Committee neural networks for porosity and permeability prediction from well logs

Neural computing has moved beyond simple demonstration to more significant applications. Encouraged by recent developments in artificial neural network (ANN) modelling techniques, we have developed committee machine (CM) networks for converting well logs to porosity and permeability, and have applied the networks to real well data from the North Sea. Simple three-layer back-propagation ANNs constitute the blocks of a modular system where the porosity ANN uses sonic, density and resistivity logs for input. The permeability ANN is slightly more complex, with four inputs (density, gamma ray, neutron porosity and sonic). The optimum size of the hidden layer, the number of training data required, and alternative training techniques have been investigated using synthetic logs. For both networks an optimal number of neurons in the hidden layer is in the range 8-10. With a lower number of hidden units the network fails to represent the problem, and for higher complexity overfitting becomes a problem when data are noisy. A sufficient number of training samples for the porosity ANN is around 150, while the permeability ANN requires twice as many in order to keep network errors well below the errors in core data. For the porosity ANN the overtraining strategy is the suitable technique for bias reduction and an unconstrained optimal linear combination (OLC) is the best method of combining the CM output. For permeability, on the other hand, the combination of overtraining and OLC does not work. Error reduction by validation, simple averaging combined with range-splitting provides the required accuracy. The accuracy of the resulting CM is restricted only by the accuracy of the real data. The ANN approach is shown to be superior to multiple linear regression techniques even with minor non-linearity in the background model.