In seismic data processing, denoising is one of the important steps to identify the earth’s subsurface layer information. The erratic noise attenuation is always challenging due to the unknown distribution of high-amplitude peaks over seismic data. In literature, the double sparsity dictionary learning (DSDL) methods were used for erratic and random noise attenuation. Here, analytical and adaptive transformations are performed sequentially to attenuate erratic and random noises. However, the DSDL technique leads to a high computational cost due to the K-SVD. Therefore, we propose a double-dictionary learning (DDL) method to denoise both random and erratic noise by preserving the signal features from seismic data. The method uses two parallel adaptive dictionaries for simultaneous denoising, and both dictionaries are concatenated further to form a comprehensive dictionary. The regularized K-SVD was used to update the dictionary and sparse coefficients for signal preservation. The DDL method effectively reduced the computational costs. The DDL method was applied to different synthetic and field datasets for denoising. The numerical results show that the proposed method provides a higher signal-to-noise ratio (SNR), lower mean squared error (MSE), and less signal leakage than existing state-of-the-art denoising methods.

In seismic data processing, denoising is one of the essential steps to identifying the earth’s subsurface layer information. The noise present in the seismic data is categorized into two types: random and erratic noise. The random noise is distributed uniformly over the seismic data. The erratic noise attenuation is always challenging due to the unknown distribution of high-amplitude peaks over seismic data. The existing double sparsity dictionary learning (DSDL) method performs with analytical and adaptive transforms; both the transforms include iterative algorithms with K-singular-value decomposition (SVD); it is computationally costly, and the dictionary is initialized with trained data. To address these limitations, we propose a novel method of dictionary learning with double regularization (DLDR) to denoise both random and erratic noise from seismic data. In double regularization, we used with$\ell _{1}$-norm and nuclear norm. The denoised data is applied to the alternating direction method of multipliers (ADMMs) to improve denoising while preserving the signal features from seismic data while reducing the computational cost. We evaluated the performance of the proposed method using signal-to-noise ratio (SNR), mean squared error (MSE), and local similarity map. The numerical results demonstrated that the proposed method resulted in higher SNR, lower MSE, and less signal leakage from seismic data. The method gives precise interpretation from the denoised seismic data.

The knowledge of hidden resources present inside the earth layers is vital for the exploration of petroleum and hydrocarbons. However, the recorded seismic data is noisy and incomplete with missing traces that leads to misinterpretation of the earth layers. In this manuscript, we consider seismic data with Gaussian, non-Gaussian noise distribution, regular and irregular missing traces. We propose a method for simultaneous noise attenuation and reconstruction of the incomplete seismic data with attention based wavelet convolutional neural network (AWUN). The wavelet transform is used as pooling layer and inverse wavelet transform is used for upsampling layers to avoid information loss. The attention module is used to obtain weights for various feature channels with higher weights assigned to the more significant information. In addition, we propose to use hybrid loss function (logcosh + huberloss) to denoise and accurately reconstruct the seismic data. Moreover, the effect of various hyper-parameters in the training process of convolutional neural networks is studied. Further, we tested the performance of proposed method on synthetically generated data and field data examples. The quantitative results demonstrated that our proposed deep learning method has shown improved signal-to-noise ratio (SNR) and mean squared error (MSE) when compared to the existing state-of-the-art methods.

In seismic data processing, denoising is one of the important steps to get the earth subsurface layers’ information accurately. The dictionary learning (DL) method is one of the prominent methods to denoise the seismic data. In the DL method, there are various parameters involved for denoising such as patch size, dictionary size, number of training patches, choice of threshold, sparsity level, computational cost, and number of iterations for DL. In this work, we study each parameter and its effects on seismic denoising in terms of signal-to-noise ratio and mean square error between the true and denoised seismic data. We examined the performance of the DL method on synthetic and field seismic data for various choices of parameters.

In seismic data processing, attenuation of erratic noise is a challenging task due to the unknown noise distribution. Erratic noise consists of high amplitude peaks and conventional sparse transforms based on least-square (LS) approach that is not appropriate for erratic noise attenuation. An alternative approach, where the data with erratic noise are transformed into pseudodata and then denoised based on fast discrete curvelet transform with structure-oriented space-varying median filtering, is performed and achieves better attenuation. However, the fast discrete curvelet transform with a fixed basis lacks the adaptivity for various data patterns of seismic data. Hence, in this article, we propose a double sparsity dictionary learning (DSDL) method which performs denoising and also preserves the original features of seismic data. The proposed method combines the strength of the analytical transform and adaptive transform to attenuate both random noise and erratic noise in data. The performance of proposed DSDL method is studied on synthetic datasets and field datasets. The numerical results demonstrate that the proposed method gives a better signal-to-noise ratio (SNR), a lower mean-squared error, and energy values for the denoised data in comparison to the existing methods.

Real seismic data consist of multiple traces captured by an array of receivers. These multiple traces are sorted by the common midpoint between the source and the receiver, and the time-lag between different traces is corrected by a normal move-out correction process. After these preprocessing steps, the sorted traces contain the same information about the earth sublayers and are corrupted by noise. The next step, termed stacking in seismic signal processing, involves the construction of an optimum trace with an improved signal-to-noise ratio (SNR) from these sorted traces. In this letter, we present an improved method for weighted stacking, where each trace is weighed in accordance with the noise variance. Using the first-order derivative property of Ramanujan sums, we perform the estimation of noise variance in each trace. Numerical results demonstrate that the method presented in this letter has better SNR for the trace obtained after stacking in comparison with existing methods.

An accurate and effective seismic wavelet estimation technique has extreme significance in the seismic data processing for analyzing the earth's subsurface layer information. The seismic wavelet to be determined is modeled as a moving average (MA) process and assumed to be driven by a zero mean, non-Gaussian, statistically independent, and identically distributed (IID) process. In order to estimate the MA model parameter from the observed noisy seismic signal, we pose this as a blind system identification (BSI) problem. In the BSI, a set of multivariate polynomial equations is obtained by matching higher order cumulant of observed noisy data with a higher order moment of blind system's impulse response. The Groebner bases that form the solution to this set of equations are obtained using the proposed algorithm. Numerical results demonstrate that the proposed method has a lower estimation error as compared to the previously reported methods.

Denoising is one of the core steps in seismic data processing flow. The seismic gather consists of multiple traces captured at different receivers. A set of receivers observe waves which are reflected from the same reflection point. Those traces need to be grouped together as they contain the same information about the earth subsurface layers. This is done by finding a common mid‐point (CMP) between the source and geophones. The time delay between CMP gathered traces are corrected by the normal move out correction method but the individual traces are corrupted by noise. In this paper we, propose a method for denoising individual traces. The set of traces can be modelled as belonging to a low‐dimensional subspace of an ambient signal space. This allows for construction of sparse representations of each trace in terms of other traces in the CMP gather. The resulting sparse representations are subsequently utilised to construct approximations of individual traces and thus, noise is suppressed. We constructed, the approximations using orthogonal matching pursuit. We applied proposed method to synthetic and field seismic data, the proposed technique performs better on established benchmarks while capturing the true locations of weak reflections and effectively attenuating the random noise.