A semianalytical approach to calculate the reflected wave of an eccentric source in a borehole

The acoustic field in a borehole is usually simulated under axisymmetric conditions. When the acoustic source deviates from the borehole axis, the field loses the axial symmetry property. We have developed a semianalytical approach to calculate the acoustic field excited by an eccentric source of limited size. The eccentric source is first decomposed into infinitely long multipole cylinder sources whose center axes pass through the eccentric point. Then, by applying the continuity of displacement and stress on the interfaces, we derive reflection coefficients by the generalized reflection and transmission coefficient method. Finally, the reflected wave is obtained after dual inverse Fourier transforms with respect to time and wavenumber. Numerical tests based on the reciprocity theorem are performed to validate this approach. The results indicate that the simulation error in every reciprocal model is negligible even if the eccentric distance of the acoustic source reaches two thirds of the radius of the borehole wall. We apply this semianalytical approach to simulate the reflected wave of an eccentric directional beam in a cased borehole.

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An efficient method for computing Green's functions for a layered half-space with sources and receivers at close depths

Bulletin of the Seismological Society of America ◽

10.1785/bssa0840051456 ◽

1994 ◽

Vol 84 (5) ◽

pp. 1456-1472 ◽

Cited By ~ 1

Author(s):

Yoshiaki Hisada

Keyword(s):

Half Space ◽

Green's Functions ◽

Green’S Functions ◽

Point Sources ◽

Asymptotic Solutions ◽

Reflection And Transmission ◽

Reflection And Transmission Coefficient ◽

Dipole Sources ◽

Coefficient Method ◽

Layered Half Space

Abstract We propose an analytical method to compute efficiently the displacement and stress of static and dynamic Green's functions for viscoelastic layered half-spaces. When source and receiver depths are close, it is difficult to compute Green's functions of the layered half-space, because their integrands, whose variable of integration is the horizontal wavenumber, oscillate with only slowly decreasing amplitude. In particular, when the depths are equal, it is extremely difficult to compute the stress Green's functions, because their integrands oscillate with increasing amplitude. To remedy this problem, we first derive the asymptotic solutions, which converge to the integrands of Green's functions with increasing wavenumber. For this purpose, we modify the generalized R/T (reflection and transmission) coefficient method (Luco and Apsel; 1983) to be completely free from growing exponential terms, which are the obstacles to finding the asymptotic solutions. By subtracting the asymptotic solutions from the integrands of the corresponding Green's functions, we obtain integrands that converge rapidly to zero. We can, therefore, significantly reduce the range of wavenumber integration. Since the asymptotic solutions are expressed by the products of Bessel functions and simple exponential functions, they are analytically integrable. Finally, we obtain accurate Green's functions by adding together numerical and analytical integrations. We first show this asymptotic technique for Green's functions due to point sources, and extend it to Green's functions due to dipole sources. Finally, we demonstrate the validity and efficiency of our method for various cases.

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Generation of 6-C Synthetic Seismograms in Stratified Vertically-Transversely-Isotropic Media Using a Generalized Reflection and Transmission Coefficient Method

Geophysical Journal International ◽

10.1093/gji/ggab044 ◽

2021 ◽

Author(s):

Le Tang ◽

Xinding Fang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Transversely Isotropic ◽

Synthetic Seismograms ◽

Seismic Modeling ◽

Reflection And Transmission ◽

Near Surface ◽

Reflection And Transmission Coefficient ◽

Coefficient Method

Summary We develop a generalized reflection and transmission coefficient method (GRTM) for generating six-component (6-C) synthetic seismograms in horizontally layered vertically-transversely-isotropic (VTI) media. Compared with the traditional seismic modeling approaches that only consider translational motion, our method can simultaneously produce three-component translational and three-component rotational data excited by a point vector force or a moment tensor source in a layered half-space. Horizontally layered models are widely used in near surface applications as the properties of near surface formations generally show small lateral variations and change mainly along the depth direction. The use of the VTI constitutive relation can make our method applicable to more general situations because it takes into account the characteristics of sedimentary formations. We compare our method with a finite-difference method (FDM) for a variety of velocity models and acquisition geometries. The numerical results demonstrate that accurate 6-C synthetic seismograms can be calculated using our method. The computational efficiency of our method for 6-C seismic modeling is much higher than the finite-difference method, because it can reduce a 3D modeling problem to 2.5D by eliminating the azimuthal dimension. Also, our method does not require to perform additional spatial interpolations to obtain the rotational components. These advantages make our method suitable to serve as a forward modeling tool for rotational seismology.

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Single Defect in Finite one Dimensional Photonic Crystals

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.614-615.1629 ◽

2012 ◽

Vol 614-615 ◽

pp. 1629-1632

Author(s):

Gang Xu ◽

Yun Sun

Keyword(s):

Photonic Crystals ◽

Transmission Coefficient ◽

Transfer Matrix Method ◽

Matrix Method ◽

Defect Mode ◽

Transmission Peak ◽

Reflection And Transmission ◽

One Dimensional ◽

Single Defect ◽

Reflection And Transmission Coefficient

Applying transfer matrix method, we get reflection and transmission coefficient of finite one dimensional photonic crystals. At the same time, we consider the position influence of single defect. We find the frequency of defect mode is same, but the height of transmission peak is not same when single defect is in different position of crystal. The transmission peak is maximum when the defect is in center of finite one dimensional photonic crystals.

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Towards the concept of hydrodynamic cavitation control

Journal of Fluid Mechanics ◽

10.1017/s0022112096004223 ◽

1997 ◽

Vol 332 ◽

pp. 377-394 ◽

Cited By ~ 21

Author(s):

Dhiman Chatterjee ◽

Vijay H. Arakeri

Keyword(s):

Acoustic Field ◽

Bubble Dynamics ◽

Hydrodynamic Cavitation ◽

Careful Study ◽

Potential Control ◽

Cavitation Phenomenon ◽

Bubble Cavitation ◽

First Results ◽

Hydrodynamic Field ◽

Pass Through

A careful study of the existing literature available in the field of cavitation reveals the potential of ultrasonics as a tool for controlling and, if possible, eliminating certain types of hydrodynamic cavitation through the manipulation of nuclei size present in a flow. A glass venturi is taken to be an ideal device to study the cavitation phenomenon at its throat and its potential control. A piezoelectric transducer, driven at the crystal resonant frequency, is used to generate an acoustic pressure field and is termed an ‘ultrasonic nuclei manipulator (UNM)'. Electrolysis bubbles serve as artificial nuclei to produce travelling bubble cavitation at the venturi throat in the absence of a UNM but this cavitation is completely eliminated when a UNM is operative. This is made possible because the nuclei, which pass through the acoustic field first, cavitate, collapse violently and perhaps fragment and go into dissolution before reaching the venturi throat. Thus, the potential nuclei for travelling bubble cavitation at the venturi throat seem to be systematically destroyed through acoustic cavitation near the UNM. From the solution to the bubble dynamics equation, it has been shown that the potential energy of a bubble at its maximum radius due to an acoustic field is negligible compared to that for the hydrodynamic field. Hence, even though the control of hydrodynamic macro cavitation achieved in this way is at the expense of acoustic micro cavitation, it can still be considered to be a significant gain. These are some of the first results in this direction.

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Study of Ultrasonic Wave Propagation Characteristics in Multilayer Bonded Structures

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.903 ◽

2012 ◽

Vol 204-208 ◽

pp. 903-907

Author(s):

Chun An Ai ◽

Yu Liu ◽

Zhi Gao Xu ◽

Jian Li

Keyword(s):

Wave Propagation ◽

Reflection Coefficient ◽

Experimental Research ◽

Bonding Strength ◽

Shear Velocity ◽

Angle Of Incidence ◽

Propagation Characteristics ◽

Reflection And Transmission ◽

Ultrasonic Wave Propagation ◽

Reflection And Transmission Coefficient

The reflection and transmission coefficient equations in multilayer bonded structures have been achieved by improved global matrix algorithm. The change of bonded strength have been simulated by the change of shear velocity in bonded layer.The curve between reflection coefficient and angle of incidence in immersion and plane ultrasonic longitudinal wave have been calculated in different bonding strength and the same frequency. The emulational graph had been compared and analyzed. The quantitative test of bonding strength and orientation of poor bonded district have been implemented. The conclusion can provide theoretic guidance for experimental research of bonded strength.

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SO-FDTD method of analyzing the reflection and transmission coefficient of weakly ionized dusty plasma layer

Acta Physica Sinica ◽

10.7498/aps.61.125201 ◽

2012 ◽

Vol 61 (12) ◽

pp. 125201

Author(s):

Li Lin-Qian ◽

Shi Yan-Xiang ◽

Wang Fei ◽

Wei Bing

Keyword(s):

Transmission Coefficient ◽

Dusty Plasma ◽

Plasma Layer ◽

Fdtd Method ◽

Reflection And Transmission ◽

Reflection And Transmission Coefficient ◽

Weakly Ionized

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A Numerical Study on the Distribution and Evolution Characteristics of an Acoustic Field in the Time Domain of a Centrifugal Pump Based on Powell Vortex Sound Theory

Applied Sciences ◽

10.3390/app9235018 ◽

2019 ◽

Vol 9 (23) ◽

pp. 5018 ◽

Cited By ~ 8

Author(s):

Chang Guo ◽

Jingying Wang ◽

Ming Gao

Keyword(s):

Centrifugal Pump ◽

Acoustic Field ◽

Time Domain ◽

Acoustic Pressure ◽

Numerical Study ◽

Source Region ◽

Centrifugal Pumps ◽

Acoustic Source ◽

Evolution Characteristics ◽

Source Component

The acoustic field distribution and evolution characteristics in a time domain inside a centrifugal pump are studied. During the fluid motion process, the acoustic source and acoustic pressure are basically less than 0, and the minimum value of the two parameters is distributed near the tongue. Additionally, the concentration, break, extend, migration and reaggregation phenomena of the minimum acoustic source region exist. Specifically, as the blade passes through the tongue, the minimum acoustic source region concentrates on the tongue firstly, then extends and migrates downstream slightly with the blade motion, and aggregates again around the tongue, which results in the similar evolution characteristics of acoustic pressure. Moreover, the standard deviation (STD) of acoustic source mainly focuses near the pressure side of blade tail and volute tongue, and the maximum STD is located at the tongue. Compared with the source component induced by stretching of the vortex, the source component induced by non-uniformity of fluid kinetic energy is closer to the overall acoustic source. Take the tongue as an example, at various rotational speeds, the STD proportions of the two components are about 5% and 95%, respectively. This study discusses the generation, distribution and evolution characteristics of acoustic field, which lays a foundation to analyze the acoustic field propagation mechanism of centrifugal pumps.

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Reconstruction and Separation in a Semi-Free Field by Using the Distributed Source Boundary Point Method-Based Nearfield Acoustic Holography

Journal of Vibration and Acoustics ◽

10.1115/1.2731403 ◽

2007 ◽

Vol 129 (3) ◽

pp. 323-329 ◽

Cited By ~ 7

Author(s):

C. X. Bi ◽

X. Z. Chen ◽

R. Zhou ◽

J. Chen

Keyword(s):

Acoustic Field ◽

Boundary Point ◽

Free Field ◽

Treatment Method ◽

Point Method ◽

Acoustic Source ◽

Acoustic Holography ◽

Distributed Source ◽

Boundary Point Method ◽

Nearfield Acoustic Holography

In a semi-free field, the acoustic field is composed of two components: the direct sound and the reflected sound. Because it is difficult to separate the direct sound from the acoustic field, conventional nearfield acoustic holography (NAH) methods cannot reconstruct an acoustic source and predict the acoustic field directly. Through utilization of the distributed source boundary point method (DSBPM)-based NAH, a treatment method for a semi-free field is proposed. In the method, the source in a semi-free field can be reconstructed correctly, and the acoustic field can be predicted and separated. An experiment on a speaker in a semi-anechoic chamber is carried out to verify the proposed method. By comparing the reconstructed and predicted results in DSBPM-based NAH with and without the proposed method, the proposed method is validated. The disadvantages of NAH without any treatment method in a semi-free field are demonstrated.

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