Patent ID: 8422745

Claim:
A computer implemented method of constructing an image representative of a distribution of a categorical physical property in a porous heterogeneous medium wherein each pixel of the image is associated with a geographic position, comprising: constructing a first training image by assigning to each pixel of the image a categorical physical property value; selecting at least two auxiliary physical properties with distributions in space representative of a distribution in space of the categorical physical property; constructing for each auxiliary physical property, an auxiliary training image by assigning to each pixel of the auxiliary training image an auxiliary physical property value determined from the first training image; defining for a central pixel for each auxiliary training image, a neighborhood of a number of pixels which are closest to the central pixel, and determining for all neighborhoods from 0 pixels to the number of pixels and for all states, a state representing values of the categorical physical property assumed by the pixels of the neighborhood, an empirical histogram of values of the categorical physical property at the center of the neighborhood conditioned by the state, and an empirical histogram of values of each auxiliary physical property at the center of the neighborhood conditioned by the state; constructing, for each auxiliary physical property, an image by assigning to each pixel of the constructed images an auxiliary physical property value obtained from measurements performed within the porous heterogeneous medium; and for each pixel of the image to be constructed: calculating a probability law of the categorical physical property from values taken by all the pixels of the neighborhood of the pixel with values at the pixel of the auxiliary physical properties obtained from the real images, and by multiplying with one another the empirical histograms of each auxiliary physical property associated at the pixel; determining a categorical physical property value at the pixel of the image to be constructed by carrying out a random selection in the calculated probability law; and constructing the image representative of the distribution of the categorical physical property by repeating the calculation of the probability law and determining a categorical physical law for each pixel of the image to be constructed; and displaying the constructed image with a computer.