A key issue in Earth Modelling is that of Multidisciplinary Data Integration, which consists of generating 3-D geologically realistic heterogeneity models compatible with both seismic and production data.
Both for the inversion of seismic and production data, the industry has gone from the use of deterministic regularization-type approaches, to Bayesian ones, then to the sampling of realizations from the posterior distribution using techniques such as Geostatistical Inversion.
The relationships between Kriging, Radial Basis Functions or Bayesian Inversion are now well-known. Kriging produces smooth 3-D models away from the data. The output of standard deterministic inversion techniques is also lower-frequency than the well data, because of the lower seismic resolution. On the other hand, Geostatistical Inversion generates 3-D heterogeneity models constrained by seismic data with the same power spectrum (or variogram) away from the wells as that at the wells. The presentation discusses the methodology and the various benefits brought by geostatistical Inversion, both in situations where the forward seismic model is linear or non-linear.
If the formal relationships between Bayesian and Geostatistical approaches are stressed by the paper, on the other hand their formal assumptions may be significantly different. We conclude by discussing these differences.
Olivier Dubrule obtained a PhD Degree in Petroleum Geostatistics at Ecole des Mines de Paris in 1981. He then worked for Sohio Petroleum Company in the USA (1982-1986), Shell International in The Netherlands (1986-1991) and, since 1991, he has been with Elf and TotalFinaElf, working in France and in the UK. During his career, he has held a variety of staff and management positions where he developed and applied new techniques for reservoir characterisation, earth modelling, risk analysis and uncertainty quantification. After leading the Earth Modelling and Uncertainty Quantification group at TotalFinaElf, Dubrule recently became manager of Geoscience Training and Communication.
Olivier Dubrule has authored more than twenty papers in the field of geostatistics and earth modelling. In 1991, he received the President's prize of the International Association of Mathematical Geology, for "Outstanding Contribution to Mathematical Geology by an individual 35 years or younger". In the last decade, he organised and chaired a number of events organised by SPE, EAGE, SEG or AAPG. Dubrule is the author of AAPG Course Notes Series #38 "Geostatistics in Petroleum Geology", and editor (with E. Damsleth) of "Petroleum Geostatistics" a Special Issue of EAGE's Petroleum Geoscience Journal, published in 2001.