Suppression of random noise in seismic data is a challenging preprocessing task. We propose a new denoising method, which includes the following steps. First, the short-time Fourier transform of the noisy seismic signal is computed. Then, a sparse low-rank matrix is estimated based on solving a nonconvex penalty function. A threshold function associated with the penalty function based on the optimal shrinkage of the singular values is employed to solve the penalty function. The nonconvex penalty function induces sparsity to the time–frequency (TF) matrix, and the optimal shrinkage optimizes the thresholding function to extract the singular values. Finally, the seismic signal is synthesized based on the estimated sparse low-rank TF matrix. We evaluate the proposed method by using a synthetic seismic section contaminated by random noise and a prestack real seismic dataset from an oil field in the southwest of Iran. The synchrosqueezed wavelet transform-OptShrink, synchrosqueezed wavelet transform-Go Decomposition, and classical $f-x$ singular spectrum analysis methods are selected to compare the performance of the proposed method. The results indicate the superiority of the proposed method compared to the other state-of-the-art noise suppression methods.

Seismic Random Noise Attenuation Using Sparse Low-Rank Estimation of the Signal in the Time–Frequency Domain

Attenuating the random noise and improving the signal-to-noise ratio (SNR) for the seismic data are of great significance in industrial exploration. In recent years, fractal conservation law (FCL) has been proposed and applied to seismic random noise suppression successfully. However, in conventional FCL, the filtering parameter selection strategy is relatively simple and a fixed parameter set is always used for the whole seismic record. In addition, it is very difficult to make an excellent tradeoff in random noise attenuation and signal preservation only by fixed parameters especially under the low-SNR conditions. Thus, accurately recognizing the effective signals and adaptively choosing appropriate filtering parameters is a feasible approach to improve the performance of the conventional FCL. In this article, an adaptive FCL methodology is proposed by combining the seismic noise analyzing theory and stationarity testing techniques. It is known that the random noise and reflection signals have different properties in stationarity and thus, the signal and noise segments can be divided by stationarity testing. As a consequence, different filtering parameters can be adopted for signal and noise segments to achieve the noise suppression and signal preservation simultaneously. Synthetic and field data experiments demonstrate that the proposed method can remove the random noise from seismic record and effectively preserve the reflection events.

Seismic Random Noise Suppression by Using Adaptive Fractal Conservation Law Method Based on Stationarity Testing

The inherent challenge of 3-D seismic noise attenuation is determining how to uncover high-dimensional concise structures that only exist in true signals to eliminate random noise. The prevailing deep learning (DL) denoising methods have achieved promising performance in revealing the compact structures underlying contaminated seismic data. However, as clean ground truth seismic data are generally unavailable in real-world settings, most existing matrix-based DL denoising schemes fail to automatically describe this type of high-dimensional structure in an unsupervised manner, potentially rendering them unable to effectively perform 3D seismic data denoising tasks. To tackle this challenge, this article presents a tensor convolutional neural network (TCNN)-based data denoising scheme using Stein’s unbiased risk estimate (SURE) (called SURE-TCNN) to learn intrinsic high-dimensional structures without ground truth seismic data. Considering that SURE provides an almost unbiased estimate of the mean squared error (MSE), SURE-TCNN has the potential to provide similar results to those of the supervised MSE-based TCNN with ground truth data. For ease of implementation, the properties of a transform-based tensor-tensor product (t-product) are followed to establish a solid theoretical connection between the SURE-TCNN tensor and matrix. Derived from this connection, the SURE-TCNN weight parameters are determined by implementing a matrix-based SURE-CNN on each frontal slice in the time-frequency domain (e.g., the wavelet domain). Synthetic and field data examples demonstrate the superior performances of the proposed model against three state-of-the-art (SOTA) methods.

Ground Truth-Free 3-D Seismic Random Noise Attenuation via Deep Tensor Convolutional Neural Networks in the Time-Frequency Domain

Erratic seismic noise, following a (known or unknown) non-Gaussian distribution, poses a formidable challenge to conventional methods of random noise attenuation. Many erratic noise cancellation methods, for instance, robust reduced-rank and sparsity-promoting filtering, have been proven to achieve promising results in overcoming this challenge. Among them, deep learning (DL) methods require no assumptions about the underlying clear seismic image and are also more robust against erratic and random noise. However, the success of existing DL-based denoising methods strongly depends on supervised learning from a large number of ground-truth seismic images affected by erratic noise and their clean counterparts, which are typically unavailable in a real-world setting. As an alternative, this article presents an unsupervised DL method for erratic-plus-Gaussian noise removal based on a robust deep convolutional autoencoder (RDCAE). In the RDCAE, the mean squared error (mse) loss in a classic DCAE is replaced by the smooth Welsch function to exploit the concept of robust image denoising. In this way, the erratic noise is downweighted by means of a curbed weight defined in terms of the Welsch function. In contrast, the random noise is diluted by combining the mean square in the Welsch function and the total variation (TV). Subsequently, the training procedures required for solving the RDCAE are derived on the basis of the backpropagation (BP) algorithm for a neural network. Experiments conducted on both synthetic and real field datasets are reported to illustrate the efficacy of the proposed method. 

Unsupervised Erratic Seismic Noise Attenuation With Robust Deep Convolutional Autoencoders

The inherent challenge of 3-D seismic noise attenuation is determining how to uncover high-dimensional concise structures that only exist in true signals to eliminate random noise. The prevailing deep learning (DL) denoising methods have achieved promising performance in revealing the compact structures underlying contaminated seismic data. However, as clean ground-truth seismic data are generally unavailable in real-world settings, most existing matrix-based DL denoising schemes fail to automatically describe this type of high-dimensional structure in an unsupervised manner, potentially rendering them unable to effectively perform 3-D seismic data denoising tasks. To tackle this challenge, this article presents a tensor convolutional neural network (TCNN)-based data denoising scheme using Stein’s unbiased risk estimate (SURE) (called SURE-TCNN) to learn intrinsic high-dimensional structures without ground-truth seismic data. Considering that SURE provides an almost unbiased estimate of the mean squared error (MSE), SURE-TCNN has the potential to provide similar results to those of the supervised MSE-based TCNN with ground-truth data. For ease of implementation, the properties of a transform-based tensor-tensor product (t-product) are followed to establish a solid theoretical connection between the SURE-TCNN tensor and matrix. Derived from this connection, the SURE-TCNN weight parameters are determined by implementing matrix-based SURE-convolutional neural networks (CNNs) on each frontal slice in the time-frequency domain (e.g., the wavelet domain). Synthetic and field data examples demonstrate the superior performances of the proposed model against three state-of-the-art (SOTA) methods. 

To whiten random noise and identify coherent noise while preserving the features of seismic events, a hybrid denoising scheme of wavelet-based higher order correlative stacking (HOCS) in the curvelet domain is proposed. The proposed algorithm uses HOCS to isolate the coefficients of seismic events in the curvelet domain. It then removes the noises and recovers signals recorded in noisy environment, without the need to choose an arbitrary threshold; the HOCS method selects a threshold automatically in the curvelet domain. Therefore, with the HOCS, it is possible to capture the features of useful signals with good correlations at all scales and all angles, then to remove the features of coherent noise with disordered correlations. Using interpretive seismic records of karst cavities and hidden sinkhole detections after artificial backfill, we show that the proposed scheme improves noisy seismic data significantly with respect to both signal-to-noise ratio and fidelity. To demonstrate the advantages of this hybrid denoising scheme, a comparison of the performances between different individual denoising methods is investigated for complex seismic records contaminated with different types of noise. Numerical case studies and three field data examples validate the effectiveness of the hybrid denoising scheme proposed in this paper.

Wavelet-Based Higher Order Correlative Stacking for Seismic Data Denoising in the Curvelet Domain

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Wavelet-Based Higher Order Correlative Stacking for Seismic Data Denoising in the Curvelet Domain