Multiple Suppression By a Wave-equation Extrapolation Method

1991 ◽  
Vol 22 (2) ◽  
pp. 481-483 ◽  
Author(s):  
B. Zhou ◽  
S. A. Greenhalgh
Keyword(s):  
Wave Equation ◽  
Extrapolation Method

A sound extrapolation method for aeroacoustics far-field prediction in presence of vortical waves

2017 ◽  
Vol 820 ◽  
pp. 424-450 ◽  
Author(s):  
Siyang Zhong ◽  
Xin Zhang
Keyword(s):  
Wave Equation ◽  
Leading Edge ◽  
Extrapolation Method ◽  
Alternative Form ◽  
Far Field ◽  
Computational Domain ◽  
Surface Integral ◽  
Inhomogeneous Wave ◽  
Computation Efficiency ◽  
Inhomogeneous Wave Equation

Off-surface integral solutions to an inhomogeneous wave equation based on acoustic analogy could suffer from spurious wave contamination when volume integrals are ignored for computation efficiency and vortical/turbulent gusts are convected across the integration surfaces, leading to erroneous far-field directivity predictions. Vortical gusts often exist in aerodynamic flows and it is inevitable their effects are present on the integration surface. In this work, we propose a new sound extrapolation method for acoustic far-field directivity prediction in the presence of vortical gusts, which overcomes the deficiencies in the existing methods. The Euler equations are rearranged to an alternative form in terms of fluctuation variables that contains the possible acoustical and vortical waves. Then the equations are manipulated to an inhomogeneous wave equation with source terms corresponding to surface and volume integrals. With the new formulation, spurious monopole and dipole noise produced by vortical gusts can be suppressed on account of the solenoidal property of the vortical waves and a simple convection process. It is therefore valid to ignore the volume integrals and preserve the sound properties. The resulting new acoustic inhomogeneous convected wave equations could be solved by means of the Green’s function method. Validation and verification cases are investigated, and the proposed method shows a capacity of accurate sound prediction for these cases. The new method is also applied to the challenging airfoil leading edge noise problems by injecting vortical waves into the computational domain and performing aeroacoustic studies at both subsonic and transonic speeds. In the case of a transonic airfoil leading edge noise problem, shocks are present on the airfoil surface. Good agreements of the directivity patterns are obtained compared with direct computation results.

Wave‐equation extrapolation‐based multiple attenuation: 2-D filtering in the f-k domain

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1377-1391 ◽  
Author(s):  
Binzhong Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Wave Equation ◽  
Prior Information ◽  
Original Data ◽  
Conventional Technique ◽  
Nonlinear Filter ◽  
Extrapolation Method ◽  
Multiple Model ◽  
Numerical Examples ◽  
Multiple Attenuation

A new nonlinear filter for wave‐equation extrapolation‐based multiple suppression is designed in the f-k domain. The realization of the new filter in the f-k domain is an extension of the conventional f-k dip filter. However, the new demultiple filter is superior to the conventional f-k dip filter in the sense that the multiple reject zones are determined automatically (based on the information of the input original data and the multiple model traces obtained by the wave‐extrapolation method) rather than by prior information on multiple moveout (dip) range. Therefore, it can easily cope with situations such as aliasing and the mixture of energy from multiples and primaries in the same quadrant. The new filter is smooth on the boundary of the reject area. Numerical examples demonstrate that the new filter is equivalent to the conventional f-k dip filter in multiple suppression for simple situations. However, when the multiples and primaries are mixed in the same quadrant and have only slight difference in dip, the new filter offers significant advantages over the conventional technique.

One-step extrapolation method for reverse time migration

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A29-A33 ◽  
Author(s):  
Yu Zhang ◽  
Guanquan Zhang
Keyword(s):  
Wave Equation ◽  
Extrapolation Method ◽  
New Method ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Order Partial Differential Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
One Step

We have proposed a new method, a one-step extrapolation algorithm, to solve the acoustic wave equation. By introducing a square-root operator, the two-way wave equation can be formulated as a first-order partial differential equation in time, which is similar to the one-way wave equation. To solve the new wave equation, we used a stable explicit extrapolation method in the time direction and handled lateral velocity variations in the space and wavenumber domains. Unlike the conventional explicit finite-difference schemes, the new method does not suffer from numerical instability or numerical dispersion problems. It can be used to design cost-effective and high-quality reverse time migration or modeling code.

scholarly journals Depth Migration Based on Two-Way Wave Equation to Image OBS Multiples: A Case Study in the South Shetland Margin (Antarctica)

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Sha Song ◽  
Jiachun You ◽  
Qing Cao ◽  
Bin Chen ◽  
Xiaomeng Cao
Keyword(s):  
Wave Equation ◽  
Extrapolation Method ◽  
Seismic Exploration ◽  
Ocean Bottom Seismometer ◽  
The South ◽  
Time Migration ◽  
Multiple Imaging ◽  
Imaging Results ◽  
Obs Data ◽  
Wavefield Extrapolation

With the development of marine seismic exploration, the ocean bottom seismometer (OBS) as a new seismic acquisition technology has been widely concerned. Although multiple waves are frequently viewed as noises, they may carry a wealth of subsurface information and produce a broader illumination than primary waves. To perform multiple wave imaging, we propose to utilize a two-way wave equation depth wavefield extrapolation method which is rarely used in this field. A simple dipping model is imaged by using primary and multiple waves, which proves the superiority of multiple waves in imaging over the primary waves and lays a foundation for practical application. Moreover, the comparison of multiple imaging results by reverse time migration and those by our proposed method demonstrates that our proposed method requires less storage space. In this study, we apply this migration method to actual OBS data collected in the South Shetland margin (Antarctica), where gas hydrates have been well documented. Firstly, the wavefield separation method is adopted to process the OBS data, so as to produce reliable primary and multiples waves; secondly, the ray-tracing method is used to derive the velocity field; and finally, the depth wavefield extrapolation method based on the two-way wave equation is applied to image primary and multiple waves. Migration results show that multiple waves provide a broader illumination and a clearer sediment structure than primary waves, especially for the highly shallow reflections.

point-Analysis Using the Extrapolation Method in the Analytical Electron microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 430-431
Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto
Keyword(s):  
Electron Microscope ◽  
Extrapolation Method ◽  
X Ray ◽  
Absorption Correction ◽  
Point Analysis ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Data Points ◽  
Identical Composition ◽  
X Ray Absorption

Absorption correction is often required in quantitative x-ray microanalysis of thin specimens using the analytical electron microscope. For such correction, it is convenient to use the extrapolation method[l] because the thickness, density and mass absorption coefficient are not necessary in the method. The characteristic x-ray intensities measured for the analysis are only requirement for the absorption correction. However, to achieve extrapolation, it is imperative to obtain data points more than two at different thicknesses in the identical composition. Thus, the method encounters difficulty in analyzing a region equivalent to beam size or the specimen with uniform thickness. The purpose of this study is to modify the method so that extrapolation becomes feasible in such limited conditions. Applicability of the new form is examined by using a standard sample and then it is applied to quantification of phases in a Ni-Al-W ternary alloy.The earlier equation for the extrapolation method was formulated based on the facts that the magnitude of x-ray absorption increases with increasing thickness and that the intensity of a characteristic x-ray exhibiting negligible absorption in the specimen is used as a measure of thickness.

Quantitative x-ray microanalysis and thickness determination using ζ factor

1996 ◽  
Vol 54 ◽  
pp. 580-581
Author(s):  
M. Watanabe ◽  
Z. Horita ◽  
M. Nemoto
Keyword(s):  
Diffusion Couple ◽  
Extrapolation Method ◽  
Thin Specimen ◽  
Beam Position ◽  
X Ray ◽  
Thickness Determination ◽  
Experimental Limitation ◽  
X Ray Absorption

X-ray absorption in quantitative x-ray microanalysis of thin specimens may be corrected without knowledge of thickness when the extrapolation method or the differential x-ray absorption (DXA) method is used. However, there is an experimental limitation involved in each method. In this study, a method is proposed to overcome such a limitation. The method is developed by introducing the ζ factor and by combining the extrapolation method and DXA method. The method using the ζ factor, which is called the ζ-DXA method in this study, is applied to diffusion-couple experiments in the Ni-Al system.For a thin specimen where incident electrons are fully transparent, the characteristic x-ray intensity generated from a beam position, I, may be represented as I = (NρW/A)Qωaist.

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