No abstract
ABSTRACT. The major difficulty with non stationary phenomena is the estimation of parameters. It is known that the simple and appealing model : variable ~ deterministic drift + random fluctuation stumbles on the problem of identification of the underlying covariance or variogram.We show how statistical in~erence is made possible by adopting another model, where the function is defined only through linear quantities named "general ized increments" . The procedure has been automatized and renders kriging a tool of easy use.Finally a brief justification is given for non-stationary conditional simulations.
A procedure combining modern wireline measurements with a lithofacies data base has been developed to produce an automatic lithologic description of the formations crossed by a well.The database lithofacies are defined from petrographic knowledge and translated in terms of log responses. The assignment of depth levels to a lithofacies is done with the data base and with a discriminant function (Bayesian decision rule). External knowledge can be taken into account by use of artificial intelligence methods'. A confidence factor is produced for each result.. Logs currently in the data base are the density, neutron, sonic transit time, gamma ray, photoelectric cross section, and concentrations of thorium, potassium, and uranium. Major lithofacies groups represented in the data base include sandstones, limestones, dolomites, shales, coals, and evaporites. These are subdivided by introducing cement and special minerals and by considering porosity ranges.The construction of the data base is a critical step. It is largely empirical and requires careful calibration against intervals with well-known lithologies (e.g., from cores). The data base can be tuned to local conditions. The procedure has been tested in several environments and compared with cores and mud log descriptions. A detailed lithologic column can be produced at the wellsite and used in decision making. The results can also serve as input for further geologic studies of facies and sequences or for quantitative evaluation of formations.
SUMMARY The size of a set is defined without ambiguity as a ratio of homothety with an elementary set having the same shape. In order to generalize this, we compare the object studied with the elements of the family {λB} of the homothetics of B. The size λ of a particular element B is going to act as a measure of the object. If the latter is made up of individualized elements, we can calculate the size of each one and construct the size histogram, assuming for example that the size of a connex component C according to B is the size of the largest B included in C. (Examples: inscribed circle radius, maximum intercept.) For any object (alveolar lung space, pore system), the size at each point x is defined as the largest λB included in the object and containing x. The set of points x of a given size λ is related to the opening with respect to λB. This geometrical transformation of opening has mathematical properties similar to those of the sieving process, and is the basis of the size distribution concept as generalized by mathematical morphology. In the plane, the texture analyser allows the above measurements.
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