## 2 Channel width Quantization Method Based on Deep Learning
### Methodology Testing  
Fundamental to the search for the candidate model with the closest match to the conditioned data is the ability to quantitatively evaluate the similarity of spatial features between the discrete points and the grid. The candidate model does not need to satisfy the conditioned data as an a priori geological model, but must have spatial features similar to the conditioned data, such as the conditional data for the stable river phase, and the non-stationary sector model is obviously not the best option. This means that the more similar the spatial features of the candidate model are to the conditional data, the more similar the spatial features of the random sample based on the candidate model are to the conditional data. Therefore, during the test, except for the parameter of the channel width, the other parameters were kept unchanged to ensure the spatial similarity between the candidate model and the conditional data, and the results were only affected by the channel width parameter. Figure 2 shows the models of four sedimentary facies with different channel widths. The parameters of the generated channel sand body model are shown in Table 1, with an NTG of 50%, an amplitude of 150 m, and a wavelength of 320 m; the width of the channel sand bodies follows the triangular distribution shown in Table 2. The channels of models A and E are densely distributed, and the width of each channel is relatively narrow. The channel widths of models B and F are medium. Models C and G have wider channel widths, and models D and H have the widest channel widths. Models E, F, G, and H are taken as virtual workspaces, and 1% of the data are randomly extracted from the virtual workspaces as conditional data. Then, 1% data points are randomly selected from candidate models A, B, C, and D, respectively, and each model is required to be sampled 100 times. Therefore, there are 400 random samples in the four models and every sample is assigned a label to recognize which candidate model it is part of. The labeling rule is that samples of the same model have the same label. Then, all 400 samples are trained in deep learning to obtain a deep convolutional network model. Figure 2: Sedimentary facies model of different channel widths. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Channel Model** & **Min. Width (m)** & **Mean Width (m)** & **Max. Width (m)** \\ \hline Models A, E & 40 & 50 & 60 \\ Models B, F & 90 & 100 & 110 \\ Models C, G & 140 & 150 & 160 \\ Models D, H & 190 & 200 & 210 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Triangular distribution of width values for four channel sand body candidate models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Recognition Rate** & **50 m Channel** & **100 m Channel** & **150 m Channel** & **200 m Channel** \\ \hline cd\_W1 & 99\% & 1\% & 0 & 0 \\ cd\_W2 & 0\% & 96\% & 2\% & 2\% \\ cd\_W3 & 0 & 7\% & 94\% & 1\% \\ cd\_W4 & 0 & 0 & 1\% & 99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Recognition rates of four different channel widths. Figure 3: Candidate model recognition rate of four different channel widths. final preferred result. As shown in Figure 4, the channel widths of models 1, 2, 3, and 4 differ significantly, and the sand body widths obey the triangular distribution in Table 1. Models 5, 6, 7, and 8 are used as virtual work zones, and data with a well density of 1% are randomly selected from the virtual work zones as conditioned data, which are used to test the model preference performance. Through 50 tests, the results are shown in Table 4 and Figure 5. According to the results, the recognition rate of the 3D channel model with 50 m width is the highest, followed by the channel model with 100 m width, and both of them have a recognition rate of more than 90%. The recognition rate of the 3D channel width models with 150 m and 200 m is poorer, and is in the range of 80-90%.