Bayesian decision theory is a statistically based theory that is used to assess the degree of certainty and the potential costs when making decisions. This paper presents a methodology, based on the Bayesian decision theory, used to infer subsurface lithofacies and saturation fluid by integrating different data sources, such as well logs data and seismic attributes, which are derived from an elastic seismic inversion. This methodology was applied on a data volume from an offshore Brazilian field to generate, as a final product, a lithofacies model and a fluid indicator for this field. Uncertainty quantification of the models was also analyzed at this work.
To infer the subsurface lithofacies, the existing facies were identified from well logs data, using the expectation maximization (EM) algorithm. This step defines the lithofacies behavior in seismic attributes domains through the use of probability density functions (PDF). Next, the subsurface lithofacies were classified by applying the maximum posterior probability (MAP) classification, using the seismic attributes as input and the PDFs computed previously. The environment was divided into cells, then the probability and uncertainty was assessed to infer the lithofacie for each cell.
After inferring the subsurface lithofacies, the fluid was inferred for the cells identified as reservoir lithofacies. Assuming an oil-water system, the fluid substitution theory and the Bayes theorem were applied to the well log data to determine the PDFs for each scenario. Following the Bayesian decision theory, the most likely fluid and the associated error was determined for each cell identified as reservoir.
Introduction
Since the first petroleum exploration studies of seismic reflexion, the seismic sensibility to lithological parameters, such as porosity, lithofacies, fluid properties, and pore pressure is notorious. However, in the 1990s, it became possible to extract these lithological parameters from seismic information. This development occurred as a result of technological progress in seismic processing and rock physics. Since then, the new challenge has been to estimate the uncertainties inherent at the quantitative seismic interpretation process in an attempt to reduce the risk linked to petroleum exploration (Avseth et al., 2001).
The methodology of reservoir properties inference, suggested in this work, is presented as a flow of processes that infers lithofacies and reservoir rock saturation fluid from the integration of pre -stack seismic data, petrophysics data, and rock physics relations. The migrated seismic data have been previously processed in an attempt to preserve or restore the relative amplitudes. The petrophysics data are in-situ observations along the wells (log data) and the rock physics models correlate the seismic attributes with the media properties.
The central idea of this work is to integrate information from different sources, each one with its own resolution and uncertainty. This work analyzes these uncertainties and its propagation for the final reservoir characterization model. The uncertainty analysis is useful for making decisions that quantify the contribution of each data source (Takahashi, 2000).
One successful solution for this kind of problem (reservoir characterization with uncertainties analysis) is the statistical probability theory application. Using the Bayesian methodology, through the Bayes theorem, is possible to develop this kind of model with a proven practical effect (Loures and Moraes, 2002).
In this context, the rock physics is used as theoretical base to characterize the seismic signature arising from variations in lithological parameters. Commonly, well log data (and core sample data), are punctual information with good resolution that serve as an information source for the necessary rock physics studies. Conversely, the seismic data represents low resolution information that covers the whole extension of the subsurface volume in study.
Figure 1 represents the workflow based on AVO inversion concepts, rock physics, and statistical methods. This work consists of two stages:Lithofacies Inference-This is developed from well data, seismic attributes, and pattern recognition techniques. With the application of the Bayesian decision theory, probability density functions (PDF) are obtained from each facies along the seismic cube. The lithofacies inferences are made from those PDFs. One example of the application of this technique can be found in the work of Braga and Loures (2005).
