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VMD-LSTM-based noise detection and predictive reconstruction for magnetotelluric signals |
LI Bo1( ), LI Chang-Wei1,2( ), LUO Run-Lin1,2, LU Yu-Zeng1,2, WANG Zhan1 |
1. College of Earth Sciences, Guilin University of Technology, Guilin 541000, China 2. Guangxi Key Laboratory of Exploration for Hidden Metallic Ore Deposits, Guilin 541000, China |
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Abstract In thereconstruction of actual subsurface structures, strong noise limits the accuracy of the magnetotelluric (MT) method,causing adverse effects on later data interpretation. Given this and the characteristics of the MT time series,this study analyzed different types of noise in the MT time series,proposing a signal denoising technique based on variational mode decomposition (VMD) and long short-term memory (LSTM) predictive reconstruction. First, baseline drift correctionwas performed for the original MT datausing the VMD signal decomposition algorithm. Then, the time series was further decomposed into multiple different intrinsic mode functions (IMFs) through VMD. The LSTM time series detection model was trained using interference-free data in the RSE component, which was then identified. Afterward, the time intervals containing noise weremarked, the increasement of noise was calculated, and the noise information wastransmitted to the original signal for truncation and removal. Finally, an LSTM multi-dimensional prediction model was trained for the IMFs, followed by the prediction of missing values under various modes. The predicted results under all modes were combined to obtain the final predicted MT signals. After signal reconstruction, a secondary signal-noise separationwas performed for spike-pulse noise that was not effectively identified through VMD. TheVMD-LSTM-based signal denoisingtechnique can accurately identify strong noise in MT signals by merely processing the time series intervals containing noise, thuseffectively preserving interference-free data. Moreover, its prediction errors can berestricted within the allowable error range of the data processing for MT signals. Therefore, this technique enjoys significant denoising effects.
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Received: 25 July 2023
Published: 26 February 2025
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Flowchart of the prediction and reconstruction model based on VMD-LSTM
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Bi-LSTM network architecture diagram
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LSTM network architecture diagram
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Time series graph of the original MT signal(a) and spectrogram of the original MT signal(b)
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Time series graph of the measured signal with added noise(a) and spectrogram of the measured signal with added noise(b)
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Time series graph and spectrogram of the VMD decomposition for the test signal with K=2 a—IMF1 time series graph;b—IMF1 spectrogram;c—IMF2 time series graph;d—IMF2 spectrogram
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Time series graph and spectrogram of the VMD decomposition for the test signal with K=3 a—IMF1 time series graph; b—IMF1 spectrogram;c—IMF2 time series graph;d—IMF2 spectrogram;e—IMF3 time series graph;f—IMF3 spectrogram
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Time series graph and spectrogram of the VMD decomposition for the test signal with K=4 a—IMF1 time series graph;b—IMF1 spectrogram;c—IMF2 time series graph;d—IMF2 spectrogram;e—IMF3 time series graph;f—IMF3 spectrogram;g—IMF4 time series graph;h—IMF4 spectrogram
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Time series graph and spectrogram of the VMD decomposition for the test signal with K=5 a—IMF1 time series graph; b—IMF1 spectrogram;c—IMF2 time series graph;d—IMF2 spectrogram;e—IMF3 time series graph;f—IMF3 spectrogram;g—IMF4 time series graph;h—IMF4 spectrogram;i—IMF5 time series graph; j—IMF5 spectrogram
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Time series graph and spectrogram of the two components for K=2, under different α values
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Time series graph and spectrogram of the two components for K=2, under different α values a、e、i、m、q—IMF1 time series graph;b、f、j、n、r—IMF1 spectrogram;c、g、k、o、s—IMF2 time series graph;d、h、l、pt—IMF2 spectrogram
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Time-domain spectrogram of the noisy original signal and RES component(a) and frequency spectrum of the noisy original signal and RES component(b)
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数据集 | K值 | α值 | 模型训练个数 | 数据集大小 | A | 2 | 2000 | 2 | 300×2400×2 | B | 3 | 2000 | 3 | 300×2400×3 | C | 4 | 2000 | 4 | 300×2400×4 | D | 5 | 2000 | 5 | 300×2400×5 | E | 6 | 2000 | 6 | 300×2400×6 | F | 7 | 2000 | 7 | 300×2400×7 |
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Experimental parameters
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K值 | 2 | 3 | 4 | 5 | 6 | 7 | RMSE | 319.684 | 288.3506 | 278.5965 | 242.9843 | 286.9627 | 293.2542 | MAE | 255.3978 | 177.6701 | 216.9816 | 175.6035 | 219.5106 | 235.4275 | MAPE | 12.0185% | 11.82071% | 11.4593% | 11.2015% | 11.3134% | 11.5241% | TIME | 3.1h | 4.4h | 6.5h | 9.8h | 13.2h | 17.6h |
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Model prediction errors for different values of K
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Comparison of LSTM predicted signal (a), VMD-LSTM predicted signal (b), and the original signal
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隐含单元数 | 求解器 | 梯度阈值 | 特征维数 | 初始学习率 | 学习因子 | 128×3 | Adam | 1 | 50 | 0.1 | 0.3 | 处理器: | AMD RADEON7 5000 SERIES | | | | | 显卡: | NVIDIA GeForce RTX 3060 | | | | | 平台: | Matlab2021a | | | | |
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Experimental parameters and training environment of LSTM model
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Addition of baseline drift component in the noisy MT signal
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VMD decomposition results with controlled α value, K = 20 000
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VMD decomposition results with controlled K value of 20 000 and gradually increasing α values
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Result of baseline drift processing
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Original test signal with the addition of 10 sharp pulse noises
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Detection results under different threshold settings a—threshold set at 90% of the maximum predicted value;b—threshold set at the maximum predicted value
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Denoising process of the measured noisy MT signal
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Comparison of apparent resistivity before and after denoising in the measured signal
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