Statistical Characterization of a Random Velocity Field Using Stacking Velocity Profiles
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Statistical Characterization of a Random Velocity Field Using Stacking Velocity Profiles D. Geraets · A. Galli · P. Ruffo
Received: 4 February 2003 / Accepted: 8 January 2007 / Published online: 24 August 2007 © International Association for Mathematical Geology 2007
Abstract 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. Keywords Covariance · Variogram · Uncertainties · Seismic velocities
D. Geraets () · A. Galli Centre de Géostatistique, Ecole des Mines de Paris, Fontainebleau, France e-mail: [email protected] P. Ruffo Exploration and Production Division, ENI, Milano, Italy
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Math Geol (2007) 39: 513–527
Introduction During the major steps of seismic and depth processing, a good estimate of the velocity field is required. This is generally obtained using velocity information of different types: sonic logs from wells and stacking velocities obtained from seismic processing. Geo-statistical tools make possible the optimal combination of velocity information of such different types, even if they have very different supports (a few meters for well velocities, hundreds of meters for seismic velocities). Amplitude preserving processing is now widely used, especially to perform Amplitude Versus Offset (AVO) studies. Shapiro and Kneib (1993) show that waves transmitted through a random media are strongly attenuated and that the correction for this effect can be computed using the covariance model of the instantaneous velocity field. In conclusion, at various phases of the processing of seismic data, it may be important to get a precise estimate of the covariance model of the instantaneous velocity field (Thore and Juliard 1999
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