8) Sedimentary Completeness

Some geoscientists continue to forget in their models the long periods of calm where nothing happens. In most stratigraphic sections, the duration of the hiatus is, generally, greater than the total duration of real deposition of the preserved sediments.

Before saying few words on sedimentary completeness, which most geoscientists, especially those working in the oil industry, completely ignore, I would like to review the concepts of geological object and geological event, as well as, the different ways of consider "time".

In "L'Ordre du Temps" (Flammarion, ISBN:978-2-0814-0920-0), Carlos Rovelli says "the world is not like a lot of things, but a set of events". The same true fin Geology. In fact, Geology is not a set of geological things, but a set of geological events.

- Geological things or geological objects continue over time ;
- Geological events are of limited duration

A block of granite, for instance, is, generally, considered as a good example of a geological thing, because geoscientists can always wonder "where" it will be tomorrow or the day after tomorrow. On the contrary, a volcanic eruption, for is instance, is a geological event and wondering "where" it will be tomorrow or after tomorrow there is no sense. The same is true when geoscientists wonder" when" a volcanic eruption take place.

Earth is made up of networks of geological events, not of geological things. In addition, geological events are not located in any particular Earth's point: they are spatially and temporally limited. In the sense of C. Rovelli, geological events are in a "where", but also in a "when".

Moreover, all things considered, even geological things, in quantum realm¹⁹ result of a set of geological events. In reality, geological things, as a block of granite, can be considered as "a complex vibration of quantum fields, momentary interaction of forces, a process, which for a brief moment, succeeds in being maintained in a identical balance before falling again into dust, an ephemeral chapter in the history of interactions between elements of the planet" C. Rovelli, 2018).

¹⁹ Realm where the scale of quantum mechanical  effects become important when studied as an isolated system, i.e., distances of 100 nanometers (10 ^-9 m) or less and cery low temperatures.

The geological and biological events characterizing the different “ages” are, often, calibrated in Sagittal time (see below). Presently, these events no longer can be interpreted from Lyell's philosophy (Uniformitarianism) or from “Catastrophic” theories (Cuvier, Agassiz, etc.). The history of our planet seems rather to be a synergistic result of geological events (unidirectional, cyclic, punctual and chaotic), in a world, where non-linear processes are frequent and the regular order alternates with chaotic order.

The highlighting of these complex geological events is one of the main missions of geoscientists. In addition, they must separate those which have a global significance from those which have a local value and determine their mutual and their chronological relations, as well as, the driving forces that are at the origin of the various geological processes.

To accomplish these tasks, geoscientist must, clearly, perceive the concepts of :

(i) Absolute Time;
       (ii) Relative Time ;
           (iii) Geological Time ;
                  (iv) Geological Event ;
                        (v) Sedimentary Completeness and
                              (vi) Preservation of stratigraphic sections.

(i) Absolute Time

Intrinsically, the absolute, true or mathematical time by its nature flows, uniformly, without any relationship to nothing outside. It is the true time of Newton, which is not accessible directly, but only indirectly, thanks to the calculus. Newton's absolute time was similar to an universal, omnipotent God-like time, one that was the same for everyone, everywhere and separated from space (a geoscientist in Portugal will live time in the same way that a geoscientist in Australia or on Moon).

Today, for us, the absolute time is obvious, because it has become, progressively, our common way of thinking, thanks to our school textbooks. However, every thing seeming obvious to us, is often, just the result of our prejudices. The existence of an uniform time, independent of things and their movement, which seems natural to us today, is not an old and natural intuition for the human being, it is a just a Newton's idea. The time before Newton (17^th century) was, completely, different. It was the Aristotle's time for whom time was just the measure of change, i.e., the way to measure how things change.

(ii) Relative Time

Disregarding the place where live on Earth, time will never be absolute. The rate at which it passes depends, entirely, on your speed and acceleration at any given moment. The relative time, which is, commonly, used in place of absolute, is the measure of part of any duration by means of movement.

In beginning of 20^th century, Einstein realizing that two celestial bodies, like Earth and Sun, do not attract each other, directly, but that each of the two acts, gradually, on what is between them (space and time). He made the assumption that Sun and Earth change space and time around them and suggested time wasn't separate from space but connected to it.

Time and space are combined to form "space-time" and everyone measures his own experience in it, differently, because the speed of light (300,000 km/s) is the same for all observers. In other words, all observers can't agree on the time it takes for other objects to travel relative to them.

Einstein also suggested, also, that space-time wasn't flat, but curved or "warped" by the existence of matter and energy. If space is sensitive to presence of the masses and modified by them, time is also.  Time moves slower near massive objects, because space-time is warped by the weight. The way time flows depends on the presence and the movement of the objects:

- Time is slowed down by the objects' mass.
- Time flow is slowed down by objects' velocit

It is for this reasons, that for for almost a century, all students learn in the University that time flows faster in mountains and slower in valleys, and any modification of the structure of time, in turn, influences the movement of all bodies, causing them to fall towards each other:

The Newton's apple²⁰ was not pulled by Earth, it fall where the time flow was slower.

²⁰We’ve all heard the story. Isaac Newton is sitting beneath an apple tree contemplating the mysterious universe. Suddenly, an apple hits him on the head. “Aha!” he shouts, or perhaps, “Eureka!” In a flash he understands that the very same force that brought the apple crashing toward the ground also keeps the moon falling toward the Earth and the Earth falling toward the sun: gravity. Or something like that. (https://conscientiousness/article/2170052-newtons-apple-the-real-story/#ixzz6Htxr7caS)

The Einstein's general relativity equations depicts not a single time, but at countless times. A different time for each point in space. The time indicated by a given clock, measured by a particular phenomenon. Each clock has its own time. Each geological event has its own time. Actually, geologists do not describe how geological things evolve over time, but how it evolves in relation to each other.

Currently, in the physical fundamental equations, the time variable does not exist. They do include variables that change relative to each other. If time is the measure of change (Aristotle's time), it is possible choose different variables to measure the change and none of these variables will have all the characteristics of the time of our experience, without avoiding the world's constant change. Physicists are looking for a theory that tells us how variables change relative to others variables not to time The fundamental equations of quantum gravity have no temporal variable and describe the world by indicating the relationships between the variable quantities, is, probably, the best approach physicists have today.

Summarizing:

In special relativity, Einstein made time even more variable with the theory of general relativity. He showed that a strong gravitational camp (in the vicinity of the Earth or the Sun, for example) makes the clocks run slower. Time is not an absolute container in which objects evolve. Time is specific to each object and depends on its movement. Just like space time becomes a relational notion. It only expresses a relation between different states of things. At the fundamental level there is no time. For any object, time is how it changes compared to other objects.

(iii) Geological Time

Since the Big Bang, i.e., about 16.5 Ga (assuming a probable value for the Hubble constant of 18 km/s to 1 My) till the Anthropocene²¹, a Planckian, Gamovian and Geological times can be differentiated (C. Emiliani, 1992, ISBN 0-521-40949-7).

²¹ Proposed geological epoch par certain geoscientist starting since Man became a significant geological agent (impact in Earth's geology and ecosystems) either with the Agriculture Revolution (12-15 ka), either with the First Industrial Revolution (roughly with the 19^th century) either with the beginning of the Atomic Age, which started in 1945.

The Planckian time, between the Big Bang and 5.390 x 10^-44  seconds after the Big Bang, is characterized by the appearance of space, time, energy and superforce.

The Gamovian time, between 10^-42 seconds after the Big Bang and 4.7 Ga (4.7 x 10⁹ years ago), is characterized by individualization of the of the four fundamental forces, inflation of the Universe, stabilization of protons and neurons, stabilization of electrons, etc. It is during this time that the universe becomes transparent, approximately, 300,000 years after the Big Bang. This period ends with the formation the solar system and evolution of stars and galaxies.

The Geological time measure the change between the Earth's formation (4.7 Ga) and the current Earth' configuration (end of Holocene beginning of the Anthropocene). It is a relative time measuring  the "when" in relation to the different geological events. Significant geological events allow several subdivisions of geological time:

a) Cryptozoic, between the formation of the solar system (4.7 Ga) and the appearance of Archaeocyatha (590 Ma). The end of Cryptozoic corresponds, roughly, to the formation of Rodhinia or Protopangea supercontinent.

b) Phanerozoic, between the appearance of Archaeocyatha (590 Ma) and the end of the Holocene (beginning of the proposed Anthropocene epoch). The Phanerozoic is characterized by two 1^st order eustatic cycles and associated continental encroachment stratigraphic cycles. The first 1^st order eustatic cycle corresponds to the Paleozoic (540 Ma- 245 Ma) and the second to the Meso-Cenozoic (245 Ma and 0 Ma).

- The first 1^st order eustatic cycle is the result of the dispersion of the continents individualized after the Rodhinia supercontinent breakup and their gathering into the Pangea new supercontinent. The associated continental encroachment stratigraphic cycle corresponds to the Paleozoic sediments (540 - 245 Ma).

- The second 1^st order eustatic cycle emphasizes the dispersion and gathering of the continents resulting from the Pangea supercontinent breakup and the associated continental encroachment stratigraphic cycle represents the Mesozoic-Cenozoic sediments (245- 0 Ma).

- In each of these stratigraphic cycle, a transgressive stratigraphic phase, with retrogradational or backstepping geometry, and a regressive stratigraphic phase, with progradational or forestepping geometry, can be considered. The limit between these phase corresponds to a major downlap surface. The transgressive stratigraphic phase is induced by the absolute sea level rise of the 1^st eustatic cycle, while the regressive stratigraphic phase is induced by the absolute sea level fall.

-In the post-Rodhinia continental encroachment cycle, the transgressive stratigraphic phase (540 - 430? Ma) encompasses the Cambrian, Ordovician and Lower Silurian sediments, while Upper Silurian, Devonian, Carboniferous and Permian sediments form the regressive stratigraphic phase (430? - 245 Ma).

-In the post-Pangea continental encroachment cycle, the transgressive stratigraphic phase (245 - 91.5 Ma) encompasses the Mesozoic sediments (except the Upper Cretaceous sediments), while the regressive stratigraphic phase (91.5 - 0 Ma) comprehends the Cenozoic sediments (excluding the Upper Cretaceous sediments, since the major downlap surface  between these stratigraphic phases has, quite often, a Cenomanian / Turonian age.

Conceiving time in an abstract and intellectual way is quite simple. Everyone knows, perfectly, well how many zeros must be added to the number ten to represent one billion of years. On the contrary, assimilating such period of time is much more difficult. The notion of Geological Time is so strange that one can only grasp it through metaphors. Let's see a simple real history: One day, when my daughters (12 and 10 years) arrived from school, the oldest told me: Papa, you know that dinosaurs died 65 million years ago.  Oh, good, can please explain that to me, I said. She took a piece of paper and wrote 65 million in numbers and then told me that dinosaurs died on that date. At that point, I took from of one of my short-courses the Universe and Earth's Calendars that I had taken, several years ago, from the Houston Chronicle, and that are illustrated here below.

Figure 032- If the Big Bang would have take place on 1^st January 2019, Galaxies would have been formed on 3 ^rd January, the Sun on 1^st August, Planets on 21^st August, the beginning of the Life on 17 ^th September and the appearance of Vertebrates on 15 ^th December. The appearance of the man would have taken place at midnight of 31 ^st December. Since the formation of the planet.

Figure 033- If the age of the Earth was one year : (i) The crust would have formed on 24^th February ; (ii) Life would have begin on 21^th March ; (iii) Evolved Plants on 14^th September ; (iv) Evolved Animals on 11 ^th November ; (v) Dinosaurs would have appeared on 12^th December and would have disappeared on 24^th December. Man would have appeared on 31^st December at 23 hr 48 m. The age of Humanity would be 12 minutes, what emphasizes the human insignificance related to the limitless of geologic time.

After describing these Calendars to my daughters, I guess they get the same feeling that a young student discover as soon as he begins to be interested in Earth Sciences, i.e., the immense temporal restriction that Geological Time (McPhee's Deep Time) imposed on the importance of man.

The classic concept of a young Earth, governed from its earliest days by human will, has, completely, disappeared since we realized the almost incomprehensible vastness at the end of which, for only a few minutes, man came to live there. Human insignificance was very well expressed by Mark Twain in his famous Eiffel Tower metaphor in his "Was the World made for Man" of 1903:

“Man has been here 32,000 years. That it took hundred million years to prepare the world for him is proof that that is what it was done for. I suppose it is, I dunno. If the Eiffel Tower were now representing the world's age , the skin of paint on the pinnacle-nob at is summit would represent man's share of that age; and anybody would perceive that that skin was what the tower was built for. I reckon they would, I dunno."

Indeed, man has started to distinguish the geological vastness which precedes him even if, to conceive it, he has little but metaphors.

“Let us imagine that the yard, an old English measure, that is to say roughly the distance separating the nose of the king from the end of his hand when he extends his arm represents the history of the earth. A simple blow of the file on the nail of his middle finger would then be enough to erase the whole history of humanity ” (McPhee, J., 1980)

S. Gould (1990) retraced this intellectual revolution, by analyzing three masters of geological literature, Thomas Burnet (17^th century), James Hutton (18^th century) and Charles Lyell (19^th century) by studying the original texts, all at the same time developers and founders of Geology. He noted that the reconstruction of the Earth's past would be unintelligible to us if we did not use two antagonistic concepts as much as necessarily complementary:

(a) Time's Arrow ²² ( linear time), whoever from the Big Bang to today, and

(b) Time's Cycle, that of immanence, of days, of seasons, of the Supercontinents, of life eternally recommenced, etc.

which are "eternal metaphors" in the understanding of time.

²²Expression introduced in 1928 by Arthur Eddington to describe the phenomenon according to which time seems to always flow in the same direction

(iv)- Geological Event

 Although the concept of geological event is trivial and not very new, its importance is, largely, underestimated by the majority of geoscientists, in particular by petroleum geologists. The importance of “rare events” in sedimentology was illustrated by the work of Hagues (1967). He showed the role of hurricanes as geological agents and demonstrated that there is a 95% chance that a hurricane hits any point on the coast of the Gulf of Mexico every 3,000 years:

" When we know the amount of sediment that a hurricane can mobilize, we must expect, at least in the Gulf of Mexico, that this type of event, rare on a human scale, will be seen as a phenomenon very common in future stratigraphic registers "

To better understand the meaning and importance of an geological event, it is important to remember that a Stratigraphic System, such as the Silurian or Cretaceous system, i.e., the sedimentary deposits of the Silurian or Cretaceous, are episodic and incomplete, with numerous hiatuses (non-deposit and erosion). Therefore, they do not translate the equivalent duration of geological time (Ager, D.V., 1984).

Irregularities in the stratigraphic registers should not be interpreted as proof of Lyell's Gradualism, but rather as a result of the ad hoc changes proposed by S. Gould (1977). Lyell, to maintain his belief in Gradualism, always maintained that appearances were deceptive and that the hiatus in the stratigraphic series could easily be explained without involving catastrophic events:

“ If a stratigraphic series only preserves one level out of 1000, the gradual changes are seen as abrupt changes ”

This interpretation of Lyell contrasts with that proposed by Gould and Eldredge (1977) who suggested that most modifications in the physics of the globe and in the history of biology are made by punctual changes, i.e., by rapid reversals of relatively stable systems. The systems absorb stresses and resist any change as long as the accumulation of stresses does not exceed the resistance threshold. If the resistance threshold is reached or exceeded, the system changes to a new stable state.

Gould (1984) did not adopt the term “catastrophism” for this type of discontinuous change. The theory of catastrophism mainly refers to global changes, such as for example the Collapse Theory of the Crust by Elie de Beaumont. Gould places more emphasis on speed than on the spread of change. He considers the terrestrial world as composed of relatively stable systems which resist constraints up to the threshold of resistance. They change very quickly towards a new system in equilibrium as soon as this threshold is reached or exceeded. The point changes emphasize the stability of the systems and the concentration of the changes during short periods which upset the previous equilibrium and quickly re-establish new systems.

To define the concept of geological event quantitatively, I will use Gretener's work on probability theory²³ and the game of dice.

²³There are several possible of interpret probabilities : (i) Bayesian interpretation, (ii) Frequentist interpretation and (iii) Propensionist interpretation. The bayesian interpretation measure our degree of conviction and our belief that something will happen. When we say that there is a 50% chance that a 5 francs coin will fall on the face it expresses our belief about tossing a coin. The frequentist interpretation is based in record sequences of repeated events (e.g., if you throw a 5 franc coin a large number of times by recording the frequency of the results this provides the proportion of the number of sides), sports or weather statistics are examples of frequentist probabilities. The propensionist interpretation, which is a consequence of theories and assumptions about nature, the propensions area considered as objective possibilities i9nherent in the initial conditions of the experiment, which may vary if these conditions are themselves modified (Lee Semolina, 2019-ISBN 978-2-10-079553-6), (Forces et dispositions, Probabilities et propensions, College DE France, http://books.openedition.org/cdf/4619?lang=fr).

Figure 034- Gretener (1967) has shown that the chance of rolling 8 six when throwing eight dice is about one in two million. In other words, in a normal dice game, where only a few rolls are allowed, it is best to bet against the eight sixes. However, as the number of throws increases, a roll of eight six becomes more likely. Indeed, there is a 95% chance of getting at least eight six in a total of around five million launched. On a human scale (duration of two or three generations) low probabilities are considered as impossibilities. However, there is no physical law that prohibits them. There is no physical law that prohibits the rolling of eight dice and the obtaining of eight six. In addition, it is absolutely essential to keep in mind that what, on a human scale is considered impossible, is only improbable on a geological time scale. For example, if we consider that each six of a dice represents a geological agent, such as a storm, hurricane, earthquake, etc., we can assume that a result of 7 six represents a less dramatic event than that produced by a result of 8 six. Likewise, a result of 6 six will be even less dramatic and more frequent than a result of 7 six, etc., etc. This makes it possible to propose a classification of geological events according to their rate of renewal: (i) Regular events ; (ii) Common events ; (iii) Recurrent events ; (iv) Occasional events and (v) Rare events. In these notes, I have used the term event several times and I hear it very often in meetings between explorers. Despite this, I will insist on its significance, because although geological agents are rare and episodic on a human scale, they induce point changes which, on a geological scale, are continuous processes. Mathematically, an episodic geological event is characterized by a duration which very rarely exceeds 1/100 of the total time considered. In other words, when we graphically express an episodic geological event (change versus time), it only represents the thickness of the pencil line. Thus, during the Phanerozoic, whose duration is approximately 600 million years, an event can be considered rare if it has a maximum duration of 6 My time duration as it is the case for instance of a stratigraphic sequence, whose time duration ranging between 3-5 million years.

For the Phanerozoic (590 Ma - 0 Ma), this concept of geological event proposed by Gretener is, reasonably, compatible with the geological resolution that we have today and that is in the best of cases is of the order of 1 Ma (1 000 000 years). If we admit that the stratigraphic records with petroleum potential vary between 1 Ma and 1,000 Ma, the geological processes have durations between 10 ka and 10 Ma, i.e., 1/100 of the total duration. In addition, this range does not take into account the "myopia" of geoscientists, which increases a lot as we descend into the depths of geological time.

Depending on the rate of renewal, i.e., the frequency of the punctuations (discontinuous processes) and taking into account the duration of geological event is, approximately, 1/100 of rate of renewal, the instantaneous geological events can be classified in five large groups:

a) Regular Events

A regular event can occurs, at least once, every 100 years and its has, generally, one year time duration. It figure in the human life as significant earthquakes, major floodings, etc..

b) Common Events

A common event, generally, occurs once every 1,000 years and is time duration is, roughly 10 years. It must appear in recorded human history, even though, usually, are no longer perceived as having, actually, happened but are rather ascribed to the vivid imagination of the ancient recorders.

c) Recurrent Events

A recurrent event happens once every 1 My (10⁶  years) and the time duration is roughly 10,000 years. They are events are important in terms of fossil stage.

d) Occasional Events 

 An occasional event takes place, at least once, every 100 My and its time duration is, approximately, 1 My years. They are the type of events that are responsible for major faunal breaks. The orogenies are typical geological occasional events.

e) Rare Events

A rare event takes place, at least once , every 1,000 My, i.e., 1Gy (10⁹ years) with a time duration of more or less, 10 My. They are the events which have occurred, at most, a very few times throughout Earth's history. A meteorite impact with the Earth is a good example of a rare geological event. The same for  the supercontinent's formation.

(v) Sedimentary Completeness

The stratigraphic completeness is the relation between the effective time of deposition and total geological time. If the time between two consecutive unconformities is, for instance, 3.0 My and the effective deposition time is 1.0 My, the sedimentary completeness is 0.3. In turbidite systems, the completeness is small, but the preservation is great. The deposition time of a deep turbiditic lobe (basin floor fan or slope fan) is practically instantaneous (in geological terms), while the time span between two consecutive lobes, during which, practically, nothing happen (from the point of view of deposition), can be thousands of years or more. The knowledge of completeness is essential to determine the sedimentation rate of a given sedimentary interval.

Geoscientist have always asked themselves the question of the continuity versus discontinuity of geological events. To the question:

Are the sedimentary records the result of more or less continuous geological processes or are they associated with extraordinary processes which take place spasmodically?

Geoscientists have, since the 18^th century, given very opposite answers. Today, the majority of geoscientists consider that the sedimentary records are incomplete and separated by important periods of calm during which nothing happens. It is surprising to note that some sedimentologists continue to forget in their models the long periods of calm where nothing happens. In most stratigraphic sections, the duration of the hiatus (non-deposition or erosion) is, generally, greater than the total duration of actual deposition of the preserved sediments.

Figure 035- In these two stratigraphic models, it is important to note that in the upper part of each section the duration of the non-deposition periods is much greater than that of the deposition. Most of the geological events that took place during this period were not preserved. The completeness can be defined as the relation between the effective time of deposition and total geological time. If the time between two consecutive unconformities is, for instance, 3.0 My and the effective deposition time is 1.0 My, the sedimentary completeness is 0.3. In turbidite systems, the completeness is small, but the preservation is great. The deposition time of a deep turbiditic lobe (basin floor fan or slope fan) is practically instantaneous (in geological terms), while the time span between two consecutive lobes, during which, practically, nothing happen (from the point of view of deposition), can be thousands of years or more. The knowledge of completeness is essential to determine the sedimentation rate of a given sedimentary interval.

Certain deposits, such as for example river deposits and, especially, overflow deposits, have a relatively low preservation. They settle above the base level. On the other hand, turbiditic deposits, which, generally, are deep water deposits (deposits associated with gravity currents are also possible in lagoon environments) are episodic geological events, have an excellent preservation, because they deposit largely below the basic level.

The stratigraphic sections are, in Sadler's metaphor (1982), local archives of geological history. The records of these archives are the sedimentary layers deposited in sequence and which are most often numbered according to their thickness rather than according to their deposition time. However, the stratigraphic sections contain numerous hiatuses induced either by erosion or by periods of non-deposition.

Three questions always come to mind of geoscientists :

1) How long does it take for a sedimentary layer to settle ?

2) How long did it take for a certain stratigraphic section to settle ?

3) Compared to the total duration of deposit of a stratigraphic section, for how long was there really deposit ?

The answers to the first two questions are, relatively, easy:

 a) A lamination of a beach deposit is settle down in approximately one second.

 b) An hummocky cross stratification (HCS) layer, characteristic of storm deposits, is deposited in a few minutes.

 c) A turbiditic layer is deposited in a few hours.

 d) Flood deposits, such as the Scablands (deposits and erosions associated with flooding induced by the rupture of the retention of lakes behind Plio-Pleistocene glaciers) in Canada, deposit for a few weeks.

e) Glacial varves are deposited for 1 year.

f) One centimeter of pelagic sediments is deposited during approximately 10³  years.

g) A continental encroachment stratigraphic subcycle is deposited between 10 and 20 million years (10⁶ years).

h) A continental encroachment stratigraphic cycle is deposited in 100-200 x 10⁶ years.

In 1982, on this subject, P. M. Sadler showed that the duration of a deposition is inversely proportional to the rate of sedimentation, i.e., the greater the rate of sedimentation the shorter the period of deposition. From this, it follows that the majority of the periods of non-deposition elude us, which led Ager to consider that the sedimentary registers correspond to short periods of terror separated by long periods of calm where nothing happens.

It is much more difficult to answer the last question (3) because it poses the problem of the completeness of the stratigraphic sections, that is to say of how many geological events, which took place during the total duration of deposit, are preserved in the section.

 (vi) Preservation of stratigraphic sections   

In large part, the preservation of the stratigraphic sections is linked to :  (a) The amplitude ; (b) The frequency and at (c) The environment in which the stratigraphic event takes place.

The stratigraphic events most represented in the stratigraphic registers are those which have a normal or low frequency, i.e., those which take place sporadically. From the point of view of frequency, the submarine cones of the basin or slope are very significant, because the turbiditic levels contrast, very strongly, with the pelagic intervals which separate them. Pelagic intervals are stratigraphic events at normal frequency, while turbiditic intervals are associated with geologically instantaneous events.

The example proposed by R. H. Dott, in 1983, gives a good picture of the magnitude / frequency ratio of turbidite deposits:

1) Imagine a stratigraphic interval composed of 100 layers of turbidite and pelagic clays, where each turbiditic layer is 10 cm thick and each pelagic layer is 5 cm thick. The total thickness being 1500 cm.

2) Given that the average deposition speed of pelagic clays is 5 cm / 1000 years and that the turbiditic currents are instantaneous stratigraphic events, we can deduce:

            a) That the total deposit time is 100,000 years and,

            b) The frequency of turbidite currents is 1000 years.

            3) It is likely to conclude:

- Two thirds of the sedimentary interval were deposited by instantaneous events whose frequency is one event per thousand years.

                - In 10 million years, 10,000 geologically instantaneous events can deposit a section of 1500 meters thick.

In this regard I remind:

" what seems impossible on a human scale becomes, on a geological time scale, possible, and the improbable becomes inevitable " (Simpson G. G. 1952)