In 3D seismic data processing, the key challenge of removing random noiseRandom noise lies in isolating the unique high-dimensional structures embedded in true signals. Deep learning (DLDeep learning (DL)) has shown significant potential in this area, particularly for extracting hidden patterns from noisy data. However, the scarcity of clean seismic data in practical applications poses a challenge. Many DLDeep learning (DL)-based denoising techniques, particularly those relying on matrix-based methods, face challenges in effectively managing complex high-dimensional structures, especially in unsupervised environments, which can limit their effectiveness in denoising 3D seismic data. To address these limitations, this chapter introduces a novel denoising strategy that integrates tensor convolutional neural networks (TCNNTensor convolutional neural network (TCNN)) with Stein’s unbiased risk estimator (SUREStein’s unbiased risk estimator (SURE)), referred to as SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN). The proposed method focuses on directly learning the intrinsic high-dimensional structures of seismic data without relying on noise-free datasets. SUREStein’s unbiased risk estimator (SURE) offers an approximately unbiased estimation of the mean squared error (MSE)Mean squared error (MSE), enabling SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN) to achieve performance comparable to supervised MSEMean squared error (MSE)-TCNN models that require clean ground truth data.This method utilizes the characteristics of tensor-tensor products (t-product)Tensor-tensor product (t-product) to build a theoretical link between tensor representations and their matrix counterparts. This connection facilitates efficient parameter optimization by processing each frontal sliceFrontal slice of the tensor in the time-frequency domainTime-frequency domain, such as the wavelet transformWavelet transform domain, using a matrix-based SUREStein’s unbiased risk estimator (SURE)-CNNConvolutional neural network (CNN). This design streamlines implementation while maintaining theoretical consistency.Experimental results on both synthetic and real-world datasets show that the proposed SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN) method significantly outperforms three leading denoising techniques in terms of its effectiveness in reducing noise. Moreover, the method exhibits strong robustness and broad applicability across various scenarios.

Transform-Based Tensor Deep Learning for Seismic Random Noise Attenuation

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发表日期：

2025年

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Feng Qian,
Shengli Pan,
Gulan Zhang

摘要

In 3D seismic data processing, the key challenge of removing random noiseRandom noise lies in isolating the unique high-dimensional structures embedded in true signals. Deep learning (DLDeep learning (DL)) has shown significant potential in this area, particularly for extracting hidden patterns from noisy data. However, the scarcity of clean seismic data in practical applications poses a challenge. Many DLDeep learning (DL)-based denoising techniques, particularly those relying on matrix-based methods, face challenges in effectively managing complex high-dimensional structures, especially in unsupervised environments, which can limit their effectiveness in denoising 3D seismic data. To address these limitations, this chapter introduces a novel denoising strategy that integrates tensor convolutional neural networks (TCNNTensor convolutional neural network (TCNN)) with Stein’s unbiased risk estimator (SUREStein’s unbiased risk estimator (SURE)), referred to as SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN). The proposed method focuses on directly learning the intrinsic high-dimensional structures of seismic data without relying on noise-free datasets. SUREStein’s unbiased risk estimator (SURE) offers an approximately unbiased estimation of the mean squared error (MSE)Mean squared error (MSE), enabling SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN) to achieve performance comparable to supervised MSEMean squared error (MSE)-TCNN models that require clean ground truth data.This method utilizes the characteristics of tensor-tensor products (t-product)Tensor-tensor product (t-product) to build a theoretical link between tensor representations and their matrix counterparts. This connection facilitates efficient parameter optimization by processing each frontal sliceFrontal slice of the tensor in the time-frequency domainTime-frequency domain, such as the wavelet transformWavelet transform domain, using a matrix-based SUREStein’s unbiased risk estimator (SURE)-CNNConvolutional neural network (CNN). This design streamlines implementation while maintaining theoretical consistency.Experimental results on both synthetic and real-world datasets show that the proposed SUREStein’s unbiased risk estimator (SURE)-TCNNTensor convolutional neural network (TCNN) method significantly outperforms three leading denoising techniques in terms of its effectiveness in reducing noise. Moreover, the method exhibits strong robustness and broad applicability across various scenarios.