Orthogonal parameters for anisotropic velocity analysis

Fowler, Paul J.; Jackson, Alexander; Hootman, Bruce W.

doi:10.1190/1.2369850

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…However, this approach, if not impossible, is extremely expensive for large‐scale seismic data sets. Furthermore, since these parameters are not orthogonal, the semblance plots might appear to be unfocused and ambiguous, hence presenting difficulties for picking (Fowler, Jackson, and Hootman, ).…”

Section: Theorymentioning

confidence: 99%

A fast algorithm for 3D azimuthally anisotropic velocity scan

Fomel

Ying

2014

Geophysical Prospecting

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The conventional velocity scan can be computationally expensive for large‐scale seismic data sets, particularly when the presence of anisotropy requires multiparameter scanning. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan by generalizing the previously proposed 2D butterfly algorithm for hyperbolic Radon transforms. To compute semblance in a two‐parameter residual moveout domain, the numerical complexity of our algorithm is roughly O(N3logN) as opposed to O(N5) of the straightforward velocity scan, with N being the representative of the number of points in a particular dimension of either data space or parameter space. Synthetic and field data examples demonstrate the superior efficiency of the proposed algorithm.

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Section: Theorymentioning

confidence: 99%

A fast algorithm for 3D azimuthally anisotropic velocity scan

Fomel

Ying

2014

Geophysical Prospecting

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“…Stovas and Ursin (2004), using another methodology, derived a different continued‐fraction approximation for the traveltime function but this approximation is only valid for short and intermediate offsets. Fowler, Jackson and Hootman (2006) provided a methodology using orthogonal parameters to describe the traveltime approximation. They studied the orthogonal approximations to Tsvankin and Thomsen 1994's equation and to the shifted hyperbola.…”

Section: Introductionmentioning

confidence: 99%

Traveltime approximations for q‐P waves in vertical transversely isotropy media*

Aleixo

Schleicher

2010

Geophysical Prospecting

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A B S T R A C TAs exploration targets have become deeper, cable lengths have increased accordingly, making the conventional two term hyperbolic traveltime approximation produce increasingly erroneous traveltimes. To overcome this problem, many traveltime formulas were proposed in the literature that provide approximations of different quality. In this paper, we concentrate on simple traveltime approximations that depend on a single anisotropy parameter. We give an overview of a collection of such traveltime approximations found in the literature and compare their quality. Moreover, we propose some new single-parameter traveltime approximations based on the approximations found in the literature. The main advantage of our approximations is that some of them are rather simple analytic expressions that make them easy to use, while achieving the same quality as the better of the established formulas. I N T R O D U C T I O NTraveltime approximations play a key role in the processing of reflection data. They are used in, for example, migration (Alkhalifah and Larner 1994; Vestrum, Lawton and Schmid 1999; Mukherjee, Sen and Stoffa 2001), moveout correction and velocity analysis (Tsvankin and Thomsen 1994;Alkhalifah and Tsvankin 1995;Fomel 2003) and remigration (Fomel 1994;Hubral, Tygel and Schleicher 1996;Schleicher and Aleixo 2007).The standard hyperbolic approximation (Dix 1955) of the P-wave reflection traveltime commonly used in seismic data processing is exact for a homogeneous isotropic medium and a planar reflector. It remains a good approximation for short offsets in layered media with not too strong lateral variations. However, as exploration targets have become deeper, cable lengths have increased accordingly. Increased offsets have made the conventional two term hyperbolic equation produce increasingly erroneous traveltimes.to the reflection moveout to guarantee an accurate determination of the model parameters.Many attempts have been made over the years to provide higher-order reflection moveout equations that provide good approximations for higher offsets. Working with a layered earth model, Bolshix (1956) obtained a sixth-order equation that approximates traveltime. Later, Taner and Koehler (1969) provided a high-order approximation for traveltimes based on an exact Taylor-series expansion of the traveltime. May and Straley (1979) used orthogonal polynomials to derive a high-order traveltime approximation. These approximations based on polynomials, Taylor series or orthogonal polynomials are rather inaccurate for larger offsets. Therefore, other approximations are necessary.To improve accuracy, particularly for large offsets, various authors proposed a shifted-hyperbola approximation (Malovichko 1978;Claerbout 1987;de Bazelaire 1988;Castle 1994). This equation describes a hyperbola that is symmetric about the t-axis and has asymptotes that intersect the time axis x = 0 at a time t = τ s that is different from the zero-offset traveltime τ 0 . The shifted hyperbola proposed by Claerbout (1987) contains a fre...

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Traveltime Approximations in VTI Media

Aleixo¹,

Schleicher²

2008

70th EAGE Conference and Exhibition Incorporating SPE EUROPEC 2008

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Orthogonal parameters for anisotropic velocity analysis

Cited by 3 publications

References 4 publications

A fast algorithm for 3D azimuthally anisotropic velocity scan

A fast algorithm for 3D azimuthally anisotropic velocity scan

Traveltime approximations for q‐P waves in vertical transversely isotropy media*

Traveltime Approximations in VTI Media

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