Nonstationary signal inversion based on shaping regularization for random noise attenuation

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry;however,it has two drawbacks.First,it assumes that the seismic signals are piecewise stationary and linear.However,the seismic signal exhibits nonstationary due to the complexity of the underground structure.Second,the method predicts noise from seismic data by convolving with a prediction error filter(PEF),which applies inconsistent noise models before and after denoising.Therefore,the assumptions and model inconsistencies weaken conventional prediction filtering's performance in noise attenuation and signal preservation.In this paper,we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation.The main idea of the method is to use the nonstationary prediction operator(NPO)to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution.Different from the convolutional predicting filtering,the proposed method uses NPO as the regularization constraint to directly invert the eff ective signal from the noisy seismic data.The NPO varies in time and space,enabling the inversion system to describe complex(nonstationary and nonlinear)underground geological structures in detail.Processing synthetic and field data results demonstrate that the method eff ectively suppresses random noise and preserves seismic refl ection signals for nonstationary seismic data.

Continuous time-varying Q-factor estimation method in the time-frequency domain

The Q-factor is an important physical parameter for characterizing the absorption and attenuation of seismic waves propagating in underground media,which is of great signifi cance for improving the resolution of seismic data,oil and gas detection,and reservoir description.In this paper,the local centroid frequency is defi ned using shaping regularization and used to estimate the Q values of the formation.We propose a continuous time-varying Q-estimation method in the time-frequency domain according to the local centroid frequency,namely,the local centroid frequency shift(LCFS)method.This method can reasonably reduce the calculation error caused by the low accuracy of the time picking of the target formation in the traditional methods.The theoretical and real seismic data processing results show that the time-varying Q values can be accurately estimated using the LCFS method.Compared with the traditional Q-estimation methods,this method does not need to extract the top and bottom interfaces of the target formation;it can also obtain relatively reasonable Q values when there is no eff ective frequency spectrum information.Simultaneously,a reasonable inverse Q fi ltering result can be obtained using the continuous time-varying Q values.

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .