Geostatistical inversion is developed for constraining a 3D geostatistical realization of acoustic impedance using a 3D seismic block. The geostatistical realization is constructed using a sequential variogram-based approach in such a way that the convolutional response of the realization fits with the actual 3D seismic data. The method is illustrated with a 3D synthetic example. The initial acoustic impedance model is generated using an unconditional simulation of one million grid cells. Then, using five wells 'drilled' in this model and the synthetic seismic obtained by convolution, the geostatistical inversion method is applied to reconstruct the initial acoustic impedance model. The 3D synthetic seismic block is matched in a matter of half-an-hour CPU on a standard workstation. Analysis of the results shows that the input geostatistical model (variograms, means and standard deviations) controls the higher and lower frequencies that are not present in the seismic amplitudes. The use of a '3D earth modelling' tool allows efficient management of the '3D earth model' constructed by geostatistical inversion, and visualization of the various inputs and outputs.

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