Seismic attribute extraction based on HHT and its application in a marine carbonate area

The Hilbert-Huang transform（HHT） is a new analysis method suitable for nonlinear and non-stationary signals.It is very appropriate to seismic signals because they show both non-stationary and nonlinear characteristics.We first introduce the realization of HHT empirical mode decomposition（EMD） and then comparatively analyze three instantaneous frequency algorithms based on intrinsic mode functions（IMF） resulting from EMD,of which one uses the average instantaneous frequency of two sample intervals having higher resolution which can determine that the signal frequency components change with time.The method is used with 3-D poststack migrated seismic data of marine carbonate strata in southern China to effectively extract the three instantaneous attributes.The instantaneous phase attributes of the second intrinsic mode functions（IMF2） better describe the reef facies of the platform margin and the IMF2 instantaneous frequency attribute has better zoning.Combining analysis of the three IMF2 instantaneous seismic attributes and drilling data can identify the distribution of sedimentary facies well.

Seismic dip estimation based on the twodimensional Hilbert transform and its application in random noise attenuation

In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.

OMHT method for weak signal processing of GPR and its application in identification of concrete micro-crack

In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method).First,according to the matching pursuit algorithm and the strong reflection-forming mechanism,and based on the sparse representation theory,a sparse dictionary,adapted to the characteristics of the strong reflection signal,was selected,and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly.Second,the Hilbert transform was used to extract multiple parameters,such as the instantaneous amplitude,the instantaneous frequency,and the instantaneous phase,from the processed signal,and the ground penetrating radar(GPR)image was comprehensively analyzed and determined from multiple angles.The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment.The resolution of the processed GPR image is greatly improved,and the reflected signal of the hidden micro-crack is easily visible,which proves the validity and accuracy of the analysis method.

Application of time–frequency entropy from wake oscillation to gas–liquid flow pattern identification

Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.

On p-ω-hyponormal Operators

In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.

Cyclostationary Feature Detection Based Spectrum Sensing Algorithm under Complicated Electromagnetic Environment in Cognitive Radio Networks

This paper focuses on improving the detection performance of spectrum sensing in cognitive radio(CR) networks under complicated electromagnetic environment. Some existing fast spectrum sensing algorithms cannot get specific features of the licensed users'(LUs') signal, thus they cannot be applied in this situation without knowing the power of noise. On the other hand some algorithms that yield specific features are too complicated. In this paper, an algorithm based on the cyclostationary feature detection and theory of Hilbert transformation is proposed. Comparing with the conventional cyclostationary feature detection algorithm, this approach is more flexible i.e. it can flexibly change the computational complexity according to current electromagnetic environment by changing its sampling times and the step size of cyclic frequency. Results of simulation indicate that this approach can flexibly detect the feature of received signal and provide satisfactory detection performance compared to existing approaches in low Signal-to-noise Ratio(SNR) situations.

Application of Hilbert-Huang Transform to the Analysis of the Landslides Triggered by the Wenchuan Earthquake

A steep rock hill with two side slopes located at DK30＋256 of National Road 213 was used as a prototype for analysis. The full process from initial deformation to sliding of the slope during ground shaking was simulated by using a new Continuum-based Discrete Element Method. During the earthquake, when shaking amplitudes were lower, the stress concentration points firstly appeared at the top of the slip mass, and then some tension failure points appeared, followed by shear failure points. At the same time, both the instantaneous frequencies of accelerations in the bedrock and that in the slip mass basically stayed in two different ranges. The energy transmittance coefficients of the sliding surface also stayed in a high range. As the ground shaking lasted, the number of failure points gradually increased until landslide occurrence. The instantaneous frequencies of accelerations in the slip mass and the energy transmittance coefficients of sliding surface gradually decreased, and both finally converged to a lower range. And then, the reasons triggering landslides are analysis in the joint time-frequency domain using Hilbert-Huang Transform, as follows： the differenees of distribution and dissipation of the earthquake energy and the inconsistency of movements between the slip mass and the bedrock were the two major influence factors.

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Controlled Probabilistic Teleportation of an Unknown Multi-Particle High-Dimensional Entangled State

We propose a protocol for controlled probabilistic teleportation of an unknown tripartite qutrit entangled state with two partial tripartite qutrit entangled states as the quantum channel. It is found that teleportation associated with the generalized qutrit Bell-basis measurement, the generalized qutrit π-state measurement and the generalized Hadamard operator in three-dimensional Hilbert space. We generalize the protocol for controlled probabilistic teleportation of an unknown k-particle qudit entangled state with a multi-particle qudit entangled state and a tripartite qudit entangled state as the quantum channel. We also calculate the classical communication cost required in both cases.

Loewner Chains Associated with the Generalized Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of typeβ and order α, almost starlikeness of order α, spirallikeness of type ofβ and starlikeness.

Analysis of Nonstationary Wind Fluctuations Using the Hilbert-Huang Transform

Climatological patterns in wind fluctuations on time scales of 1–10 h are analyzed at a meteorological mast at the Yangmeishan wind farm, Yunnan Province,China, using a 2-yr time series of 10-min wind speed observations. For analyzing the spectral properties of nonstationary wind fluctuations in mountain terrain, the Hilbert-Huang transform(HHT) is applied to investigate climatological patterns between wind variability and several variables including time of year, time of day, wind direction, and pressure tendency. Compared with that for offshore sites, the wind variability at Yangmeishan wind farm has a more distinct diurnal cycle, but the seasonal discrepancies and the differences according to directions are not distinct, and the synoptic influences on wind variability are weaker. There is enhanced variability in spring and winter compared with summer and autumn. For flow from the main direction sector, the maximum wind variability is observed in spring. And the severe wind fluctuations are more common when the pressure tendency is rising.

Embryonic and larval development in barfin flounder Verasper moseri (Jordan and Gilbert)

Broodstock of Verasper moseri （Jordan and Gilbert） aged 3-4 years old were selected, and reinforced cultivation was conducted to promote maturation under controlled water temperature and photoperiod conditions. Fertilized eggs were obtained by artificial fertilization, and the development of embryos, larvae and juveniles was observed continuously. The results showed that the fertilized eggs of V. moseri were spherical, with transparent yolk and homogeneous bioplasm, and had no oil globule inside. The average diameter of the eggs was 1.77＋0.02 mm. The eggs of V. moseri were buoyant in water with salinity above 35. The cleavage type was typical discoidal. Young pigment cells appeared when olfactory plates began to form. Hatching occurred at 187 h after fertilization at a water temperature of 8.5℃. The newly hatched larvae, floating on the water surface, were transparent with an average total length of 4.69±0.15 mm. During the cultivation period, when the water temperature was raised from 9 to 14.5℃, 4-day old larvae showed more melanophores on the body surface, making the larvae gray in color. The pectoral fins began to develop, which enabled the larvae to swim horizontally and in a lively manner. On days 7-8, the digestive duct formed. The yolk sac was small and black. The yolk sac was absorbed on day 11. Larvae took food actively, and body length and body height clearly increased. The rudiments of dorsal and anal fin pterygiophores were discernible and caudal fin ray elements formed on day 19. On day 24, the larval notochord flexed upwards, and the rays of unpaired fins began to differentiate. Pigment cells converged on the dorsal and anal fin rays, and the mastoid teeth on the mandible appeared. On day 29, the left eyes of juveniles began to move upwards. Depigmentation began in some juveniles and they became sandy brown in color on day 37. Most juveniles began to settle on the bottom of the tank. The left eyes of juveniles migrated completely to the right side on day 50, when the average body length attained 2.5±0.18 cm, and juveniles accomplished metamorphosis to young. The embryonic and larval characters of several flounder species are compared.

On the Ground State of Spin Systems with Orbital Degeneracy

In order to understand the properties of the spin system with orbital degeneracy, we first study the ground state of the SU(4) spin-orbital model on a square lattice. The mean-field results suggest that for a small Hund's interaction, the flavor liquid state is stable against the solid state, but with sufficient deviation from the SU(4) limit the long-range order may be attained in 2D system. Furthermore, we employ a variational approach to calculate the phase diagram of the ground state and the temperature-dependent susceptibility by taking into account the Hund's interaction and the anisotropy in orbital wavefunctions. Finally, the implications for the experimental observations on the material, , are discussed.

An Existence Theorem for Strongly Nonlinear Implicit Complementarity Problems

A class of strongly nonlinear implicit complementarity problems for set-valued mappings in Hilbert spaces is studied,Thereupon a new existence theorem is established and proved to be a solution to that kind of problems.

A Note on the Difference of Gaussian Measure of Two Balls in Hilbert Spaces

Let H be a separable Hilbert space, μ be a symmetric Gaussian measure on H. Applying the meathod of sum of independent random variables. A finer estimate of the difference of Gaussian measure of two balls is obtained.

Teleportation with an Arbitrary Mixed Resource as a Trace－Preserving Quantum Channel

General conditions are given in order to perform a perfect teleportation process in the case where the Hilbert spaces involved have different dimensions. An explicit expression is obtained for the quantum channel associated with the standard teleportation protocol T0 with an arbitrary mixed state resource. The transmission fidelity of the corresponding quantum channel is given.

Decomposable Multipliers on a Banach Algebra

The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].

Shafting misalignment fault diagnosis by means of motor speed signal and SVD-HT method

Aiming at the deficiency of diagnosis method based on vibration signal,a novel method based on speed signal with singular value decomposition and Hilbert transform(SVD-HT)is proposed.The fault diagnosis mechanism based on the speed signal is obtained by constructing the shaft misalignment fault model firstly.Then the SVD-HT method is applied to the processing of the speed signal.The accuracy of the SVD-HT method is verified by comparing the diagnosis results of the order spectrum method and the SVD-HT method.After that,the diagnosis results based on vibration signal and speed signal under no-load and load patterns are compared.Under the no-load pattern,the amplitudes of the speed signal components f_(r),2f_(r) and 4f_(r) are linear with the misalignment.In addition,under the load pattern,the amplitudes of the speed signal components f_(r),2f_(r) and 4f_(r) have a linear relationship with the load.However,the diagnosis result of the vibration signal does not have the above characteristics.The comparison results verify the robustness and reliability of the speed signal and SVD-HT method.The method presented in this paper provides a novel way for misalignment fault diagnosis.

Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces.The cost function consists of a separable term, in which each component is modeled through its own potential,and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals.An algorithm with guaranteed weak convergence to a solution to the problem is provided.Various multicomponent signal decomposition and recovery applications are discussed.