Mathematical Geosciences

, Volume 40, Issue 7, pp 831–844 | Cite as

Conditioned Simulations of Random Velocity Fields

  • D. GeraetsEmail author
  • C. Lajaunie
  • P. Ruffo


In petroleum exploration and production, it is essential to have good estimations of the uncertainties on the reserves. Uncertainties on the velocity model used during the data processing are of major importance in this estimation. The generation of several velocity fields gives access to a quantified estimation of the uncertainties due to the velocity model inversion. The use of statistical methods helps in generating several important, equiprobable velocity fields, matching all the available velocity information. This paper presents an efficient simulation algorithm to generate instantaneous velocity fields, constrained by the distribution of values measured at the wells, and calibrated by the stacking velocities, taken as root-mean-square velocities. The simulations also match the covariance model given for the instantaneous velocity fields. The method is developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is shown, using data provided by ENI–Agip Division, and the efficiency of the proposed simulation method is discussed.


Simulation Stacking velocity Uncertainties 


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  1. Al-Chalabi M (1997) Instantaneous slowness versus depth functions. Geophysics 62(1):270–273 CrossRefGoogle Scholar
  2. Chilès J-P, Delphiner P (1999) Geostatistics, modelling spatial uncertainty. Wiley-Interscience, New York, 695 p Google Scholar
  3. Galli A, Gao H (2001) Rate of convergence of the Gibbs Sampler in the Gaussian case. Math Geol 33(6):653–677 CrossRefGoogle Scholar
  4. Geraets D, Galli A (2002) Statistical traveltime tomography in terms of stacking velocity. Pure Appl Geophys 159(7–8):1617–1636 CrossRefGoogle Scholar
  5. Geraets D, Galli A, Ruffo P (2007) Statistical characterization of a random velocity field using velocity profiles. Math Geol 39(5):513–527 CrossRefGoogle Scholar
  6. Lajaunie C (1999) Simulation of velocity constrained by stack analysis: models, methods and case study. Technical report N-20/99/G, Centre de Géostatistique Google Scholar

Copyright information

© International Association for Mathematical Geology 2008

Authors and Affiliations

  1. 1.Petit-RosièreBelgium
  2. 2.Centre de GéostatistiqueEcole des Mines de ParisFontainebleauFrance
  3. 3.ENI–Agip DivisionSan Donato MilaneseItaly

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