Multi-layer Gaussian Mixture Model algorithm and its application in lithology classification

Figures & data

Table

ALGOL 1. Exact process of GMM

Input: Missing data $Z=\{Z_1,Z_2,\dots ,Z_n\}$.

Output: The category of each data point in $Z=\{Z_1,Z_2,\dots ,Z_n\}$.

01. Fixed $2\le c\le n$, $\epsilon >0$. Give initial value ${\hat{z}}^{(0)}=({\hat{z}}_1^{(0)},\dots ,{\hat{z}}_c^{(0)})$. And let $s=1$.

02. Use a convenient normal distribution matrix $||\cdot ||$ to compare ${\hat{z}}^{(s)}$ and ${\hat{z}}^{(s-1)}$.

03. Set the threshold for model iteration $\epsilon$.

07. While $(||{\hat{z}}^{(s)}-{\hat{z}}^{(s-1)}||>\epsilon )$

08. The ${\alpha }^{(s)}$ and ${\mu }^{(s)}$ is calculate by formula (4)(6)

${\displaystyle \sum ^{(s)}}$ is calculate by formula (7)

${\hat{z}}^{(s)}$ is calculate by formula (2)

if $||{\hat{z}}^{(s)}-{\hat{z}}^{(s-1)}||<\epsilon$

Break

else:

s = s+1

continue

End if

End while

(a) 09. Output the category of each data point in $Z=\{Z_1,Z_2,\dots ,Z_n\}$.

Figure 1. Multiple GMM flowchart.

Figure 2. Double GMM flowchart.

Figure 3. Schematic diagram of the influence of outliers.

Figure 4. Block well diagram.

Figure 5. BIC assessment results.

Figure 6. The difference between single and multiple GMM.

Figure 7. The clustering results correspond to the classification of XI well lithofacies.

Figure 8. The clustering results correspond to the classification of XII well lithofacies.

Figure 9. XII lithology multi-layer GMM classification results and actual comparison.

Figure 10. Operation efficiency of XI as an initialization well.

Figure 11. Operation efficiency of XIII as an initialization well.