投审稿入口
VMD-TCN-Transformer-based approach for logging curve reconstruction under complex conditions
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摘要:
声波测井曲线，尤其是纵波时差（DTC）与横波时差（DTS），是岩石物理分析、地震合成记录制作及储层精细表征的重要基础资料，但在实际钻井过程中，受井眼条件及复杂测量环境噪声等因素影响，声波测井曲线易发生畸变或缺失，从而制约其工程应用效果。传统经验公式与统计回归方法难以刻画测井曲线之间复杂的非线性关系，近年来引入的机器学习与深度学习方法虽在一定程度上提升了重构精度，但在复杂井况条件下，对测井信号非平稳特征、局部变化特征及长程地质相关性的综合表征仍存在一定局限。针对上述问题，本文提出一种基于变分模态分解（VMD）与时域卷积网络（TCN）-Transformer融合架构的声波测井曲线重构方法。该方法通过VMD对原始测井信号进行多尺度分解，在最大程度保留地层有效信号的同时，滤除高频环境噪声，引入TCN刻画测井曲线的局部变化特征，并结合Transformer多头自注意力机制提取测井序列的长程依赖信息，从而实现对复杂沉积旋回特征的整体建模。基于山西某区块实测测井资料，开展模型对比分析、消融实验、井径异常条件下的曲线重构实验及盲井预测验证。结果表明，所提出方法在声波测井曲线重构精度与稳定性方面表现优异，测试井段中DTC与DTS预测的决定系数（
R2 ）分别达到0.9142 和0.9165 ；VMD信号分解与TCN-Transformer混合架构对模型性能提升均有显著贡献；在井径异常发育井段，模型能够有效抑制环境噪声干扰，重构的曲线形态连续合理；盲井预测结果生成的合成地震记录与实测地震剖面在波组特征与相位特征上具有较好一致性。该方法在复杂井况条件下具有较好的适应性与实用性，可为低质量测井资料校正、补全及后续地震反演与储层精细表征提供可靠基础数据支持。Abstract:ObjectiveAcoustic logging curves, particularly compressional wave slowness (DTC) and shear wave slowness (DTS), serve as fundamental data for petrophysical analysis, synthetic seismogram generation, and refined reservoir characterization. However, during actual drilling operations, these curves are prone to distortion or gaps due to factors such as borehole conditions and complex environmental measurement noise, which constrains their practical application. Traditional empirical formulas and statistical regression methods struggle to capture the complex nonlinear relationships between logging curves. Although machine learning and deep learning methods introduced in recent years have improved reconstruction accuracy to some extent, they still exhibit limitations in comprehensively representing the non-stationary features, local variations, and long-range geological dependencies of logging signals under complex borehole conditions.
MethodsTo address these issues, this study proposed an acoustic logging curve reconstruction method based on a fusion architecture combining variational mode decomposition (VMD) and temporal convolutional network (TCN)-Transformer. The method first employed VMD to perform multi-scale decomposition of the original logging signals, preserving the effective formation signals to the greatest extent while effectively filtering out high-frequency environmental noise. Subsequently, TCN was introduced to characterize the local variation features of the logging curves, while the Transformer’s multi-head self-attention mechanism was employed to extract long-range dependencies within the logging sequences, enabling holistic modeling of complex sedimentary cyclicity. Based on measured logging data from a block in Shanxi, comparative model analysis, ablation experiments, curve reconstruction experiments under conditions of severe borehole enlargement, and blind-well prediction validation were conducted.
ResultsThe results demonstrated that the proposed method performed well in terms of accuracy and stability for acoustic logging curve reconstruction. The coefficients of determination (
R2 ) for DTC and DTS predictions in the test intervals reached0.9142 and0.9165 , respectively. Both the VMD signal decomposition and the TCN-Transformer hybrid architecture contributed significantly to the model’s performance. In intervals with significant borehole enlargement, the model effectively suppressed environmental noise interference, producing reconstructed curves with continuous and geologically reasonable morphology. The synthetic seismograms generated from the blind-well prediction results showed good consistency with the measured seismic profile in terms of wavelet characteristics and phase features.ConclusionThe proposed method exhibits strong adaptability and practicality under complex borehole conditions. It can provide reliable foundational data for the correction and completion of low-quality logging data, as well as for subsequent seismic inversion and refined reservoir characterization.
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图 2 Transformer编码器（Encoder）结构示意图
Add & Norm为残差连接与层归一化；Feed Forward Network为前馈神经网络；Multi-Head Attention为多头注意力机制；Q，K，V分别为查询、键与值矩阵；下同
Figure 2. Schematic diagram of Transformer Encoder structure
图 3 基于VMD-TCN-Transformer的测井曲线预测流程图
Input为输入；VMD为变分模态分解；IMF1，IMF2，…，IMFN为N个模态分量；R为残余分量；Dilated Causal Conv为膨胀因果卷积；BatchNorm为批量归一化；GELU为高斯误差线性单元激活函数；Dropout为随机失活；1×1 Conv为1×1卷积层；TCN Block为时域卷积网络块；Positional Encoding为位置编码；Transformer Block为Transformer 模块；Attention Pooling为注意力池化层；Output为输出；下同
Figure 3. Flowchart of VMD-TCN-Transformer-based logging curve prediction
图 4 LX-53井的测井曲线(a)-(h)分别为井径、自然伽马、光电吸收截面、补偿中子、密度、电阻率、纵波时差、横波时差
CAL为井径；GR为自然伽马；Pe为光电吸收截面；CNCF为补偿中子；DEN为密度；M2RX为深感应电阻率；DTC纵波时差；DTS为横波时差；黑色虚线框内为扩径区；下同
Figure 4. Logging curves of well LX-53 (a)-(h) represent the caliper, natural gamma ray, photoelectric factor, compensated neutron porosity, bulk density, resistivity, compressional wave slowness, and shear wave slowness, respectively.
图 5 测井曲线互信息分析（a）和自相关系数（b）
Figure 5. Mutual information analysis (a) and autocorrelation coefficient (b) of logging curves
图 6 原始信号幅值(a)、VMD 算法分解所得各固有模态函数（IMF）分量的幅值(b～k)及皮尔逊相关系数绝对值|r| (l)
Figure 6. Amplitude of original signal (a), amplitude of each intrinsic mode function (IMF) component decomposed by VMD algorithm (b-k), and absolute value of Pearson correlation coefficient ∣r∣ (l)
图 7 6种方法对纵波时差（DTC）(a～f)和横波时差（DTS）(g～l)曲线的重构效果对比
黑色曲线为实测声波曲线；红色曲线为重构的DTC曲线；蓝色曲线为重构的DTS曲线
Figure 7. Comparison of reconstruction performance of DTC (a-f) and DTS (g-l) curves using six methods The black curves represent the measured data, while the red and blue curves represent the reconstructed DTC and DTS, respectively.
图 8 5种网络模型训练损失函数曲线对比
Figure 8. Comparison of training loss function curves for five network models
图 10 LX-61井DTC、DTS曲线校正分析(a1～k1)和LX-59井DTC、DTS曲线预测分析(a2～j2)
黑色实线为实测测井曲线；红色虚线为本研究方法重构曲线；蓝色虚线为多元线性回归法重构曲线；下同
Figure 10. Correction analysis of DTC and DTS curves for Well LX-61 (a1-k1) and prediction analysis of DTC and DTS curves for Well LX-59 (a2-j2)
表 1 实验环境与工具
Table 1. Experimental environment and tools
项目 配置 操作系统 Windows 11 CPU Intel(R) Core(TM) i7-14650HX GPU NVIDIA GeForce RTX 4060 8GB编程语言 Python3.9 CUDA版本 11.3 工具包 PyTorch、NumPy、Pandas、Scikit-learn、
Matplotlib、Seaborn、VMDpy、SciPy等
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表 2 模型超参数
Table 2. Model hyperparameters
模块 关键参数 设置值 TCN 层数 4 卷积核大小 5 Transformer 编码器层数 2 注意力头数 2 回归器 结构 64→32→2 激活函数 GELU 数据参数 时间窗长度 64 训练策略 学习率 0.001 优化器 AdamW Batch大小 64 训练轮数 100 正则化 Dropout（0.1）
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表 3 各模型预测DTC、DTS曲线的评估指标
Table 3. Evaluation indicators of each model for predicting DTC and DTS curves
模型方法 DTC DTS 参数量/106 计算复杂度/GFLOP R2 RMSE MAE R2 RMSE MAE MLR 0.6345 4.9669 4.2230 0.7025 14.5676 12.4837 < 0.0001 < 0.0001 GRU 0.8565 3.0046 2.2360 0.8728 4.7593 3.8748 0.1032 0.0539 LSTM 0.8773 2.8784 2.1542 0.8764 4.7378 3.3009 0.1374 0.0716 Informer 0.8801 2.7354 2.1198 0.8779 4.3191 3.5587 0.2001 0.0391 TCN-BiGRU-Attention 0.8907 2.5523 1.9406 0.9006 4.1956 3.1229 0.1779 0.0879 TCN-Transformer 0.9142 2.4064 1.7611 0.9165 3.8931 2.8234 0.1822 0.0661
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表 4 消融实验评估指标
Table 4. Evaluation indicators for ablation experiments
模型方法 DTC DTS 参数量/106 计算复杂度/GFLOP R2 RMSE MAE R2 RMSE MAE TCN 0.7763 2.5741 1.7541 0.7706 7.1682 5.9686 0.1112 0.0550 Transformer 0.8048 2.3582 1.5721 0.7972 6.5491 5.3059 0.2343 0.0648 TCN-Transformer 0.8539 2.0042 1.3719 0.8487 6.1137 4.9542 0.1822 0.0661 VMD-TCN-Transformer 0.8872 1.8341 1.3068 0.8734 5.5723 4.2967 0.1822 0.0661 注：VMD为信号预处理模块，不增加模型的可训练参数量，也不显著增加计算复杂度，故VMD-TCN-Transformer与TCN-Transformer的参数量和计算复杂度保持一致
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[1] 雍世和, 张超谟. 测井数据处理与综合解释[M]. 山东东营: 中国石油大学出版社, 2007.YONG S H, ZHANG C M. Logging data processing and comprehensive interpretation[M]. Dongying, Shandong: China University of Petroleum Press, 2007. (in Chinese) [2] 马天寿, 向国富, 石榆帆, 等. 基于双向长短期记忆神经网络的水平地应力预测方法[J]. 石油科学通报, 2022, 7(4): 487-504.MA T S, XIANG G F, SHI Y F, et al. Horizontal in-situ stress prediction method based on the bidirectional long short-term memory neural network[J]. Petroleum Science Bulletin, 2022, 7(4): 487-504. (in Chinese with English abstract [3] 赖锦, 苏洋, 肖承文, 等. 地球物理测井在地质领域应用经典案例解析[J]. 地质科技通报, 2024, 43(5): 279-288.LAI J, SU Y, XIAO C W, et al. Analysis of typical applications of geophysical well logs in geological fields[J]. Bulletin of Geological Science and Technology, 2024, 43(5): 279-288. (in Chinese with English abstract [4] HE J B, LI H, MISRA S. Data-driven in-situ sonic-log synthesis in shale reservoirs for geomechanical characterization[J]. SPE Reservoir Evaluation & Engineering, 2019, 22(4): 1225-1239. doi: 10.2118/191400-PA [5] SHI W R, WANG X Z, SHI Y H, et al. Application of dipole array acoustic logging in the evaluation of shale gas reservoirs[J]. Energies, 2019, 12(20): 3882. doi: 10.3390/en12203882 [6] LIU J X, EGHBALI A, TORRES-VERDÍN C. Axial resolution enhancement of borehole acoustic measurements via inversion-based interpretation supported with ultrasonic data[J]. Geophysics, 2024, 89(1): D43-D59. doi: 10.1190/geo2023-0313.1 [7] 黎子豪, 蒋恕. 基于机器学习和SHAP算法的声波测井曲线重构及可解释性分析[J]. 地质科技通报, 2025, 44(1): 321-331. doi: 10.19509/j.cnki.dzkq.tb20230504LI Z H, JIANG S. Reconstructing and interpreting analysis of sonic logging curves based on machine learning and SHAP algorithm[J]. Bulletin of Geological Science and Technology, 2025, 44(1): 321-331. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.tb20230504 [8] CASTAGNA J P, BATZLE M L, EASTWOOD R L. Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks[J]. Geophysics, 1985, 50(4): 571-581. doi: 10.1190/1.1441933 [9] HAN D H, NUR A, MORGAN D. Effects of porosity and clay content on wave velocities in sandstones[J]. Geophysics, 1986, 51(11): 2093-2107. doi: 10.1190/1.1893163 [10] 廖茂辉. 多元回归方法校正扩径对密度曲线声波曲线的影响[J]. 物探与化探, 2014, 38(1): 174-179. doi: 10.11720/j.issn.1000-8918.2014.1.32LIAO M H. The application of multiple regression method to the calibration of the influence of hole enlargement on density and acoustic logs[J]. Geophysical and Geochemical Exploration, 2014, 38(1): 174-179. (in Chinese with English abstract doi: 10.11720/j.issn.1000-8918.2014.1.32 [11] 夏竹, 赵磊, 李凯, 等. Atlas测井仪GR曲线扩径校正方法的改进及应用效果[J]. 石油地球物理勘探, 2016, 51(增刊1): 93-99. doi: 10.13810/j.cnki.issn.1000-7210.2016.s.016XIA Z, ZHAO L, LI K, et al. Improvement of GR curve enlargement correction method for Atlas logging tool and its application effect[J]. Oil Geophysical Prospecting, 2016, 51(S1): 93-99. (in Chinese with English abstract doi: 10.13810/j.cnki.issn.1000-7210.2016.s.016 [12] 高刚, 杨亚华, 赵彬, 等. 砂岩敏感识别因子的建立及直接提取方法[J]. 石油地球物理勘探, 2019, 54(6): 1329-1338. doi: 10.13810/j.cnki.issn.1000-7210.2019.06.017GAO G, YANG Y H, ZHAO B, et al. A method for establishing and directly extracting sensitive identification factors of unconsolidated sandstones[J]. Oil Geophysical Prospecting, 2019, 54(6): 1329-1338. (in Chinese with English abstract doi: 10.13810/j.cnki.issn.1000-7210.2019.06.017 [13] 翟晓岩, 高刚, 李勇根, 等. 融合注意力机制的二维卷积神经网络测井曲线重构方法[J]. 石油地球物理勘探, 2023, 58(5): 1031-1041. doi: 10.13810/j.cnki.issn.1000-7210.2023.05.001ZHAI X Y, GAO G, LI Y G, et al. Reconstruction method of logging curves by 2D convolutional neural network integrating attention mechanism[J]. Oil Geophysical Prospecting, 2023, 58(5): 1031-1041. (in Chinese with English abstract doi: 10.13810/j.cnki.issn.1000-7210.2023.05.001 [14] HE J B, MISRA S. Generation of synthetic dielectric dispersion logs in organic-rich shale formations using neural-network models[J]. Geophysics, 2019, 84(3): D117-D129. doi: 10.1190/geo2017-0685.1 [15] 杨怀杰, 乔宝强. 基于多元回归模型的拟声波时差测井曲线重构方法研究[J]. 铀矿地质, 2021, 37(3): 500-505. doi: 10.3969/j.issn.1000-0658.2021.37.053YANG H J, QIAO B Q. Study on reconstruction method of quasi-acoustic time difference log based on multiple regression model[J]. Uranium Geology, 2021, 37(3): 500-505. (in Chinese with English abstract doi: 10.3969/j.issn.1000-0658.2021.37.053 [16] FAUST L Y. A velocity function including lithologic variation[J]. Geophysics, 1953, 18(2): 271-288. doi: 10.1190/1.1437869 [17] WYLLIE M R J, GREGORY A R, GARDNER L W. Elastic wave velocities in heterogeneous and porous media[J]. Geophysics, 1956, 21(1): 41-70. [18] 黄小平, 高玉春. 对Garden公式应用条件的探讨[J]. 新疆石油地质, 2000, 21(3): 233-234.HUANG X P, GAO Y C. An approach to application considerations of Garden's relation[J]. Xinjiang Petroleum Geology, 2000, 21(3): 233-234. (in Chinese with English abstract [19] YANG Y H, YIN X Y, GAO G, et al. Shear-wave velocity estimation for calciferous sandy shale formation[J]. Journal of Geophysics and Engineering, 2019, 16(1): 105-115. doi: 10.1093/jge/gxy009 [20] 陈钢花, 王永刚. Faust公式在声波曲线重构中的应用[J]. 勘探地球物理进展, 2005, 28(2): 125-128.CHEN G H, WANG Y G. Application of Faust equation in rebuilding of acoustic curve[J]. Progress in Exploration Geophysics, 2005, 28(2): 125-128. (in Chinese with English abstract [21] CRANGANU C, BAUTU E. Using gene expression programming to estimate sonic log distributions based on the natural gamma ray and deep resistivity logs: A case study from the Anadarko Basin, Oklahoma[J]. Journal of Petroleum Science and Engineering, 2010, 70(3/4): 243-255. doi: 10.1016/j.petrol.2009.11.017 [22] FENG R H, GRANA D, BALLING N. Imputation of missing well log data by random forest and its uncertainty analysis[J]. Computers & Geosciences, 2021, 152: 104763. doi: 10.1016/j.cageo.2021.104763 [23] 刘建建, 周军, 余卫东, 等. 基于超参数优化LSTM的声波测井曲线生成技术[J]. 石油物探, 2024, 63(5): 1061-1074. doi: 10.12431/issn.1000-1441.2024.63.05.015LIU J J, ZHOU J, YU W D, et al. Acoustic log curve reconstruction based on hyperparameter optimized LSTM[J]. Geophysical Prospecting for Petroleum, 2024, 63(5): 1061-1074. (in Chinese with English abstract doi: 10.12431/issn.1000-1441.2024.63.05.015 [24] 周欣, 曹俊兴, 王兴建, 等. 基于双向门控循环单元神经网络的声波测井曲线重构技术[J]. 地球物理学进展, 2022, 37(1): 357-366.ZHOU X, CAO J X, WANG X J, et al. Acoustic log reconstruction based on bidirectional gated recurrent unit (GRU) neural network[J]. Progress in Geophysics, 2022, 37(1): 357-366. (in Chinese with English abstract [25] HAN J, DENG Y, ZHENG B, et al. Well logging super-resolution based on fractal interpolation enhanced by BiLSTM-AMPSO[J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2025, 11(1): 54. doi: 10.1007/s40948-025-00969-9 [26] 王欢欢, 赵彬, 刘建新, 等. 基于多头注意力机制的TCN-BiGRU密度测井曲线重构方法[J]. 地球物理学进展, 2025, 40(2): 592-604. doi: 10.6038/pg2025II0114WANG H H, ZHAO B, LIU J X, et al. Density logging curve reconstruction method based on TCN-BiGRU with multi-head attention mechanism[J]. Progress in Geophysics, 2025, 40(2): 592-604. (in Chinese with English abstract doi: 10.6038/pg2025II0114 [27] CHEN T F, GAO G, WANG P, et al. Prediction of shear wave velocity based on a hybrid network of two-dimensional convolutional neural network and gated recurrent unit[J]. Geofluids, 2022, 2022(1): 9974157. doi: 10.1155/2022/9974157 [28] 吕泽富, 钟阳阳, 王攀. 基于奇异谱分析和图注意力网络的测井曲线补全研究[J]. 地球物理学进展, 2025, 40(4): 1788-1799.LYU Z F, ZHONG Y Y, WANG P. Logging curves completion based on singular spectrum analysis and graph attention networks[J]. Progress in Geophysics, 2025, 40(4): 1788-1799. (in Chinese with English abstract [29] WANG Z J, WANG Y F. Integrating unsupervised learning and transformer for missing log prediction[J]. Geophysics, 2025, 90(4): D85-D100. doi: 10.1190/geo2024-0558.1 [30] 陈雪菲, 辛显康, 喻高明, 等. 基于模态分解融合机器学习的测井曲线预测[J]. 科学技术与工程, 2025, 25(17): 7132-7141. doi: 10.12404/j.issn.1671-1815.2404440CHEN X F, XIN X K, YU G M, et al. Logging curve prediction based on modal decomposition fused with machine learning[J]. Science Technology and Engineering, 2025, 25(17): 7132-7141. (in Chinese with English abstract doi: 10.12404/j.issn.1671-1815.2404440 [31] LIAO W L, GAO C Q, FANG J D, et al. A TCN-BiGRU density logging curve reconstruction method based on multi-head self-attention mechanism[J]. Processes, 2024, 12(8): 1589. doi: 10.3390/pr12081589 [32] DRAGOMIRETSKIY K, ZOSSO D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62(3): 531-544. doi: 10.1109/TSP.2013.2288675 [33] 史洪岩, 李尚达, 潘多涛, 等. 基于VMD-COMTBO-BiLSTM光伏阵列故障诊断研究[J]. 太阳能学报, 2026, 47(2): 18-29.SHI H Y, LI S D, PAN D T, et al. Research on photovoltaic array fault diagnosis based on VMD-COMTBO-BiLSTM[J]. Acta Energiae Solaris Sinica, 2026, 47(2): 18-29. (in Chinese with English abstract [34] 农高海. 基于VMD-BiLSTM的短期电力负荷预测[J]. 电脑知识与技术, 2025, 21(15): 107-110. doi: 10.16086/j.cnki.issn1000-0380.2024120122NONG G H. Short-term power load forecasting based on VMD-BiLSTM[J]. Computer Knowledge and Technology, 2025, 21(15): 107-110. (in Chinese with English abstract doi: 10.16086/j.cnki.issn1000-0380.2024120122 [35] 孔宪正, 黄国勇, 邓为权, 等. 基于SSA-VMD预处理的TCN-Informer短期风速多步预测混合模型[J]. 太阳能学报, 2026, 47(2): 527-538.KONG X Z, HUANG G Y, DENG W Q, et al. Hybird model based on SSA-VMD preprocessing of TCN-Informer short-term wind speed prediction[J]. Acta Energiae Solaris Sinica, 2026, 47(2): 527-538. (in Chinese with English abstract [36] LEA C, FLYNN M D, VIDAL R, et al. Temporal convolutional networks for action segmentation and detection[C]//Anon. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017: 1003-1012. [37] BAI S J, KOLTER J Z, KOLTUN V. Convolutional sequence modeling revisited[C]//Anon. International Conference on Learning Representations. [S. l. ]: [s. n. ], 2018. [38] 汪敏, 郭鑫平, 唐洪明, 等. 深度Transformer迁移学习的页岩气储层核心参数预测案例[J]. 地球物理学报, 2023, 66(6): 2592-2610. doi: 10.6038/cjg2022Q0054WANG M, GUO X P, TANG H M, et al. Case study of core parameter prediction for shale gas reservoirs based on deep Transformer transfer learning[J]. Chinese Journal of Geophysics, 2023, 66(6): 2592-2610. (in Chinese with English abstract doi: 10.6038/cjg2022Q0054 [39] 庞振宇, 鲁玉清, 徐颖晋, 等. 基于CNN-Transformer的致密砂岩储层孔隙度参数预测研究[J]. 石油地球物理勘探, 2025, 60(6): 1399-1408.PANG Z Y, LU Y Q, XU Y J, et al. Porosity prediction of tight sandstone reservoirs based on CNN-Transformer[J]. Oil Geophysical Prospecting, 2025, 60(6): 1399-1408. (in Chinese with English abstract [40] 于水, 韩府宏, 罗宇晨, 等. 基于Transformer多尺度融合网络的暖通空调能耗预测模型[J]. 太阳能学报, 2026, 47(2): 300-309. doi: 10.19912/j.0254-0096.tynxb.2024-1746YU S, HAN F H, LUO Y C, et al. Energy consumption prediction model for heating ventilation air conditioning based on transformer multi-scale fusion network[J]. Acta Energiae Solaris Sinica, 2026, 47(2): 300-309. (in Chinese with English abstract doi: 10.19912/j.0254-0096.tynxb.2024-1746 -
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