Synthetic seismic sections for acoustic, elastic, anisotropic, and vertically inhomogeneous layered media

Hron, F.; May, B. T.; Covey, J. D.; Daley, P. F.

doi:10.1190/1.1442124

Cited by 18 publications

(7 citation statements)

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“…The e¡ect of spherical divergence we consider is the e¡ect of a ray tube propagating through a horizontally layered medium, in which the P-wave velocity varies vertically. In this 1-D case, the relative geometrical spreading is de¢ned by (det Q) 1a2~y p dy dp cos 0 0 cos 0 N 1a2 (A1) (C í erveny¨1985; Hron et al 1986), where p is the ray parameter, y is the source^receiver horizontal separation, 0 0 is the take-o¡ angle of the ray, 0 N is the angle to the vertical axis of the ray at the receiver point, and Q can be understood as a transformation matrix from global ray coordinates to local ray-centred coordinates. The e¡ect of spherical divergence in the de-migration process can be expressed as the reciprocal of the normalized geometrical spreading, (Ursin 1990), where o 0 is the P-wave velocity at the source point.…”

Section: Appendix A: the De-migration Of Amplitudesmentioning

confidence: 99%

Seismic amplitude inversion for interface geometry: practical approach for application

Wang¹,

White²,

Pratt³

2000

Geophys. J. Int.

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Summary This paper presents a practical approach for the application of real seismic amplitude data in the context of reflection seismic tomography. The estimation of recorded seismic amplitudes from reflection seismic gathers is performed with the aid of pre‐stack time migration, which enhances continuity and reflection strength and reduces reflection point dispersal and diffraction effects. Moreover, contraction of the Fresnel zone by migration brings the amplitudes closer to the ray amplitudes assumed in the inversion. De‐migration of the amplitudes follows, so that we recover a set of ‘true’ observations for input to inversion. To make the amplitude inversion robust, the effect of noise in the amplitude data is mitigated by applying iteratively a locally reweighted regression, which can efficiently reject amplitude outliers. This approach is applied to a reflection seismic profile from the North Sea to constrain the geometry of a stack of interfaces by using both the amplitude inversion and a joint inversion with traveltime data. The application example represents a valuable contribution to the discussion of how the combined effort of imaging and inversion of seismic data should be organized when we are dealing with field data.

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Section: Appendix A: the De-migration Of Amplitudesmentioning

confidence: 99%

Seismic amplitude inversion for interface geometry: practical approach for application

Wang¹,

White²,

Pratt³

2000

Geophys. J. Int.

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“…With at most one turning point, the Fourier transform of the received waveform is given by (Cervenjr et al 1977;Hron et al 1986; Cervenjr1987)…”

Section: Asymptotic Modelling Of P R I M a R Y Multiple A N D Convementioning

confidence: 99%

“…We consider seismic waves which have been multiply reflected with possible mode conversions in a horizontally layered elastic medium where the layer parameters may vary continuously with depth in each layer. With at most one turning point, the Fourier transform of the received waveform is given by (Cervenjr et al 1977;Hron et al 1986; Cervenjr1987)…”

Section: Asymptotic Modelling Of P R I M a R Y Multiple A N D Convementioning

confidence: 99%

SEISMIC REFLECTION AMPLITUDES¹

Ursin¹,

Dahl

1992

Geophysical Prospecting

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URSIN, B. and DAHL, T. 1992. Seismic reflection amplitudes. Geophysical Prospecting 40,483-512.Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset.Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel-time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P-wave, S-wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter.For primary reflected P-waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant.The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth-order polynomial in offset, the traveltime by the normal square-root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.

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“…Fryer and Frazer (1984) calculated synthetic seismograms for stratified anisotropic media using a slightly modified version of the reflectivity method introduced by Kennett (1983). Hron et al (1986) computed the kinematic and dynamic properties of seismic body waves in elliptical anisotropic media employing the zero-order approximation of ART. Recently, Gajewski and Psencik (1987) presented a very elegant method, also based on ART, to compute synthetic seismograms in 3D laterally inhomogeneous anisotropic media.…”

Section: Introductionmentioning

confidence: 99%

ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES¹

Tsingas

Vafidis²,

Kanasewich

1990

Geophysical Prospecting

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TSINGAS, C., VAFIDIS, A. and KANASEWICH, E.R. 1990. Elastic wave propagation in transversely isotropic media using finite differences. Geophysical Prospecting 38,933-949.When treating the forward full waveform case, a fast and accurate algorithm for modelling seismic wave propagation in anisotropic inhomogeneous media is of considerable value in current exploration seismology. Synthetic seismograms were computed for P-SV wave propagation in transversely isotropic media. Among the various techniques available for seismic modelling, the finite-difference method possesses both the power and flexibility to model wave propagation accurately in anisotropic inhomogeneous media bounded by irregular interfaces. We have developed a fast high-order vectorized finite-difference algorithm adapted for the vector supercomputer. The algorithm is based on the fourth-order accurate MacCormacktype splitting scheme. Solving the equivalent first-order hyperbolic system of equations, instead of the second-order wave equation, avoids computation of the spatial derivatives of the medium's anisotropic elastic parameters. Examples indicate that anisotropy plays an important role in modelling the kinematic and the dynamic properties of the wave propagation and should be taken into account when necessary.

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Synthetic seismic sections for acoustic, elastic, anisotropic, and vertically inhomogeneous layered media

Cited by 18 publications

References 0 publications

Seismic amplitude inversion for interface geometry: practical approach for application

Seismic amplitude inversion for interface geometry: practical approach for application

SEISMIC REFLECTION AMPLITUDES¹

ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES¹

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Synthetic seismic sections for acoustic, elastic, anisotropic, and vertically inhomogeneous layered media

Cited by 18 publications

References 0 publications

Seismic amplitude inversion for interface geometry: practical approach for application

Seismic amplitude inversion for interface geometry: practical approach for application

SEISMIC REFLECTION AMPLITUDES1

ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES1

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SEISMIC REFLECTION AMPLITUDES¹

ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES¹