## 3 Methodology
### Prepare the Logging Data  
Based on the analysis of sedimentary characteristics of the target strata in the study area (Figure 3), three sedimentary subfacies, delta front, delta plain and shore-shallow lake, were selected as the label values for this classification task. When the label values were determined, the natural gamma-ray (GR) curve was chosen as the logging curve to extract the logging facies elements, and six logging facies elements were selected to quantitatively describe the shape of the logging curve. The curve was sampled at equal depth intervals from top to bottom to form an \(n+1\) logging data sequence. In this way, the depth sequence \(d_{0}\), \(d_{1}\),..., \(d_{n}\) and its corresponding log amplitude sequence \(a_{0}\), \(a_{1}\),..., \(a_{n}\) can be obtained. The thickness was recorded as \(h_{i}=d_{i}-d_{i\text{-}1}\) (\(i=1,2\),..., \(n\)). After obtaining the depth sequence and corresponding logging amplitude sequence, the corresponding parameters could be quantified. (1) Variance  
This property is expressed by the standard deviation of the curve:  
\[\sigma=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(a_{i}-\overline{a})^{2}} \tag{1}\]  
The standard deviation of the curve actually reflects the sorting of the grain sizes. If the grain sizes of the sediment are sorted well and the physical property changes little, then the logging curve is an approximately straight line. The mean value of the logging data is mainly concentrated in the middle of the curve. Only the top and bottom data deviate from the mean value slightly, so the value of \(\sigma\) is smaller. At this time, it corresponds to the box curve. On the contrary, if the separation of sediment grain sizes is poor, the physical properties change greatly. It shows certain fluctuations in logging curves and the shape of the curves may be a funnel, bell or finger. At this time, the logging data are relatively scattered, and a considerable section of the data points are deviate greatly from the  
Figure 4: Conceptual framework for the modeling process [27; 28]. mean, which will inevitably lead to a larger value of \(\sigma\). The calculation shows that the variance of large mudstone layers is the smallest in all sedimentary environments, which corresponds to the deposition of mudstone between rivers or deltas [29]. (2) Relative Center of Gravity  
The relative center of gravity (RM) reflects the curve shape and can also explain the graded sequence of the sedimentary rock grains. It can be expressed as follows:  
\[\text{RM}=\frac{\sum_{i=1}^{n}\text{i}a_{i}}{n\sum_{i=1}^{n}a_{i}}\ (i=1,2, \ldots,n) \tag{2}\]  
The grain sequence of sedimentary facies is different between positive and negative. Generally, the center of gravity of the positive grain order is lower than that of the reverse grain order, and the center of gravity of the reverse grain order is higher than that of the normal grain order. However, because the length of each section is different, the relative center of gravity is taken here to facilitate a comparison [30]. When RM \(>\) 0.5, the center of gravity is lower, and the curve is bell-shaped. When RM \(<\) 0.5, the curve is funnel-shaped, and the center of gravity is higher. When RM \(\approx\) 0.5, the curve shape is a box type [11]. (3) Ratio Amplitude  
Ratio amplitude refers to the ratio of the amplitude of a curve to its thickness. Different curve shapes have different ratios, which reflect lithological changes to a certain extent. By calculation, the maximum and minimum values are found. Taking the GR curve as an example, the ratio of minimum value to thickness is defined as the left ratio amplitude (\(\lambda_{\text{L}}\)), and the ratio of maximum value to thickness is defined as the right ratio amplitude (\(\lambda_{\text{R}}\)). Obviously, the larger the left ratio amplitude, the coarser the grain size of the sediment; the smaller the left ratio, the smaller the grain size of the sediment [31].