Random noise elimination acts as an important role in the seismic signal processing. Generally, noise in seismic data can be divided into two categories of coherent and incoherent or random noise. Suppression of wide-band noise which is characterized by random oscillation in seismic data over time is one of the challenging issues in the seismic data processing. This paper describes a new noise suppression algorithm for seismic data denoising. The seismic data, trace-by-trace are transformed into sparse subspace using the synchrosqueezed wavelet transform, then the obtained sparse time-frequency representation is decomposed into semilow-rank and sparse components using the Optshrink algorithm. Finally, the denoised seismic trace can be recovered by back-transforming the semilow-rank component to the time domain using inverse synchrosqueezed wavelet transform. The proposed method is assessed using a single synthetic seismic trace and a synthetic seismic section with two crossover linear and curve events with two discontinuities that are buried in the random noise. We have also evaluated the method using a prestack real seismic data set from an oil field in the southwest of Iran. A comparison is performed between the proposed method and the semisoft GoDec algorithm, classical f-x singular spectrum analysis, and prediction Wiener filter. The results visually and quantitatively confirmed the superiority of the proposed method in contrast to the other well-established noise reduction methods.

Representation of a signal in a sparse way is a useful and popular methodology in signal-processing applications. Among several widely used sparse transforms, dictionary learning (DL) algorithms achieve most attention due to their ability in making data-driven nonanalytical (nonfixed) atoms. Various DL methods are well-established in seismic data processing due to the inherent low-rank property of this kind of data. We have introduced a novel data-driven 3D DL algorithm that is extended from the 2D nonnegative DL scheme via the multitasking strategy for random noise attenuation of seismic data. In addition to providing parts-based learning, we exploit nonnegativity constraint to induce sparsity on the data transformation and reduce the space of the solution and, consequently, the computational cost. In 3D data, we consider each slice as a task. Whereas 3D seismic data exhibit high correlation between slices, a multitask learning approach is used to enhance the performance of the method by sharing a common sparse coefficient matrix for the whole related tasks of the data. Basically, in the learning process, each task can help other tasks to learn better and thus a sparser representation is obtained. Furthermore, different from other DL methods that use a limited random number of patches to learn a dictionary, the proposed algorithm can take the whole data information into account with a reasonable time cost and thus can obtain an efficient and effective denoising performance. We have applied the method on synthetic and real 3D data, which demonstrated superior performance in random noise attenuation when compared with state-of-the-art denoising methods such as MSSA, BM4D, and FXY predictive filtering, especially in amplitude and continuity preservation in low signal-to-noise ratio cases and fault zones.

Attenuation of random noise is a major concern in seismic data processing. This kind of noise is usually characterized by random oscillation in seismic data over the entire time and frequency. We introduced and evaluated a low-rank and sparse decomposition-based method for seismic random noise attenuation. The proposed method, which is a trace by trace algorithm, starts by transforming the seismic signal into a new sparse subspace using the synchrosqueezing transform. Then, the sparse time-frequency representation (TFR) matrix is decomposed into two parts: (a) a low-rank component and (b) a sparse component using bilateral random projection. Although seismic data are not exactly low-rank in the sparse TFR domain, they can be assumed as being of semi-low-rank or approximately low-rank type. Hence, we can recover the denoised seismic signal by minimizing the mixed ${\ell }_1‐{\ell }_2$ norms’ objective function by considering the intrinsically semilow-rank property of the seismic data and sparsity feature of random noise in the sparse TFR domain. The proposed method was tested on synthetic and real data. In the synthetic case, the data were contaminated by random noise. Denoising was carried out by means of the $f\text{-}x$ classical singular spectrum analysis (SSA) and $f\text{-}x$ deconvolution method for comparison. The $f\text{-}x$ deconvolution and the classical $f\text{-}x$ SSA method failed to properly reduce the noise and to recover the desired signal. We have also tested the proposed method on a prestack real data set from an oil field in the southwest of Iran. Through synthetic and real tests, the proposed method is determined to be an effective, amplitude preserving, and robust tool that gives superior results over classical $f\text{-}x$ SSA as conventional algorithm for denoising seismic data.

Reducing uncertainty in geologic interpretation of petroleum reservoir containing thin layers requires increasing vertical resolution via appropriate advanced resolution enhancement methods. This problem was resolved here by introducing an alternative approach in resolution enhancement. Our method uses Gabor deconvolution (GD) combined with wavelet scaling. First, the seismic trace is transformed in the time-frequency domain using the Gabor transform. Subsequently, the Gabor magnitude spectrum of the seismic trace is smoothed to estimate the wavelet magnitude, which is then divided by the original value on the Gabor magnitude spectrum along the frequency axis to design a scale transformation filter. Finally, the filtered Gabor magnitude spectrum of the seismic trace is transformed back to the time domain using an inverse Gabor transformation. The result of using this technique is an increase of the dominant frequency, which produces a higher resolution of the seismic trace compared with using only the original GD. This method was applied to two synthetic and one field seismic data sets and compared with using only a GD. After applying the new approach, all three data sets indicate an extension in bandwidth (BW) and an enhancement in the resolution adequate for thin-layer seismic interpretation. When compared with the data sets using only a GD, the new approach produced comparable extension in the effective BW, while it pushing the dominant frequency to higher values. This allowed the imaging of many thin layers and geologic intervals in the field data example that could not be interpreted by the GD method.