New formulas derived from seismic interferometry to simulate phase velocity estimates from correlation methods using microtremor

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. SA71-SA83 ◽  
Author(s):  
Toshiaki Yokoi
Keyword(s):  
Fundamental Mode ◽  
Normal Modes ◽  
Single Mode ◽  
Partition Ratio ◽  
Dispersion Curves ◽  
Seismic Interferometry ◽  
Waveform Data ◽  
Correlation Methods ◽  
Theoretical Consequence ◽  
Better Than

I have developed two theoretical formulas on the basis of the power partition ratios among different modes of Rayleigh waves that are newly derived theoretically from seismic interferometry (SI). These formulas, one for the spatial autocorrelation method (SPAC) and another for the centerless circular array method (CCA), are used to simulate the estimates of the dispersion curves that can be obtained from the correlation methods using microtremor in situations when the higher normal modes are present along with the fundamental mode. The formulas can provide a way to overcome the problem caused by the assumption of the dominance of the fundamental mode, which is not always true. In addition, I have conducted a numerical validation check using the synthetic microtremor waveform data that were produced by the finite-difference method. I have found that the CCA can be an alternative to the SPAC to estimate the dispersion curves. The formula for the CCA can well simulate the dispersion curves estimated by the SPAC and CCA methods, and are better than the formula based on the above-mentioned assumption. Moreover, using the data mentioned above, I have discovered that the dual-mode inversion, which considers the presence of the fundamental and first higher modes on the basis of the formula for the CCA, performs better than the conventional single-mode inversion, which rests on the above-mentioned assumption. These positive results partially support the theoretical consequence of SI, i.e., the power partition ratio, and, further, SI itself on which the theoretically derived formulas fully rely.

THEORETICAL INVESTIGATION OF MODAL SEISMOGRAMS FOR A LAYER OVER A HALF‐SPACE

Geophysics ◽  
1965 ◽  
Vol 30 (4) ◽  
pp. 571-596 ◽  
Author(s):  
Stanley J. Laster ◽  
Joe G. Foreman ◽  
A. Frank Linville
Keyword(s):  
Half Space ◽  
Arrival Time ◽  
Normal Modes ◽  
Single Mode ◽  
Dispersion Curves ◽  
Leaky Modes ◽  
The Individual ◽  
Propagation Of Elastic Waves

The use of normal modes to represent the propagation of elastic waves at large horizontal offset is well known. By addition of the relevant leaky modes, the mode theory is shown to be useful for representation of the seismograms at shorter range. A theoretical model consisting of a 2‐cm brass layer over a steel half‐space is considered. Dispersion curves and excitation functions are computed for the first four normal modes and the first three PL modes. Attenuation as a function of frequency also is computed for the PL modes. A suite of seismograms is computed for the distance range 50–70 cm, showing each mode individually and their sum (the total seismogram). It is found that, for the distances used, the individual modes do not approximate transients with a definite “arrival” time. Only their sum is required to exhibit this physical behavior. In addition, at short distances, the dispersion of a single mode is not visually obvious although the dispersion curve may be recovered by use of Fourier transform methods. Determination of the dispersion curves from the total seismogram is more difficult and requires some seperation of the modes, as they overlap in frequency and velocity. This work shows the preponderance of the leaky modes in the early part of the seismogram and indicates their importance in the later part of the seismogram for short horizontal offset.

Large Amplitude Vibrations of Circular Plate on a Uniform Elastic Foundation

1972 ◽  
Vol 94 (1) ◽  
pp. 43-49 ◽  
Author(s):  
R. Bolton
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Single Mode ◽  
Linear Mode ◽  
Mode Amplitude ◽  
Plate Vibrations ◽  
Edge Conditions ◽  
Large Amplitude Vibrations ◽  
Mode Response

Herrmann’s equations, the dynamic analogues of the von Karman equations, are solved for a circular plate on a linear elastic foundation by assuming a series solution of the separable form involving unknown time functions. The spatial functions include both regular and modified Bessel functions and are chosen to satisfy the linear mode shape distributions of the plate as well as the usual edge conditions. Total differential equations governing the symmetric plate motions are derived using the Galerkin averaging techniques for a spatially uniform load. By extending the concept of normal modes to nonlinear plate vibrations, comparisons between normal mode response and single mode response, as functions of the first mode amplitude, are shown for different values of the elastic foundation parameter. Results are obtained for plates with simply supported and clamped edges and with both radially moveable and immoveable edges. These results are used to discuss the limitations of single-mode response of circular plates, both with and without an elastic foundation.

scholarly journals Microwave enhanced roasting for pyrite ore samples with dielectric properties strongly dependent on temperature

2015 ◽  
Vol 20 (1) ◽  
Author(s):  
Manuel Diaz ◽  
Ivan Amaya ◽  
Rodrigo Correa
Keyword(s):  
Experimental Data ◽  
Dielectric Properties ◽  
Processing Time ◽  
Gaussian Model ◽  
Single Mode ◽  
Electrical Energy ◽  
Electrical Energy Consumption ◽  
Pilot Plant Scale ◽  
Heating Behavior ◽  
Better Than

<p>This article shows the main experimental results related to the measurement of dielectric properties of Pyrite ore mineral samples as a function of temperature, and their effect on the heating behavior of the samples. It was found that the sample’s dielectric properties strongly depend on temperature. The best model for  and  that fitted the experimental data, was a Gaussian model. Besides, and under certain conditions, it was possible to roast the mineral even better than with an electric furnace, while requiring less processing time and with lower electrical energy consumption. Additional exploratory tests revealed that microwaves can be used to smelt a roasted mineral ore with time reductions of about 90%, while keeping recovery margins above 95%. Thus, we conclude that, as a next stage, the process should be directed to using a single mode applicator, for processing higher volumes of mineral at pilot plant scale.</p>

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Interpreting Proper Orthogonal Modes in Vibrations

1997 ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Distributed System ◽  
Normal Modes ◽  
Single Mode ◽  
Dominant Mode ◽  
Coordinate Space ◽  
Nonlinear Simulation ◽  
Principal Axes ◽  
Linear And Nonlinear ◽  
Proper Orthogonal Modes ◽  
Proper Orthogonal

Abstract We investigate the interpretation of proper orthogonal modes (POMs) of displacements in both linear and nonlinear vibrations. The POMs in undamped linear symmetric systems can represent linear natural modes if the mass distribution is known. This is appoximately true in a distributed system if it is discretized uniformly. If a single mode dominates, the dominant POM approximates the dominant mode. This is also true if a distributed system is discretized arbitrarily. Generally, the POMs represent the principal axes of inertia of the data in the coordinate space. For synchronous nonlinear normal modes, the dominant POM represents a best fit of the nonlinear modal curve. Linear and nonlinear simulation examples are presented.

scholarly journals Generation of (3, 1) Vector Signal Based on Probabilistic Shaping Technology without Precoding

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jiangnan Xiao ◽  
Xu Dong ◽  
Bo Liu ◽  
Xingxing Feng ◽  
Chuang Zhao ◽  
...  
Keyword(s):  
Forward Error Correction ◽  
Single Mode ◽  
Optical Carrier ◽  
Error Ratio ◽  
Bit Error Ratio ◽  
Optical Carrier Suppression ◽  
Forward Error ◽  
Rf Signal ◽  
Vector Signal ◽  
Better Than

In this paper, we introduce the probabilistic shaping (PS) technique to the normal (3, 1) vector signal and simulate the generated PS (3, 1) photonic vector signal on an optical transmission system. The PS (3, 1) photonic vector signal is generated by a radio frequency (RF) signal at 12 GHz driving a Mach–Zehnder modulator- (MZM-) based optical carrier suppression (OCS) doubling, and the PS (3, 1) photonic vector signal is not precoding. The PS (3, 1) photonic vector signal and the normal (3, 1) photonic vector signal are used to transmit in 5 km, 10 km, and 20 km single-mode fibers (SMF), respectively. The simulation results demonstrate that the bit error ratio (BER) of the PS (3, 1) vector signal is less than the forward error correction (FEC) threshold of 3.8  ×  10−3, and the BER performance is better than that of the normal (3, 1) vector signal at 4 Gbit/s and 8 Gbit/s transmission rates.

scholarly journals Research on a Rail Defect Location Method Based on a Single Mode Extraction Algorithm

2019 ◽  
Vol 9 (6) ◽  
pp. 1107 ◽  
Author(s):  
Bo Xing ◽  
Zujun Yu ◽  
Xining Xu ◽  
Liqiang Zhu ◽  
Hongmei Shi
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Single Mode ◽  
Dispersion Curves ◽  
Modal Identification ◽  
Propagation Time ◽  
Location Method ◽  
Defect Location ◽  
Extraction Algorithm ◽  
Mode Extraction

This paper proposes a rail defect location method based on a single mode extraction algorithm (SMEA) of ultrasonic guided waves. Simulation analysis and verification were conducted. The dispersion curves of a CHN60 rail were obtained using the semi-analytical finite element method, and the modal data of the guided waves were determined. According to the inverse transformation of the excitation response algorithm, modal identification under low-frequency and high-frequency excitation was realized, and the vibration displacements at other positions of a rail were successfully predicted. Furthermore, an SMEA for guided waves is proposed, through which the single extraction results of four modes were successfully obtained when the rail was excited along different excitation directions at a frequency of 200 Hz. In addition, the SMEA was applied to defect location detection, and the single reflection mode waveform of the defect was extracted. Based on the group velocity of the mode and its propagation time, the distance between the defect and the excitation point was measured, and the defect location was predicted as a result. Moreover, the SMEA was applied to locate the railhead defect. The detection mode, the frequency, and the excitation method Were selected through the dispersion curves and modal identification results, and a series of signals of the sampling nodes were obtained using the three-dimensional finite element software ANSYS. The distance between the defect and the excitation point was calculated using the SMEA result. When compared with the structure of the simulated model, the errors obtained were all less than 0.5 m, proving the efficacy of this method in precisely locating rail defects, thus providing an innovated solution for rail defect location.

Erratum: Reply to Comment on ‘Fundamental mode spot-size measurement in single-mode optical fibres’

1982 ◽  
Vol 18 (21) ◽  
pp. 936
Author(s):  
F. Alard ◽  
L. Jeunhomme ◽  
M. Monerie ◽  
P. Sansonetti ◽  
C. Vassallo
Keyword(s):  
Fundamental Mode ◽  
Single Mode ◽  
Spot Size ◽  
Optical Fibres ◽  
Size Measurement

scholarly journals Mode parameterization of structures with very low symmetry: PZT and magnetite

2014 ◽  
Vol 70 (a1) ◽  
pp. C501-C501
Author(s):  
J. Manuel Perez-Mato ◽  
Balazs Kocsis ◽  
Emre Tasci ◽  
Mois Aroyo
Keyword(s):  
Degrees Of Freedom ◽  
Parent Phase ◽  
Normal Modes ◽  
Single Mode ◽  
Irreducible Representations ◽  
Mode Decomposition ◽  
Stringent Test ◽  
Low Symmetry ◽  
Distorted Phase

The parameterization of distorted structures in terms of symmetry modes is an effective and efficient method for both their description and refinement [1]. A basis of symmetry-adapted modes transforming according to irreducible representations not only provides a hierarchical division of the degrees of freedom consistent with the mechanism at the origin of the distorted phase, but it allows the avoidance of false refinement minima, typical of highly pseudo-symmetric phases. A reduction of the number of free parameters by setting to zero negligible marginal modes is also possible. The mode description is nowadays easily applicable through freely available programs [2,3], while direct single crystal and powder diffraction refinements under this parameterization are possible combining these programs with some of the most popular refinement codes. The mode description is especially effective when dealing with distorted structures of very low symmetry compared with that of the parent phase. In these cases, the hierarchy between strong primary modes and weak marginal ones is specially pronounced, minimizing the role of many secondary modes. The physical origin of each primary distortion is usually a set of unstable degenerate normal modes. This introduces correlations among the different phases in the phase diagram that become patent in a mode description and can be used both to characterize the evolution of the relevant order parameters and as a stringent test of proposed structural models. Furthermore, the fact that each of the primary mode distortions is basically associated with the activity (instability) of a single normal mode can yield a "single mode" signature in the mode decomposition, which represents a set of subtle additional structural constrains beyond conventional crystallography. We will illustrate these considerations using the examples of the monoclinic phases of ferroelectric PbZr1-xTixO3 (PZT) and the Verwey phase of magnetite.

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