Frequency-domain Green’s functions for radar waves in heterogeneous 2.5D media

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. J13-J22 ◽  
Author(s):  
Karl J. Ellefsen ◽  
Delphine Croizé ◽  
Aldo T. Mazzella ◽  
Jason R. McKenna
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Frequency Domain ◽  
Hybrid Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Homogeneous Model ◽  
Electromagnetic Properties ◽  
Perfectly Matched Layers ◽  
Phase Errors

Green’s functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the [Formula: see text]- and [Formula: see text]-directions, but not in the [Formula: see text]-direction. Wave propagation in the [Formula: see text]- and [Formula: see text]-directions is simulated with the finite-difference method, and wave propagation in the [Formula: see text]-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Green’s functions is assessed by comparing them with independently calculated Green’s functions. For a homogeneous model, the magnitude errors range from [Formula: see text] through 0.44%, and the phase errors range from [Formula: see text] through 4.86%. For a layered model, the magnitude errors range from [Formula: see text] through 2.06%, and the phase errors range from [Formula: see text] through 2.73%. These numerical Green’s functions might be used for forward modeling and full waveform inversion.

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

2.5D AND 3D GREEN'S FUNCTIONS FOR ACOUSTIC WEDGES: IMAGE SOURCE TECHNIQUE VERSUS A NORMAL MODE APPROACH

2013 ◽  
Vol 21 (01) ◽  
pp. 1250025 ◽  
Author(s):  
A. TADEU ◽  
E. G. A. COSTA ◽  
J. ANTÓNIO ◽  
P. AMADO-MENDES
Keyword(s):  
Wave Propagation ◽  
Normal Mode ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Element Formulation ◽  
Two Dimensional ◽  
Image Source ◽  
Point Pressure ◽  
Fluid Channel

2.5D and 3D Green's functions are implemented to simulate wave propagation in the vicinity of two-dimensional wedges. All Green's functions are defined by the image-source technique, which does not account directly for the acoustic penetration of the wedge surfaces. The performance of these Green's functions is compared with solutions based on a normal mode model, which are found not to converge easily for receivers whose distance to the apex is similar to the distance from the source to the apex. The applicability of the image source Green's functions is then demonstrated by means of computational examples for three-dimensional wave propagation. For this purpose, a boundary element formulation in the frequency domain is developed to simulate the wave field produced by a 3D point pressure source inside a two-dimensional fluid channel. The propagating domain may couple different dipping wedges and flat horizontal layers. The full discretization of the boundary surfaces of the channel is avoided since 2.5D Green's functions are used. The BEM is used to couple the different subdomains, discretizing only the vertical interfaces between them.

scholarly journals VISCO-ACOUSTIC MODELING IN THE FREQUENCY DOMAIN USING A MIXED-GRID FINITE-DIFFERENCE METHOD AND ATTENUATION-DISPERSION MODEL

2019 ◽  
Vol 37 (2) ◽  
Author(s):  
S.K. Avendaño ◽  
M.A. Ospina ◽  
J.C. Muñoz-Cuartas ◽  
H. Montegranario
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Frequency Domain ◽  
Difference Method ◽  
Seismic Attenuation ◽  
Numerical Dispersion ◽  
Acoustic Medium ◽  
Time Migration ◽  
Point Scheme

ABSTRACT. Seismic modeling is an important step in the process used for imaging Earth sub-surface. Current applications require accurate models associated with solutions of the equation of wave propagation in realistic medium. In this work, we propose a modeling for 2D wave propagation in a visco-acoustic medium with variable velocity and density, handled in the frequency domain under conditions that describe dissipation depending on the quality factor Q. We use mixed-grid finite-difference method and optimize it for the case of the visco-acoustic medium with the aim to minimize numerical dispersion. We present solutions for test cases in homogeneous media and compare the analytic solutions. Further, we compare the solution using conventional grid (5-point scheme) and our mixed grid implementation (9-point scheme), finding a better response with the mixed grid 9-point scheme. We also studied the characteristics of the numerical solution, wave fields for P-waves are discussed for different velocity profiles, damping functions and Q values finding that the method performs very well with potential in applications that require full knowledge of the wave field such as Full Waveform Inversion or Reverse Time Migration. Keywords: seismic attenuation, wave propagation modeling, visco-acoustic medium, quality factor.RESUMO. A modelagem sísmica é um passo importante no processo da construção de imagens da sub-superfície da Terra. Aplicações atuais exigem modelos de exatidão associados a soluções da equação de propagação de ondas em meio realista. Neste trabalho, nós propomos uma modelagem para propagação de ondas 2D em um meio visco-acústico com velocidade e densidade variáveis, manipuladas no domínio da frequência sob condições que descrevem a dissipação dependendo do fator de qualidade Q. Utilizamos o método de diferenças finitas em redes mistas e otimizamos para o caso do meio visco-acústico com o objetivo de minimizar a dispersão numérica. Apresentamos soluções para casos de teste em meios homogêneos e comparamos com as soluções analíticas. Além disso, comparamos a solução usando uma rede convencional (5-pontos) e nossa implementação de redes mistas (9-pontos), encontrando uma melhor resposta com o esquema de 9-pontos da rede mista. Também estudamos as características da solução numérica, campos de onda para ondas P são discutidos para diferentes perfis de velocidade, funções de amortecimento e valores de Q, descobrindo que o método funciona muito bem com potencial em aplicações que exigem conhecimento completo do campo de onda, como inversão de forma de onda completa ou Migração de Tempo Inverso.Palavras-chave: atenuação sísimica, modelagem de propagação de onda, meio visco-acústico, fator de qualidade.

Source locations of microseisms in the North Atlantic from Matched Field Processing using full Green's Functions.

2021 ◽  
Author(s):  
Sven Schippkus ◽  
Céline Hadziioannou
Keyword(s):  
Wave Propagation ◽  
Travel Time ◽  
North Atlantic ◽  
Seismic Noise ◽  
Green's Functions ◽  
Green’S Functions ◽  
Regional Scale ◽  
Matched Field Processing ◽  
The North ◽  
The North Atlantic

<p>Precise knowledge of the sources of seismic noise is fundamental to our understanding of the ambient seismic field and its generation mechanisms. Two approaches to locating such sources exist currently. One is based on minimizing the misfit between estimated Green's functions from cross-correlation of seismic noise and synthetically computed correlation functions. This approach is computationally expensive and not yet widely adopted. The other, more common approach is Beamforming, where a beam is computed by shifting waveforms in time corresponding to the slowness of a potentially arriving wave front. Beamforming allows fast computations, but is limited to the plane-wave assumption and sources outside of the array.</p><p>Matched Field Processing (MFP) is Beamforming in the spatial domain. By probing potential source locations directly, it allows for arbitrary wave propagation in the medium as well as sources inside of arrays. MFP has been successfully applied at local scale using a constant velocity for travel-time estimation, sufficient at that scale. At regional scale, travel times can be estimated from phase velocity maps, which are not yet available globally at microseism frequencies.</p><p>To expand MFP’s applicability to new regions and larger scales, we replace the replica vectors that contain only travel-time information with full synthetic Green's functions. This allows to capture the full complexity of wave propagation by including relative amplitude information between receivers and multiple phases. We apply the method to continuous recordings of stations surrounding the North Atlantic and locate seismic sources in the primary and secondary microseism band, using pre-computed databases of Green's functions for computational efficiency. The framework we introduce here can easily be adapted to a laterally homogeneous Earth once such Green’s function databases become available, hopefully in the near future.</p>

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