MORPHOLOGIE MATHEMATIQUE ET GENESE DES CONCRETIONS CARBONATEES DES MINERAIS DE PER DE LORRAINE

Abstract

SUMMARY Matheinatical morphology and genesis of Lorraine iron ore carbonated concretions Mathematical morphology provides strong theoretical tools for the description of geological structures. Here, the intrinsic function of MATHERON'S (1965) regionalized variables theory, is used to describe a limestone migration phenomcnon, and the genesis of carbonate nodules in the sedimentary ore deposits of Lorraine. In this intrinsic function: is x a moving point through the mineraliLed space v, and k(x) a boolean value associated to x. The characteristics of γ (h) represent the structure of the regionalisation k(x). This descriptive step leads to models of stochastic processes to interpret the genesis of those migrations. The theoretical models allow to resolve or to compute the intrinsic functions and to confront them with experimental data. In conclusion mathematical morphology - the acute efficiency of which is manifest in the description of the evolutions - appears to be unable to explain why those evolutions occur. The different steps of this study can be presented as follows. The beginning is shown by the pictures of Fig. I. White limestone concretions can be distinguished set against a dark background of iron ore. It is clear that the structure of the concretion is the same in Fig.lA and 1B though the two photos are different. How could this structural identity be measured? For this purpose we shall use the “variogram”-concept of Matheron's theory (FORTET et al., 1953). The “regionalized variable” is the function k(x), of wich the value is 1 when x is in the concretions, and zero when not. “x” is a moving point through the mineralized space v. The intrinsic function, or “half variogram”, γ (h) is then: which depends only on the vector h and not on the moving point x. y(h) represents an increment variance. It mathematizes the concept of the influence zone of the sample. The average “variogram” of Fig.1, and of a series of twelve photos taken in the same neighbourhood is giien by Fig.3B, in the vertical direction. The origin tangents of curves measure in each direction the diametral variation, whose average value in all directions of space represents the specific surface of concretions (cf. SERRA, 1966a). Practically the variograms do not increase after 50 cm in horizontal direction, and 25 cm in the vertical one. Those values mean average lengths of concretions in those directions. On the other hand, the curve of Fig. 3B represents a maximum, which reflects the limestone migration process itself. This last remark leads to the establishment of stochastic models of the genesis of limestone migration. Realisations of those random functions are giwn in Fig. 9A, B, C, D. Their variograms are similar to those of Fig.3A and 3B. Such a model is, therefore, an adequate representation of natural regionalization, and expresses the genetic hypothesis. This mathematical method finally allows an easy and clear translation of structural notions in a quantitative language.