Image-based velocity estimation of rock using Convolutional Neural Networks.

Digital images of rock samples have been using extensively in Digital Rock Physics (DRP) to evaluate physical parameters of rock such as permeability, P- and S-wave velocities and formation factor. The parameters are numerically computed by simulation of the corresponding physical processes through segmented image of rock, which provide a direct and accurate evaluation of rock properties. However, recent advances in machine learning and Convolutional Neural Networks (CNN) allow using images as input. Such networks, however, require a considerable number of images as input. In this paper, CNNs are used to estimate the P- and S-wave velocities from images of rock medium. To deal with lack of input data, a hybrid pattern- and pixel-based simulation (HYPPS) is used as an efficient data augmentation method to increase the training data set. For each input image, 10 stochastic realizations are produced. Compare to the case wherein the stochastic models are not used, the new results from the enhanced network indicate a sharp improvement in the estimations such that R2 is increased to 0.94. Furthermore, the newly developed CNN network, unlike the one with the small data set (R2=0.75), manifests no over/underestimation. The estimated properties, in comparison with the computational results, indicate that CNNs perform outstandingly in predicting the physical parameters of rock without conducting any time-demanding forward modeling if enough input data are provided.