Scientific drilling helps people know complete subsurface information about fluid transport through coring a complete sample in the region of interest (ROI), but due to limited technology and rocks’ vulnerable feature, these samples are always intervallic or broken. Porosity measured by geophysical data is easily available and reflects certain pore space information of rocks, so we proposed a U-Net with spatiotemporal long short-term memory cells (ST-UNet) to reconstruct a 3D large-size digital rock with complex pore structure from a limited number of discrete 2D digital rock images in intervallic samples according to continuous 1D porosity distribution. The results show that the reconstructed sample outperforms the homogeneous algorithm in term of the structural similarity (SSIM), peak signal-to-noise ratio (PSNR), accuracy, mean square error (MSE), reconstructed pore space is essentially identical to that of the ground truth in terms of morphology. Additionally, the gap between the reconstructed model permeability and the real model permeability is only 0.03 D in the transport properties, and in the elastic properties, the acoustic velocities error is only 3.0%, and the porosity error is only 0.07%. When a large number of 2D information are missing, a digital sample is reconstructed only by the 1D porosity distribution, and its variation in porosity remained in strong consistency with that of the ground truth, and the total porosity error is only 0.8%.

Seismic inversion plays an essential role in the exploration and development of oil and gas reservoirs. With the development of neural networks, deep learning has achieved a wide range of applications in seismic inversion due to its powerful feature extraction and nonlinear fitting capabilities. However, when applying the traditional deep learning methods to seismic inversion based on trace-by-trace, problems such as overfitting and poor continuity of prediction results are prone to occur. To address these problems, we propose a closed-loop Unet with geophysical constraints based on spatial background information, called SG-CUnet. In SG-CUnet, sparse reflection coefficients and seismic forward modeling process are used as geophysical constraints of the network to improve the stability and accuracy of prediction results. Meanwhile, the spatial information of seismic data is added to the training process of SG-CUnet to improve the lateral continuity of prediction results. The effectiveness of proposed SG-CUnet is verified by synthetic Marmousi2 and field data examples. In synthetic data applications, the SG-CUnet proposed in this paper can give more accurate impedance estimation results than other methods. Furthermore, in the field area application, we combine the proposed SG-CUnet with a transfer learning strategy for semi-supervised training to solve the limited labeled data problem. The predicted results show that the semi-supervised SG-CUnet has better reservoir structure details and lateral continuity.

When the spatial response variables are discrete, the spatial logistic autoregressive model adds an additional network structure to the ordinary logistic regression model to improve the classification accuracy. With the emergence of high-dimensional data in various fields, sparse spatial logistic regression models have attracted a great deal of interest from researchers. For the high-dimensional spatial logistic autoregressive model, in this paper, we propose a variable selection method with for the spatial logistic model. To identify important variables and make predictions, one efficient algorithm is employed to solve the penalized likelihood function. Simulations and a real example show that our methods perform well in a limited sample.

In recent years, spatial data widely exist in various fields such as finance, geology, environment, and natural science. These data collected by many scholars often have geographical characteristics. The spatial autoregressive model is a general method to describe the spatial correlations among observation units in spatial econometrics. The spatial logistic autoregressive model augments the conventional logistic regression model with an extra network structure when the spatial response variables are discrete, which enhances classification precision. In many application fields, prior knowledge can be formulated as constraints on the parameters to improve the effectiveness of variable selection and estimation. This paper proposes a variable selection method with linear constraints for the high-dimensional spatial logistic autoregressive model in order to integrate the prior information into the model selection. Monte Carlo experiments are provided to analyze the performance of our proposed method under finite samples. The results show that the method can effectively screen out insignificant variables and give the corresponding coefficient estimates of significant variables simultaneously. As an empirical illustration, we apply our method to land area data.

In the field of seismic inversion, Convolutional Neural Network (CNN) has been extensively applied for their powerful capability of feature extraction and nonlinear fitting. However, the insufficient amount of labeled seismic inversion dataset impedes the application of CNN in seismic elastic inversion. Besides, the lack of effective geophysical constraints in conventional CNN will make the network prone to over-fitting, leading to unstable inversion results. In this paper, a workflow is developed for generating sufficient and diverse datasets for pre-stack seismic inversion with limited log and seismic data. The Sequential Gaussian Co-Simulation algorithm is used to simulate the changes in the reservoir space under the constraints of the low-frequency model. At the same time, the Elastic Distortion algorithm is used to simulate the complex geological structures. This can increase the diversity of the strata longitudinal combination by enriching the combination mode of stratigraphic parameters. Besides, the combination of a U-net and three fully connected networks (UCNN) is proposed to predict the elastic parameters from seismic data. In UCNN, the sparse reflection coefficient is used as a constraint to improve the accuracy of the network. The performance of this method was evaluated by synthetic and field data examples. The results show not only the effectiveness of the proposed method but also demonstrate its outperformance over the conventional deep learning method. The R2 scores of density, Vp and Vs are 0.94, 0.98, 0.98.