# In search of rhythms in the chalk

When we contemplate certain cliffs, for example the high cliff between the Door of Upstream of Etretat and the Rock Vaudieu, we are struck by the regular and periodic repetition of flints. This rythmicité can be understandable only of two manners:

-Either what it is an autocyclic phenomenon: for example, when a certain quantity of mud settled, then a new flint forms;

-either what it is a phenomenon allocyclique: for example, the flint forms every time a climatic parameter is reached.

What have just noticed we about flints can extend to other types of rocks or to a physical parameter. Mange and al. (1999) perfectly analyzed the series cénomanienne of the South of England which presents alternations chalk / marl on strong thicknesses.

Robaszynki observes the following alternations in Cénomano-Turonien of the Course White-nose.

The porosity is a physical parameter measured in the drillings by logging. Gold, the low porosities are often bound to a presence more marked with clayey minerals. Logs diagraphiques in the chalk shows cyclic variations of the porosity. But other parameters: sonic, gamma ray, can be analyzed.

Certain mathematical methods (Weedon, on 2003) ) allow to extract the fundamental frequencies of a signal, a geologic series by being only a particular case

Shepherd and Otter (1989) modelled the periods of the various climatic cycles during the geological times. Here are 4 main periods for the upper Cretaceous:

- Long eccentricity: 400 ka,
- Short eccentricity: 115 ka (that is by rounding off 100 ka),
- Obliquité: 51,1 + 39,3 ka (that is approximately 40 ka),
- Climatic precession: 22,4 + 18,6 ka (that is approximately 20 ka).

By supposing a rate of 2, 3 and 4 cm sedimentation / 1000 years, the thicknesses calculated for every period are:

2 cms / 1000 years | 3 cms / 1000 years | 4 cms / 1000 years | |

E_{400} |
8 m | 12 m | 16 m |

E_{100} |
2 m | 3 m | 4 m |

O_{40} |
0,8 m | 1,2 m | 1,6 m |

P_{20} |
0,4 m | 0,6 m | 0,8 m |

Thus the elementary cycle would be a cycle précessionnel. But flints often group together by packages of 4 in 5 suggesting a modulation by a cycle of longer period (short eccentricity 100 ka).

The mathematical methods leading to the extraction of the fundamental cycles in Norman chalks were never tried today. The technique is heavy and it is especially practised on long carrots of drilling. We can quote the article of Wu *and al. *(2012) carrying on lakeside series of Turonien-Campanien in China which creates by filtering the cycles of long eccentricity (405 ka) and of short eccentricity (100 ka). The cycles of 405 ka are numbered:

Santonien: E_{405} 0 in E_{405} 6

Coniacien: E_{405} 7 in E_{405} 15