Fractal Analysis and Depositional Cycles from Stratigraphic Sequences of the Upper Cretaceous at the Iberian Range (Spain)

A fractal approach to the study of cyclicity from twenty stratigraphic sections of the Upper Turonian of the Iberian Basin is presented. The strata thickness distribution (D_t) of these sections conforms to power law distributions of the form N_t≈Ct^-D, where N_t is the number of strata with thickness>t, which may be interpreted in terms of self-affine fractal scaling. D_t is an exponent related to the fractal dimension of the system, obtained from the previous equation applying logarithms.

Values of D_t obtained from the total thickness of each stratigraphic section range from 0.64 to 1.37. D_t is higher (0.8 to 1.37) in the central area of the Basin, and is lower (0.8 to 0.64) towards the southern coastal margin. These values can be considered as a parameter which reflects the geometrical organization of the 4th-order parasequences in each section.

Values of D_t ranging from 0.8 to 0.64 correspond to sections with both a wide range in bed thickness and thicker strata (around 0.4 m). Values of D_t ranging from 1.37 to 0.8 correspond to sections with more homogeneous bed thickness, composed mainly of thinner strata (around 0.2 m).

Lower D_t values reflect sections with heterogeneous accommodation within mixed terrigenous-carbonate environments. Meanwhile, those sections with higher D_t values correspond to carbonate platform environments with more homogeneous accommodation. Besides, the sections with lower D_t are more sensitive to lateral displacements of the carbonate platform facies belts (progradation or retrogradation).

These preliminary results show that fractal analysis may be a new tool of critical importance in the stratigraphic and dynamic analysis of stratigraphic successions. Fractal analysis can be utilized to get a better insight into the stratigraphical and sedimentological interpretations. It can also be used as a quality control parameter of field data, detecting sections with exposure problems.