Axisymmetric Body-Force Fields in Elastodynamics of Transversely Isotropic Media

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Morteza Eskandari-Ghadi ◽  
Ronald Y. S. Pak
Keyword(s):  
Wave Equations ◽  
Transversely Isotropic ◽  
Axisymmetric Body ◽  
Material Condition ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axisymmetric Problems ◽  
Elastodynamic Solution ◽  
Limiting Case ◽  
Recent Extension

In this paper, a complete elastodynamic solution for axisymmetric problems under axial body-forces in terms of two retarded potential functions in transversely isotropic media is extended to the case of general torsionless axisymmetry. Allowing for both axial and radial distributed internal loads through the use of an extra potential, the new solution retains its completeness via the theory of repeated wave equations. By virtue of its analytical design, the formulation can be reduced to the corresponding elastostatic case by simply suppressing the time-dependence of its potentials as well as the case of isotropy. In the limiting case of the latter material condition, the proposed representation for elastostatic problem degenerates to a recent extension of Love’s potential function.

Efficient mixed-domain pure P-wave equations for 2D and 3D tilted transversely isotropic media

2020 ◽  
Vol 68 (3) ◽  
pp. 605-618
Author(s):  
Bowen Li ◽  
Deli Wang ◽  
Jinju Zhou ◽  
Qianxiang Zhang ◽  
Rui Wang
Keyword(s):  
Wave Equations ◽  
Transversely Isotropic ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
2D And 3D

scholarly journals Pure P‐ and S‐wave equations in transversely isotropic media

2020 ◽  
Vol 68 (9) ◽  
pp. 2762-2769
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah ◽  
Umair bin Waheed
Keyword(s):  
Wave Equations ◽  
Transversely Isotropic ◽  
S Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

A one-way dual-domain propagator for scalar qP-waves in VTI media

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. D9-D17 ◽  
Author(s):  
Qiyu Han ◽  
Ru-Shan Wu
Keyword(s):  
Dispersion Relation ◽  
Phase Shift ◽  
Wave Equations ◽  
Large Angle ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Elastic Wave Equations ◽  
Dual Domain ◽  
Vti Media

In this paper, we present an anisotropic one-way propagator for modeling and imaging quasi-P (qP) waves in transversely isotropic media with a vertically symmetric axis (VTI media). We derive the dispersion relation for a scalar qP-wave using elastic wave equations for anisotropic media. By applying a rational approximation to the dispersion relation, we obtain a one-way, dual-domain, scalar qP-wave propagator for heterogeneous VTI media. The propagator includes a phase-shift term and both phase-screen and large-angle correction terms. The phase-shift term is implemented in the wavenumber domain, while the other terms are implemented in the space domain. Fourier transformations are used to shuttle the wavefield between the two domains. This propagator can be used to propagate qP-wavefields within an isotropic or a VTI medium, with either medium containing lateral heterogeneities. Error analysis of the impulse response and dispersion relations demonstrates that the propagator is accurate and stable and has a wide-angle capability. The application of the propagator to the imaging of qP-wave data with VTI models which contain complex structures and large perturbations of velocity and anisotropy results in excellent image quality. This demonstrates the potential value of the propagator for use in modeling and imaging qP-wavefields within strongly heterogeneous VTI media.

scholarly journals Anisotropic viscoacoustic wave modelling in VTI media using frequency-dependent complex velocity

2020 ◽  
Author(s):  
Yabing Zhang ◽  
Yang Liu ◽  
Shigang Xu
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Wave Equations ◽  
Transversely Isotropic ◽  
P Wave ◽  
Low Rank ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Rank Decomposition ◽  
Low Rank Decomposition

Abstract Under the conditions of acoustic approximation and isotropic attenuation, we derive the pseudo- and pure-viscoacoustic wave equations from the complex constitutive equation and the decoupled P-wave dispersion relation, respectively. Based on the equations, we investigate the viscoacoustic wave propagation in vertical transversely isotropic media. The favourable advantage of these formulas is that the phase dispersion and the amplitude dissipation terms are inherently separated. As a result, we can conveniently perform the decoupled viscoacoustic wavefield simulations by choosing different coefficients. In the computational process, a generalised pseudo-spectral method and a low-rank decomposition scheme are adopted to calculate the wavenumber-domain and mixed-domain propagators, respectively. Because low-rank decomposition plays an important role in the simulated procedure, we evaluate the approximation accuracy for different operators using a linear velocity model. To demonstrate the effectiveness and the accuracy of our method, several numerical examples are carried out based on the new pseudo- and pure-viscoacoustic wave equations. Both equations can effectively describe the viscoacoustic wave propagation characteristics in vertical transversely isotropic media. Unlike the pseudo-viscoacoustic wave equation, the pure-viscoacoustic wave equation can produce stable viscoacoustic wavefields without any SV-wave artefacts.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

Variation of stacking velocity in transversely isotropic media

1995 ◽  
Vol 26 (2-3) ◽  
pp. 431-436 ◽  
Author(s):  
Patrick N.(Jr). Okoye ◽  
N. F. Uren ◽  
W. Waluyo
Keyword(s):  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Elastic Least-Squares Imaging in Tilted Transversely Isotropic Media for Multicomponent Land and Pressure Marine Data

2020 ◽  
Vol 41 (4) ◽  
pp. 805-833 ◽  
Author(s):  
Jidong Yang ◽  
Biaolong Hua ◽  
Paul Williamson ◽  
Hejun Zhu ◽  
George McMechan ◽  
...  
Keyword(s):  
Least Squares ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Marine Data
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