Seismic data denoising based on mixed time-frequency methods

Deconvolution denoising in the f-x domain has some defects when facing situations like complicated geology structure, coherent noise of steep dip angles, and uneven spatial sampling. To solve these problems, a new filtering method is proposed, which uses the generalized S transform which has good time-frequency concentration criterion to transform seismic data from the time-space to time-frequency-space domain （t-f-x）. Then in the t-f-x domain apply Empirical Mode Decomposition （EMD） on each frequency slice and clear the Intrinsic Mode Functions （IMFs） that noise dominates to suppress coherent and random noise. The model study shows that the high frequency component in the first IMF represents mainly noise, so clearing the first IMF can suppress noise. The EMD filtering method in the t-f-x domain after generalized S transform is equivalent to self-adaptive f-k filtering that depends on position, frequency, and truncation characteristics of high wave numbers. This filtering method takes local data time-frequency characteristic into consideration and is easy to perform. Compared with AR predictive filtering, the component that this method filters is highly localized and contains relatively fewer low wave numbers and the filter result does not show over-smoothing effects. Real data processing proves that the EMD filtering method in the t-f-x domain after generalized S transform can effectively suppress random and coherent noise of steep dips.

Geometric Phases Corrected by Stochastic Dephasing

We analyze the effect of stochastic dephasing on geometric phases. The result implies that the correction of geometric phases relies on not only the fluctuation of the random variable in the stochastic process, but also the frequency of the system.

A Stochastic Description of Transition Between Granular Flow States

Two-dimensional granular flow in a channel with small exit is studied by molecular dyhamics simulations. We firstly define a key area near the exit, which is considered to be the choke area of the system. Then we observe the time variation of the local packing fraction and flow rate in this area for several fixed inflow rate, and find that these quantities change abruptly when the transition from dilute flow state to dense flow state happens. A relationship between the local flow rate and the local packing fraction in the key area is also given. The relationship is a continuous function under the fixed particle number condition, and has the characteristic that the flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at a high value with negative slope. By use of the relationship, the properties of the flow states under the fixed inflow rate condition are discussed in detail, and the discontinuities and the complex time variation behavior observed＇in the preexisting works are naturally explained by a stochastic process.

Coefficient of Partial Correlation and Its Calculation

This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.

Phase Transitions Induced by Top-Priority of Randomization

We study the characteristics of phase transition to take the top-priority of randomization in the rules of NaSch model （i.e. noise-first model） into account via computing the relaxation time and the order parameter. The scaling exponents of the relaxation time and the scaling relation of order parameter, respectively, are obtained.

Dynamics of Entanglement of Qutrit-Qutrit States with Stochastic Dephasing

The effect of stochastic dephasing on the dynamics of entanglement of qutrit-qutrit states is investigated by using negativity and bound entanglement defined with realignment criterion, From the analysis, we, find that the time evolution of quantum free entanglement and bound entanglement depends on the fluctuations of the stochastic variables and the parameters of the particular initial states of concern. Our results imply that some qutrits states display both distillability sudden death and entanglement sudden death, while some states do not display distillability sudden death but only entanglement sudden death.

Asymptotics for the Tail Probability of Random Sums with a Heavy-Tailed Random Number and Extended Negatively Dependent Summands

Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ： k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P（X〉x）/P（τ〉x）→0 as x →∞.

THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.

CHOVER'S LAW OF THE ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED SEQUENCES

Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.

Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.

Randomly Weighted Sums for Negatively Associated Random Variables with Heavy Tails

In 2003, Tang Qihe et al. obtained a simple asymptotic formula for independent identically distributed (i.i.d.) random variables with heavy tails. In this paper, under certain moment conditions, we establish a formula as the same as Tang’s, when random variables are negatively associated (NA).

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 < qc< 0.25 separating the two phase transition types.

THE LIMIT THEOREM FOR DEPENDENT RANDOM VARIABLES WITH APPLICATIONS TO AUTOREGRESSION MODELS

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.