Method For Random Noise Attenuation Research Articles

Adaptive Damped Rank-Reduction Method for Random Noise Attenuation of Three-Dimensional Seismic Data

Adaptive Damped Rank-Reduction Method for Random Noise Attenuation of Three-Dimensional Seismic Data

A common-reflection-point gather random noise attenuation method based on the synchrosqueezing wavelet transform

Common-reflection-point (CRP) gather is one extensively used prestack seismic data type. However, CRP suffers more noise than a poststack seismic data set. The events in the CRP gather are always flat, and the effective signals from neighboring traces in the CRP gather have similar forms not only in the time domain, but also in the time-frequency (TF) domain. Therefore, we first use the synchrosqueezing wavelet transform (SSWT) to decompose seismic traces to the TF domain because the SSWT has better TF resolution and reconstruction properties. Then, we use the similarity of neighboring traces to smooth and threshold the SSWT coefficients in the TF domain. Finally, we used the modified SSWT coefficients to reconstruct the denoised traces for the CRP gather. Synthetic and field data examples indicate that our method can effectively attenuate random noise with a better attenuation performance than the commonly used principal component analysis, [Formula: see text] filter, and the continuous wavelet transform method.

Unsupervised 3-D Random Noise Attenuation Using Deep Skip Autoencoder

Effective random noise attenuation is critical for subsequent processing of seismic data, such as velocity analysis, migration, and inversion. Thus, the removal of seismic random noise with an uncertainty level is meaningful. Attenuating 3-D random noise in a supervised way based on deep learning (DL) is challenging because clean labels are difficult to obtain. Therefore, it is necessary to develop an adaptive unsupervised-based method for random noise attenuation. In this article, we propose a deep-denoising unsupervised learning (DDUL) network to attenuate random noise in 2-D/3-D seismic data. A patching technique is used to split 2-D/3-D seismic data into several patches to be fed into the network, which helps to expand the number of samples for training. We use the fully symmetrical structure of the autoencoder to construct the network. In each corresponding encoder and decoder layer, skip connections are added to enhance the learning of seismic data features. We construct three blocks to extract waveform features in seismic data, i.e., encoder, decoder, and skip blocks. Among them, the skip is connected between the encoder and decoder blocks of each hidden layer. The use of multiple blocks not only improves the network’s ability to extract seismic data features but also solves the problem of excessive training parameters caused by hidden layer stacking. Five 2-D/3-D synthetic and field seismic datasets are used to test the denoising performance of our proposed method. The denoising results demonstrate that our proposed method has good signal-preserving and noise attenuation capabilities in real-world applications.

Application of the local maximum synchrosqueezing transform for seismic data

Seismic signal analysis is the main step in data processing through the petroleum exploration via costly seismic investigations. Precision of target delineation by seismic data for exploratory drilling strongly depends on resolution of the seismic image. However, resolution of the seismic image is restricted by the band-limited nature of the seismic signal and inherent deficiencies in signal enhancement and random noise attenuation methods. Generally, it is required to increase resolution of the seismic data both in time and frequency domains. General solution to achieve this goal is employing time – frequency transformation (TFT) methods. The most applicable and conventional TFT method is the short time Fourier transform (STFT). Nevertheless, the STFT method does not provide sufficient resolution for further seismological interpretation on data. Thus, reassignment and simultaneous synchrosqueezing transform methods were introduced that increase resolution in time by reassignment of coefficients to their true position. However, they are still not appropriate for obtaining required resolution in seismic signal. The local maximum synchrosqueezing transform (LMSST) was introduced as an efficient method for signal analysis. The LMSST method yet was not used for analysis of seismic data and the procedure of its parameters optimization for applying on seismic data is unclear. Therefore, in the presented study, we propose a strategy for defining optimum parameters of the LMSST method and the procedure of its application on seismic data, where high resolution seismic image is required for hydrocarbon exploration. The proposed strategy was applied on two synthetic data examples, considering the quality factor expression and contamination by random noise and a field data example from a natural gas reservoir. Result of applying the proposed strategy on synthetic and field data examples and comparison of results with the leading-edge methods, revealed that this strategy could be considered as an alternative to the common signal enhancement methods. Additionally, the proposed method consists of the advantage of easy implementation and full reconstruction of the original signal. It was also proved that the proposed strategy is a robust method against added random noise compared to other competitive methods when applied on nonstationary seismic signal.

Nonstationary signal inversion based on shaping regularization for random noise attenuation

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry; however, it has two drawbacks. First, it assumes that the seismic signals are piecewise stationary and linear. However, the seismic signal exhibits nonstationary due to the complexity of the underground structure. Second, the method predicts noise from seismic data by convolving with a prediction error filter (PEF), which applies inconsistent noise models before and after denoising. Therefore, the assumptions and model inconsistencies weaken conventional prediction filtering’s performance in noise attenuation and signal preservation. In this paper, we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation. The main idea of the method is to use the nonstationary prediction operator (NPO) to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution. Different from the convolutional predicting filtering, the proposed method uses NPO as the regularization constraint to directly invert the effective signal from the noisy seismic data. The NPO varies in time and space, enabling the inversion system to describe complex (nonstationary and nonlinear) underground geological structures in detail. Processing synthetic and field data results demonstrate that the method effectively suppresses random noise and preserves seismic reflection signals for nonstationary seismic data.

Structure-Oriented DTGV Regularization for Random Noise Attenuation in Seismic Data

Noise attenuation is a very important step in seismic data processing, which facilitates accurate geologic interpretation. Random noise is one of the main factors that lead to reductions in the signal-to-noise ratio (SNR) of seismic data. It is necessary for seismic data, including complex geological structures, to develop a number of new noise attenuation technologies. In this article, we concern with a new variational regularization method for random noise attenuation of seismic data. Considering that seismic reflection events often have spatially varying directions, we first employ the gradient structure tensor (GST) to estimate the spatially varying dips point by point and propose the structure-oriented directional total generalized variation (DTGV) (SODTGV) functional. Then, we employ the SODTGV as a regularizer to establish an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -SODTGV model and develop the primal-dual algorithm for solving this model. Next, the choice of the model parameters is discussed. Finally, the proposed model is applied to restore noisy synthetic and field data to verify the effectiveness of the proposed workflow. For contrastive methods, we select the structure adaptive median filtering (SAMF), anisotropic total variation (ATV), total generalized variation (TGV), DTGV, median filtering, KL transform, SVD transform, and curvelet transform. The synthetic and real seismic data examples indicate that our proposed method can preferably improve the vertical resolution of seismic profiles, enhance the lateral continuity of reflection events, and preserve local geologic features while improving the SNR. Moreover, the proposed regularization method can also be applied to other inverse problems, such as image processing, medical imaging, and remote sensing.

Seismic Random Noise Attenuation Based on PCC Classification in Transform Domain

Random noise attenuation of seismic data is an essential step in the processing of seismic signals. However, as the exploration environment is becoming more and more complicated, the energy of valid signals is weaker and the signal to noise (SNR) is much lower, which brings great difficulty to seismic data processing and interpretation. To this end, we propose an unconventional and effective seismic random noise attenuation method based on proximal classifier with consistency (PCC) in transform domain. Firstly, we analyze various transforms for seismic data from traditional wavelet transform and curvelet transform to emerging non-subsampled shearlet transform (NSST) and non-subsampled contourlet transform (NSCT). And, we select the excellent NSST to decompose the noisy seismic data into different sub-bands of frequency and orientation responses. Secondly, unlike traditional sparse transform based seismic denoising methods that often directly use a thresholding operator and corresponding inverse transform to denoise seismic data, our proposed method employs a superior performance PCC to classify the NSST coefficients of seismic data before thresholding operator. The added step can effectively divide the NSST coefficients into reflected useful signal coefficients and noise-related coefficients, which can preserve the edge of reflected signals and keep the information of events intact as much as possible. In addition, we also introduce an adaptive threshold computing method and a soft-thresholding method to achieve seismic data denoising better. Finally, the experimental results on the typical synthetic example and real seismic data show the superior performance of the proposed method.

Signal-to-noise ratio enhancement for downhole microseismic data based on 3D shearlet transform

Downhole microseismic data are characterized for their high frequency and small amplitude, which bring great difficulty for noise suppression. We present a random noise attenuation method for downhole microseismic data based on the 3D shearlet transform (3DST). In contrast to the 2D shearlet, 3DST takes into account the correlation among three components of downhole microseismic. With the help of correlation among the data, downhole microseismic data are reassembled into a new 3D matrix and then transformed to the shearlet domain. After the analysis of the coefficients’ energy and the high-order cumulant on each scale, an efficient threshold function is proposed. We apply a small threshold to the coefficients associated with the signal’s scales, and a large threshold is chosen for the scales of the noise. Experimental results indicate that the algorithm significantly improves the signal-to-noise ratio of the microseismic data and effectively preserves a valid signal.

Seismic Random Noise Attenuation Method Based on Variational Mode Decomposition and Correlation Coefficients

Seismic data is easily affected by random noise during field data acquisition. Therefore, random noise attenuation plays an important role in seismic data processing and interpretation. According to decomposition characteristics of seismic signals by using variational mode decomposition (VMD) and the constraint conditions of correlation coefficients, this paper puts forward a method for random noise attenuation in seismic data, which is called variational mode decomposition correlation coefficients VMDC. Firstly, the original signals were decomposed into intrinsic mode functions (IMFs) with different characteristics by VMD. Then, the correlation coefficients between each IMF and the original signal were calculated. Next, based on the differences among correlation coefficients of effective signals and random noise as well as the original signals, the corresponding treatment was carried out, and the effective signals were reconstructed. Finally, the random noise attenuation was realized. After adding random noise to simple sine signals and the synthetic seismic record, the improved complementary ensemble empirical mode decomposition (ICEEMD) and VMDC were used for testing. The testing results indicate that the proposed VMDC has better random noise attenuation effects. It was also used in real-world seismic data noise attenuation. The results also show that it could effectively improve the signal-to-noise ratio (SNR) of seismic data and could provide high-quality basic data for further interpretation of seismic data.

A compound method for random noise attenuation

ABSTRACTRandom noise attenuation, preserving the events and weak features by improving signal‐to‐noise ratio and resolution of seismic data are the most important issues in geophysics. To achieve this objective, we proposed a novel seismic random noise attenuation method by building a compound algorithm. The proposed method combines sparsity prior regularization based on shearlet transform and anisotropic variational regularization. The anisotropic variational regularization which is based on the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation attenuates noises while preserving the events of seismic data and it effectively avoids the fine‐scale artefacts due to shearlets from the restored seismic data. The proposed method is formulated as a convex optimization problem and the split Bregman iteration is applied to solve the optimization problem. To verify the effectiveness of the proposed method, we test it on several synthetic seismic datasets and real datasets. Compared with three methods (the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation, shearlets and shearlet‐based weighted anisotropic total variation), the numerical experiments indicate that the proposed method attenuates random noises while alleviating artefact and preserving events and features of seismic data. The obtained result also confirms that the proposed method improves the signal‐to‐noise ratio.

Inversion-based data-driven time-space domain random noise attenuation method

Conventional time-space domain and frequency-space domain prediction filtering methods assume that seismic data consists of two parts, signal and random noise. That is, the so-called additive noise model. However, when estimating random noise, it is assumed that random noise can be predicted from the seismic data by convolving with a prediction error filter. That is, the source-noise model. Model inconsistencies, before and after denoising, compromise the noise attenuation and signal-preservation performances of prediction filtering methods. Therefore, this study presents an inversion-based time-space domain random noise attenuation method to overcome the model inconsistencies. In this method, a prediction error filter (PEF), is first estimated from seismic data; the filter characterizes the predictability of the seismic data and adaptively describes the seismic data’s space structure. After calculating PEF, it can be applied as a regularized constraint in the inversion process for seismic signal from noisy data. Unlike conventional random noise attenuation methods, the proposed method solves a seismic data inversion problem using regularization constraint; this overcomes the model inconsistency of the prediction filtering method. The proposed method was tested on both synthetic and real seismic data, and results from the prediction filtering method and the proposed method are compared. The testing demonstrated that the proposed method suppresses noise effectively and provides better signal-preservation performance.

Seismic arrival enhancement through the use of noise whitening

A constant feature in seismic data, noise is particularly troublesome for passive seismic monitoring where noise commonly masks microseismic events. We propose a statistics-driven noise suppression technique that whitens the noise through the calculation and removal of the noise’s covariance. Noise whitening is shown to reduce the noise energy by a factor of 3.5 resulting in microseismic events being observed and imaged at lower signal to noise ratios than originally possible – whilst having negligible effect on the seismic wavelet. The procedure is shown to be highly resistant to most changes in the noise properties and has the flexibility of being used as a stand-alone technique or as a first step before standard random noise attenuation methods.

Improved random noise attenuation using f−x empirical mode decomposition and local similarity

Conventional f−x empirical mode decomposition (EMD) is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events. However, when a seismic event is not horizontal, the use of f−x EMD is harmful to most useful signals. Based on the framework of f−x EMD, this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals. Compared with conventional f−x EMD, f−x predictive filtering, and f−x empirical mode decomposition predictive filtering, the new approach can preserve more useful signals and obtain a relatively cleaner denoised image. Synthetic and field data examples are shown as test performances of the proposed approach, thereby verifying the effectiveness of this method.

The seismic random noise attenuation method based on enhanced bandelet transform

The 2D separable wavelet transform used in bandelet transform, has low angular resolution and suffers from aliasing. We propose an enhanced bandelet transform, which replaces the 2D separable wavelet transform used in bandelet transform with nonsubsampled contourlet transform (NSCT, NSCT can decompose 2D signal to a series of bandpass directional components). Based on the enhanced bandelet transform, we developed a new seismic random noise attenuation method. The method is applied to synthetic seismic data and field data. The numerical results show that our method can outperform the random noise attenuation method based on bandelet transform.

Matching-Pursuit-Based Spatial-Trace Time-Frequency Peak Filtering for Seismic Random Noise Attenuation

Time-frequency peak filtering (TFPF) is an effective seismic random noise attenuation method at low signal-to-noise ratio (SNR). However, the conventional TFPF is biased for seismic signals with high frequency. We propose a spatial-trace TFPF (ST-TFPF) algorithm for reducing random noise in seismic data and simultaneously the bias of TFPF. The proposed method takes into consideration the lateral coherence between the neighboring traces as constraint of TFPF. To reduce bias, this algorithm takes TFPF along seismic events. The first stage of the proposed method preliminarily identifies the position of seismic reflection events using matching pursuit. The second stage consists of analyzing time delay of neighboring traces to construct spatial traces along seismic events. The last stage of algorithm consists of encoding seismic data along the constructed spatial traces and detecting the pseudo-Wigner-Ville distribution peaks of the encoded signals to reduce random noise. We assess our method on the synthetic and field data. The results illustrate that the ST-TFPF extends the signal preserving ability of TFPF in a wider range of window length at low SNR. Furthermore, comparison with conventional TFPF and wavelet denoising method shows that our method outperforms the two methods in random noise attenuation and seismic signal enhancement.

Robust reduced-rank filtering for erratic seismic noise attenuation

Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of [Formula: see text] deconvolution, the classical SSA method, and the proposed robust SSA method. The [Formula: see text] deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.

A new method for random noise attenuation in seismic data based on anisotropic fractional-gradient operators

Abstract In this paper, we first introduce an anisotropic fractional-gradient operator, from which, we propose a new method for random noise attenuation of seismic data. Then we derive the Euler–Lagrange equation for solving the proposed minimization problem and present the corresponding numerical algorithm. Finally, we apply our proposed method to the random noise attenuation for synthetic and real seismic sections. In addition, we also provide the selection strategies of the parameters involved in our proposed method. The theoretical analysis and experimental results indicate that our method can enhance the coherence of seismic events in the horizontal direction and preserve the texture structure and detailed useful information in the vertical direction while improving the signal-to-noise ratio. This provides a reliable basis for seismic data interpretation.

Random noise attenuation using f-x regularized nonstationary autoregression

We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space ([Formula: see text]) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using [Formula: see text] RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional [Formula: see text] domain prediction technique. The conventional [Formula: see text] domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The new method does not require windowing strategies in spatial direction. We implement the algorithm by an iterated scheme using the conjugate-gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in the [Formula: see text] domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of [Formula: see text] RNA. There are two key parameters in the proposed method: filter length and radius of shaping operator. Tests on synthetic and field data examples showed that, compared with [Formula: see text] domain and time-space domain prediction methods, [Formula: see text] RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.

Multicomponent f-x seismic random noise attenuation via vector autoregressive operators

We propose an extension of the traditional frequency-space ([Formula: see text]) random noise attenuation method to three-component seismic records. For this purpose, we develop a three-component vector autoregressive (VAR) model in the [Formula: see text] domain that is applied to the multicomponent spatial samples of each individual temporal frequency. VAR model parameters are estimated using the least-squares minimization of forward and backward prediction errors. VAR modeling effectively identifies the potential coherencies between various components of a multicomponent signal. We use the squared coherence spectrum of VAR models as an indicator to determine these coherencies. Synthetic and real data examples are provided to show the effectiveness of the proposed method.