Mapping of seismic and lithologic facies from 3D reflection seismic data plays a key role in depositional environment analysis and reservoir characterization during hydrocarbon exploration and development. Although a variety of machine-learning methods have been developed to speed up interpretation and improve prediction accuracy, there still exist significant challenges in 3D multiclass seismic facies classification in practice. Some of these limitations include complex data representation, limited training data with labels, imbalanced facies class distribution, and lack of rigorous performance evaluation metrics. To overcome these challenges, we have developed a supervised convolutional neural network (CNN) and a semisupervised generative adversarial network (GAN) for 3D seismic facies classification in situations with sufficient and limited well data, respectively. The proposed models can predict 3D facies distribution based on actual well log data and core analysis, or other prior geologic knowledge. Therefore, they provide a more consistent and meaningful implication to seismic interpretation than commonly used unsupervised approaches. The two deep neural networks have been tested successfully on a realistic synthetic case based on an existing reservoir and a real case study of the F3 seismic data from the Dutch sector of the North Sea. The prediction results show that, with relatively abundant well data, the supervised CNN-based learning method has a good ability in feature learning from seismic data and accurately recovering the 3D facies model, whereas the semisupervised GAN is effective in avoiding overfitting in the case of extremely limited well data. The latter seems, therefore, particularly adapted to exploration or early field development stages in which labeled data from wells are still very scarce.

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.

Among the large variety of mathematical and computational methods for estimating reservoir properties such as facies and petrophysical variables from geophysical data, deep machine-learning algorithms have gained significant popularity for their ability to obtain accurate solutions for geophysical inverse problems in which the physical models are partially unknown. Solutions of classification and inversion problems are generally not unique, and uncertainty quantification studies are required to quantify the uncertainty in the model predictions and determine the precision of the results. Probabilistic methods, such as Monte Carlo approaches, provide a reliable approach for capturing the variability of the set of possible models that match the measured data. Here, we focused on the classification of facies from seismic data and benchmarked the performance of three different algorithms: recurrent neural network, Monte Carlo acceptance/rejection sampling, and Markov chain Monte Carlo. We tested and validated these approaches at the well locations by comparing classification predictions to the reference facies profile. The accuracy of the classification results is defined as the mismatch between the predictions and the log facies profile. Our study found that when the training data set of the neural network is large enough and the prior information about the transition probabilities of the facies in the Monte Carlo approach is not informative, machine-learning methods lead to more accurate solutions; however, the uncertainty of the solution might be underestimated. When some prior knowledge of the facies model is available, for example, from nearby wells, Monte Carlo methods provide solutions with similar accuracy to the neural network and allow a more robust quantification of the uncertainty, of the solution.

We have developed a time-lapse seismic history matching framework to assimilate production data and time-lapse seismic data for the prediction of static reservoir models. An iterative data assimilation method, the ensemble smoother with multiple data assimilation is adopted to iteratively update an ensemble of reservoir models until their predicted observations match the actual production and seismic measurements and to quantify the model uncertainty of the posterior reservoir models. To address computational and numerical challenges when applying ensemble-based optimization methods on large seismic data volumes, we develop a deep representation learning method, namely, the deep convolutional autoencoder. Such a method is used to reduce the data dimensionality by sparsely and approximately representing the seismic data with a set of hidden features to capture the nonlinear and spatial correlations in the data space. Instead of using the entire seismic data set, which would require an extremely large number of models, the ensemble of reservoir models is iteratively updated by conditioning the reservoir realizations on the production data and the low-dimensional hidden features extracted from the seismic measurements. We test our methodology on two synthetic data sets: a simplified 2D reservoir used for method validation and a 3D application with multiple channelized reservoirs. The results indicate that the deep convolutional autoencoder is extremely efficient in sparsely representing the seismic data and that the reservoir models can be accurately updated according to production data and the reparameterized time-lapse seismic data.