scholarly journals DISCRETE TIME SOLUTION OF PLANE P‐SV WAVES IN A PLANE LAYERED MEDIUM

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 197-219 ◽  
Author(s):  
Clint W. Frasier
Keyword(s):  
Free Surface ◽  
Discrete Time ◽  
Acoustic Waves ◽  
Plane Waves ◽  
Normal Incidence ◽  
Small Time ◽  
Body Waves ◽  
Response Matrix ◽  
Constant Matrix ◽  
P And Sv Waves

For plane waves at normal incidence to a layered elastic medium, both the forward and inverse discrete time problems have been previously solved. In this paper the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer. Vertical traveltimes for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment Δτ. This gives a 4×4 layer matrix analogous to the 2×2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses recorded at the free surface of a layered half space are derived as matrix series in integer powers of the Fourier transform variable [Formula: see text]. These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. It is shown that the reflection response matrix generated by a source at the free surface equals the product of a constant matrix and the positive time part of the autocorrelation matrix of the transmission response matrix due to a deep source. This is an extension to nonnormal incidence of a theorem proved by Claerbout for acoustic waves at normal incidence.

Effect of inertial coefficients in the propagation of plane waves in micropolar porous materials

2017 ◽  
Vol 06 (01) ◽  
pp. 1750007 ◽  
Author(s):  
R. Lianngenga
Keyword(s):  
Free Surface ◽  
Porous Materials ◽  
Plane Waves ◽  
Body Waves ◽  
Plane Body ◽  
Reflected Waves ◽  
Phase Velocities ◽  
Energy Ratios

The problem of phase velocities and attenuations of plane body waves and its reflection from a stress-free surface has been investigated in the micropolar porous materials. The amplitude and energy ratios of reflected waves are obtained analytically. The effect of inertial coefficients in the propagation of plane body waves is computed numerically for a particular model.

Polarization analysis of high-frequency, three-component seismic data

1991 ◽  
Vol 81 (2) ◽  
pp. 622-642
Author(s):  
K. Bataille ◽  
J. M. Chiu
Keyword(s):  
High Frequency ◽  
Time Windows ◽  
Random Noise ◽  
Polarization State ◽  
Principal Component ◽  
Small Time ◽  
Body Waves ◽  
Local Data ◽  
Principal Component Approach ◽  
Component Approach

Abstract We present a method to determine the polarization of body waves from three-component, high-frequency data and examples of its application. The method is based on the principal component approach. One advantage of this approach is that the polarization state can be determined for small time windows compared with the predominant period of the wave. This is particularly useful for identifying converted waves within the crust. The stability of the result is analyzed with synthetic cases by adding simultaneous arrivals from waves and random noise. The method works well with both synthetic and local data in the detection of the polarization of the wave by separating arrivals from different directions. From the local data, some seismic phases related to crustal conversions are observed that require strong lateral variations.

Calculation of Acoustic Efficiency of Exhaust Silencers for Automotive Internal Combustion Engines

2021 ◽  
pp. 41-47
Author(s):  
Vladimir Tupov ◽  
O. Matasova
Keyword(s):  
Acoustic Waves ◽  
Internal Combustion Engines ◽  
Combustion Engine ◽  
Control Point ◽  
Plane Waves ◽  
Exhaust System ◽  
Internal Combustion ◽  
Combustion Engines ◽  
Exhaust Noise ◽  
Insertion Losses

Insertion losses as the main characteristic that mathematically describes the acoustic efficiency of a noise silencer has been considered. This characteristic shows the reduction of noise generated by its source, in particular by the internal combustion engine’s exhaust system, at the control point as a silencer use result. Has been presented a mathematical description of the insertion losses, and have been considered parameters necessary for calculating this characteristic. Has been demonstrated the analytical dependence of impedance for the sound emission by the exhaust system’s end hole from the coefficient of acoustic waves reflection by this hole. The performed analysis of the widely used formulas for calculating the coefficient of sound reflection by the end hole has showed their insufficient accuracy for project designs performing. Have been proposed calculation dependences providing high accuracy for calculations of the reflection coefficient modulus, and the attached length of the channel end hole without a flange in the entire range of the existence of plane waves in it. It has been shown that the end correction of this hole at ka = 0 is 0.6127, and not 0.6133, as it was mistakenly believed until now in world acoustics. Has been proposed a method for calculation the exhaust noise source internal impedance. This method more accurately, in comparison with the already known ones, describes the acoustic processes in the internal combustion engine’s exhaust manifold, thanks to increases the accuracy of calculation the silencer acoustic efficiency, that allows develop the silencer at the early stages of the design of an automotive internal combustion engine.

Nonlinear Water Waves in the Presence of Submerged Elliptic Cylinder

2004 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Boundary Integral Equations ◽  
Fluid Velocity ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Boundary Integral ◽  
Nonlinear Water Waves ◽  
Wave Elevation ◽  
Boundary Equations

The fully nonlinear problem on unsteady two-dimensional water waves generated by elliptic cylinder, that is horizontally submerged beneath a free surface, is considered. An analytical boundary integral equations method using a version of Milne-Thomson transformation is developed. Boundary equations (the BEq system) determine immediately exact wave elevation and fluid velocity at free surface. Small-time solution expansion is obtained in the case of accelerated cylinder starting from rest.

Effective Extinction Distances in Zone Axis Silicon

2000 ◽  
Vol 6 (S2) ◽  
pp. 1028-1029
Author(s):  
Z. Yu ◽  
R. R. Vanfleet ◽  
J. Silcox
Keyword(s):  
Electron Microscopy ◽  
Plane Waves ◽  
Normal Incidence ◽  
Sample Surface ◽  
Bloch Wave ◽  
Zone Axis ◽  
Image Recording ◽  
Intensity Measurements ◽  
Digital Image Recording ◽  
Convergent Beam

Many scientific questions encountered in electron microscopy require quantitative deductions from the observations. Comparisons of experimental observations with simulations are however, still relatively rare since measurements of intensity are normally difficult. In this paper we discuss the use of experimental observations of the effective extinction distances for zone axis silicon using a convergent beam STEM mode for comparison with a number of simulations. On the experimental side, the measurements were made with a STEM that provides accurate intensity measurements directly with a digital image recording system. Two theoretical schemes widely used in electron microscopy simulations, multislice simulation and Bloch-wave calculation, were employed for the simulations. In each case, both a TEM case and a STEM case were calculated for comparison.The multislice simulations were carried out using codes available from Kirkland. For the TEM case with plane waves at normal incidence on the sample surface, the unscattered (0,0) exit beam gives the Bright Field (BF) intensity.

Passive Seismic Marchenko Imaging

2020 ◽  
Author(s):  
Zhongyuan Jin
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Low Cost ◽  
Body Waves ◽  
Seismic Survey ◽  
Significant Difference ◽  
Passive Seismic ◽  
Seismic Acquisition ◽  
Imaging Property ◽  
Internal Multiples

<p>In recent years, seismic interferometry (SI) has been widely used in passive seismic data, it allows to retrieve new seismic responses among physical receivers by cross-correlation or multidimensional deconvolution (MDD). Retrieval of reflected body waves from passive seismic data has been proved to be feasible. Marchenko method, as a new technique, retrieves Green’s functions directly inside the medium without any physical receiver there. Marchenko method retrieves precise Green’s functions and the up-going and down-going Green’s functions can be used in target-oriented Marchenko imaging, and internal multiples related artifacts in Marchenko image can be suppressed. </p><p>Conventional Marchenko imaging uses active seismic data, in this abstract, we propose the method of passive seismic Marchenko imaging (PSMI) which retrieves Green’s functions from ambient noise signal. PSMI employs MDD method to obtain the reflection response without free-surface interaction as an input for Marchenko algorithm, such that free-surface multiples in the retrieved shot gathers can be eliminated, besides, internal multiples don’t contribute to final Marchenko image, which means both free-surface multiples and internal multiples have been taken into account. Although the retrieved shot gathers are contaminated by noises, the up-going and down-going Green’s functions can be still retrieved. Results of numerical tests validate PSMI’s feasibility and robustness. PSMI provides a new way to image the subsurface structure, it combines the low-cost property of passive seismic acquisition and target-oriented imaging property of Marchenko imaging, as well as the advantage that there are no artifacts caused by internal multiples and free-surface multiples.</p><p>Overall, the significant difference between PSMI and conventional Marchenko imaging is that passive seismic data is used into Marchenko scheme, which extends the Marchenko imaging to passive seismic field. Passive seismic Marchenko imaging avoids the effects of free-surface multiples and internal multiples in the retrieved shot gathers. PSMI combines the low-cost property of passive seismic acquisition and target-oriented imaging property of Marchenko imaging which is promising in future field seismic survey.</p><p>This work is supported by the Fundamental Research Funds for the Central Universities (JKY201901-03). </p>

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