GEOSTATISTICAL SEISMIC INVERSION In reservoir modelling and characterization different seismic inversion techniques are conditioned by the available existing data provided by seismic surveys and the subsurface Petro-elastic properties obtained by wells, the inversion solution tries to provide a subsurface model that fits equally all the existing observed data. A geostatistical framework is a natural solution to integrate both data within the same framework while assessing the spatial uncertainty of the inverted property. The objective of this thesis is to develop and implement machine learning (Functional Data Analysis) method in order to reduce the computational time of subsurface models (acoustic impedance). The proposed method uses Principal component Analysis to reduce the dimension of the data (Dimensionality Reduction).