Abstract: |
Following the idea presented in the paper of Allard D. and al. (this conference), we present a procedure to estimate a most likely lithofacies map consistently with auxiliary information. Although truncated pluri-Gaussian models have been proposed two decades ago, their practical use has been limited by three major impediments: first, the difficulty to relate underlying Gaussian variables to physically interpretable processes; second, the estimation of a truncation diagram from data or concepts is not intuitive for geologists; third, updating a truncation diagram according to current proportions could be a challenge (current practice is to simplify truncation diagrams with rectangular domains). The paper of Allard D. and al. provides a solution to build the truncation diagram from auxiliary variables and lithofacies at wells; they also provide a technique to update this diagram in order to fit target proportions. Using the same methodology, it is possible to go one step further in restoring a physical meaning for underlying Gaussian variables. Assuming that auxiliary variables are known everywhere in the area of interest, it is possible to build a most likely facies map consistent with auxiliary data of course but also consistent with geological prior proportions and honoring lithofacies well data. The technique can be described by the following steps: - uniform transform of auxiliary variables; - indicator kriging (simple kriging) of prior proportion maps to honor well data indicators and to obtain updated proportion maps; - adjustment of truncation diagrams to local updated proportions; - truncation of transformed auxiliary variables to obtain most likely lithofacies map. The procedure is explained in more details and then applied on two case studies (with one and two geophysical attributes respectively). |
