Approche fractale du karst des Grands Causses, Massif Central, France

Abstract

Six regions (3 big limestone plateaus : Sauveterre, Méjean, Noir and 3 valleys : Lot, Tarn, Jonte) of the sedimentary basin of Grands Causses are analyzed. This article is a part of a research. This research tries to revalue the respective importance of chronological paradigm and the spatial paradigm in the geomorphology. Naturalist s method must be gradually replaced by the construction of a theory deducted from universal principles. The fractal dimension (Ap) of all the contour lines is calculated by using the relation : S vs PA. Valleys have contour lines more irregular than those of the big limestone plateaus. A rectilinear relation appears between the height of these curves and the value of Δp. For the Lot, the Sauveterre and the Tarn when the height increases Ap decrease. For the Lot, the Sauveterre and the Tarn when the height increases Ap increase. These two relations correspond to 2 types of morphogenesis. The relation between the height and the fractal dimension thus appears as sturdy and frequents. The S vs P relation is curved in the case of Jonte. This curvature can be modeled by a polynomial relation of the second degree like : y = ax2 + bx + c. The curvature can then enter in a calculation (g) to balance the value of Δp : g = l/(Δp/(Cc x b) ; Cc is the coefficient of curvature and Ce = a in ax2 and b = b in bx. The relation enters -g-and the height for the Jonte valley becomes very good (r2 = 0.87)). This shows that AP is not sufficient information because contour lines are covariant, not self-similar.