## 1 Introduction
Deep sequence correlation graphs are undirected graphs constructed in the spatial domain, where each node denotes a collection of features at a given time point. By handling graphs of deep sequence correlations, GCNs can synthesize various features from multiple time points, thereby accounting for profound sequence dependencies in the prediction of porosity. Feature correlation graphs are undirected graphs constructed within feature channels, where each node corresponds to an individual depth-wise sequence attribute. By processing these graphs, GCNs are able to combine analogous features, enabling the model to capture and incorporate feature correlations for more accurate porosity prediction [26]. In summary, our proposed model has proven to be effective for porosity prediction. For instance, [PERSON] et al. [27] designed an adaptive spatio-temporal graph neural network (ASTGNN), which effectively captures the spatial and temporal dependencies among available logging measurements by integrating GCNs and temporal convolutional networks (TCNs). Their experimental results validated the method's accuracy and superior performance in both univariate and multivariate regression logging predictions on a Norwegian oilfield dataset and China's Daqing dataset. However, enhancing the accuracy and robustness of the model requires overcoming two key issues. First, existing GCNs depend on a single graph type, be it a deep sequence correlation graph or a feature correlation graph, which restricts their capacity to capture the full spectrum of sequence and feature correlations in logging data [27]. Second, traditional GCNs heavily rely on predefined graphs for feature aggregation, where the graph topology can vary based on the thresholds of cosine similarity or covariance, potentially affecting the precision and stability of the predictions [28,29]. To address these issues, this study concurrently considers two key factors for predicting porosity from logging curves: the correlation between deep sequences, and the correlation between features. We input the deep sequence correlation graph into GCNs to capture non-Euclidean features in logging data, extract inherent spatiotemporal relationships within formation data, and thereby construct dependency relationships within complex geological structures. The input features are physical quantities measured by logging tools, used to derive the physical properties of subsurface rocks for interpreting the structure and characteristics of the formation. The feature correlation graph, an undirected structure formed within feature channels, assigns each node to a distinct time series attribute. The GCNs processing the feature correlation graph can aggregate similar features to account for the feature correlation in porosity prediction. Taking both factors into account offers significant advantages for handling logging tasks with complex geological structures and intricate dependencies among different physical quantities. Furthermore, to overcome the limitations of predefined graphs, we use an adaptive mechanism that can automatically construct temporal correlation graphs and feature correlation graphs without setting thresholds. This mechanism enables the predictive model to dynamically learn the graph structure during training, substantially boosting the accuracy and robustness of its predictions. Finally, to prevent redundancy in processing both deep sequence correlation graphs and feature correlation graphs, we employ an attention-based selection method to pinpoint and extract the key features emerging from the attention graph convolution operations and dynamically adjust their contributions to porosity prediction, thus improving the model's accuracy and robustness.