The self-organizing map (SOM) is one of the most effective pattern recognition techniques, and is commonly used tool for non-supervised seismic facies analysis. Early SOM implementations required estimating the number of clusters. Current implementations avoid this choice by over-defining the number of clusters and mapping them against continuous 1D, 2D and 3D colorbars, which the interpreter then visually clusters. We generate SOM clusters based on the wavelet shape, on the spectral component and the GLCM attributes of the Red-Fork formation and correlate the results with the knowledge of geology from extensive well control in the area.
SOM (Kohonen, 2001) clusters data such that the statistical relationship between multidimensional data is converted into a much lower dimensional latent space that preserves the geometrical relationship among the data points. Mathematically, each SOM unit preserves the metric relationships and topologies of the multidimensional input data. SOM prototype vectors or neurons have the same dimension as the input data, and are arranged in a regular low-dimensional grid or map, thereby topologically connecting it to its neighbors. In this paper, we apply this workflow to seismic amplitude, spectral component volumes and Grey Level Cooccurrence Matrix attributes for a seismic survey acquired over the Anadarko Basin, Oklahoma, USA. We interpret these results using extensive well control and geological information in this area (Suarez et al., 2008).
The Kohonen SOM (Kohonen, 2001) is not only an effective way of visualizing multidimensional data but also preserves the original topological structure, making it amenable for seismic facies analysis. Initially we assume the input seismic attributes are represented by J vectors in the space Rn, xj=[xj1, xj2, xj3 …. xjN] where N is the number of input seismic attributes and j=1,2,…,J is the number of seismic traces analyzed. These vectors are in turn represented by P prototype vectors mi, mi= [mi1, mi2…. miN], where i=1,2,…,P. Prototype vectors are organized on a grid of lower dimension than P. After initializing the SOM prototype vectors to reasonably span the data space, the first training step in SOM is to choose a representative subset of the J input vectors. Each training vector is associated with the nearest prototype vector. After each iteration of the training, the mean and standard deviation of the input vectors associated with each prototype vector is accumulated, after which the prototype vectors are updated using a function of the distance between it and its neighbors. This iterative process stops either when the SOM converges or the training process reaches a predetermined number of iterations. One way to evaluate the SOM clustering results is to plot the distance between the neighboring prototype vectors thereby generating the Unified Matrix distance (U-Matrix) map. While the Umatrix can be used to estimate the number of clusters or data classes in the data, in this paper, we project the SOM to a 2D or 3D colorbar using Principal Component Analysis (PCA) after which the results are visually clustered in the interpreter’s brain.
