SEG/EAGE Distinguished Instructor Short Course 2003

Olivier Dubrule


Geostatistics for Seismic Data Integration in Earth Models


Olivier Dubrule

In recent years, the use of geostatistics has spread from the world of reservoir characterisation to that of velocity analysis, time-to-depth conversion, seismic inversion, uncertainty quantification, and more generally to that of seismic data integration in earth models. Nevertheless, many geoscientists still regard geostatistics as little more than a statistical black-box. By explaining the concepts and applications, the goal of this course is to clarify the benefits of geostatistics and help spread its use.

The course will cover the use of geostatistics for interpolation (kriging…), heterogeneity modelling, uncertainty quantification (simulation…), and data integration (cokriging, external drift, geostatistical inversion…). A variety of applications and examples will be presented, including velocity mapping, time-to-depth conversion, heterogeneity modelling, and seismic data integration in stochastic earth models. The relationships between geostatistics and approaches more familiar to geophysicists, such as filtering or bayesian methods, will also be discussed, without entering into mathematical details. A number of case studies will be presented, covering examples from various parts of the world. This will be a lively course, illustrated by examples, exercises and discussion sessions.

The short-course presentation, limited to one-day, will provide an overview of basic concepts and applications. The course document will provide a support to the course, and further extend some of the more technical considerations.

As a result of following this course, geoscientists, and more specifically geophysicists will better understand how geostatistics fits into their workflow, what tools and techniques they should use depending on the problem at hand, and what added-value may result from its use.

O. Dubrule has significant teaching experience, through his AAPG sponsored course "Geostatistics in Petroleum Geology" and through courses he has given internally at TotalFinaElf, at the Geological Society (through Japec) and at academic institutions such as Imperial College (London) and Ecole des Mines (France).

This course comes at a time when the use of geostatistics is spreading in geophysics, as shown by the increase in the number of geostatistics papers submitted to Geophysics or Geophysical Prospecting. It should raise significant interest among both SEG and EAGE members.

Who should attend?

This is a great opportunity for those interested in solving practical problems involving data interpolation, earth modelling, multidisciplinary data integration or uncertainty quantification



  • Earth Modelling, the meeting point for data integration.
  • The role of geostatistics at different steps of the Earth Modelling workflow
  • Basics of statistics

The covariance and the variogram

  • Stationarity vs non-stationarity, what does this mean practically ?
  • Variogram and covariance. Interpreting the sill, the range, the nugget effect.
  • How to compute a variogram.
  • Various variogram and covariance models, how to fit them, their relation with fractals.


  • Kriging, for property interpolation in 2D or 3D.
  • Error Cokriging and Factorial Kriging for velocity analysis and mapping.
  • Time-to-depth conversion using the External Drift method.
  • Collocated Cokriging, for integration of seismic attributes information in reservoir models
  • How Kriging relates to other deterministic interpolation techniques (multiquadrics, splines…)

Conditional Simulation for Heterogeneity Modelling and Uncertainty Quantification

  • Conditional Simulation, what is it, and when should it be applied?
  • Conditional Simulation for 3D geological facies modelling.
  • Stochastic Earth Modelling integrating all subsurface uncertainties.

Geostatistical Inversion

  • Geostatistical Inversion, for acoustic impedance inversion at reservoir scale
  • Geostatistical Inversion versus other geophysical inversion techniques


  • Geostatistical websites and software
  • The "do's and dont's" of geostatistics.
  • The current and future role of geostatistics in the reservoir modelling workflow.

The SEG/EAGE Distinguished Instructor Short Course is sponsored by SEG and EAGE.