Seismic data denoising is a crucial and challenging task for high-quality seismic exploration. Recent advancements in deep learning methods have demonstrated promising results in seismic denoising. However, the acquisition of ground truth data required for training remains unavailable, especially in field tests. We propose an unsupervised deep denoiser called the iterative diffusion denoising model (IDDM) based on a diffusion model to remove random noise. We present the diffusion process of IDDM according to the seismic noise model and the two-stage reverse process to iteratively train a deep restorer with the data pair created solely from the observed data. Hence, the IDDM is learned to approximate the reverse diffusion process of the seismic data, which leads to the effective seismic signal recovery and robustness to the variant noise level and complex distribution of the field seismic data. Moreover, the invariant features between adjacent states are introduced to the generative denoising model by the signal preserving module, enabling IDDM to gradually recover the effective seismic signals in high fidelity while thoroughly suppressing noise using only noisy data. The proposed approach shows excellent denoised results in synthetic and field data tests at low signal-to-noise ratios (SNRs), demonstrating its potential for practical applications in seismic data processing.

Seismic random noise attenuation is an essential procedure when processing seismic data. Due to various acquisition environments and complex geological conditions, random noise in seismic field data exhibits spatiotemporal levels, significantly increasing the difficulty of extracting seismic signals. The deep learning (DL) methods have shown excellent performances for seismic denoising. However, most existing discriminative DL methods cannot fit field data with noise levels and signal structures that differ from the training set. To tackle the unmatching challenge, we propose a self-supervised deep denoising model named noise estimation-based convolution neural network (NE-CNN), which contains a multiscale denoising module as a pretrained model and a dual-path noise estimation module that estimates the noise level of each data patch with a generalized Gaussian distribution and gray-level co-occurrence matrix (GLCM). With Stein’s unbiased risk estimate (SURE), we can fine-tune the pretrained denoising module according to the estimated noise levels in a self-supervised style solely on data to be processed, leading to a boost of robustness to nonstationary seismic noise. In synthetic and field data tests, NE-CNN performed satisfactorily compared with discriminative DL methods in denoising effects on seismic data with nonstationary noise.

Seismic random noise suppression presents two main challenges: achieving thorough noise suppression while simultaneously ensuring complete restoration of effective signal content. However, due to the complexity of random noise, existing denoising methods often only achieve an awkward balance between removing random noise and restoring effective signals. In this paper, we propose a novel random noise suppression model based on downsampling and super-resolution. By decoupling the denoising and signal restoration processes, our method reduces the difficulty of addressing these two challenges and mitigates the likelihood of suboptimal results. On the one hand, the high fitting-capacity Downsampling network uses non-linear transformations to separate random noise and effective signals while purifying the high-order features of effective signals. On the other hand, the Super-resolution network expands the low-dimensional seismic signal content containing the high-order features of the signal to restore the signal structure. Moreover, we propose a new adversarial loss by introducing the gradient between the generated data and the real data, which enhances the perceptual quality of the super-resolution results and recovers the content of effective signals better. Because both subnetworks are not affected by signal/noise features during processing, the model exhibits strong fitting and generalization abilities. The experimental evaluation on four different types of seismic data demonstrates the superiority of our method in suppressing random noise and restoring the content of effective signals.

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.

Low-frequency random noise in the desert seismic data severely obscures the effective information contained in the seismic data due to its similarity to seismic signals. To suppress desert seismic random noise, we propose a novel mask-guided seismic data denoising model (MGDNet) by introducing the signal semantics to guide the deep denoising network. The MGDNet consists of two subnetworks. The first subnetwork utilizes a shallow convolutional network to predict the mask that represents the semantics of the signal contained in the noisy seismic data. The second subnetwork based on the Siamese network combines the global location information of the signal in the mask to learn the difference between low-frequency noise features and signal features so that the following denoising network can estimate the seismic signals. The MGDNet utilizes the signal semantics to guide the denoising process so that the global features associated with the seismic events can be preserved well even obscured by random noise with similarity. The results on the simulated data, public dataset, and field seismic data show that our method achieves significant effects on the suppression of desert random noise and the restoration of the signal structure.

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.

Seismic random noise reduction is an indispensable step in seismic data processing. Due to complex geological condition and acquisition environment, random noise in the desert seismic data has spatiotemporally variant noise levels and weak similarity to the signals, which severely obscures the seismic signals and increases the difficulty to extract the reflected seismic signals. This letter focuses on suppressing the desert random noise based on a convolutional neural network (CNN) and proposes a branch construction-based denoising network (BCDNet). The BCDNet contains a denoising main network and a branched network added to the downsampled layer of the main network. With the branched network, the global context feature of the seismic data is obtained early in the network to guide the denoising task of the subsequent main network, which allows a flexible denoising for the desert random noise. Moreover, the downsampled layer is able to enlarge the receptive field of the network without increasing the network depth, thus leading to the better retention of the structural features in the seismic records. The extensive experiments and the field desert data application confirm that our BCDNet not only has a significant denoising capacity to desert seismic data but also is competitive in training time and memory cost.

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.

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.

In this letter, we have applied a new filtering method for the simultaneous noise reduction and enhancement of seismic signals using a fractal conservation law, which is simply a partial differential equation (PDE) modified by a nonlocal fractional antidiffusive term of lower order. By using an integral formula, which is based on Taylor-Poisson's formula and Fubini's theorem for an antidiffusive term, and then taking the fast Fourier transform of the PDE, the filter in the frequency domain can be derived. The study showed that this filter eliminates the high frequencies, amplifies the medium frequencies, and preserves the low frequencies. Thus, some features of the signal, such as relative maxima or minima, can be preserved or even amplified. Usually, these features are flattened by other denoising methods. The properties of this novel method are tested on both synthetic seismic data and real common shot point seismic records. Additionally, we compared this method with time-frequency peak filtering (TFPF), which has a good performance under low signal-to-noise ratio. The experimental results illustrate the superior performance of our method versus TFPF in the recovery of seismic events by removing random noise and enhancing valid signal.

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) 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.

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.

The time-frequency peak filtering (TFPF) technology is applied for recovering seismic events without loss of valid information. By using frequency modulation signal encoding and taking peak of Wigner-Ville distribution (WVD) of encoded analytic signal, valid reflect signals constructing seismic events are estimated. To reduce the deterministic bias of TFPF resulted from nonlinearity of seismic reflect signal, the pseudo WVD (PWVD) TFPF is utilized. The reduced bias window length is derived by analyzing bias from experimental resulting. Testing of this method on synthetic seismic data and common shot point recordings indicates that TFPF technique significantly enhances signals from noisy seismic data and improves the continuity of seismic events by filtering out most of the additive noise. The resulting shows the clean recovery of seismic events in noise level down to a signal-to-noise ratio of-2.4dB.