Gaussian mixture model deep neural network and its application in porosity prediction of deep carbonate reservoir

To estimate the spatial distribution of porosity, model-driven or data-driven methods are usually used to establish the relationship between porosity and seismic elastic parameters. However, due to the strong heterogeneity and complex pore structures of carbonate reservoirs, porosity estimation of carbonates still represents a great challenge. The existing conventional model-driven and data-driven-based porosity estimation methods have high uncertainty. To characterize the complex statistical distribution of porosity, the nonlinear relationship between porosity and seismic elastic parameters, and the uncertainty of porosity estimation, we have used a Gaussian mixture model deep neural network (GMM-DNN) to invert porosity from seismic elastic parameters. We use a Gaussian mixture model to describe the complex distribution of porosity, and we apply a deep neural network to establish the nonlinear relationship among seismic compressional-wave (P-wave) velocity, density, and porosity. The outputs of the GMM-DNN provide an estimated probability distribution of porosity conditioned on the input seismic elastic parameters. The synthetic data example verifies the feasibility of this method. We further apply the GMM-DNN-based porosity inversion method to a deep complex carbonate reservoir in the Tarim Basin, Northwest China. The well-logging data are used to train the GMM-DNN; then, the P-wave velocity and density obtained by prestack amplitude-variation-with-offset inversion are fed into the trained network to reasonably estimate the porosity distribution of the whole target reservoir and evaluate its uncertainties. © 2022 Society of Exploration Geophysicists.