A new paper is added to the collection of reproducible documents: Noniterative f-x-y streaming prediction filtering for random noise attenuation on seismic data

Random noise is unavoidable in seismic exploration, especially under complex-surface conditions and in deep-exploration environments. The current problems in random noise attenuation include preserving the nonstationary characteristics of the signal and reducing computational cost of broadband, wide-azimuth, and high-density data acquisition. To obtain high-quality images, traditional prediction filters (PFs) have proved effective for random noise attenuation, but these methods typically assume that the signal is stationary. Most nonstationary PFs use an iterative strategy to calculate the coefficients, which leads to high computational costs. In this study, we extended the streaming prediction theory to the frequency domain and proposed the f-x-y streaming prediction filter (SPF) to attenuate random noise. Instead of using the iterative optimization algorithm, we formulated a constraint least-squares problem to calculate the SPF and derived an analytical solution to this problem. The multi-dimensional streaming constraints are used to increase the accuracy of the SPF. We also modified the recursive algorithm to update the SPF with the snaky processing path, which takes full advantage of the streaming structure to improve the effectiveness of the SPF in high dimensions. In comparison with 2D f-x SPF and 3D f-x-y regularized nonstationary autoregression (RNA), we tested the practicality of the proposed method in attenuating random noise. Numerical experiments show that the 3D f-x-y SPF is suitable for large-scale seismic data with the advantages of low computational cost, reasonable nonstationary signal protection, and effective random noise attenuation.

A new paper is added to the collection of reproducible documents: Seismic data interpolation using streaming prediction filter in the frequency domain

Surface conditions and economic factors restrict field geometries, so seismic data acquisition typically obtains field data with irregular spatial distribution, which can adversely affect the subsequent data processing and interpretation. Therefore, data interpolation techniques are used to convert field data into regularly distributed data and reconstruct the missing traces. Recently, the mainstream methods have implemented iterative algorithms to solve data interpolation problems, which require substantial computational resources and restrict their application in high dimensions. In this study, we proposed the f-x and f-x-y streaming prediction filters (SPFs) to reconstruct missing seismic traces without iterations. According to the streaming computation framework, we directly derived an analytic solution to the overdetermined least-squares problem with local smoothness constraints for estimating SPFs in the frequency domain. We introduced different processing paths and filter forms to reduce the interference of missing traces, which can improve the accuracy of filter coefficients. Meanwhile, we utilized a two-step interpolation strategy to guarantee the effective interpolation of the irregularly missing traces. Numerical examples show that the proposed methods effectively recover the missing traces in seismic data when compared with the traditional Fourier Projection Onto Convex Sets (POCS) method. In particular, the frequency domain SPFs are suitable for high-dimensional seismic data interpolation with the advantages of low computational cost and reasonable nonstationary signal reconstruction.

A new paper is added to the collection of reproducible documents: Seismic data interpolation without iteration using t-x-y streaming prediction filter with varying smoothness

Although there is an increase in the amount of seismic data acquired with wide-azimuth geometry, it is difficult to achieve regular data distributions in spatial directions owing to limitations imposed by the surface environment and economic factor. To address this issue, interpolation is an economical solution. The current state of the art methods for seismic data interpolation are iterative methods. However, iterative methods tend to incur high computational cost which restricts their application in cases of large, high-dimensional datasets. Hence, we developed a two-step non-iterative method to interpolate nonstationary seismic data based on streaming prediction filters (SPFs) with varying smoothness in the time-space domain; and we extended these filters to two spatial dimensions. Streaming computation, which is the kernel of the method, directly calculates the coefficients of nonstationary SPF in the overdetermined equation with local smoothness constraints. In addition to the traditional streaming prediction-error filter (PEF), we proposed a similarity matrix to improve the constraint condition where the smoothness characteristics of the adjacent filter coefficient change with the varying data. We also designed non-causal in space filters for interpolation by using several neighboring traces around the target traces to predict the signal; this was performed to obtain more accurate interpolated results than those from the causal in space version. Compared with Fourier Projection onto a Convex Sets (POCS) interpolation method, the proposed method has the advantages such as fast computational speed and nonstationary event reconstruction. The application of the proposed method on synthetic and nonstationary field data showed that it can successfully interpolate high-dimensional data with low computational cost and reasonable accuracy even in the presence of aliased and conflicting events.

A new paper is added to the collection of reproducible documents: Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter

Complex field conditions always create different interferences during seismic data acquisition, and there exist several types of noise in the recorded data, which affect the subsequent data processing and interpretation. To separate an effective signal from the noisy data, we adopted a pattern-based method with a two-step strategy, which involves two adaptive prediction-error filters (APEFs) corresponding to a nonstationary data pattern and noise pattern. By introducing shaping regularization, we first constructed a least-squares problem to estimate the filter coefficients of the APEF. Then, we solved another constrained least-square problem corresponding to the pattern-based signal-noise separation, and different pattern operators are adopted to characterize random noise and ground-roll noise. In comparison with traditional denoising methods, such as FXDECON, curvelet transform and local time-frequency (LTF) decomposition, we examined the ability of the proposed method by removing seismic random noise and ground-roll noise in several examples. Synthetic models and field data demonstrate the validity of the strategy for separating nonstationary signal and noise with different patterns.