This paper presents a novel method for seismic signal denoising based on the dual-tree complex wavelet transform. The advantages of shift invariance, adequate directions and anti-aliasing enable the dual-tree complex wavelet to effectively represent seismic data. However, the fixed threshold in each sub-band leads to the attenuation of the useful signal or residual noise. In this paper, noise attenuation strategies are discussed for all sub-bands in different directions and scales. In this approach, block matching is combined with singular value decomposition to handle the noisy coefficients in high-frequency scales based on local and non-local similarity. An adaptive threshold is used to divide the signal from the noise at lowfrequency scales. The method is applied to synthetic seismic data and field data to verify its performance. The experimental results illustrate that the proposed method improves the signal-to-noise ratio by 3-4 dB compared with fixed threshold denoising in all sub-bands.

To achieve a high level of seismic random noise suppression, the conventional time-frequency peak filtering (TFPF) has been adequately studied and applied in previous researches in recent years. A window is used to improve linearity, thereby achieving the unbiased estimates. However, applying a fixed window length to all frequencies signals will result in serious loss of effective components. The recently proposed the parabolic-trace TFPF (PT-TFPF) resample seismic record along parabolic-trace to enhance linearity. But complex events in field data have different curvatures, and it is difficult to fit parabolic-trace. To resolve these problems, we present an adaptive linear TFPF (AL-TFPF) in this paper. In this novel method, the linearity of the effective signals is implemented by grouping instead of window or filtering trace. Based on temporal continuity and spatial correlation, grouping is able to adaptively resample. The AL-TFPF stores the similar blocks into a new matrix. In this approach, degree of improvement of linearity is related to the accuracy of block matching. Finally, we evaluate the performance of our method on both synthetic records and field data. The experimental results illustrate that our proposed method realizes the retention of useful components and attenuation of the noise simultaneously, compared with the conventional TFPF and the PT-TFPF.

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Comparing with the linear Black-Scholes model, the fractional option pricing models are constructed by taking account some more parameters like, for example, the transaction cost, so that it becomes more difficult to find the exact analytical solution. In this paper, we analyze a nonlinear fractional Black and Scholes model, and we find the solution by using a novel numerical method, based on a mixture of efficient techniques. In particular, we combine (1) Haar wavelet integration method which transforms the PDEs into a system of algebraic equations, (2) the homotopy perturbation method in order to linearize the problem, and (3) the variational iteration method which will be used to solve the large system of algebraic equations efficiently. We will also show that, in comparison with other popular methods, our coupling technique has a higher efficiency and calculation precision.