基于四阶累积量的同相轴自动拾取方法

针对强随机噪声干扰情况下地震勘探资料中同相轴无法正确拾取的问题,提出了基于四阶累积量的同相轴自动拾取方法。该方法利用四阶累积量进行时间延迟估计,避免了相关高斯噪声的影响;同时在参考道的选择上,以一定的间隔设置多个参考道,减少了同相轴拾取过程中的累积误差。理论模型计算表明:该方法相对于互相关方法,对相关高斯噪声有更强的抑制能力,信噪比达到-5dB。在实际资料应用中,拾取了与同相轴有关的参数:同相轴位置,该参数为地震资料的属性分析和精确定量解释提供了依据。

基于高阶累积量一维切片的地震信号初至自动拾取方法

将现代重要的统计信号处理理论高阶累积量理论引入到地震信号的分析与处理中,提出了一种基于互四阶累积量一维切片的地震信号初至自动拾取方法,并给出了该方法的基本原理与具体算法。该方法利用地震信号横向波形的相似性以及互四阶累积量对高斯色噪声不敏感的特点,实现地震信号初至时间的自动拾取。理论模型计算表明,在强高斯色噪声干扰下该方法仍能对地震信号初至起跳时间进行有效拾取,信噪比达到-3dB;在实际资料应用中,该方法能快速准确地确定地震信号初至点的位置,与人工拾取结果基本一致。

Mixed noise removal for color images using quaternion representation

In order to effectively restore color noisy images with the mixture of Gaussian noise and impulse noise,a new algorithm is proposed using the quaternion-based holistic processing idea for color images.First,a color image is represented by a pure quaternion matrix.Secondly,according to the different characteristics of the Gaussian noise and the impulse noise,an algorithm based on quaternion directional vector order statistics is used to detect the impulse noise. Finally,the quaternion optimal weights non-local means filter （QOWNLMF）for Gaussian noise removal is improved for the mixed noise removal.The detected impulse noise pixels are not considered in the calculation of weights.Experimental results on five standard images demonstrate that the proposed algorithm performs better than the commonly used robust outlyingness ratio-nonlocal means （ROR-NLM）algorithm and the optimal weights mixed filter （OWMF）.

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.

Frequency Domain TOA Estimation Algorithm Based on Cross-HOC

High-Order Cumulants （HOC） and cross-correlation was combined to suppress the Gaussian color noises and the tin-related noises in real applications. The cross-HOC TOA estimation model was developed based on the diagonal slice of the forth-cross-cumu-lant. The eigen analysis was carried out, and the eigea noise space and the eigen signal space was achieved. Then the Frequency Domain TOA estimation algorithm based on Cross-HOC was developed. Different simulation experiments were carried out to draw out the conclusions.

Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.