Measurement of interstation phase velocity by wavelet transformation

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.

Seismic tomography of Yunnan region using short-period surface wave phase velocity

The data of short-period (1~18 s) surface waves recorded by 23 stations belonging to the digital seismic network of Yunnan Province of China are used in this paper. From these data, the dispersion curves of phase velocities of the fundamental mode Rayleigh wave along 209 paths are determined by using the two-station narrowband filtering cross-correlation method. Adopting tomography method, the distribution maps of phase velocities at various peri-ods in Yunnan region are inverted. The maps of phase velocities on profiles along 24N, 25N, 26N, 27N and 100.5E and the distribution maps of phase velocities at 3 periods in the study region are given. The results show that the phase velocity distribution in Yunnan region has strong variations in horizontal direction, and the phase velocity distribution in short-period range is closely related to the thickness of sedimentary layers in the shallow crust. The phase velocity in southern part of the Sichuan-Yunnan rhombic block encircled by the Honghe fault and Xiaojiang fault is obviously lower than that in surrounding areas. The epicentral locations of strong earthquakes in Yunnan region are mainly distributed in transitional zones between low and high phase velocities.

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

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

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.

Phase Velocity and Rest Energy of Schrödinger Equation Seen from Neutrino Oscillations

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.

Changes of the acoustic modal phase velocity,group velocity and interference distance in an eddy

Using the modal dispersion equation with the phase-integral approaches, and con-sidering an eddy (or water mass) as a sound channel disturbance, the effects of the undisturbed channel, cold-core eddy and warm-core eddy on the acoustic propagation characteristics are dis-cussed. According to the solutions of the dispersion equation, the relation between the modal Parameters (phase velocity, group velocity and interference distance) and the eddy intensity is obtained. When the plane wave (with an incident angle a) travels toward the center of a warm-core eddy (disturbed intensity BM ) 'double channel phenomenon' will take place in case of sin2 α < BM < 2(1 - cosα), and then the modal phase velocity and interference distance will have anomalous changes which are completely different from the case of the cold-core eddy.

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

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 masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,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 masses.The 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 technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The 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 masses.Finally,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 models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

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

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 equations.We 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 wave.Fluid 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.

Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

The statistical laws of strong seismic motion phase characteristics

Under the assumption of an effective point source model,this paper introduces a conception of equivalent phase velocity to describle the average propagation processes and dispersion properties of seismic waves from seismic source to the site,then illuminates the relation between the phase properties of seismic motion and equivalent phase velocity and obtains a simple formula of estimating the equivalent phase velocity through the use of the phase difference spectrum of seismic motion.After the parts of strong seismic records in the western American and the SMART-1 array are used to identify the method presented by this paper in reason,the statistical relations of equivalent phase velocity are given in the above two regions.The results of the paper have demonstrated that the phase spectrum of seismic motion has its inner law as same as the amplitude spectrum does.

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham＇s rheology equation of liquid phase and Bagnold＇s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

Tests of relative vertical offsets for several types of GPS receiver antenna phase centers

The correction for antenna phase center is considered in processing Global Positioning System （GPS） data collected from a network of GPS ultra-short baselines. Compared with the leveling measurements, the GPS results show that the relative vertical offsets for the pairs of GPS receiver antenna phase centers still exist, although absolute calibration of the antenna phase center variations （PCVs） has been considered. With respect to the TPS CR.G3 antenna, the relative vertical offset for the LEI AT504 antenna is 8.4 mm, the offset for the ASH701945C_M antenna is 5.5 mm, and those for the ASHY00936E_C and ASH701945B_M antennas are approximately between 2 mm and -3 mm. The relative offsets for the same type of antennas are approximately 1 mm. By correcting the absolute PCVs, the existing relative offset becomes negligible for horizontal positioning.

A review of the wave gradiometry method for seismic imaging

As dense seismic arrays at different scales are deployed,the techniques to make full use of array data with low computing cost become increasingly needed.The wave gradiometry method(WGM)is a new branch in seismic tomography,which utilizes the spatial gradients of the wavefield to determine the phase velocity,wave propagation direction,geometrical spreading,and radiation pattern.Seismic wave propagation parameters obtained using the WGM can be further applied to invert 3D velocity models,Q values,and anisotropy at lithospheric(crust and/or mantle)and smaller scales(e.g.,industrial oilfield or fault zone).Herein,we review the theoretical foundation,technical development,and major applications of the WGM,and compared the WGM with other commonly used major array imaging methods.Future development of the WGM is also discussed.

Quantum Mechanics: Internal Motion in Theory and Experiment

Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E2 = p2c2 + m2c4. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon;while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, vp⋅vg = c2 with vp ≥ c because vg ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for vp = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if vp is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy;h = Planck’s constant;ν = frequency;ω = angular momentum;p = momentum;λ = wavelength;k = wave vector;c = speed of light;m = particle rest mass;vp = phase velocity;vg = group velocity].

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

Previously Unknown Formulas for the Relativistic Kinetic Energy of an Electron in a Hydrogen Atom

Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.

Structure of Periodic Flows through a Channel with a Suddenly Expanded and Contracted Part

With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.

Crustal structure of the northeastern Tibetan plateau,the Ordos block and the Sichuan basin from ambient noise tomography

We apply ambient noise tomography to significant seismic data resources in a region including the northeastern Tibetan plateau, the Ordos block and the Sichuan basin. The seismic data come from about 160 stations of the provincial broadband digital seismograph networks of China. Ambient noise cross-correlations are performed on the data recorded between 2007 and 2009 and high quality inter-station Rayleigh phase velocity dispersion curves are obtained between periods of 6 s to 35 s. Resulting Rayleigh wave phase velocity maps possess a lateral resolution between 100 km and 200 kin. The phase velocities at short periods （〈20 s） are lower in the Sichuan basin, the northwest segment of the Ordos block and the Weihe graben, and outline sedimentary deposits. At intermediate and long periods （〉25 s）, strong high velocity anomalies are observed within the Ordos block and the Sichuan basin and low phase velocities are imaged in the northeastern Tibetan plateau, reflecting the variation of crustal thickness from the Tibetan plateau to the neighboring regions in the east. Crustal and uppermost mantle shear wave velocities vary strongly between the Tibetan plateau, the Sichuan basin and the Ordos block. The Ordos block and the Sichuan basin are dominated by high shear wave velocities in the crust and uppermost mantle. There is a triangle-shaped low velocity zone located in the northeastern Tibetan plateau, whose width narrows towards the eastern margin of the plateau. No low velocity zone is apparent beneath the Qinling orogen, suggesting that mass may not be able to flow eastward through the boundary between the Ordos block and the Sichuan basin in the crust and uppermost mantle.

Study on characteristics of internal solitary waves in the Malacca Strait based on Sentinel-1 and GF-3 satellite SAR data

The study of the characteristics of internal solitary waves happened in the Malacca Strait is an urgent problem for submarine, ship navigation and marine engineering. Based on SAR remote sensing data obtained from the high spatial resolution Sentinel-1 and GF-3, the internal solitary wave characteristics of the Malacca Strait are investigated. By use of 20 Sentinel-1 SAR images from June 2015 to December 2016 and 24 GF-3 images from April2018 to March 2019, the spatial distribution characteristics of internal solitary wave s are statistically analyzed. It is found that the internal solitary waves are usually in the form of wave packets and single solitary waves, and the maximum crest length of the leading wave can reach 39 km. The amplitude and group velocity of internal solitary wave s can be calculated by the inversion model of high-order nonlinear Schrodinger(NLS) equation, and the calculated amplitude of the internal solitary wave s and the propagation group velocity of the wave packets range from 4.7 m to 23.9 m and 0.12 m/s to 0.40 m/s, respectively. The range of phase velocity of single internal solitary waves obtained by Kd V equation is 0.26 m/s to 0.60 m/s. In general, the amplitude and the velocity of internal solitary wave s in Malacca strait are related to the topography.