Azimuthally dependent anisotropic velocity model update

Koren, Zvi; Ravve, Igor

doi:10.1190/geo2013-0178.1

Cited by 25 publications

(13 citation statements)

References 34 publications

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“…This equation is also derived in Koren and Ravve (), Ravve and Koren (), and Stovas (). To extend the kinematic properties of converted waves for multi‐layered media, we have to apply the technique similar to equation (12),

\begin{matrix} true \\ left \frac{1}{V_{0}} = (〈〉, \frac{1}{v_{0 j}}), \frac{V_{1}^{2}}{V_{0}} = (〈〉, \frac{v_{1 j}^{2}}{v_{0 j}}), \frac{V_{2}^{2}}{V_{0}} = (〈〉, \frac{v_{2 j}^{2}}{v_{0 j}}), \\ left \frac{((), 1 + 8 η_{((), eff) 1}) V_{1}^{4}}{V_{0}} = (〈〉, \frac{(1 + 8 η_{1 j}) v_{1 j}^{4}}{v_{0 j}}), \\ left \frac{((), 1 + 8 η_{((), eff) 2}) V_{2}^{4}}{V_{0}} = (〈〉, \frac{(1 + 8 η_{2 j}) v_{2 j}^{4}}{v_{0 j}}), \\ left \frac{((), 1 + 4 η_{((), eff) x y}) V_{1}^{2} V_{2}^{2}}{V_{0}} = (〈〉, \frac{(1 + 4 η_{x y j}) v_{1 j}^{2} v_{2 j}^{2}}{v_{0 j}}), \end{matrix}

where

false⟨ m false⟩ = false(\sum_{j = 1}^{N} z_{j} m_{j} false) / false(\sum_{j = 1}^{...}

…”

Section: Converted Wavesmentioning

confidence: 79%

“…I derive the relation between the phase and group azimuths defined at zero offset that is valid for any wave mode in ORT media. Koren and Ravve () derived the same relation for compressional waves. I show how the on‐vertical‐axis singularity and on‐vertical‐axis triplication affect the kinematic properties of single‐mode and converted‐mode waves.…”

Section: Introductionmentioning

confidence: 77%

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Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

Stovas

2016

Geophysical Prospecting

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I derive the kinematic properties of single‐mode P, S1, and S2 waves as well as converted PS1, PS2, and S1S2 waves in elastic orthorhombic media including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross‐term one). I show that the azimuthal dependence of normal moveout velocity and anellipticity is different in phase and group domains. The effects on‐vertical‐axis singularity and on‐vertical‐axis triplication are considered for pure‐mode S1 and S2 waves and converted‐mode S1S2 waves. The conditions and properties of on‐vertical‐axis triplication are defined in terms of kinematic parameters. The results are illustrated in four homogeneous orthorhombic models and one multilayered orthorhombic model with no variation in azimuthal orientation for all the layers.

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\begin{matrix} true \\ left \frac{1}{V_{0}} = (〈〉, \frac{1}{v_{0 j}}), \frac{V_{1}^{2}}{V_{0}} = (〈〉, \frac{v_{1 j}^{2}}{v_{0 j}}), \frac{V_{2}^{2}}{V_{0}} = (〈〉, \frac{v_{2 j}^{2}}{v_{0 j}}), \\ left \frac{((), 1 + 8 η_{((), eff) 1}) V_{1}^{4}}{V_{0}} = (〈〉, \frac{(1 + 8 η_{1 j}) v_{1 j}^{4}}{v_{0 j}}), \\ left \frac{((), 1 + 8 η_{((), eff) 2}) V_{2}^{4}}{V_{0}} = (〈〉, \frac{(1 + 8 η_{2 j}) v_{2 j}^{4}}{v_{0 j}}), \\ left \frac{((), 1 + 4 η_{((), eff) x y}) V_{1}^{2} V_{2}^{2}}{V_{0}} = (〈〉, \frac{(1 + 4 η_{x y j}) v_{1 j}^{2} v_{2 j}^{2}}{v_{0 j}}), \end{matrix}

where

false⟨ m false⟩ = false(\sum_{j = 1}^{N} z_{j} m_{j} false) / false(\sum_{j = 1}^{...}

…”

Section: Converted Wavesmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 77%

Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

Stovas

2016

Geophysical Prospecting

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“…As a result, we obtain the residual NMO velocity

δ V_{2} (ψ_{phs})

that makes it possible to update the effective fast and slow NMO velocities and the effective slow azimuth, related to the given top and bottom horizons. One can then use a generalized Dix‐type inversion (e.g., Koren and Ravve , for compressional waves) to obtain the local fast and slow NMO velocities of the layer and the orientation of its lateral orthorhombic axes. Alternatively, the residual moveout can be used as input for global tomography.…”

Section: Discussion: Residual Moveoutmentioning

confidence: 99%

“…This statement follows from Snell's law, and it holds for both pure‐mode and converted waves. In our previous study (Koren and Ravve ), we derived an analytic relationship for the azimuthal deviation between the phase and ray velocities in each individual layer. This azimuthal lag

Δ ψ = ψ_{ray} - ψ_{phs}

depends on the local fast and slow NMO velocities and the local “slow azimuth” (azimuth of the slow NMO velocity).…”

Section: Introductionmentioning

confidence: 99%

“…Our main aim in this work is to derive the phase-domain NMO velocities to establish explicit approximations for azimuthally dependent second-order residual moveout analysis in this domain, for all types of pure-mode and converted waves. Indeed, for compressional waves in layered orthorhombic media, higher order moveout approximations for longer offsets (wider angles) and for surface-offset azimuths have already been derived (Al-Dajani, Tsvankin, and Toksoz 1998;Grechka and Tsvankin 1998;Pech and Tsvankin 2004), and for phase azimuth by Ravve and Koren (2014) and Koren and Ravve (2015). However, in this work, in addition to compressional waves, we mainly concentrate on shear-wave propagation and converted P-S waves.…”

mentioning

confidence: 98%

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Normal moveout velocity for pure‐mode and converted waves in layered orthorhombic medium

Ravve

Koren

2015

Geophysical Prospecting

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We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi‐compressional, quasi‐shear, and converted waves in one‐dimensional multi‐layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface‐offset azimuth and applying our derived relationship between the surface‐offset azimuth and phase‐velocity azimuth, we obtain the normal moveout velocity versus the phase‐velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time‐domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local‐angle‐domain common image gathers. The angle and azimuth parameters of the local‐angle‐domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψphs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi‐layer structure is based on the fact that, for a one‐dimensional model assumption, the horizontal slowness ph and the azimuth of the phase velocity ψphs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface‐offset azimuth and phase‐velocity azimuth domains.

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All that wobbles isn’t necessarily azimuthal anisotropy

Debenham¹,

Badry

Megebry

2019

ASEG Extended Abstracts

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Onshore 3D seismic data is often acquired with rich azimuth coverage by utilising orthogonal shooting (or cross-spread) layouts. This means that azimuthal anisotropy, if present, can be readily observed and its effects on the data can be quantified and accounted for as part of the processing and imaging flow. In this example from the Canning Basin, the data appeared initially to be exhibiting the effects of azimuthal anisotropy. However, with careful handling and honouring of the azimuths of the acquired data during the PreSDM velocity model building, it was possible to correct for most of the variation simply with a laterally variable velocity model, without the need to invoke the presence of azimuthal anisotropy.

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Azimuthally dependent anisotropic velocity model update

Cited by 25 publications

References 34 publications

Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

Normal moveout velocity for pure‐mode and converted waves in layered orthorhombic medium

All that wobbles isn’t necessarily azimuthal anisotropy

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