The low-rank approximation method is one of the most effective approaches recently proposed for attenuating random noise in seismic data. However, the low-rank approximation approach assumes that the seismic data has low rank for its f - x domain Hankel matrix. This assumption is seldom satisfied for the complicated seismic data. Besides, the low-rank approximation approach is usually implemented in local windows in order to satisfy the principal assumption required by the algorithm itself. When implemented in local windows, the rank is even more difficult to choose because the seismic data is highly nonstationary in both time and spatial dimensions and the optimal rank for different local windows is not consistent with each other. In order to preserve enough useful energy, one needs to set a relatively large rank when implementing the low-rank approximation method, which makes the traditional method incapable of attenuating enough noise. Considering such difficulties described above, we propose an empirical low-rank approximation approach. We adaptively decompose the input data into several components that have truly low ranks via empirical mode decomposition. An interpretation of the proposed empirical low-rank approximation method is that we empirically decompose a multi-dip seismic image that is not of low rank into multiple single-dip seismic images that are low-rank individually. We use both synthetic and field data examples to demonstrate the superior performance of the proposed approach over traditional alternatives.

The cost of obtaining a complete porosity value using traditional coring methods is relatively high, and as the drilling depth increases, the difficulty of obtaining the porosity value also increases. Nowadays, the prediction of fine reservoir parameters for oil and gas exploration is becoming more and more important. Therefore, high-efficiency and low-cost prediction of porosity based on logging data is necessary. We have developed a machine-learning method based on the traditional long short-term memory (LSTM) model, called multilayer LSTM (MLSTM), to perform the porosity prediction task. We used three different wells in a block in southern China for the prediction task, including a training well and two test wells. One test well has the same logging data type as the training well, whereas the other test well differs from the training well in the logging depth and parameter types. Two different types of test data sets are used to detect the generalization ability of the network. A set of data was used to train the MLSTM network, and the hyperparameters of the network were adjusted through experimental accuracy feedback. We also tested the performance of the network using two sets of log data from different regions, including generalization and sensitivity of the network. During the training phase of the porosity prediction model, the developed MLSTM establishes a minimized objective function, uses the Adam optimization algorithm to update the weight of the network, and adjusts the network hyperparameters to select the best target according to the feedback of the network accuracy. Compared with conventional sequence neural networks, such as the gated recurrent unit and recurrent neural network, the logging data experiments show that MLSTM has better robustness and accuracy in depth sequence prediction. Especially, the porosity value at the depth inflection point can be better predicted when the trend of the depth sequence was predicted. This framework is expected to reduce the porosity prediction errors when data are insufficient and log depths are different.

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.

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.

Empirical wavelets transform (EWT) is a fully adaptive signal-analysis approach, which is similar to the empirical mode decomposition (EMD) but has a consolidated mathematical theory, and is appealing in designing automatic algorithm for a variety of signal processing tasks. EWT first estimates the frequency components presented in the given signal, then computes the boundaries, and extracts the oscillatory components based on the computed boundaries. Because of the superb performance of the EWT in decomposing nonlinear and non-stationary signals, it has been successfully applied into a number of problems. The last 6 years have seen the development of EWT. This paper presents a general overview of the recent advancements made in research on the EWT algorithm and its state-of-the-art applications in a wide range of areas such as machine fault diagnosis, seismic data analysis, image processing, power system monitoring and medical disease diagnosis, which aims at providing some comprehensive references for reader concerning with EWT. We place emphasis on the applications of using such signal-analysis algorithm throughout with illustrative examples. Finally, the potential avenues for the future trends and directions associated with EWT are discussed.

We have determined an approach for simultaneous reconstruction and denoising of 3D seismic data with randomly missing traces. The core in simultaneous reconstruction and denoising of 3D seismic data is the choice of constraint method. Recently, there have been two types of popular approaches to choose such a constraint: sparsity-promoting transforms using a sparsity constraint and rank reduction methods using a rank constraint. Although the sparsity-promoting transform enjoys the direct advantage of high efficiency, it lacks adaptivity to a variety of data patterns. On the other hand, the rank reduction method can be adaptively applied to different data sets, but its computational cost is quite high. We investigate multiple constraints for simultaneous seismic data reconstruction and denoising based on a novel hybrid rank-sparsity constraint (HRSC) model, which aims at combining the benefits of the sparsity-promoting transforms and rank reduction methods. Also, we design the corresponding HRSC algorithmic framework to effectively solve our new model via tightly combining a sparsity-promoting transform and a rank reduction method, which is more powerful in simultaneous reconstruction and denoising of 3D seismic data. Our HRSC framework aims at providing an extra level of constraint and, thus, can significantly improve the signal-to-noise ratio (S/N) of the reconstructed results with higher efficiency. Application of the HRSC framework on synthetic and field 3D seismic data demonstrates superior performance in terms of S/N and visual observation compared with the well-known rank reduction method, known as multichannel singular spectrum analysis.