scholarly journals Transformation to zero offset in transversely isotropic media

1995 ◽  
Author(s):  
T. Alkhalifah
Keyword(s):  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Zero Offset

scholarly journals Large-offset P-wave traveltime in layered transversely isotropic media

Geophysics ◽  
2021 ◽  
pp. 1-49
Author(s):  
Mohammad Mahdi Abedi ◽  
David Pardo
Keyword(s):  
Asymptotic Series ◽  
Transversely Isotropic ◽  
Velocity Estimation ◽  
Horizontal Velocity ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
Heterogeneity Parameter ◽  
Zero Offset

Large-offset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with vertical symmetry axis (VTI), the accuracy of traditional traveltime approximations is limited to near offsets. Herein, we propose a new traveltime approximation that maintains the accuracy of the classical equations around zero offset, and exhibits the correct curvilinear asymptote at infinitely large offsets. Our approximation is based on the conventional acoustic assumption. Its equation incorporates six parameters. To define them, we use the Taylor series expansion of the exact traveltime around zero offset, and a new asymptotic series for infinite offset. Our asymptotic equation shows that the traveltime behavior at infinitely large offsets is dominated by the properties of the layer with the maximum horizontal velocity in the sequence. The parameters of our approximation depend on: the effective zero offset traveltime, the normal moveout velocity, the anellipticity, a new large-offset heterogeneity parameter, and the properties of the layer with the maximum horizontal velocity in the sequence. We apply our traveltime approximation: (1) to directly calculate traveltime and ray parameter at given offsets, as analytical forward modeling; and (2) to estimate the first four of the aforementioned parameters for the layers beneath a known high-velocity layer. Our large-offset heterogeneity parameter includes the layering effect on the reflections traveltime.

scholarly journals A transversely isotropic medium with a tilted symmetry axis normal to the reflector

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. A19-A24 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Paul Sava
Keyword(s):  
Closed Form ◽  
Model Building ◽  
Incidence Angle ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
Reflection Angle ◽  
Velocity Model Building ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Zero Offset

The computational tools for imaging in transversely isotropic media with tilted axes of symmetry (TTI) are complex and in most cases do not have an explicit closed-form representation. Developing such tools for a TTI medium with tilt constrained to be normal to the reflector dip (DTI) reduces their complexity and allows for closed-form representations. The homogeneous-case zero-offset migration in such a medium can be performed using an isotropic operator scaled by the velocity of the medium in the tilt direction. For the nonzero-offset case, the reflection angle is always equal to the incidence angle, and thus, the velocities for the source and receiver waves at the reflection point are equal and explicitly dependent on the reflection angle. This fact allows for the development of explicit representations for angle decomposition as well as moveout formulas for analysis of extended images obtained by wave-equation migration. Although setting the tilt normal to the reflector dip may not be valid everywhere (i.e., on salt flanks), it can be used in the process of velocity model building, in which such constrains are useful and typically are used.

scholarly journals NMO‐velocity surfaces and Dix‐type formulas in anisotropic heterogeneous media

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 939-951 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Cross Sections ◽  
Heterogeneous Media ◽  
Transversely Isotropic ◽  
Radius Vector ◽  
P Wave ◽  
Reflection Data ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Anisotropic Layers ◽  
Zero Offset

Reflection moveout of pure modes recorded on conventional‐length spreads is described by a normal‐moveout (NMO) velocity that depends on the orientation of the common‐midpoint (CMP) line. Here, we introduce the concept of NMO‐velocity surfaces, which are obtained by plotting the NMO velocity as the radius‐vector along all possible directions in 3‐D space, and use it to develop Dix‐type averaging and differentiation algorithms in anisotropic heterogeneous media. The intersection of the NMO‐velocity surface with the horizontal plane represents the NMO ellipse that can be estimated from wide‐azimuth reflection data. We demonstrate that the NMO ellipse and conventional‐spread moveout as a whole can be modeled by Dix‐type averaging of specifically oriented cross‐sections of the NMO‐velocity surfaces along the zero‐offset reflection raypath. This formalism is particularly simple to implement for a stack of homogeneous anisotropic layers separated by plane dipping boundaries. Since our method involves computing just a single (zero‐offset) ray for a given reflection event, it can be efficiently used in anisotropic stacking‐velocity tomography. Application of the Dix‐type averaging to layered transversely isotropic media with a vertical symmetry axis (VTI) shows that the presence of dipping interfaces above the reflector makes the P‐wave NMO ellipse dependent on the vertical velocity and anisotropic coefficients ε and δ. In contrast, P‐wave moveout in VTI models with a horizontally layered overburden is fully controlled by the NMO velocity of horizontal events and the Alkhalifah‐Tsvankin coefficient η ≈ ε − δ. Hence, in some laterally heterogeneous, layered VTI models P‐wave reflection data may provide enough information for anisotropic depth processing.

Fowler DMO and time migration for transversely isotropic media

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 835-845 ◽  
Author(s):  
John Anderson ◽  
Tariq Alkhalifah ◽  
Ilya Tsvankin
Keyword(s):  
Transverse Isotropy ◽  
Computing Time ◽  
Transversely Isotropic ◽  
P Wave ◽  
Effective Parameters ◽  
Weak Anisotropy ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Zero Offset

The main advantage of Fowler’s dip‐moveout (DMO) method is the ability to perform velocity analysis along with the DMO removal. This feature of Fowler DMO becomes even more attractive in anisotropic media, where imaging methods are hampered by the difficulty in reconstructing the velocity field from surface data. We have devised a Fowler‐type DMO algorithm for transversely isotropic media using the analytic expression for normal‐moveout velocity. The parameter‐estimation procedure is based on the results of Alkhalifah and Tsvankin showing that in transversely isotropic media with a vertical axis of symmetry (VTI) the P‐wave normal‐moveout (NMO) velocity as a function of ray parameter can be described fully by just two coefficients: the zero‐dip NMO velocity [Formula: see text] and the anisotropic parameter η (η reduces to the difference between Thomsen parameters ε and δ in the limit of weak anisotropy). In this extension of Fowler DMO, resampling in the frequency‐wavenumber domain makes it possible to obtain the values of [Formula: see text] and η by inspecting zero‐offset (stacked) panels for different pairs of the two parameters. Since most of the computing time is spent on generating constant‐velocity stacks, the added computational effort caused by the presence of anisotropy is relatively minor. Synthetic and field‐data examples demonstrate that the isotropic Fowler DMO technique fails to generate an accurate zero‐offset section and to obtain the zero‐dip NMO velocity for nonelliptical VTI models. In contrast, this anisotropic algorithm allows one to find the values of the parameters [Formula: see text] and η (sufficient to perform time migration as well) and to correct for the influence of transverse isotropy in the DMO processing. When combined with poststack F-K Stolt migration, this method represents a complete inversion‐processing sequence capable of recovering the effective parameters of transversely isotropic media and producing migrated images for the best‐fit homogeneous anisotropic model.

Multicomponent stacking‐velocity tomography for transversely isotropic media

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1564-1574 ◽  
Author(s):  
Vladimir Grechka ◽  
Andres Pech ◽  
Ilya Tsvankin
Keyword(s):  
Velocity Field ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Accurate Estimation ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Inversion Procedure ◽  
Important Processing ◽  
Zero Offset

Accurate estimation of the velocity field is the most difficult step in imaging of seismic data for anisotropic media. Here, the velocity‐analysis problem is examined for the most common anisotropic model of sedimentary formations—transverse isotropy (TI) with arbitrary orientation of the symmetry axis. We show that supplementing wide‐azimuth reflected PP data with mode‐converted (PS) waves yields more stable estimates of the anisotropic coefficients and, in many cases, helps to constrain the model in depth. An important processing step preceding the inversion is computation of the traveltimes of the pure SS‐waves from those of the PP‐, and PS‐waves based on a technique recently developed by Grechka and Tsvankin. This procedure allows us to replace PS‐wave moveout, which is generally asymmetric with respect to zero offset, with the symmetric (hyperbolic on short spreads) moveout of the pure SS reflections. Then, generalizing the algorithm previously suggested for PP data, we develop a joint tomographic inversion of the normal‐moveout (NMO) ellipses and zero‐offset traveltimes of PP‐ and SS‐waves. Application of the method to wide‐azimuth PP and PS reflections from a dipping interface beneath a homogeneous TI layer shows that for a range of reflector dips and tilt angles of the symmetry axis, it is possible to build the anisotropic velocity field in the depth domain. We also extend our inversion procedure to layered TI media with curved interfaces and study its stability in the presence of noise and heterogeneity.

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
Sign in / Sign up

Export Citation Format

Share Document