For subsequent seismic data processing and interpretation, it is important to obtain high-quality distributed acoustic sensing (DAS) signals from down-hole DAS data containing various complex noises. Model-based denoising methods mainly treat this signal estimation issue as a maximum a posteriori (MAP) optimization problem, for its relatively transparent mathematical model and wide range of applications. However, the manually designed prior assumption in MAP cannot accurately describe the actual distribution of DAS data, so the optimization parameters for obtaining high-quality solutions are difficult to determine, making it unavailable in DAS signal estimation. To solve these problems, we propose to emulate the optimization process of MAP with neural networks and accomplish the signal estimation task in feature space via some customized optimization modules. Specifically, we first construct an optimization unit (OPTU) to simulate the optimization process. And then, in order to further obtain the signal distribution of DAS data, we design in each OPTU, a multiscale dense feature aggregation (MDFA) module with the idea of back-projection fusion. With the help of OPTU, the optimization estimation process would be implemented more finely and automatically, expanding the application of MAP for accurate DAS signal estimation. Experiments on both synthetic and field DAS data demonstrate that our method can successfully estimate the high-quality signals from DAS data corrupted by complex noises, with less energy loss.

Nowadays, one of the predominant deep learning approaches to improve the quality of DAS VSP seismic data is executed through supervised learning, which requires paired training set including data simulation with relevant parameters and solutions of elastic wave equations. However, differences between simulated data and field data in terms of signal regulations and noise distributions often leads to poor results. An alternative approach is self-supervised learning, such as the representative framework--Blind Spot Network (BSN), but unfortunately, the effective information in blind spots cannot be fully utilized. To solve this problem, this paper considers BSN as a basis and establishes a novel self-supervised network--blind spot visualization (BSV) to suppress random noise and improve the quality of DAS VSP data. In BSV, one branch is dedicated to first produce more denoised data with blind spots and then recover the valid information covered by the blind spots, assuming that the signal is partially data-dependent and the DAS noise is conditionally data-independent. The other branch is designed to generate a target for training without blind spots, so that the dual-branch network can accomplish a self-supervised task in the way of supervised learning. More than that, unlike BSN, we utilize a tailor-made blind spot mapper (BSM) to recover effective information in the blind spots. Results of field data testing prove BSV’s advantages in suppressing random noise and improving the quality of DAS VSP data, although test on synthetic data is nearly identical to supervised learning.

The random noise attenuation is an essential step in seismic data processing. Due to complex geological conditions and acquisition environment, the intensity of effective signal and random noise varies in time and space. Additionally, the morphology of seismic event is complex and diverse, such as large dips and fast changes. These complex conditions necessitate that the denoiser adjust filtering policy dynamically. In this paper, we propose a reinforcement learning-based seismic denoising (RLSD) model with the framework of asynchronous advantage actor-critic (A3C). In A3C framework, the RLSD agent utilizes a policy network to learn a denoising policy for the state that is the sample of seismic data and selects a suitable filter from the preset action space composed of multiple simple and effective seismic filters with different parameters. Moreover, the RLSD agent utilizes a value network and a region-adaptive weighted reward function to accurately evaluate the denoising effect of nonstationary seismic signals. A curriculum learning approach is adopted to achieve convergence of the proposed RLSD model under complex seismic data by training from the stationary training data to nonstationary training data, and make the model more suitable to the data to be processed by using a local similarity-based reward function to fine-tune the model. The synthetic and field seismic data applications confirm that the proposed RLSD model achieves a significant performance in preserving nonstationary signals and suppressing noise by adaptively adjusting the denoising policy according to the complex structural features and noise levels. The source code is available on https://github.com/liangc-code/RLSD.

Distributed acoustic sensing (DAS) has been gradually applied to vertical seismic profiling (VSP), where the generated DAS VSP seismic data contains types of complex noise. Therefore, data denoising plays an important role in collecting high-quality geological information. Generative adversarial network(GAN) has been widely used in seismic exploration data denoising these years, but problems such as insufficient optimization objectives, poor signal retention continuity, and insufficient accuracy still remains when processing DAS VSP data. To address these problems, this paper proposes DuGAN, a deep learning network for multi-scale feature extraction and global information discrimination, to better meet the requirements of high-precision in DAS VSP data denoising. Our method takes GAN as the basic architecture and chooses the multi-scale codec network U-net to explore the potential correlation of DAS data at different scales and a more robust feature representation of DAS signals. In addition, DuGAN is more inclined to emphasize the global role of discriminator so that the entire network ensures the integrity of effective signal structure from a global perspective. Also, for more accurate recovery of the DAS reflected signal, we adjust the loss function in adversarial training and tilt the target optimized space towards the discriminator. Experiments on synthetic and field DAS seismic data show that DuGAN has better denoising performance-not only the noise-covered signal can be recovered, but also the overall effective events are better preserved.

Since seismic data will be interfered with by a host of complicated noise during the acquisition process, the quality of the acquired seismic data is usually poor. The overlap of signals and noise makes it difficult to extract effective signals from desert seismic records. Therefore, the suppression of seismic noise and the retention of seismic signals are key issues in seismic signal processing. In order to improve the quality of the data obtained, we propose an unsupervised relative attributes-based generative adversarial network (RAGAN), which includes a generator, a discriminator, and an attribute match-aware discriminator. By encoding the data of different attributes in seismic records, the denoising task can be regarded as the conversion process of the data corresponding to the attributes. The relative attributes obtained by the difference between the target attribute and the original attribute are used to control the attributes of the data generated by the generator, so as to achieve the purpose of noise suppression. Experimental results of both synthetic and field seismic records show that the proposed method performs better than part of conventional methods.

In recent years, the denoising of low-frequency desert noise has been the significant and difficult point in processing seismic data. Traditional random noise suppression methods could not get a good result in processing seismic data in desert areas. Moreover, convolutional neural network (CNN) has made notable achievements in many fields recently. In order to denoise seismic data in desert areas and improve the signal-to-noise ratio (SNR), CNN is introduced to process seismic data. According to the characteristics of desert seismic data, we designed a new network suitable for desert seismic data training and denoising, which is named DnResNeXt. Then, to form a mapping from the noisy data to the pure desert noise, we build a mass of training sets to train the denoising network. Thus, the network can predict the noise, then by subtracting the predicted noise from the noisy data, the denoised data are obtained. Consequently, compared with the traditional methods in suppressing random noise, DnResNeXt network has obvious advantages in both simulation and actual experiments.

Desert seismic data are often characterized by low signal-to-noise ratio (SNR) due to the fickle surface conditions and desert random noise with nonstationarity, nonlinearity, spatial directivity, and low-frequency characteristics. This low SNR is likely to affect the following inversion and interpretation. Therefore, robust noise attenuation is crucial to improve the SNR of desert seismic data. We propose a novel method alternating direction method of multipliers-based denoising convolutional neural network (ADMM-CNN) by combining low-rank decomposition with feed-forward denoising convolutional neural network (DnCNN). DnCNN is a deep-learning-based method for noise removal, which can make good noise attenuation performance through training. However, there is no feature extraction procedure before model learning in its structure, so DnCNN cannot make full use of the prior information of signals. Combining low-rank decomposition just addresses this issue. Compared with DnCNN, our method has two main novelties. First, we use the synthetic seismic data that resemble the characteristics of field desert seismic data and desert noise to train the ADMM-CNN. Second, we use ADMM to decompose the data into three layers (low-rank, sparse, and perturbation) which are used as the inputs of three channels neural network. Through this decomposition, the neural network can capture more features and prior information of desert seismic data. Both synthetic field data tests demonstrate the robuster performance of ADMM-CNN compared to traditional methods and DnCNN, also that the ADMM-CNN method suppresses the desert noise more thoroughly and greatly improves SNR of desert seismic data at the same time.

The low-frequency seismic noise has partially overlapping frequency band and similar waveform with seismic signals, making identification of seismic signals difficult in the seismic data at low signal-to-noise ratio (SNR). For improving the quality of seismic data, a deep complex reaction–diffusion (DCRD) model is proposed by combining the convolutional neural network (CNN) with the complex shock diffusion (CSD) which consists of a diffusion term and a shock term. By introducing a reaction term with an adjustable weight into the CSD, the CNN model can be embedded to learn the reaction term, leading to more effective signal preservation. The DCRD feeds smoothed signal components to the evolution process, by fusing the intermediate result based on low-level seismic features of data to be processed and the result of CNN model that learns deep seismic features. Moreover, the learnable reaction term facilitates the DCRD to apply effective diffusion for filtering out low-frequency seismic noise with spatiotemporally variable levels. Finally, the diffusion and shock terms in the DCRD can adjust the deviation of CNN model when the noise statistics of noisy seismic data having spatiotemporally variable levels deviate from training data, which also expand the practical application of CNN model. The DCRD is tested on synthetic and field seismic data and the results demonstrate that the DCRD achieves a great performance in suppressing low-frequency seismic noise with spatiotemporally variable levels and preserving seismic signals.

High-quality seismic exploration data are the basis of geological exploration. However, due to the increasingly complex environment in the exploration area, the signal-to-noise ratio (SNR) of seismic data is getting lower and lower. Eliminating noise is the most direct mean to improve the SNR and quality of seismic data. The Tarim Basin with a desert surface in China is rich in energy, but due to the variability of surface conditions, the desert noise has nonstationary, nonlinear, spatial directivity, low frequency, and other characteristics, which make noise attenuation very difficult. Aiming at this problem, we develop an extension of complex diffusion filter, namely approximate-message-passing-based complex diffusion, which is used to eliminate noise in desert seismic exploration data and enhance effective signals. Compared with the traditional complex diffusion, this letter adds a noise estimate in its diffusion processing, which improves the algorithm's ability to eliminate desert noise. The experimental results of synthetic and field seismic data show that the proposed method is more effective than other methods. Not only it can remove the noise and surface wave in the desert seismic record but also can preserve the effective signal. Therefore, we believe that the proposed method can provide a new idea for desert seismic signal processing.

In desert seismic records, random noise with complex characteristics such as nonstationary, non-Gaussian, nonlinear, and low-frequency will contaminate effective signals, which will greatly reduce the continuity and resolution of the seismic events. In order to achieve the requirements of high signal-to-noise ratio (SNR), high resolution, and high fidelity of seismic records after denoising, and to obtain high quality seismic exploration data, we present a method for suppressing low-frequency noise of desert seismic data, which combines variational mode decomposition (VMD) with low-rank matrix approximation algorithm. This method can further avoid the effect of spectrum aliasing on the denoising results because of using VMD. At first, the proposed method decomposes seismic signals into different modes by VMD and then arranges all modes into a signal matrix. An algorithm named OptShrink is used to extract the low-rank noise components, and great denoising effect is achieved by making a difference between the low-rank noise components and the original seismic record. The method is applied to synthetic desert seismic data and real desert seismic data. The experimental results show that the denoising effect of this method is better than that of previous methods in desert low-frequency noise. The effective signal remains intact, the resolution and continuity of the seismic events are improved obviously. The suppression of surface wave is also very thorough.

The convolutional neural network (CNN) has achieved excellent performance in many fields, which has attracted much attention. CNN is a kind of feedforward neural network with convolution computation and depth structure. In this letter, aiming at the intense interference of seismic exploration noise in the desert of China, a desert seismic noise reduction system based on deep residual encoder-decoder network is proposed. In order to extract the characteristics and variation law of desert seismic noise, a noise set containing a large number of desert seismic noise is utilized for training the network so that the network forms the end-to-end mapping between the noisy records and the noise. Consequently, the effective signals are obtained by subtracting noise from the noisy records so as to achieve a satisfactory denoising performance. Compared with the traditional random noise suppression methods, the advantages of the proposed method are fully demonstrated in the processing of the synthetic records and the field records. Especially when the signal-to-noise ratio (SNR) is very low, this proposed method can still have a very good denoising effect.

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.

The expected patch log likelihood (EPLL) is a patch-prior based denoising method which ensures denoising performance in ensemble approximation by local patch denoising. Basing on that, we propose a classification based EPLL method to attenuate seismic random noise, of which the level varies spatiotemporally. In EPLL method, the Gaussian mixture model (GMM) learned from samples is taken as a prior to statistically model patches, then the seismic signal is reconstructed by weighted averaging the noisy image and summation of denoised patches. Since the accuracy of the local statistic modeling and global signal reconstruction is related to the variance of the noise of the patches that have various noise variance in seismic image, we classify the patches into several groups in order to minimize the within-class variance. Therefore, appropriate regularization parameter and most likely prior are assigned to each patch according to the noise variance of the patch in EPLL. Experimental results of synthetic and field seismic data show that the classification based EPLL achieves a desired performance in seismic events preservation and nonstationary random noise attenuation.

Time picking is of great concern in the processing of microseismic data. However, the traditional method based on time/frequency domain cannot pick the first arrival time accurately in low signal-to-noise ratio. Besides, the traditional time picking methods which based on clustering are sensitive to selecting the initial clustering centers and easy to converge to local optimal value. To solve the above problems, we propose a time picking method for microseismic data based on locally linear embedding (LLE) and improved particle swarm optimization (PSO) clustering algorithm. First, the LLE algorithm can obtain the inherent characteristics and the rules hidden in high-dimensional data by calculating Euclidean distances and reconstruction weights between microseismic data points. The input is represented in a low-dimensional form. Then, the improved PSO clustering algorithm is used to select the optimal clustering centers from low-dimensional data through global search method. After that, the low-dimensional data can be classified into noise cluster and signal cluster by the K-means algorithm. Finally, the initial time of the signal cluster can be considered as the first arrival time of microseismic data. The experimental results show that accuracy of the proposed method is higher than that of the improved PSO clustering algorithm, Akaike information criterion method, and short- and long-time window ratio method (short-time window averaging/long-time window averaging).

Recently, the time-frequency peak filtering (TFPF) has been frequently applied to seismic random noise attenuation. Conventionally, TFPF recovers seismic events in association with a fixed window length along the time direction. Thus, the spatial information of the events is ignored. Moreover, TFPF is approximately equivalent to a time-invariant low-pass filter, which cannot adapt quickly enough to track the rapidly changing signal. To solve these problems, we propose a spatiotemporal adaptive TFPF (ST-ATFPF) algorithm. In this approach, we recover the events by the ATFPF, which is based on convex sets and Viterbi algorithm in intercept time-slowness domain. The high-resolution Radon transform concentrates the energy of the events effectively, and the correlations between wavelets, which form the events in a seismic record, are exploited by ST-ATFPF, consequently. Additionally, ST-ATFPF can track the rapidly changing signal. Numerical results have demonstrated the validity of our algorithm with higher output SNR and less signal information loss than the traditional TFPF, Radon TFPF, and ATFPF.

Seismic signals are nonlinear, and the seismic state-space model can be described as a nonlinear system. The particle filter (PF) method, as an effective method for estimating the state of a nonlinear system, can be applied to deal with seismic random noise attenuation. However, PF suffers from sample impoverishment caused by resampling, which results in serious loss of valid seismic information and leads to inaccurate representation of the reflected signal. To address the impoverishment issue and to further improve the particle quality, we propose a novel method to suppress seismic random noise-the adaptive fission particle filter (AFPF). In AFPF, all the particles undergo a fission process and produce “offspring” particles to maintain particle diversity. To implement the adaptation and to monitor the degree of fission, we apply a fission factor, which takes into account weights that indicate the quality of the particles. This leads to significant improvements in the particle quality, i.e., the proportion of highly weighted particles is increased. The effective seismic information provided by the resulting particles reproduces the true signal more reliably, reducing the bias of PF. In addition, we establish a dynamic state-space model suitable for seismic signals. Experimental results on synthetic records and field data illustrate the superior performance of AFPF in noise attenuation and reflected signal preservation compared with the PF.

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.

The time–frequency peak filtering (TFPF) algorithm is an effective method for seismic random noise attenuation. The conventional TFPF filters seismic data only along the channel direction, ignoring the spatial characteristics of the reflection events, which results in the loss of directional information. In order to improve the filtering performance of TFPF, we adopt a Radon transform to implement spatiotemporal 2-D TFPF, which is doing TFPF in the Radon domain. Since this method takes the spatial correlation of the reflection events into account, it could extract the reflection events better than the conventional TFPF. As the conventional Radon transform may produce a smearing phenomenon, we apply an improved least squares high-resolution Radon transform to assist TFPF in this letter. Thus, the events can be highly focused to energy points in different positions of the Radon domain. Then we identify the signal parts and process them by TFPF with short window length (WL). The other parts are considered as noise, and we process them by TFPF with long WL. By virtue of this new method, we can preserve the valid signal better and suppress the random noise more effectively. Through experiments on the synthetic seismic records and the field seismic data, the new method possesses a superior performance in random noise attenuation and seismic event preservation compared with the conventional TFPF and Radon TFPF methods.

Time-frequency peak filtering (TFPF) has been widely applied to suppress the random noise in seismic data in recent years. Conventional TFPF adopts a pseudo-Wigner-Ville distribution to ensure the approximate linearity of the signal. However, a short window length (WL) cannot effectively attenuate the random noise and a long WL can hardly recover the subtle structures of seismic events. In this letter, we discuss the different correlation integral values of signal and noise in the radial-trace domain for identifying the noise and signal segments. Then, a longer WL according to the noise intensity is used to remove the random noise and a shorter WL according to the frequency characteristics of the signal is used to preserve the details of the signal. The experiment results on both the synthetic model and the field seismic data show that this method can effectively remove noise from seismic record and maintain the amplitude of the valid signal.

Time-frequency peak filtering (TFPF) with fixed window length effectively attenuates random noise in seismic data, but performs well only for slow-varying seismic signals. To surmount the limitation, we propose the adaptive time-frequency peak filtering with the signal-dependent window length related to the belongings of seismic data to the signal, the signal nonlinearity and the local noise variance. The fuzzy c-means clustering algorithm is used to obtain the belongings in feature space, which incorporates spatial information including local similarity feature, local mean and local median in immediate neighborhood. As a result, the window length is set different for signal and noise and relatively small for the signal with high nonlinearity. We test the proposed method on both synthetic and field seismic data, and our experimental results illustrate that the adaptive method achieves better performance over the conventional TFPF both in random noise attenuation and the effective components preservation.

Time-frequency peak filtering (TFPF) is a classical filtering method in time-frequency domain. It applies Wigner-Ville distribution to estimate the instantaneous frequency of an analytical signal. There is a pair of contradiction in this method, i.e., selecting a short window length may lead to good preservation for signal amplitude but bad random noise reduction whereas selecting a long window length may lead to serious attenuation for signal amplitude but effective random noise reduction. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, we adopt empirical mode decomposition (EMD) to improve the TFPF results. The new idea is to utilize the decomposition characteristic of EMD which decomposes a signal to several modes from high to low frequency and to take advantage of the time-frequency filtering characteristic of TFPF which can recognize the valid signal component in the time-frequency plane in order to achieve effective random noise reduction together with good amplitude preservation. Through some experiments on synthetic seismic models and field seismic records, we show the better performance of the new method compared with the conventional TFPF.

In this letter, we research a spatiotemporal-domain-based time-frequency peak filtering (TFPF) method in order to remove the large error (bias) of the conventional TFPF in intermediate-frequency seismic record discrimination. An intermediate-frequency seismic signal is one whose dominant frequency is about 40 Hz or higher. To find a balance between noise attenuation and reflected signal preservation, the radial-trace TPFT (RT-TFPF) takes both the unbiased condition and the adjacent seismic traces' correlation into consideration, and uses the RT transform to obtain a reduced-frequency input to decrease the TFPF error. Therefore, this method can discriminate some reflection events weakened by the conventional TFPF algorithm. First, we decrease the intermediate frequencies along RTs nearly aligned with the reflection event. Then, we obtain a less biased TFPF estimation with suitable window length τ. Finally, we recover the original intermediate frequency with the inverse RT transform. With the RT-TFPF, we can enhance reflection events without sacrificing frequency components while attenuating as much random noise as possible. Experiments on both synthetic model and field data demonstrate that the RT-TFPF performs well both in random noise attenuation and intermediate-frequency preservation, in addition to presenting advantages over the conventional TFPF.

A novel method based on nonnegative matrix factorization (NMF) spectral unmixing is proposed for land seismic additive random noise attenuation. In the method, the noisy seismic signal is first decomposed into a collection of intrinsic mode functions (IMFs) instead of being directly processed. These IMFs can be considered as a new set of observations. In the short-time Fourier transform (STFT) spectrum of each IMF, the degree of mixing from the effective signal and the random noise is considerably reduced. Then, a sparse NMF is used to unmix the STFT spectrum of each IMF. We get the subsignals out of the separated subspectrums by the inverse STFT. Finally, the desired signal is reconstructed from the subsignals by$K$-means clustering algorithm. Experimental results of both synthetic and real seismic records show that the proposed method can significantly suppress random noise and preserve the effective signal components. Comparisons with time–frequency peak filtering and$f{-}x$filtering further verify its better performance.