Determination of geometrical spreading from traveltimes

Vanelle, C.; Gajewski, Dirk

doi:10.1016/j.jappgeo.2003.02.002

Cited by 19 publications

(11 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Geometrical spreading in the time-offset domain is related to the convergence or divergence of ray beams (Gajewski and Pšenčík, 1987) and can be obtained directly from the spatial traveltime derivatives. For example, an algorithm to compute geometrical spreading from coarsely-gridded traveltime tables was introduced by Vanelle and Gajewski (2003). Ursin and Hokstad (2003) represented the geometrical-spreading factor of P-waves in horizontally layered VTI media in terms of reflection traveltime described by the Tsvankin-Thomsen nonhyperbolic moveout equation 3.3.…”

Section: Geometrical Spreading In Azimuthally Anisotropic Mediamentioning

confidence: 99%

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Tsvankin¹,

Grechka²

2011

182

View full text Add to dashboard Cite

Section: Geometrical Spreading In Azimuthally Anisotropic Mediamentioning

confidence: 99%

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Tsvankin¹,

Grechka²

2011

182

View full text Add to dashboard Cite

“…Its accuracy, as well as the accuracy of the parabolic formula, are tested by Gjøystdal et al (1984). More recently, the hyperbolic formula has been used to interpolate traveltimes (Vanelle and Gajewski, 2002) and for the determination of the geometrical spreading (Vanelle and Gajewski, 2003) in inhomogeneous isotropic or anisotropic media. The coefficients of the Taylor expansion are evaluated from traveltimes specified in known nodes of a coarse grid.…”

Section: Introductionmentioning

confidence: 99%

Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: Tests of accuracy

et al. 2013

View full text Add to dashboard Cite

On several simple models of isotropic and anisotropic media, we have studied the accuracy of the two-point paraxial traveltime formula designed for the approximate calculation of the traveltime between points S 0 and R 0 located in the vicinity of points S and R on a reference ray. The reference ray may be situated in a 3D inhomogeneous isotropic or anisotropic medium with or without smooth curved interfaces. The twopoint paraxial traveltime formula has the form of the Taylor expansion of the two-point traveltime with respect to spatial Cartesian coordinates up to quadratic terms at points S and R on the reference ray. The constant term and the coefficients of the linear and quadratic terms are determined from quantities obtained from ray tracing and linear dynamic ray tracing along the reference ray. The use of linear dynamic ray tracing allows the evaluation of the quadratic terms in arbitrarily inhomogeneous media and, as shown by examples, it extends the region of accurate results around the reference ray between S and R (and even outside this interval) obtained with the linear terms only. Although the formula may be used for very general 3D models, we concentrated on simple 2D models of smoothly inhomogeneous isotropic and anisotropic (∼8% and ∼20% anisotropy) media only. On tests, in which we estimated twopoint traveltimes between a shifted source and a system of shifted receivers, we found that the formula may yield more accurate results than the numerical solution of an eikonal-based differential equation. The tests also indicated that the accuracy of the formula depends primarily on the length and the curvature of the reference ray and only weakly depends on anisotropy. The greater is the curvature of the reference ray, the narrower its vicinity, in which the formula yields accurate results.

show abstract

“…Geometric spreading in the time-offset domain is related to the convergence or divergence of ray beams (Gajewski and Pšenčík, 1987) and, therefore, can be computed directly from the spatial derivatives of traveltime (Vanelle and Gajewski, 2003). This ray-theory result is exploited in the moveout-based geometricspreading correction devised for horizontally layered VTI models by Ursin and Hokstad (2003) and extended to wide-azimuth, long-spread PP and PS data from azimuthally anisotropic media by Xu andTsvankin (2006, 2008).…”

Section: Prestack Amplitude Analysismentioning

confidence: 99%

Seismic anisotropy in exploration and reservoir characterization: An overview

Gaiser²,

et al. 2010

View full text Add to dashboard Cite

Recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods. In particular, vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms, especially those based on the wave equation. Here, we briefly review the state of the art in modeling, processing, and inversion of seismic data for anisotropic media. Topics include optimal parameterization, body-wave modeling methods, P-wave velocity analysis and imaging, processing in the τ -p domain, anisotropy estimation from vertical seismic profiling (VSP) surveys, moveout inversion of wide-azimuth data, amplitude-variation-with-offset (AVO) analysis, processing and applications of shear and mode-converted waves, and fracture characterization. When outlining future trends in anisotropy studies, we emphasize that continued progress in data-acquisition technology is likely to spur transition from transverse isotropy to lower anisotropic symmetries (e.g., orthorhombic). Further development of inversion and processing methods for such realistic anisotropic models should facilitate effective application of anisotropy parameters in lithology discrimination, fracture detection, and time-lapse seismology.

show abstract

Determination of geometrical spreading from traveltimes

Cited by 19 publications

References 19 publications

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: Tests of accuracy

Seismic anisotropy in exploration and reservoir characterization: An overview

Contact Info

Product

Resources

About