Summary
We apply a common statistical tool, Principal Component Analysis (PCA) to the problem of direct property estimation from three-dimensional (3D) seismic-amplitude data. We use PCA in a novel way to successfully make detailed effective porosity predictions in channelized sand and shale.
The novelty of this use revolves around the sampling method, which consists of a small vertical sampling window applied by sliding along each vertical trace in a cube of seismic-amplitude data. The window captures multiple, vertically adjacent amplitude samples, which are then treated as vectors for purposes of the PCA analysis. All vectors from all sample window locations within the seismicdata volume form the set of input vectors for the PCA algorithm.
Final output from the PCA algorithm can be a cube of assigned classes, whose clustering is based on the values of the most significant principal components (PC's). The clusters are used as a categorical variable when predicting reservoir properties away from well control. The novelty in this approach is that PCA analysis is used to analyze covariance relationships between all vector elements (neighboring amplitude values) by using the statistical mass of the large number of vectors sampled in the seismic data set.
Our approach results in a powerful signal-analysis method that is statistical in nature. We believe it offers data-driven objectivity and a potential for property extraction not easily achieved in model-driven fourier-based time-series methods of analysis (digital signal processing).
We evaluate the effectiveness of our method by applying a cross-validation technique, alternately withholding each of the three wells drilled in the area and computing predicted effective porosity (PHIE) estimates at the withheld location by using the remaining two wells as hard data. This process is repeated three times, each time excluding only one of the wells as a blind control case. In each of the three blind control wells, our method predicts accurate estimates of sand/shale distribution in the well and effective porosity-thickness product values. The method properly predicts a low sand-to-shale ratio at the blind well location, even when the remaining two hard data wells contain only high sand-to-shale ratios.
Good predictive results from this study area make us optimistic that the method is valuable for general reservoir property prediction from 3D seismic data, especially in areas of rapid lateral variation of the reservoir. We feel that this method of predicting properties from the 3D seismic is preferable to traditional, solely variogram-based geostatistical estimation methods. Such methods have difficulty capturing the detailed lithology distribution when limited by the hard data control's sampling bias. This problem is especially acute in areas where rapid lateral geological variation is the rule. Our method effectively overcomes this limitation because it provides a deterministic soft template for reservoir-property distributions.
