An example of the application of neural networks of a simple architecture to unfocused well electrometry probes

Abstract

An effective method of finding stable solutions of inverse problems of electric and induction logging along the well is proposed, which allows avoiding the influence of the resistance values of the neighboring formations on the determination of the geoelectrical parameters of the object under study. A highly efficient method was proposed for solving such an unstable inverse problem. This method is based on the application of a neural network with inverse error propagation of a simple architecture. Namely three-layer. The mathematical statement of the problem is given, both the topology of the neural network and all its parameters are described in detail. In the course of the numerical experiment, they were selected as optimal. The process of building a base for training a neural network is described in detail. Namely, how each of the examples of the learning base is built by solving a direct problem. With this cut parameter, the training for each example is chosen arbitrarily, which guarantees a comprehensive range for training the neural network. The number of examples in the training base is one hundred thousand examples. As the activation function, the sigmoid is chosen due to the fact that it is differentiable everywhere. The results of testing the written program are given. The learning rate was estimated to obtain the required small error. It is shown that this approach is stably convergent. For testing, the parameters of the layers of the cut, which are inherent to the geophysical parameters of the cuts of the Dnipro-Donetsk depression, were chosen. A complex of lateral logging sounding was chosen as the electrical logging equipment. Four-probe low-frequency induction logging equipment was chosen as induction logging equipment. Examples for induction and electrical logging are given separately. The obtained results are analyzed in detail. Ways of further improvement of the obtained neural network and its use for other problems of geophysics are given.