Because a high signal-to-noise ratio (SNR) is beneficial to the subsequent processing procedures, the noise attenuation is important. We propose an adaptive random noise attenuation framework based on convolutional neural networks (CNNs). The framework transforms the target function from effective signal learning to noise learning through residual learning, so as to improve the training efficiency. After sufficient training, the network transfers the learned seismic data features using a large synthetic data set to the testing of complex field data with unknown noise levels and, thus, attenuates the noise in an unsupervised way. Unsupervised noise reduction requires certain representativeness of the training data and a sufficient amount of training data sets. In the network architecture, we introduce residual learning and batch normalization (BN) to reduce the training parameters of the network, thereby shortening the time for feature learning. The activation function with leakage correction function can effectively retain negative information, and its combination with the double convolutional residual block can enhance the generalization ability and feature extraction performance of the network. In the test of synthetic data and complex field data with unknown noise levels, by comparing the noise reduction results of some classic denoising algorithms, the adaptive CNN proposed in this article can more effectively attenuate the noise and reconstruct the seismic waveform.

A sparse dictionary is more adaptive than a sparse fixed-basis transform since it can learn the features directly from the input data in a data-driven way. However, learning a sparse dictionary is time-consuming because a large number of iterations are required in order to obtain the dictionary atoms that best represent the features of input data. The computational cost becomes unaffordable when it comes to high-dimensional problems, e.g., 3-D or even 5-D applications. We propose an efficient high-dimensional dictionary learning (DL) method by avoiding the singular value decomposition (SVD) calculation in each dictionary update step that is required by the classic K-singular value decomposition (KSVD) algorithm. Besides, due to the special structure of the sparse coefficient matrix, it requires a much less expensive sparse coding process. The overall computational efficiency of the new DL method is much higher, while the results are still comparable or event better than those from the traditional KSVD method. We apply the proposed method to both 3-D and 5-D seismic data reconstructions and demonstrate successful and efficient performance.

We have developed a new method for simultaneous denoising and reconstruction of 5D seismic data corrupted by random noise and missing traces. Several algorithms have been developed for seismic data restoration based on rank-reduction (RR) methods. More recently, a damping operator has been introduced into the conventional truncated singular-value decomposition (TSVD) formula to further remove residual noise, the presence of which disturbs the quality of the seismic results. Despite the success of the damped RR (DRR) method when the observed data have an extremely low signal-to-noise ratio (S/N), random noise is still a limiting factor for obtaining a perfect quality of the result. Therefore, how to accurately solve the simultaneous denoising and reconstruction problem with high fidelity is still challenging. We assume that introducing only the damping operator into the TSVD formula is not enough to remove the random noise and restore the useful signal well. By combining the soft thresholding (ST) operator and the moving-average (MA) filter, we have developed a new operator, which we call the STMA operator. Then, by introducing the STMA operator into the DRR framework, we have developed a new algorithm known as the robust DRR method, which aims at mixing the advantages of the STMA operator and the damping operator. The STMA operator is applied to the Hankel matrix after damped TSVD to better remove residual noise. Examples of our approach on synthetic and field 5D seismic data demonstrate the better performance in terms of the visual examination and numerical test compared with the DRR approach. Our method aims at producing an effective low-rank filter and, thus, can perfectly enhance the S/N of the simultaneously denoised and reconstructed results with higher accuracy.

Predictive filtering (PF) in the frequency domain is one of the most widely used denoising algorithms in seismic data processing. PF is based on the assumption of linear or planar events in the time-space domain. In traditional PF methods, a predictive filter is fixed across the spatial dimension, which cannot deal with spatial variations in seismic data well. To handle the curved events, the predictive filter is either applied in local windows or extended into a nonstationary version. The regularized nonstationary autoregression (RNAR) method can be treated as a nonstationary extension of traditional PF, in which the predictive filter coefficients are variable in different spatial locations. This highly underdetermined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to the more general case, in which we can apply more constraints to the filter coefficients according to the features of seismic data. First, apart from the smoothness in space, we also apply a smoothing constraint in frequency, considering the coherency of the coefficients in the frequency dimension. Second, we apply a frequency-dependent smoothing radius in the spatial dimension to better take advantage of the nonstationarity of seismic data in the frequency axis and to better deal with noise. The effectiveness of our method is validated using several synthetic and field data examples.

Distributed acoustic sensing (DAS) is a new technology for recording vibration signals using optical fibers, and is advantageous over traditional seismic geophones given high spatial sampling density, real-time monitoring capabilities and relatively low cost for large-scale data acquisition. In recent years, progress in applications of the DAS technique has been achieved in near-surface imaging, earthquake detection, and urban traffic monitoring. In this study, we propose to apply a machine learning (ML) method to recognize and extract vehicle signals from DAS data acquired in a typical urban environment in Hangzhou, China. To design an efficientML framework, we apply a series of processing steps to eliminate noise and strengthen the vehicle signal, which is crucial for preparing high-quality labels. Initially, a total of 190 features (62 1-D features and 128 2-D features) are extracted from raw data, which are filtered down to 31 through univariate feature selection, random forest, and similarity analyses. These selected features are classified into (traffic) signal or (non-traffic) noise using the classic ML method of support vector machine (SVM). The resulting model enables robustly extracting vehicle signals with only a small (e.g., 10) training dataset and achieve an overall accuracy of about 80% on the test data. We further demonstrate the application of city traffic monitoring by considering the slope and coherence of the extracted vehicle signals. The preservation of car signals leads to a more accurate estimate in vehicle speed and volume. This study highlights the potential of real-time monitoring of speed and volume of traffic flow using existing city infrastructure and sheds light on the promising applications of the DAS technique in developing smart cities.

Local slope is an important attribute that can help distinguish seismic signals from noise. Based on optimal slope estimation, many filtering methods can be designed to enhance the signal-to-noise ratio of noisy seismic data. We present an open-source MATLAB code package for local slope estimation and corresponding structural filtering. This package includes 2D and 3D examples with two main executable scripts and related subfunctions. All code files are in the MATLAB format. In each main script, local slope is estimated based on the well-known plane-wave destruction algorithm. Then, the seismic data are transformed to the flattened domain by utilizing this slope information. Furthermore, the smoothing operator can be effectively applied in the flattened domain. We introduce the theory and mathematics related to these programs and present the synthetic and field data examples to show the usefulness of this open-source package. The results of local slope estimation and structural filtering demonstrate that this package can be conveniently and effectively applied to the seismic signal analysis and denoising.