## 2 Methods
### Adaptive Construction of Deep Sequence and Feature Correlation Graphs  
Two spectrogram convolution operations were initialized from deep sequence correlation and feature correlation graphs. To construct the feature space, we extracted features from the well-logging data using a sliding window with a length of \(S\) and a step size of 1. The \(i\)-th sampling is denoted as \(X_{i}\in\mathbb{R}^{S\times F}\), where \(S\) represents the moving window length and \(F\) denotes the number of features extracted. Typically, deep correlation and feature covariance graphs are initialized by calculating the cosine similarity matrix \(C_{i}\in\mathbb{R}^{S\times S}\) and the covariance matrix \(E_{i}\in\mathbb{R}^{F\times F}\). These two matrices can be computed from \(X_{i}\). The matrix element \(c_{s,s^{\prime}}^{(i)}\) of \(C_{i}\) can be obtained using Equation (1), where \(x_{s}^{(i)}\) refers to the \(s\)-th column vector associated with the \(i\)-th group of extracted features. \[c_{s,s^{\prime}}^{(i)}=\Big{(}x_{s}^{(i)}\cdot x_{s^{\prime}}^{(i)}\Big{)}/ \Big{(}\|x_{s}^{(i)}\|\|x_{s^{\prime}}^{(i)}\|\Big{)},\quad s=1,\dots,S, \tag{1}\]  
The matrix element \(e_{f,f^{\prime}}^{(i)}\) of \(E_{i}\) can be derived from Equation (2), where \(x_{f}^{(i)}\) represents the \(f\)-th row vector of the \(i\)-th extracted feature; \(E[\cdot]\) denotes the expectation of a vector. \[e_{f,f^{\prime}}^{(i)}=E\bigg{[}\Big{(}x_{f}^{(i)}-E\Big{[}x_{f}^{(i)}\Big{]} \Big{)}\Big{(}x_{f^{\prime}}^{(i)}-E\Big{[}x_{f^{\prime}}^{(i)}\Big{]}\Big{)}^ {\top}\bigg{]},\quad f=1,\dots,S, \tag{2}\]  
The cosine similarity matrix \(C_{i}\) can be used to derive the depth sequence correlation adjacency matrix \(A_{d}\in\mathbb{R}^{S\times S}\) through Equation (3), where \(a_{s,s^{\prime}}\) represents an element of the adjacency matrix \(A_{d}\). The value of this matrix is determined by the threshold \(\theta\). If \(a_{s,s^{\prime}}=1\), an edge exists between nodes \(s\) and \(s^{\prime}\) in the deep sequence graph \(G_{d}\), whereas if \(a_{s,s^{\prime}}=0\), no edge is present between them in \(G_{d}\). If there is no edge, the two nodes are not correlated  
Figure 1: The computational framework for the adaptive graph convolution operation with sequence and feature correlation graphs includes (**A**) feature extraction and sampling, (**B**) adaptive construction of graphs, (**C**) spectral graph convolution operations for both graphs, and (**D**) porosity prediction based on multi-head attention. along the depth sequence. If there is an edge, this means the two nodes are correlated along the depth sequence. \[a_{s,s^{\prime}}= \begin{cases}1,&c_{s,s^{\prime}}^{(i)}\geq\theta\\ 0,&c_{s,s^{\prime}}^{(i)}<\theta^{\prime}\end{cases}  \tag{3}\]  
The covariance matrix \(E_{i}\) can be used to derive a feature correlation adjacency matrix \(A_{f}\in\mathbb{R}^{F\times F}\) through Equation (4), where \(a_{f,f^{\prime}}\) represents an element of the adjacency matrix \(A_{f}\). If two features are correlated by \(E_{i}\), \(a_{f,f^{\prime}}\) is set to 1; otherwise, it is set to 0. When \(a_{f,f^{\prime}}=1\), an edge exists between nodes \(f\) and \(f^{\prime}\) in the depth sequence correlation graph \(G_{f}\), indicating feature correlation. If \(a_{f,f^{\prime}}=0\), no edge exists between the nodes, signifying that the features are uncorrelated. \[a_{f,f^{\prime}}= \begin{cases}1,&e_{f,f^{\prime}}^{(i)}>0\\ 0,&e_{f,f^{\prime}}^{(i)}\leq 0^{\prime}\end{cases}  \tag{4}\]  
The topological structure of the graphs preconstructed through the cosine similarity matrix \(C_{i}\) and the covariance matrix \(E_{i}\) may vary due to the predefined threshold \(\theta\), which may affect the precision and reliability of porosity prediction. (A quantitative analysis of the graph determinacy for these two preconstruction methods is provided in Appendix A.)