Prediction of porosity and lithology in siliciclastic sedimentary rock using cascade neural assemblies

A novel approach to porosity and lithology prediction in siliciclastic sedimentary rocks is discussed here. It is based on the use of multi-element neural assembly with multiple inputs and a single output. In experiments with porosity prediction, the writers used one-, two- and three-dimensional input vector-parameters with coordinates (1) Vp or Vs; (2) Vp and Vs, and (3) petrophysical group index, Vp and Vs. When the neural assembly was trained to predict lithology, the input parameters were: (1) Vp or Vs; (2) Vp and Vs, and (3) Vp, Vs, and porosity. The writers utilized the training data-sets containing only 20 to 30 elements. To be able to work efficiently with such small training sets the writers used cascading neural assemblies specifically designed to work with small training data-sets. Each element of the neural assembly is a neural network of a simple structure. The elements of the assembly are combined in such a way that the approximation error of the assembly obtained during training session decreases with increasing number of elements. This allows for a simple and a well-defined methodology of estimating of a necessary number of neural elements in the assembly. The cost function of each element of neural assembly was taken as a sum of two terms. The first term was an estimate of the prediction error (a standard cost function of the predictive neural net), whereas the second term was a regularization term equal to the weighted sum of the squared norms of the transform matrixes. The neural network-based prediction of rock parameters was tested on a variety of training and test data-sets. Best results were achieved when the training data-set included representatives of all lithologies (petrophysical groups) contained in the test data-set and when the input parameters included independent data on the type of lithology or porosity in addition to seismic velocities.