# A Case Study Comparing Methods for Coal Thickness Identification in Complex Geological Conditions
## 4 Results and Discussion
### Seismic Multi-Attribute Prediction Result  
#### 4.2.1 Attribute Optimization Result  
**Normalization:** Seismic layer attributes were extracted and normalized for the No. 2 coal seam target layer. Eleven seismic attributes were selected with absolute correlation coefficients exceeding 0.6, as detailed in Table 1.  
**Attribute Optimization:** Following correlation coefficient calculations among seismic attributes and their correlations with coal thickness, a refined selection process was undertaken. Attributes demonstrating significant correlations were retained or merged, while those showing high mutual independence, but substantial correlation, were excluded. Figure 10: Section of impedance. Figure 9: Comparison between synthetic records and seismic profiles: (**a**) density log; (**b**) velocity log; (**c**) seismogram synthesis; and (**d**) seismic trace. This process identified seven independent and sensitive attributes crucial for constructing a robust decision model. Table 2 illustrates the outcomes of mutual correlation computations, highlighting attributes such as arc length, decile frequency, maximum amplitude, maximum energy level, high cross-section, and total energy. **Optimal Attribute Combination:** Utilizing results from mutual correlation assessments, an exhaustive search approach was employed to determine the optimal attribute combination. The methodology involved sequentially selecting the most relevant attribute from the set of seven identified attributes: (a) beginning with attribute 1; (b) assessing combinations with the remaining six attributes to minimize prediction errors, identifying attribute 2 with minimal error; and (c) continuing to evaluate combinations with attributes 1 and 2 to identify the top three combinations with the smallest prediction errors, thereby establishing attribute 3. Stepwise regression further refined subsequent attribute combinations. **Effectiveness Analysis:** Effectiveness analysis methods can determine the most suitable number of attributes based on actual conditions, thereby improving the accuracy and reliability of the model, and avoiding overfitting phenomena. For the No. 2 coal seam, the optimal combination of attributes includes length, percentile frequency (2), maximum amplitude, and total energy as shown in Figure 10.  
In Figure 11, the horizontal axis represents the number of seismic attributes, while the vertical axis represents the average error. It can be observed that when the number of attributes increases to five, the actual error significantly rises. Therefore, it is concluded that additional attributes beyond the fourth attribute may lead to overfitting. Hence, the optimal number of attributes was determined to be four. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Seismic Attribute**} & \multicolumn{1}{c}{\
\begin{tabular}{c} **Correlation Coefficient** \\ **2° Coal Seam** \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} **Correlation Coefficient** \\ **2° Coal Seam** \\ \end{tabular} } \\ \hline Root Mean Square Amplitude & \(0.708\) & Decile Frequency (2) & \(0.636\) \\ Maximum Energy Level & \(0.74\) & Decile Frequency (3) & \(0.595\) \\ Instanceous Frequency & \(-0.622\) & Decile Frequency (7) & \(0.307\) \\ Maximum Amplitude & \(0.743\) & Dominant Frequency & \(0.399\) \\ Average Energy Level & \(0.681\) & High Cross-section & \(-0.63\) \\ Bandwidth Deviation Ratio & \(-0.607\) & Low Cross-Section & \(0.311\) \\ Arc Length & \(0.768\) & Total Energy & \(0.657\) \\ Bandwidth Ratio (4) & \(-0.465\) & Asymmetry & \(-0.131\) \\ Bandwidth Ratio (5) & \(0.269\) & Area above Half Peak & \(-0.346\) \\ Bandwidth Ratio (9) & \(0.706\) & Slope above Half Peak & \(0.56\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation coefficients between coal thickness and seismic attributes.