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

Due to the limitation of the seismic data acquisition environment and instrument, seismic data are often subjected to random noise interference. At the same time, random noise is inevitably introduced in the processing of seismic data. To solve the problem, this paper proposes a seismic data denoising approach based on bidimensional empirical mode decomposition (BEMD) and shearlet transform. In the beginning, the BEMD is used to decompose the seismic data with noise, and several intrinsic modal functions (IMFs) are obtained according to the frequency distribution from high to low. Then, the shearlet transform is applied to reduce the noise of the high-frequency IMF. Finally, the denoised high-frequency IMF component and the low-frequency IMF component are accumulated and reconstructed to achieve the noise reduction of seismic data. The proposed method was used to perform noise reduction experiments on seismic data. The results show that the proposed method performs better and can reduce the uneven deformation of seismic wavefront compared with other methods.

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Random Noise Reduction in Seismic Data by Using Bidimensional Empirical Mode Decomposition and Shearlet Transform

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

In seismic exploration, effective seismic noise attenuation along with seismic signal preservation is a key problem for seismic signal processing. The seismic data acquired from complex environments usually have a low signal-to-noise ratio (SNR) and nonstationary random noise that makes it difficult to accurately restore seismic signals. For enhancing seismic signals and filtering nonstationary random noise, we propose a structure-adaptive nonlinear complex diffusion method (ANCD) based on the regularized complex shock diffusion (CSD) by exploiting the structure-adaptive diffusion coefficients. The proposed complex diffusion method makes use of the imaginary value which is generated by a complex diffusion process as a directional structure indicator to guide the diffusion coefficients, by cooperating with spatially variant structure factors associated with the eigenvalues and eigenvectors of the structure tensor. In this way, the structural-adaptive diffusion term of ANCD allows the diffusion process along seismic structures, and the resulting imaginary part in turn enables the shock term to enhance the seismic signals with steep dips and rapidly varying slopes. The proposed method is tested on the synthetic seismic data and field seismic data acquired from the forest belt and desert area. The results show that the ANCD achieves a superior tradeoff between suppressing complicated random noise and preserving the seismic structures compared with the state-of-the-art seismic denoising methods.

Seismic Signal Enhancement and Noise Suppression Using Structure-Adaptive Nonlinear Complex Diffusion

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

To improve the denoising performance of seismic data contaminated with random and coherent
noises, a hybrid denoising scheme is proposed in this paper. It aims to whiten the random noise
and identify the coherent noise for the preserved or prominent seismic features. With the wavelet
and curvelet basis functions in curvelets alternately, the hybrid denoising scheme utilises the
representation of edges and singularities along curves. Then it adapts the wavelet-based higher-order
correlative stacking denoising method from seismic exploration sequentially. In regard to
interpretive seismic records of bedrock surface detection after the artificial backfill, the noisy data
are significantly improved both in denoising and fidelity. To prove the advantage of the hybrid
denoising scheme, a comparison of the performances between the different individual denoising
methods, including the higher-order correlative stacking method, curvelets with wavelet and
curvelet basis functions, has been discussed for the complex seismic records contaminated with
different noises. Numerical case studies and a field data analysis have been used to show that the
proposed hybrid denoising scheme is prominent for seismic data containing complex features
than the individual denoising methods.

Yu-Jie Zhang

Papers

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

Higher-order correlative stacking for seismic data denoising based on the multiple-domain combination