6 th International Geosciences Student Conference, 13 – 16 July 2015, Prague Shale Volume Estimation Using Factor Analysis and Neural Network V. Srivardhan, S. K. Pal email: vardhan.sri@gmail.com Department of Applied Geophysics, Indian School of Mines, Dhanbad-826004, India. Summary Estimation of volume of shale is a crucial step in reservoir characterization. Shale volume is generally estimated using gamma ray logs, as they directly measure shale radioactivity. But it does not mean that other log signatures do not record the presence of shale, and implies that they are not as easily interpretable as done using only gamma ray logs. In this study a methodology using factor analysis and backpropagation neural network is proposed for the estimation of shale volume using gamma ray logs, density logs, and P-wave velocity. Utilization of several logs gives a better estimation of volume of shale and the accuracy of these techniques is discussed and compared with conventional methods Factor Analysis A N by K matrix D is decomposed in factor analysis by the following equation (Szabo et al, 2014)          Here the factor scores (N by M matrix) are represented F, factor loadings by L (K by M matrix), and E (N by K matrix) is the matrix of residuals. The dimension M determines the number of factors such that M<K. The matrix L is determined through the covariance matrix S and obtained by the approximation algorithm of Jöreskog (2007) defined by the below equations.                              The eigenvalues and eigenvectors of matrix S* are represented as λ and ω, the matrix of sorted M eigenvalues and eigenvectors is Γ M and Ω M , an arbitrary orthogonal M by M matrix is U, and θ represents the smallest number of factors satisfying the condition given in the below equation.             The factor scores are obtained using Bartlett's method (1937) and defined by the below equations.                             The Kaiser varimax rotation is applied for accounting the variations in the factor loadings with the log responses which ensures that a unique log response is majorly characterized by a unique factor and enhances the interpretability of the results. The volume of shale in this study was estimated using Larionov (1969) relation for Pre-Tertiary and Tertiary rocks and is defined below.                      Neural Network Backpropagation Technique Non-linear modelling is carried out using neural networks for input x and weights w. A linear relationship, between the weights and the input is defined in Equation 8 (Luthi and Bryant, 1997).             Here w o is the connection weight bias term which is generally 1. There is a nonlinear relationship between the weighted input and the output y=f(φ(x,w)) given by Equation 9 and 10. The output varies between 0 and 1 and in this study represents the volume of shale.             The first layer of processing is called the input layer, which leads to a layer of processing which finally connects to the output layer. The connections between the layers are facilitated through the