Method for quickly forming a stochastic method representating the distribution of a physical variable in a heterogeneous environment by appropriate selection of a geostatistic realizations

1) A method for forming a Gaussian or Gaussian-related type stochastic numerical model giving an image of a distribution of a physical quantity in a porous heterogeneous medium, which is calibrated in relation to data obtained by means of measurements performed in the medium or by prior observations, and characteristic of the fluid displacement in the medium, comprising an iterative gradual deformation process wherein an initial realization y and a number (N−1)(N>1) of other realizations yi (with i=1, . . . ,(N−1)), independent of the initial realization, are linearly combined, at each iteration, by applying constraints to linear combination coefficients, and an objective function measuring a difference between a set of non linear data deduced from the combination by means of a simulator and the dynamic data is minimized, the iterative process being repeated until an optimum realization of the stochastic model is obtained, whrein, in order to select geostatistical realizations allowing a minimization of objective function and obtaining a convergence of the model

• a number N# (N#>>N) of realizations is generated and (N−1) other realizations having indicators of larger absolute value are selected from among the realization and the indicator associated with each realization corresponds to a scalar product between the realization and a geostatistical gradient of the objective function in relation to the initial geostatistical realization y, arbitrarily selected and conditioned to the data.