Statistical Characterization of a Random Velocity Field Using Stacking Velocity Profiles
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In petroleum exploration and production, it is important to have good estimations of the uncertainties on the reserves. Uncertainties in the velocity model used during the data processing are of major importance in this estimation. The use of geo-statistical tools can help in dealing with these uncertainties. Up to now, a strong limitation has been the inability to properly merge velocity functions measured in the wells with seismic velocity data. This was due to the different “supports” among the two, i.e. the well velocity may be regarded as a direct measurement of the instantaneous velocity field, while the seismic velocities correspond to an “average along the travelled paths” of this field. The problem is that, apart from the well positions, the instantaneous velocity field is out of reach. Luckily, for many practical applications, it is enough to know just its covariance model. However, no algorithmic method is available in the literature to yield the covariance model, and geologists are forced to use arbitrary distributions. The present paper proposes an original method to obtain a good estimate of this covariance model, using widely available information, mainly seismic stacking velocities. This method was first developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is performed, which highlights the robustness of the resulting estimation.
KeywordsCovariance Variogram Uncertainties Seismic velocities
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