voicesof denial become progressively weaker, and may disappearentirely; still no explanation is forthcoming of the nature ofthe events.

1.5. A single mechanism?

The phenomena that lie behind the practice of stratigraphyshould be of considerable interest to physicists, who are notconstrained by the ‘dangerous doctrine of uniformitarianism’(Ager 1993b, p xvi). In addition, I propose that a singlemechanism is responsible for all three types of events—thoseunderlying biostratigraphy, magnetostratigraphy and sequence

stratigraphy. This proposal is based on the following empiricalevidence. (For brevity, the word ‘mass’ will be omitted fromnow on, ‘extinction’ always meaning ‘mass extinction’.)

The ‘strong correlation between extinctions and magneticreversals’ is well known to geologists (Ager 1993a, p 37), butremains unexplained. Equally well known and unexplained isthe correlation between extinctions and sequence boundaries:

‘In the seven cores studied the magnetic reversalsand faunal boundaries are consistently related to eachother . . . The coincidence or near coincidence offaunal changes with reversals in these cores suggestsa causal relation.’ (Opdyke et al 1966)

‘Many geologists expect sequence boundaries tocorrespond with system, series, and stage boundariesand . . . zonal subdivisions . . . ’ (Gradstein et al 2004,p 236)

‘The most often recognized surface is the combinedsequence boundary and subsequent flooding (trans-gressive) surface. Most standard stage type sectionslocated in passive-margin settings, have a transgres-sive surface as their lower boundary.’ (Hardenbol et al1998, p 4)

‘The regional and the global stage boundaries aresequence boundaries that reflect the global event ofthe sea-level fall.’ (Vakarcs et al 1998, p 215)

‘The initiation of each major transgressive episodecoincides with a major mass extinction . . . ’(Gradstein et al 2004, p 288)

The geological record, in fact, contains multiple instances ofperfect coincidence. Here are a few examples, listing the dates,in million years ago, of a polarity reversal, a stage boundaryand a sequence boundary: 28.45, 28.45, 28.45; 23.80, 23.80,23.80; 20.52, 20.52, 20.52; 14.80, 14.80, 14.80 (Gradsteinet al 2004, pp 69–71; de Graciansky et al 1998, Chart 2). TheOligocene–Miocene boundary, dated 23.03 Myr ago, coincideswith a polarity reversal (Gradstein et al 2004, p 424). ThePermian–Triassic boundary coincides with a polarity reversal(Ward et al 2005). The four most recent stage boundaries,dated 3.60, 2.59, 1.81 and 0.78 Myr ago, all coincide withpolarity reversals (Gradstein et al 2004, pp 28–9; ICS 2009);the last three—also with sequence boundaries. The list couldbe continued.

The above is strong evidence that all three types of eventsare caused by the same mechanism. The alternative—threeseparate mechanisms, which often act at exactly the sametime—is so improbable that it hardly deserves attention.

It is also true that not every stage boundary will coincidewith a polarity reversal and/or a sequence boundary. Thereasons are simple: all three types of events being causedby the same mechanism does not mean that all three mustoccur, and leave a clear record, every time the mechanismacts. For example, a slight variation in the mortality producedby the event may cause it to leave no trace in the fossil record(see above). Polarity reversal need not occur each time themechanism acts (see below). And some of the events mayhave left a poor record yet to be discovered.

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1.6. The problem of accurate dating

An additional problem is the difficulty of mapping thesedimentary column to the time axis. Radiometric dating hasachieved spectacular successes in geology, but sedimentaryrocks cannot be dated in this way. Only igneous rocksor volcanic ashes can be dated radiometrically because theradioactive isotope and its decay products must be ‘lockedin’ within the crystalline matrix; otherwise their ratioswill be distorted by diffusion and other effects (Bourgeois1990). Radiometric dating in stratigraphy is typically limitedto volcanic ash horizons that bracket biostratigraphicallycalibrated sedimentary sections (Gradstein et al 2004, p 89).If one uses the assumption of constant sedimentationrate between such horizons, a catastrophic, geologicallyinstantaneous deposit will be interpreted as representingthousands or even millions of years (Bourgeois 1990,Ager 1993a, 1993b). Then the ages assigned, say, to abiostratigraphic boundary and a polarity reversal may fail tocoincide, even though the extinction and the reversal occurredsimultaneously.

Currently, no reliable technique exists for mapping thesedimentary column, between the radiometrically dated tiepoints, to the time axis. A case in point is provided by the strataassociated with the Cretaceous–Tertiary boundary—probably,the most thoroughly studied segment of the geological record.In several geographical locations, a particular sedimentarycomplex within these strata is interpreted by some geologistsas deposited over 0.3 Myr, by others—over a few hours ordays (by a mega-tsunami). The debate on this issue hasbeen going on for over two decades, and shows no sign ofabating, with world-class experts in both camps marshallingthe ever increasing amounts of data to support their respectiveinterpretations. (For the latest salvos from each side of thedebate, see Keller et al 2009a, 2009b and Schulte et al 2010.)The implied sedimentation rates differ by eight orders ofmagnitude.

1.7. Playing with time

One immediate conclusion is this: with the exception of theradiometrically dated tie points, the mapping t (z) of thesedimentary column to the time axis must be viewed as anunknown function, which is monotonically increasing butotherwise of the most general nature. This function possessesmultiple jump discontinuities, corresponding to the periods oftime when either no deposition occurred or the deposited stratawere subsequently removed (eroded). The sedimentary recordis ‘more gaps than record . . . a lot of holes tied together withsediment’ (Ager 1993a, Ch. 3). The discontinuities of t (z)—the periods of ‘lost time’—are marked in the sedimentaryrecord by unconformities (figure 3). Unconformities are ofparamount importance in interpretation of the sedimentaryrecord; in particular, they define sequence boundaries insequence stratigraphy.

While t (z) is piecewise continuous, the value of itsderivative may range over many orders of magnitude, and thereis no reason to expect t (z), or its inverse, to possess any degreeof smoothness. As noted above, between the radiometrically

Figure 3. An example of unconformity. An unconformity is aburied erosional surface separating strata of different ages; itindicates that sediment deposition was not continuous. In an angularunconformity, such as the one shown here, younger strata ofsedimentary rock rest upon the eroded surface of tilted or foldedolder rocks. Not all unconformities are angular; often, the youngerand the older strata are essentially parallel. Unconformities areclearly visible in the seismic reflection record; they define sequenceboundaries in sequence stratigraphy. The mapping t (z) of thesedimentary column to the time axis possesses multiplediscontinuities, corresponding to the periods of ‘lost time’; thesediscontinuities are marked in the sedimentary record byunconformities.(Image © Copyright Patrick Mackie and licensed under CreativeCommons License; see http://www.geograph.org.uk/photo/107618)

dated tie points t (z) is essentially unknown. It is impossibleto use a function like that for any practical purposes (e.g.construction of graphs), so one often assigns to t (z) maximalsmoothness—linearity—between the tie points (which isequivalent to assuming the constant sedimentation rate). Thisis only a consequence of the currently unavoidable ignorance,and should not preclude contemplation of phenomena thatwould lead to highly non-smooth t (z).

Consider, for example, the sea-level curve of sequencestratigraphy. In its construction, of both the original saw-tooth version and the ‘more sinusoidal’ version, constantsedimentation rates were assumed. As discussed above, thereis no rational basis for this assumption; if it is dropped, thetime axis can be locally stretched or compressed at will, withthe sea-level curve being deformed as a result. Imagine nowthe sea-level curve transformed into a comb-like series ofinstantaneous peaks, coinciding in time with the abrupt sea-level falls of the original saw-tooth (‘onlap’) curve (Haq et al1987, Haq and Schutter 2008, see figure 2). In other words,could an entire cycle of sea-level rise and fall be geologicallyinstantaneous?

It could not, of course—if the sea level is understood in itsusual sense of a global, quasi-static datum. But things changedramatically if fluid dynamics is brought into the picture. Aspointed out by Dott (1996), and also by Ager (1993a, 1993b),the sequences of sequence stratigraphy could be deposited bymega-tsunamis. Such a scenario immediately resolves thegreat controversy over the sea-level changes in the absence ofcontinental ice sheets (see above). And it is fully supported by

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the field data: the strata directly overlying a sequence boundarytypically contain pebble conglomerates, lag gravels, and rip-up clasts of the underlying lithologies (Baum and Vail 1988),which all signify a fast, high-energy flow. Such a flow occurswhen coastal areas are flooded by a tsunami (Bourgeois 2009),not during a quasi-static sea-level rise ∼100 m in a millionyears.

The mega-tsunami scenario also solves another long-standing puzzle, the presence of erratics (boulders, etc.),normally interpreted as glacial dropstones, in deposits fromthe ice-free epochs:

‘Concentrations of erratics and [fossilized] woodappear to occur in distinct horizons or boulderbeds. These coincide with the basal portions oftransgressive units.’ (Markwick and Rowley 1998)

‘Allochthonous logs . . . occur in extraordinary abun-dance as sedimentary components in transgressivemarine shelf deposits . . . ’ (Savrda 1991)

1.8. Summary of part 1

There are strong indications that a single mechanism isresponsible for the mass extinctions, geomagnetic polarityreversals and mega-tsunamis that underlie biostratigraphy,magnetostratigraphy and sequence stratigraphy. Thismechanism has been acting quasi-periodically over at least542 Myr, on timescales close, in the order of magnitude, to1 Myr. The mechanism is fast, and involves a significantenergy release. It is unlikely to have astronomical causes, bothbecause of the energies involved, and because it acts quasi-periodically. It must then be sought within the Earth itself.

This already looks like a problem of considerable interest,but the intrinsic interest is not the only motivation here: unlesswe understand the mechanism, we shall have no chance ofpreventing it from acting again. And it may act again, strictlyspeaking, any moment: the last four of its actions are dated3.60, 2.59, 1.81 and 0.78 Myr ago. Still, on the margins of amillion-year timescale, there is probably some time left.

2. A common origin for the Earth’s magnetic fieldand stratigraphic boundaries

2.1. Geomagnetism as a problem of physics

The origin of the Earth’s magnetic field is one of the oldestproblems of physics. In 1269, Petrus Peregrinus (Pierre deMaricourt) wrote Epistola de Magnete (Peregrinus 1269), ‘thefirst scientific treatise describing observations and experimentscarried out for the purpose of clarifying natural phenomenon.The conclusions were derived logically based on observationsand experiments’ (Kono 2007). Written 400 years beforescientific journals were invented, Epistola de Magnete hada form of a letter to a friend, and spread via manuscriptcopies. Peregrinus discovered (and named) the poles of amagnet, as well as the impossibility of separating them, i.e.the nonexistence of magnetic charges. In order to explainthe propensity of the magnetic needle to align along themeridian, he proposed that ‘it is from the poles of the heavens

that the poles of the magnet receive their virtue’. (In thegeocentric system, the celestial sphere rotates about the axispassing through the celestial poles.) He further proposed thatthe magnet as a whole is influenced by ‘the whole heavens’and, if properly oriented on frictionless pivots, would ‘moveaccording to the motion of the heavens’—in essence, the firsthint at Mach’s principle (Peregrinus 1269).

Peregrinus’s explanation of the magnetic needle behaviorremained a reasonable hypothesis until the discoveryof declination in the 15th century; the first recordedmeasurements of declination were made by ChristopherColumbus, who also discovered the dependence of declinationon the geographic location (Kono 2007). In 1600, WilliamGilbert in De Magnete, the first scientific monograph, proposedthat the Earth itself is a ‘great [permanent] magnet’ (Gilbert1600, pp 211–212). Gilbert’s hypothesis suffered a majorsetback when secular variation of the Earth’s main magneticfield was discovered by Henry Gellibrand (1635). It wasultimately abandoned because (Chapman and Bartels 1940,chapter 21):

(a) secular variation could not be explained;(b) the required magnetization of the lithosphere appeared

to be too high (since temperature increases with depth,only the outer shell of the Earth can be permanentlymagnetized);

(c) ‘it would be hard to explain how the magnetization couldbe everywhere so nearly parallel to the magnetic axis,unless some powerful hypothetical process was assumedby which the Earth was magnetized at some past epoch,although no trace of this process is now left’.

It would be even harder to explain the polarity reversals, buttheir reality was largely denied at the time.

In the early decades of the 20th century, the origin ofthe Earth’s magnetic field was considered one of the mostimportant problems of physics (Einstein 1924). Some far-reaching proposals were made but only one survived to thisday, by Joseph Larmor (1919), who suggested the followingorigin for magnetic fields of celestial bodies: electric currentsare induced in a conducting fluid moving through a magneticfield; these currents give rise to secondary magnetic fields,which add to the original field. If amplification of the field isfaster than its resistive decay, the flow may act as a generatorof magnetic field—a hydromagnetic dynamo. The initial fieldcan be arbitrarily small; the field growth is exponential untilits back action on the flow (via the Lorentz force) becomessignificant.

With regard to the Earth in particular, Larmor (1919)singled out secular variation as ‘the very extraordinary featureof the earth’s magnetic field’, and suggested that the abovemechanism would account for secular variation ‘merely bychange of internal conducting channels; though, on the otherhand, it would require fluidity and residual circulation in deep-seated regions’.

Larmor did not develop this conjecture in any detail;more than 25 years passed before it was applied to theEarth’s core, by Frenkel (1945) and independently by Elsasser(1946). At the turn of the century, hydromagnetic dynamo

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action was finally demonstrated in the laboratory (Stefani et al2008), though neither the flow nor the magnetic field in theexperiments bear much resemblance to their counterparts incelestial bodies.

Currently, the consensus is that the geomagnetic main fieldis produced by the hydromagnetic dynamo in the Earth’s fluidouter core (Roberts and Glatzmaier 2000). Secular variationis used to estimate the characteristic large-scale velocity inthe outer core, and to conclude that dynamo action is possible.This model has not been seriously questioned for decades, eventhough it makes no testable predictions. (With one exception:the characteristic timescale of magnetic diffusion in the core,∼10 kyr, imposes an approximate lower limit on the durationof a polarity reversal.)

In Ryskin (2009), I proposed a different mechanism ofsecular variation: ‘ocean water being a conductor of electricity,the magnetic field induced by the ocean as it flows throughthe Earth’s main field may depend on time and manifest itselfglobally as secular variation’. This proposal was supportedby calculation of secular variation using the equations ofmagnetohydrodynamics, and by analysis of observational data.‘If secular variation is caused by the ocean flow, the entireconcept of the dynamo operating in the Earth’s core is calledinto question: there exists no other evidence of hydrodynamicflow in the core’ (Ryskin 2009).

Note that it is impossible to determine the location ofthe source by observing the field at the Earth’s surface. Forexample, the external field of a uniformly magnetized sphericalshell is exactly that of a point dipole, and depends only on theproduct of magnetization and volume; the radii of the shellcannot be inferred. In addition, there exists an infinite varietyof magnetizations of a spherical shell that produce no externalfield at all (Runcorn 1975). The commonly assumed separationof the observed field, on the basis of its spherical harmonicrepresentation, into the field produced in the Earth’s core andthe crustal field, has no theoretical basis.

Below I show that a vast amount of seemingly unconnectedgeophysical and geological data can be understood in aunified way if the source of the Earth’s main magneticfield is a ∼200 km thick lithosphere, repeatedly magnetizedas a result of methane-driven oceanic eruptions (Ryskin2003), which produce ocean flow capable of dynamo action.Polarity reversals, extinctions and sequence boundaries areconsequences of these eruptions. Unlike the consensus model,this scenario is consistent with the paleomagnetic data showingthat

‘directional changes during a reversal can beastonishingly fast, possibly occurring as a nearlyinstantaneous jump from one inclined dipolar stateto another in the opposite hemisphere’ (Acton et al2000).

2.2. The magnetizable lithosphere

At the atmospheric pressure, the Curie temperature of ironoxides and other iron-containing minerals is not higherthan 675 ◦C, but it rises with pressure; rates of increase∼23 K GPa−1 have been measured (Schult 1970). This means

that at a depth of 200 km, the Curie temperature of iron oxidescan be ∼800 ◦C. Metal alloys that form in the deep lithospheremay have the Curie temperature as high as 1100 ◦C (Haggerty1978). The actual temperature variation with depth is notwell constrained. Temperatures inferred from seismic data are∼800 to 1000 ◦C at 200 km depth (Goes et al 2005, Kuskovet al 2006). Observations suggest that the upper mantle is,in fact, magnetic (Pochtarev et al 1997, Blakely et al 2005).Thus, a deep Curie isotherm is not ruled out by the data; let ustake for its depth 200 km.

The volume of the 200 km thick outer shell of the Earthis ∼1020 m3. The dipole moment of the Earth’s magneticfield is ∼0.8 × 1023 A m2. If the source of the field is the200 km thick lithosphere, the average magnetization of thislithosphere must be ∼1 kA m−1. This is a very large value,much larger than the average magnetization of the near-surfacerock. However, under the conditions of high temperature andpressure prevalent in the deep lithosphere, iron-oxide mineralsmay acquire remanent magnetizations ∼102 to 103 kA m−1

(Robinson et al 2002, Gilder and LeGoff 2008), provided themagnetizing field is much stronger than the geomagnetic field.Since iron oxides make up a few percent of the lithosphere,the average magnetization of the lithosphere ∼1 kA m−1 isfeasible, if only barely. Just barely accounting for the observedintensity of the Earth’s magnetic field is, however, not a flawbut a virtue: the important question of why the field has thisparticular intensity is then resolved.

Thus, objection (b) is not fatal to Gilbert’s hypothesis. Butwhat could magnetize the lithosphere, and do so repeatedly,reversing the field polarity?

2.3. Methane-driven oceanic eruption as dynamo

In Ryskin (2003), I proposed the existence of methane-drivenoceanic eruptions, a quasi-periodic Earth-based phenomenoncapable of causing extinctions and climate perturbations. Inmost of the world ocean, methane, CH4, continuously entersthe water column from the seafloor, dissolves in seawater andis oxidized by microbes. In some oceanic regions prone tostagnation and anoxia, methane may escape oxidation andaccumulate in the water column for a very long time, untilsaturation is reached. Since the saturation concentrationincreases with depth (due to Henry’s law), a water columnsaturated with dissolved gas is in a metastable state (Ryskin2003). A transition from this metastable state must eventuallyoccur; the mechanism of transition is the water-columneruption, driven by the interplay of buoyancy forces andexsolution of dissolved gas (Ryskin 2003). A similar process isresponsible for the most violent, explosive volcanic eruptions;these are driven by exsolution of water vapor dissolved in theliquid magma (Gilbert and Sparks 1998).

Extinctions are among the most important effects of themethane-driven oceanic eruptions. The eruption brings to thesurface deep anoxic waters that cause extinctions in the marinerealm. Terrestrial extinctions are caused by the eruption-triggered mega-tsunamis, by the explosions and conflagrationsthat follow the massive release of methane, and by the ensuingclimate perturbations. In a large eruption, combustion and

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explosion of the released methane would liberate energyequivalent to 108 Mt of TNT; this is greater than the world’sstockpile of nuclear weapons (implicated in the nuclear-winterscenario) by a factor ∼104 (Ryskin 2003).

In addition to the supporting evidence discussed inRyskin (2003), this scenario is also in accord with otherextinctions data: the preferential survival among vertebratesof the burrowing, swimming and diving species (Sheehan andFastovsky 1992, Retallack et al 2003, Robertson et al 2004),and the evidence for massive combustion of hydrocarbons(Cisowski 1990, Belcher et al 2009).

Methane-driven oceanic eruption may produce a short-lived ocean flow of sufficient intensity to act as ahydromagnetic dynamo. Ocean water has a substantialelectrical conductivity, σ ≈ 3.2 S m−1. One importantvelocity scale is the speed of propagation of tsunamis,∼200 m s−1. Another is the maximum vertical velocity withinthe erupting fluid column, ∼100 m s−1. For the ocean depthH of a few thousand meters, the vertical travel time is then∼1 min, whereas the time needed for a tsunami to cross theocean is ∼1 day. These timescales should be comparedwith the timescales of resistive decay or magnetic diffusion.Magnetic diffusivity η ≡ (µ0σ)−1, where µ0 is a constant ofSI. For ocean water η ≈ 0.25 km2 s−1, so that the timescale onwhich magnetic diffusion penetrates through the ocean depthis H 2/η ∼ 1 min. More important for dynamo action isthe global diffusion timescale. For the ocean viewed as athin spherical shell of thickness H and radius R (the Earth’sradius), this is RH/η ∼ 1 day (Callarotti and Schmidt 1983).Comparison of the timescales shows that dynamo action cannotbe ruled out. Below I assume that it does occur (though notnecessarily in every eruption), and explore the consequences.This assumption is the only hypothetical element in the presentscenario.

2.4. Dynamo field and the lithosphere

Direct numerical simulations show that turbulent flow of aconducting fluid can generate a large-scale magnetic field viathe inverse-cascade mechanism (Brandenburg 2001). The timenecessary to build up the large-scale field is comparable to thelongest magnetic diffusion timescale; for the ocean it should bemeasured in days. The simulations also show that the overallevolution of the large-scale field is well described by the α2

model of the mean-field dynamo theory. This model was usedby Schubert and Zhang (2001) to calculate the magnetic fieldgenerated by turbulent flow in a spherical fluid shell, with eitherconducting or non-conducting material occupying the interiorof the shell.

As a rough approximation, the ocean during a methane-driven eruption can be viewed as such a shell. Then the interiorof the shell contains the Earth’s highly conducting metallic coreand the essentially non-conducting mantle and crust. If theinterior were entirely non-conducting, the generated magneticfield would be approximately uniform in it (figure 2(c) ofSchubert and Zhang 2001). The highly conducting corechanges the picture, but only slightly: the short-lived magneticfield generated by the ocean flow during the eruption (‘the

dynamo field’) cannot enter it, except for a skin depth. Themagnetic diffusivity in the core is η ∼ 1 m2 s−1 (Roberts andGlatzmaier 2000); the penetration depth of a dynamo field witha lifetime, say, t = 10 days is (ηt)1/2 ∼ 1 km, whereas theradius of the core is ∼ 3500 km. Thus, throughout its lifetimethe dynamo field avoids the Earth’s core.

Due to the Coriolis force dominance in the large-scaleocean flow, the direction of the dynamo field ought to beroughly aligned with the Earth’s axis of rotation, with arandomly chosen polarity. (The axis of rotation provides apreferred direction, but no preferred polarity.) The magnitudeof the dynamo field can be estimated by assuming that it stopsgrowing when its back action on the flow—the Lorentz force—becomes comparable to the Coriolis force (Elsasser 1946). Theratio of the two forces is characterized by the Elsasser numberσB2/ρ�, where B is the characteristic field value, ρ is thedensity of the fluid, and � is the angular velocity of the Earth’srotation. The order-of-magnitude estimate of the dynamo field(given originally by Elsasser (1946) for the Earth’s core model)is then (ρ�/σ)1/2; with ρ and σ of the ocean water this yields∼0.1 T. The dynamo field is thus greater than the geomagneticfield observed today by a factor ∼103.

After the dynamo field disappears, there remains the weakfield due to the lithosphere, which was magnetized by thedynamo field. To a first approximation, the lithosphere can beviewed as a spherical shell with uniform magnetic properties.The dynamo field avoids the Earth’s core, but this makes it onlyslightly non-uniform within the lithosphere. Thus, to a firstapproximation, after the dynamo field disappears, a uniformlymagnetized lithosphere is left. In the present scenario, the fieldproduced by this lithosphere is the geomagnetic field observedtoday, and in the intervals between the dynamo-producingoceanic eruptions in the past.

2.5. Geomagnetic and geological implications

The earliest evidence of the geomagnetic field dates to 3.5 Gyrago (Tarduno et al 2010). The ocean was in existence by 3.7Gyr ago (Fedo et al 2001, Moorbath 2009). Methane may havebeen entering the ocean water column since very early times; itcertainly was present in the seafloor sediments by 3.5 Gyr ago(Ueno et al 2006), though its origin—microbial or abiotic—isa matter of dispute (Kutcherov and Krayushkin 2010).

The magnetized lithosphere being the source of thecurrently observed main geomagnetic field explains whythe field is so stable; such stability would not be expected if thefield were produced by a currently operating hydromagneticdynamo (Zhang and Gubbins 2000). The present scenarioalso explains the dominance of the axial dipole, and theobserved correlations between the gravitational anomalies andthe long-wavelength geomagnetic anomalies. The sources ofthe anomalies appear to lie at the base of the crust and in theupper mantle (Pochtarev et al 1997, Blakely et al 2005).

The polarity of each dynamo field being arbitrary, thegeomagnetic field should have reversed its direction manytimes throughout the Earth’s history. The lifetime of thedynamo field and the duration of the polarity reversal are likelymeasured in days. These durations cannot be inferred on the

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basis of sedimentary record because during the eruption, andfor some time after it, sedimentation rates can be much higherthan average.

Only volcanic lava flows that erupted before or during apolarity transition, and cooled below the Curie temperature asthe transition was occurring, may provide reliable informationabout the speed of the transition. Such lava flows have beenfound in Oregon, North America, in Afar, Africa, and in theCanary Islands. All show ‘astonishingly rapid field change’(Coe et al 1995). In central Afar, ‘one lava flow has recordedboth of the antipodal transitional components’, and so theduration of the transition could be estimated knowing the lava’scooling rate (Acton et al 2000). The results show that

‘directional changes during a reversal can beastonishingly fast, possibly occurring as a nearlyinstantaneous jump from one inclined dipolar stateto another in the opposite hemisphere. . . . For theSite ET040 lava flow, which is ∼4.5 m thick, to haverecorded nearly antipodal transitional componentsabove and below ∼500 ◦C would indicate thatthe jump from a northern-hemisphere transitionalstate to a southern-hemisphere one occurred inless than a few weeks. . . . Reheating and partialremagnetization by the overlying flow cannot explaineither of the transitional directions because both differsignificantly from that of the reversely magnetizedoverlying flow.’ (Acton et al 2000).

In the Canary Islands, if the ‘peculiar’ magnetization directionsobserved in several lava flows ‘could have a geomagneticorigin’ (Valet et al 1998), these flows

‘would have recorded an almost complete fieldreversal. . . .Given the time taken by a 3–4 m thick lavaflow to cool, this scenario would imply an extremelyshort duration for the reversal process.’ In particular,‘a 160◦ angular deviation of the field direction wouldhave been recorded’ while the lava flow was coolingfrom 580 ◦C to 500 ◦C, a time interval that ‘cannotexceed . . . 10 days’ (Valet et al 1998).

Having considered this interpretation of the data, Valet et al(1998) rejected it because ‘the hypothesis of such an extremelyrapid field reversal is very unlikely, if not impossible’.They presented arguments in favor of remagnetization by theoverlying flow, but made the following remark: ‘One maywonder why atypical rock magnetic properties would prevailonly within flows associated with reversals.’

The data of Coe et al (1995), Acton et al (2000), and Valetet al (1998) cannot be reconciled with the Earth’s core beingthe source of the geomagnetic field: the diffusion timescaleof the core, ∼10 kyr, would then determine the duration ofreversal. In the present scenario, the Earth’s core is screenedfrom the geomagnetic field: by Runcorn’s theorem, a sphericalshell (the lithosphere) magnetized by a field whose sourceswere outside of it (the dynamo field) does not produce anyfield in its interior (Runcorn 1975). The core is not screenedfrom the dynamo field, but the dynamo field is short-lived anddoes not enter it.

Given that methane-driven oceanic eruptions cause extinc-tions, polarity reversals should coincide with biostratigraphicboundaries. Not every oceanic eruption will produce a dynamofield (depending on the paleogeography, the magnitude of theeruption, etc.); even when it does, not always the resultinglithospheric field will have a polarity different from the pre-vious one. Thus, not every biostratigraphic boundary will bemarked by a geomagnetic reversal. Nor will every reversalcoincide with a biostratigraphic boundary: some oceanic erup-tions may result in a polarity reversal or excursion, but onlya regional extinction, or none at all. Nevertheless, signifi-cant correlation between extinctions and reversals should beobservable in the geological record. In addition, biostrati-graphic boundaries and polarity reversals should coincide withsequence boundaries because oceanic eruptions produce mega-tsunamis.

Conflagrations and explosions that follow methane-drivenoceanic eruptions produce metallic or glassy microspherulesor microtektites (Cisowski 1990, Ryskin 2003); thusgeomagnetic polarity reversals ought to be correlated withmicrotektite horizons. Such correlations are indeed observed.The Permian–Triassic boundary coincides with a polarityreversal (Ward et al 2005) and is marked by high concentrationsof microspherules (Jin et al 2000). Preisinger et al (2002)found magnesioferrite spinels at all four polarity reversalsthat they studied. Haines et al (2004) describe microtektite-bearing deposits that coincide with the last reversal, 0.78 Myrago. They note ‘abundant organic debris, including whole treetrunks’, and envision rapid deposition by high-energy floods,exactly as suggested by the present scenario.

2.6. Conclusion

The only hypothetical element in the present scenario is themethane-driven oceanic eruption capable of dynamo action;the rest follows inescapably. Note that the present scenario isin accord with all the available geomagnetic, paleomagneticand geological data. In fact, the present scenario will alsobe in accord with most of the conventional interpretation ofthese data, provided one abandons the assumption of constantsedimentation rate.

Nevertheless, it is far too early to declare the problemsolved. Alternative scenarios may be possible, and the presentscenario may eventually be found deficient on one or morecounts. A theory intended to explain phenomena in the realmof a historical science can be neither falsified nor confirmed(because experiment is impossible), and must always remainunder scrutiny. But this does not mean that an attempt to buildsuch a theory is not worth while.

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