An automatic fitting method for a variogram based on deep learning
ZHAO Li-Fang1,2(), YU Si-Yu1,2(), LI Shao-Hua1,2
1. Key Laboratory of Exploration Technologies for Oil and Gas Resources, Ministry of Education, Yangtze University, Wuhan 430100, China 2. School of Geosciences, Yangtze University, Wuhan 430100, China
A variogram serves as a crucial tool for quantifying spatial correlations. However, existing variogram fitting methods often yield unstable results. This study proposed an automatic variogram fitting method based on deep learning, aiming to enhance the precision and stability of automatic fitting. The fitting of the experimental variogram is essentially a nonlinear optimization problem, which involves optimizing the matching between the experimental and theoretical variograms. The proposed method generated substantial training datasets using several sets of theoretical variograms with varying parameter values for training and learning in deep neural networks. The trained model was then used for the automatic fitting of the experimental variogram. Multiple sets of experimental results demonstrate that based on the robust fitting capability of deep neural networks, the proposed method manifested superior fitting stability and computational efficiency compared to the least squares method, providing a novel approach for automatic variogram fitting in geostatistics.
Li-Fang ZHAO,Si-Yu YU,Shao-Hua LI. An automatic fitting method for a variogram based on deep learning[J]. Geophysical and Geochemical Exploration,
2024, 48(5): 1359-1367.
Parameters of each data of the experimental variance function
Comparison of the fitting effect of the two different methods a—range mapping relationship between the least squares method and the deep learning method when the variogram function's range is 25~50, with red points indicating outliers; b—range mapping relationship between the least squares method and the deep learning method when the variogram function's range is 35~60, with red points indicating outliers; c—range mapping relationship between the least squares method and the deep learning method when the variogram function's range is 35~60, with red points indicating outliers; a1—the x and y coordinates of the red outliers in a correspond to the values of the least squares fitting curve and the deep learning curve, respectively; b1—the x and y coordinates of the red outliers in b correspond to the range values of the least squares fitting curve and the deep learning curve, respectively; c1—the x and y coordinates of the red outliers in c correspond to the range values of the least squares fitting curve and the deep learning curve, respectively
参数
第一组
第二组
第三组
理论变差函数
最小二乘法
深度学习
理论变差函数
最小二乘法
深度学习
理论变差函数
最小二乘法
深度学习
C0
0
0
-0.13
20.00
1.67
17.97
0
0
0.2
range
28.22
6.40
30.01
37.63
4.98
32.47
58.93
8.78
57.62
sill
84.27
78.11
83.86
85.17
78.25
81.24
96.83
53.18
94.37
Comparison of the parameters of the variational functions C0, range, and sill
Comparison of root mean square error and average error of the two methods
Efficiency comparison chart of two methods
Depth learning interpolated fit plot a—data points of 10 experimental variogram functions interpolated to 20 data points, with red indicating original points and blue indicating interpolated points; b—fitting effect diagram of fig.a interpolated data points; c—data points of 15 experimental variogram functions interpolated to 20 data points, with red indicating original points and blue indicating interpolated points; d—fitting effect diagram of fig.c interpolated data points.
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