Wide-Angle Phase-Slowness Approximations in VTI Media

Pedersen, Ørjan; Ursin, Bjørn; Stovas, Alexey

doi:10.3997/2214-4609.201402323

Cited by 3 publications

(6 citation statements)

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“…Let us keep the approximate behaviour of function S ( p ) at p = 0 given in and preserve the value of S ( p ) at p = P qSV (corresponding to the horizontal propagation of qSV‐waves). It gives the new approximation for function S ( p ): The corresponding equation for the derivative from is: Substituting into the expression for vertical slowness, , results in: A similar equation has been derived in Pedersen et al (2007).…”

Section: Slowness Surface Approximations Of Qsv‐wavesmentioning

confidence: 95%

“…The vertical slowness squared for qP‐ and qSV‐waves can be given as (Stovas and Ursin 2003): where: and: The notations in are valid only for the range of horizontal slownesses [0, P qSV ], with P qSV = 1/β 0 . With the condition: the horizontal slowness could be larger than P qSV with the maximum slowness defined by Q ( p ) = 0 and is no longer valid (Pedersen et al 2007). In our further computations we consider the horizontal slowness in the range of [0, P qSV ], therefore, the vertical slowness for qP‐ and qSV‐waves can be defined by .…”

Section: The Qp‐wave Quasi‐acoustic Approximationmentioning

confidence: 99%

“…There are many approximations to the slowness surface in a transversely isotropic (VTI) medium both for qP‐ and qSV‐waves (Schoenberg and de Hoop 2000; Fowler 2003; Pedersen, Ursin and Stovas 2007). The quasi‐acoustic approximation introduced by Akhalifah (1998) is of great help for the processing, modelling and interpretation of qP‐wave data in a VTI medium.…”

Section: Introductionmentioning

confidence: 99%

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Slowness surface approximations for qSV‐waves in transversely isotropic media

Stovas

Roganov²

2008

Geophysical Prospecting

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A B S T R A C TThe vertical slowness approximations are widely used in phase-shift migration methods for quasi P-and quasi SV-waves in transversely isotropic medium. The description of the vertical slowness needed for the migration application for shear waves in transverse isotrophy media is generally complicated. The reason is that this type of approximations results in much simpler expressions for the vertical slowness and, which is most important, they contain fewer parameters than exact expressions.We derive slowness surface approximations valid for qSV-wave propagation in transversely isotropic and tilted transversely isotropic media by applying an approximation extracted from acoustic approximation for qP-wave propagation. One approximation has the same accuracy as a qP-wave acoustic approximation for the same range of horizontal slowness, the other approximations are wide-angle ones.

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Section: Slowness Surface Approximations Of Qsv‐wavesmentioning

confidence: 95%

Section: The Qp‐wave Quasi‐acoustic Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Slowness surface approximations for qSV‐waves in transversely isotropic media

Stovas

Roganov²

2008

Geophysical Prospecting

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“…With no horizontal on-axis shear-wave triplication, the negative sign in front of the radical corresponds to the qP slowness and the positive sign corresponds to the qSV slowness. In case of a horizontal on-axis shear-wave triplication, q β is multivalued for some values of p (Pedersen et al, 2007). To get the vertical wave-number k z , the vertical slowness q can be written as q = k z /ω, while the horizontal-slowness p can be written p = k x /ω where k x is the lateral wave-number.…”

Section: Theorymentioning

confidence: 99%

“…a quasiacoustic approximation (Alkhalifah, 1998). In the quasiacoustic approximation, we assume that γ 2 0 1, and a simplified slowness expression for qP waves can be provided by (Alkhalifah, 1998;Pedersen et al, 2007)…”

Section: Simplified Slowness Expressions For Qp -Wavesmentioning

confidence: 99%

One-way wave-equation migration of compressional and converted waves in a VTI medium

2010

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In seismic reflection surveying, by recording both pressure and shear-wave reflections, one can increase the amount of information obtained about the subsurface rather than by recording pressure waves alone. Geologic structures that are not visible by using conventional pressure-data may possibly be imaged using shear waves, thus mitigating the risk in oil and gas exploration and production. Horizontally layered sedimentary rocks exhibit anisotropy that can be approximated by an effective transverse isotropic medium with a vertical axis of symmetry. Taking into account a vertically transverse isotropic earth, we derive phase-slowness expressions for quasi-P and quasi-SV waves that are used in a one-way wave-equation migration scheme. We derive simplified slowness-expressions that are useful for processing of conventional pressure data. Numerical examples demonstrate that the slowness approximations are valid for wide-angle propagation, and the resulting one-way propagators are validated on a series of synthetic tests and applied on a field ocean-bottom seismic data set. The results show that the method accurately images both compressional and converted waves in OBS data over a vertically transverse isotropic medium.

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Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

Koren

Ravve

2018

Geophysical Prospecting

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Considering horizontally layered transversely isotropic media with vertical symmetry axis and all types of pure‐mode and converted waves we present a new wide‐angle series approximation for the kinematical characteristics of reflected waves: horizontal offset, intercept time, and total reflection traveltime as functions of horizontal slowness. The method is based on combining (gluing) both zero‐offset and (large) finite‐offset series coefficients. The horizontal slowness is bounded by the critical value, characterised by nearly horizontal propagation within the layer with the highest horizontal velocity. The suggested approximation uses five parameters to approximate the offset, six parameters to approximate the intercept time or the traveltime, and seven parameters to approximate any two or all three kinematical characteristics. Overall, the method is very accurate for pure‐mode compressional waves and shear waves polarised in the horizontal plane and for converted waves. The application of the method to pure‐mode shear waves polarised in the vertical plane is limited due to cusps and triplications. To demonstrate the high accuracy of the method, we consider a synthetic, multi‐layer model, and we plot the normalised errors with respect to numerical ray tracing.

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Wide-Angle Phase-Slowness Approximations in VTI Media

Cited by 3 publications

References 0 publications

Slowness surface approximations for qSV‐waves in transversely isotropic media

Slowness surface approximations for qSV‐waves in transversely isotropic media

One-way wave-equation migration of compressional and converted waves in a VTI medium

Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

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