**Probabilistic Seismic Facies Estimation of a Mississippian Tripolitic Chert Reservoir through Generative Topographic Mapping**

**Roy, Atish; Kwiatkowski, Tim J.; Marfurt, Kurt**

The Mississippian chert reservoirs are highly heterogeneous reservoirs with much of the lime been altered to a dense, non-porous chert. However the tripolitic chert found within this formation have high porosity and low-permeability forming sweet spots in the reservoirs. The aim of this study is to create a probabilistic estimation of the sweet spots of a heterogeneous Mississippian tripolitic chert reservoir through Generative Topographic Mapping (GTM). The GTM is a non-linear dimensionality reduction technique proposed by Bishop et al, in 1998.

The goal of the GTM model is dimensionally reduction of a D-dimensional data and its representation in the 2-D latent space in terms of probability distribution. Initially a grid of latent space variables are defined with a prior probability assigned to each of them. They are then non-linearly mapped to the data-space where the mapped reference vectors form a confined 2-D manifold. Each of the reference vectors is then convolved with a Gaussian noise distribution (PDF) to include the data-vector. The next step is integrating these PDFs for all the reference vectors and we get the probability distribution of a data-vector in the data space. Later by subsequent iteration, each component of the mixture is moved to towards the data-vector for which it is most responsible to. After fitting the GTM model to the data the posterior probabilities of the reference vectors are calculated through Bayes' theorem and are projected as the most likely occurrence in the 2-D latent space.

In our case we have considered the "best attribute" volumes for input to the GTM clustering program, which does a proper analysis of the heterogeneous chert reservoir. After the final iteration different clusters, formed from the posterior projections of the data-vectors, are identified and color-coded in the 2-D latent space and the corresponding occurrence in the 3-D seismic volume can be identified. Further quantitative estimation of the probability of occurrence of tripolitic chert in the reservoir can also be determined from the posterior probability projections of the data in the 2-D latent space. The results are then verified from the well information in the survey.

AAPG Search and Discovery Article #90163©2013AAPG 2013 Annual Convention and Exhibition, Pittsburgh, Pennsylvania, May 19-22, 2013