In this letter, an improved differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional evolutionary algorithms, an individual is treated as a whole, and all its variables (genes) are evaluated with a uniform fitness function. This evaluation criterion is not effective for a high-dimensional individual. Therefore, for high-dimensional waveform inversion, we incorporate the decomposition strategy of cooperative coevolution into DE to decompose the individual into some subcomponents. Another novel feature that we introduce is a local fitness function for each subcomponent, and a new mutation operator is designed to guide the mutation direction of each subcomponent with the corresponding local fitness value. Coevolution among different subcomponents is realized in the selection operation with the global fitness function. Many experiments have been carried out to evaluate the performance of this new algorithm. The results clearly show that, for high-dimensional waveform inversion, this algorithm is effective and performs better than some other methods. Finally, the new method has been applied to real seismic data.

When reconstructing seismic data, the traditional singular value decomposition (SVD) denoising method has the challenge of difficult rank selection. Therefore, we propose a seismic data denoising method that combines SVD and deep learning. In this method, seismic data with different signal-to-noise ratios (SNRs) are processed by SVD. Data sets are created from the decomposed right singular vectors and data sets divided into two categories: effective signal and noise. The lightweight MobileNetV2 network was chosen for training because of its quick response speed and great accuracy. We forecasted and categorized the right singular vectors by SVD using the trained MobileNetV2 network. The right singular vector (RSV) corresponding to the noise in the seismic data was removed during reconstruction, but the effective signal was kept. The effective signal was projected to smooth the RSV. Finally, the goal of low SNR denoising of two-dimensional seismic data was accomplished. This approach addresses issues with deep learning in seismic data processing, including the challenge of gathering sample data and the weak generalizability of the training model. Compared with the traditional denoising method, the improved denoising method performs well at removing Gaussian and irregular noise with strong amplitudes.

S waves travel slower than P waves and have a lower dominant frequency. Therefore, applying common techniques such as time–frequency filtering and f-k filtering to separate S waves from ground roll is difficult because ground roll is also characterized by slow velocity and low frequency. In this study, we present a method for attenuating ground roll using a polarization filtering method based on the t-f-k transform. We describe the particle motion of the waves by complex vector signals. Each pair of frequency components, whose frequencies have the same absolute value but different signs, of the complex signal indicate an elliptical or linear motion. The polarization parameters of the elliptical or linear motion are explicitly related to the two Fourier coefficients. We then extend these concepts to the t-f-k domain and propose a polarization filtering method for ground roll attenuation based on the t-f-k transform. The proposed approach can define automatically the time-varying reject zones on the f-k panel at different times as a function of the reciprocal ellipticity. Four attributes, time, frequency, apparent velocity and polarization are used to identify and extract the ground roll simultaneously. Thus, the ground roll and body waves can be separated as long as they are dissimilar in one of these attributes. We compare our method with commonly used filtering techniques by applying the methods to synthetic and real seismic data. The results indicate that our method can attenuate ground roll while preserving body waves more effectively than the other methods.

As a powerful optimization algorithm for solving nonlinear, complex and tough global optimization problems, differential evolution (DE) has been widely applied in various science and engineering fields. In this paper, considering that the evolution direction of each individual is not fully exploited to guide the search process in most DE algorithms, a new DE variant ( named ADEwSE), which incorporates the successful experience of evolved individuals into classic “current-to-pbest/1” mutation strategy to reduce the randomness of search direction, is proposed. Moreover, crossover matrix sorting scheme based on real crossover rate, opposition learning of crossover rate and adaptive adjustment of top p% values are combined with the new mutation strategy to improve the global search ability. In addition, to improve the searching ability of ADEwSE further, an ADEwSE variant by introducing the linear reduction of population size is proposed. In order to verify and analyze the performance of ADEwSE, numerical experiments on a set of 29 test problems from CEC2017 benchmark for 30, 50 and 100 dimensions are executed. And the experimental results are compared with that of 21 state-of-art DE-based algorithms. Comparative analysis indicates that the ADEwSE and its improved version are competitive with these state-of-art DE variants in terms of solution quality obtained.

Reduced-rank filtering is a common method for attenuating noise in seismic data. Because conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio (S/N) is very low or when data contain high levels of isolate or coherent noise. Therefore, we have developed a novel and robust reduced-rank filtering method based on singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of the singular values and the singular vectors. The left and right singular vectors corresponding to large singular values are selected first. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and it is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing, or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes such as main frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of the event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low S/N, strong isolated noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.