Evaluation of Radial Basis Function Neural Networks in Subsurface Seismic Characterization

Neural network provides a mathematical non-linear mapping technique that has been employed in many scientific and engineering studies. A radial basis function (RBF) neural network is a kind of supervised non-linear neural network with two main advantages: mathematically simple and computationally cheap. The structure of a typical RBF network has three parts: an input layer, an output layer and a hidden layer. In this study we are interested in the performance of a RBF neural network with respect to hidden layers and arrive at an optimal structure for a RBF network with a fixed number of nodes. Subsurface seismic characterization requires building a relationship (commonly non-linear) between seismic attributes and rock/fluid properties. With such a relationship, the rock/fluid properties computed from well logs can be extended to interwell points. Neural networks are powerful tools to obtain this non-linear relationship. Well logs are separated into two groups, a training group and a test group. Optimized seismic attributes and logs from training group act as inputs and outputs, respectively, to train the RBF network; then the network is deployed to the whole data set and the misfit between the calculated results and the test group is obtained. This overall misfit is utilized to evaluate the performance of networks with different structures. The data we use in this study is a part of the Boonsville 3-D seismic data contributed by the Bureau of Economic Geology of the University of Texas at Austin. Since there are limited numbers of wells with sonic curves, a log prediction using RBF networks is used. A typical single-layer RBF network is used for simplicity. An impedance inversion is applied to constrain the characterization process.