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phase velocity maps of Rayleigh waves in the Ordos block and adjacent regions

Earthquake Science 2018年第5期31卷 234-241页

作者： Shaoxing Hui Wenhua Yan Yifei Xu Liping Fan Hongwu Feng Shaanxi Earthquake Agency Xi'an 710068China Institute of Geophysics China Earthquake AdministrationBeijing 100081China

We analyze continuous waveform data from 257 broadband stations of the portable seismic array deployed under the "China Seismic Array-northern part of NS seismic belt" project as well as data from a permanent seismic network from January 2014 to December 2015. The phase velocity dispersion curve of 7,185 Rayleigh waves is obtained with a method based on the image analysis of phase velocity extraction, and the inversion is obtained. The period of Rayleigh wave phase velocity distribution has a range of 5–40 s, and minimum resolution close to 20 km. The results show that the phase velocity structure image well reflects the geological structural characteristics of the crust and uppermost mantle, and that the phase velocity distribution has obvious lateral heterogeneity. The phase velocity of the 5–15 s period is closely linked to the surface layer and sedimentary layer, the low-velocity anomalies correspond to loose sedimentary cover, and the high-velocity anomalies correspond to orogenic belts and uplifts and the boundary between high and low velocity anomalies is consistent with the block boundary. The phase velocity of the 5–15 s period is strongly affected by the crust layer thickness, the northeastern Tibetan plateau has low-velocity anomalies in the middle to lower crust, the west side of the Ordos block is consistent with the northeastern Tibetan plateau, which may imply the material exchange and fusion in this area. The velocity variation is inversely related to the Moho depth in the 40 s period of Swave, and the lateral velocity heterogeneity represents the lateral variation of the Moho depth. The Ordos block and the northern margin of Sichuan basin are located in the uppermost mantle at this depth, and the depth in the transition zone is still located in the lower crust.

关键词： Ordos block ambient noise tomography Rayleigh wave phase velocity

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High-resolution Rayleigh wave phase velocity maps from ambient noise tomography in North China

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Earthquake Science 2012年第3期25卷 241-251页

作者： Jiatie Pan Institute of Geophysics, China Earthquake Administration, Beijing 100081, China 1. Institute of Geophysics China Earthquake Administration Beijing 100081 China

We presented high-resolution Rayleigh wave phase velocity maps at periods ranging from 5 s to 30 s in the northeast part of the North China Craton (NNCC). Continuous time-series of vertical component between October 2006 and December 2008, recorded by 187 broadband stations temporarily deployed in the NNCC region, have been cross-correlated to obtain estimated fundamental mode Rayleigh wave Green’s functions. Using the frequency and time analysis technique based on continuous wavelet transformation, we measured 3 667 Rayleigh wave phase velocity dispersion curves. High-resolution phase velocity maps at periods of 5, 10, 20 and 30 s were reconstructed with grid size 0.25°× 0.25°, which reveal lateral heterogeneity of shear wave structure in the crust and upper mantle of NNCC. For periods shorter than 10 s, the phase velocity variations are well correlated with the principal geological units in the NNCC, with low-speed anomalies corresponding to the major sedimentary basins and high-speed anomalies coinciding with the main mountain ranges. Within the period range from 20 s to 30 s, high phase velocity observed in eastern NCC is coincident with the thin crust, whereas low phase velocities imaged in central NCC is correlated to the thick crust. However, the low-velocity anomaly in the Beijing-Tianjin-Tangshan region displayed in the 20 s and 30 s phase maps may be associated with fluids.

关键词： Rayleigh wave phase velocity ambient noise tomography wavelet transformation North China Craton

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Measurement of interstation phase velocity by wavelet transformation

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Earthquake Science 2009年第4期22卷 425-429页

作者： Qingju Wu Xiufen Zheng Jiatie Pan Fengxue Zhang Guangcheng Zhang vInstitute of Geophysics China Earthquake Administration Beijing 100081 China

In this paper, we present wavelet transformation method to measure interstation phase velocity. We use Morlet wavelet function as mother wavelet to filter two seismograms at various period of interest, and correlate the wavelet filtered seismograms to form cross-correlogram. If both wavelet filtered signals are in phase at that period, the phase of the cross-correlogram is a minimum. Using 3-spline interpolation to transform cross-correlation matrix to a phase velocity verse period image, it is convenient for us to measure interstation phase velocity.

关键词： dispesion phase velocity wavelet transform

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phase velocity and Rest Energy of Schrödinger Equation Seen from Neutrino Oscillations

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Journal of Modern Physics 2016年第6期7卷 473-476页

作者： Shan Zhou School of Physics and Electrical Information Shangqiu Normal University Shangqiu China

The phase velocity is discussed using de Broglie relations and Schrödinger equation. We argue that in non-relativistic quantum mechanics the Hamiltonian should be added by a rest-energy term when Schrödinger equation is used to study the interference between particles of different masses. From neutrino oscillation experiments, we find that the phase velocity can be related to a measurable quantity (the flavor transition probability), therefore, the phase factor originated from the rest energy can’t be omitted. Correspondingly, the energy in de Broglie relations should always be total energy rather than kinetic energy, contrary to some textbooks of quantum mechanics.

关键词： De Broglie Relation phase velocity Neutrino Oscillation

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Where Is phase velocity in Minkowski Space?

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Journal of Modern Physics 2024年第10期15卷 1555-1566页

作者： Antony J. Bourdillon Ultra-High Resolution Lithography San Jose CA USA

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: *** = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ,

关键词： Event Horizon Scattering Range Wave Packet phase velocity Group velocity Dispersion Dynamics Quantum Physics

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Study on relationship between the phase velocity of different lamb wave and the fatigue of plate

Study on relationship between the phase velocity of differen...

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2011年全国压电和声波理论及器件应用研讨会

作者： Wei Lin~* Xu LI Jia-qi Wang Dept.Applied Physics,Nanjing University of Aeronautics and Astronautics,Nanjing,211100,P.R.China

＜正＞The elastic coefficients,one of the material parameters to characterize mechanical behavior,are important parameter in studies of the materials *** order to study of the influences on the phase velocities of dif... 详细信息

关键词： High order Lamb wave Elastic coefficients phase velocity

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Study on pressure wave propagation in two-phase flow in liquid oxygen feed pipe between pumps

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航空动力学报 2010年第10期25卷 2352-2357页

作者： WEI Xin SUN Bing FANG Jie School of Astronautics Beijing University of Aeronautics and Astronautics Beijing 100191 China

A study on the character of pressure wave propagation was proposed for the gas liquid oxygen two-phase flow in the pipe between *** to the practical working conditions,the homogenous model based on the compressibility theory regarding a single bubble in an infinite liquid,and Redlich-Kwong gas equation was derived a model for the low temperature and high pressure case,especially considering the change of the ratio of density of gas to one of *** numerical tests were *** results not only show the agreement between numerical simulation for this model and experiment at the normal temperature and pressure is good,but also show that the modifications of the model for the low temperature and high pressure condition are *** study is of reference to further study of oscillation restrain and relative pipe tests.

关键词： two-phase flow pressure wave pipe between pumps phase velocity attenuation

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Research on propagation properties of elastic waves in two-phase anisotropic media

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Acta Seismologica Sinica(English Edition) 1999年第4期12卷 405-412,494页

作者：刘洋李承楚 1. Department of Geoscience University of Petroleum 102200 Beijing China

With the development of seismic engineering and seismic exploration of energy, the underground media that westudy are more and more complicated. Conventional anisotropy theory or two-phase isotropy theory is difficult todescribe anisotropic media containing fluid, such as fractures containing gas, shales containing water Based onBlot theory about two-phase anisotropy, with the use of elastic plane wave equations, we get Christoffel *** calculate and analyze the effects of frequency on phase velocity, attenuation, amplitude ratio and polarizationdirection of elastic waves of two-phase, transversely isotropic media. Results show that frequency affects slow Pwave the greatest among the four kinds of waves, i.e., fast P wave, slow P wave, fast S wave and slow S *** phase amplitude to solid phase amplitude ratio of fast P wave, fast S wave and slow S wave approaches unitfor large dissipation coefficients. Polarization analysis shows that polarization direction of fluid phase displacement is different from, not parallel to or reverse to, that of solid phase displacement in two-phase anisotropic media.

关键词： two-phase anisotropy elastic wave phase velocity attenuation amplitude ratio polarization

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Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

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Applied Mathematics and Mechanics(English Edition) 2024年第4期45卷 633-648页

作者： E.GHAVANLOO S.EL-BORGI School of Mechanical Engineering Shiraz UniversityShiraz 71963-16548Iran Mechanical Engineering Program Texas A&M University at QatarDoha 23874Qatar

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed *** developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a *** inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed ***,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed *** discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization *** subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed *** novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed ***,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum *** parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

关键词： nonlinear mass-spring chain discrete model continuum model LindstedtPoincare method(LPM) method of multiple scales(MMS) dispersion phase velocity

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An analytical study on the Rayleigh wave generation in a stratified structure

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Applied Mathematics and Mechanics(English Edition) 2020年第7期41卷 1039-1054页

作者： A.MANDI S.KUNDU P.PATI P.C.PAL Department of Mathematics and Computing Indian Institute of Technology(Indian School of Mines)Dhanbad 826004India

In this paper,an analytical method is used to investigate the Rayleigh wave generation in a stratified structure and the wave generation in a dry sandy layer constrained between the couple stress and inhomogeneous orthotropic *** study is devoted to analyzing the impact of various effective parameters associated with the media on the phase velocities of the *** displacement components for each medium are derived by implementing the separable variable *** frequency equa-tion is secured by using the displacement components in the boundary conditions,imposed at the interfaces between the layer and ***,the secured equation is the relation between the phase velocity and the wave *** computations are performed,and graphical representations are demonstrated between the phase velocity and the wave number for both phase velocities with different values of the *** comparison between the phase velocities is observed for the same value of each pa-rameter.

关键词： Rayleigh wave dry sandy layer couple stress orthotropic phase velocity wave number

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