基于深度学习的变差函数自动拟合方法研究

doi:10.11720/wtyht.2024.1522

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Abstract

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.

Key words： variogram automatic fitting deep learning geostatistics

Received: 01 December 2023 Published: 21 October 2024

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	Li-Fang ZHAO
	Si-Yu YU
	Shao-Hua LI

Cite this article:

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.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2024.1522 OR https://www.wutanyuhuatan.com/EN/Y2024/V48/I5/1359

Neural network structure

1 000×20 experimental variational function data

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

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.

1 000×6 experimental variational function data

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