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58th EAGE Conference and Exhibition
- Conference date: 03 Jun 1996 - 07 Jun 1996
- Location: Amsterdam, Netherlands
- ISBN: 978-90-73781-07-8
- Published: 04 June 1996
1 - 20 of 604 results
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The tip wave superposition method based on the refraction transform
Authors A. Aizenberg, H. B. Helle, K. D. Kiem-Musatov and J. PajchelIn seismic modelling is widely used the diffraction Kirchhoffs integral with the spherical Green function obtained from the exact Kirchhoffs integral by means of replacement of the integral boundary values with their high-frequency asymptotics. This approach is only applicable in homogeneous medium because the Green function in the inhomogeneous medium is non-spherical. In [1] we introduced the tip wave superposition method (TWS) for seismic simulation in 3-D geological models with structurally complex target but with a homogeneous overburden. In this paper we generalize the TWS to account for an inhomogeneous overburden but restricted to the scalar case.
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A Pertubation technique for travel time computation with FD-Eikonal solvers
Authors N. Ettrich and D. GajewskiThe theory of first order perturbation is well known and commonly used in classical ray tracing techniques. Desired quantities in a perturbed medium are calculated along rays which propagate through a reference medium. Reference and perturbed medium differ only slightly. First order traveltime perturbation can be used, e.g., for pre-stack Kirchhoff-type migration. In general in migration the correct subsurface model is unknown. Therefore, a simultaneous migration with several macro models should be performed. The results can be used for velocity estimation techniques. The time consuming procedure of computing traveltimes from sources to all subsurface points is performed directly only in one model. For the other slightly deviating models the traveltimes are computed efficiently by perturbation. Moreover, most of the recently developed methods for fast computation of traveltimes are designed for isotropic media. For Kirchhoff-type migration of data from anisotropic media perturbation techniques provide a fast way to compute diffraction surfaces for slightly anisotropic media where the reference medium is isotropic. Here existing tools to compute traveltimes in isotropic media can be used. For highest computational speed we implemented the perturbation formulas into Vidale's method (Vidale, 1988) and call it FD-perturbation method.
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Hard and smooth models for seismic imaging based on raytracing
More LessUnderstanding of wave propagation is essential in geophysical imaging techniques. Most of these techniques require an a priori model of the subsurface. Conventional imaging techniques usually employ a highfrequency approximation: only the wave front is considered. In the limit of infinite frequency, only discontinuous variations of the velocity produce reflections. It therefore seems an obvious choice to require the velocity model to be smooth: all reflection data are caused by discontinuities that can be considered as perturbations on the smooth background model.
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Multiple scattering of seismic waves in thinly layered media
Authors S. A. Shapiro and S. TreitelWe study the influence of higher order multiple scattering in 1-D layered structures on the transmissivity and the reflectivity of normally incident delta-pulse plane waves. For the case of the transmissivity we obtain an approximation which is more accurate than the familiar O'Doherty-Anstey formula. We derive also an approximation of the reflectivity, which clarifies the nature of this imp rtant quantity. We show how our results have implications for both forward and inverse modeling.
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Heterogeneous modelling behaviour at an interface in porous media
Authors G. Quiroga-Goode and J. M. CarcioneHeterogeneous numerical modeling satisfies implicitly the boundary conditions at physical interfaces. In models including a one-phase rheology, i.e., solids or fluids, where only one kind of boundary condition is satisfied, heterogeneous modeling has proved very useful.
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Theoretical description and numerical simulation of elastic wave propagation in random media
Authors E. Burr, N. Gold and S. A. ShapiroA wave propagating through a random medium is scattered due to its interactions with the spatial variations in material properties of the medium. We split the wave u into a scattered part u f and a coherent part < u > , the so-called Meanfield. The Meanfield is carrying information about the attenuation due to scattering and implicit about irregularities in the structure of the medium. Our aim is to extract this information.
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Waves in scaling media - The implication of non-differentiability
Authors F. Herrmann and J. StaalDifferentiability forms the predominant cornerstone on which many laws of physics are based. The wave equation, as such, does not form an exception. The main goal of this paper is to validate whether this important presupposition of differentiability is met with in the seismic context. For this purpose the rather new concept of wavelets is reviewed. Given this theoretical body it is shown that it is possible to not only estimate the local degree of regularity (differentiability) of the well - log measurement, but also the singularity spectrum, capturing the hierarchy of scaling exponents. Application of these analyzing techniques to the well data shows that their behaviour is singular within the seismic scale range and beyond. The implication of this observation is that when these profiles are submitted as coefficients in the wave equation, one is confronted with a fundamental problem. In our judgement this problem lies in the fact that the constitutent parameters, the coefficients in the wave equation, show a too strong spatial fluctuation with respect to the characteristic scale of the seismic disturbance. This may not only result in a possible instability of the wave equation but also in a new type of reflection and dispersion mechanism which has to be related, from first principles, to the local and global apparent degree of non-differentiability.
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Time-domain representation of waves in media with frequency power law of dispersion
By V. E. RokAs it was observed and theoretically proved the dispersion of sound in microinhomogeneous media may be connected with relaxation process that leads to equalization an additional thermodynamic parameter ξ that depends on wave pressure (or stress) differently in inclusions and host medium.
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Non hyperbolic reflection move out for horizontal transverse isotropy
Authors A. F. Al-Dajani and I. TsvankinRecent experimental studies (Lynn et al., 1995) have shown that P-wave signatures, including reflection moveout, are sensitive to the presence of azimuthal anisotropy. Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model caused by vertical penny-shaped cracks embedded in an isotropic matrix.
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Wave polarization in transversely isotropic and orthorhombic media
Authors J. M. Carcione and K. HelbigElastic waves can, in principle, be classified according to their propagation velocity, e.g., through the values of the slowness or the group velocity surfaces along a given direction. Generally, in media of relatively high symmetry (isotropic to orthorhombic), the fastest wave is quasi-compressional and the slower wave is quasi-transverse.
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Frequency-dependent anisotropy of seismic waves in transversely isotropic multilayering
Authors U. Werner and S. A. ShapiroOur goal is to find out whether a multilayered medium can be substituted by, a frequency-dependent equivalent averaged TI-medium. To achieve this we formulate the influence of multilayering on elastic wave propagation analytically and compare our results with numerical simulations of wave propagation in multilayered media.
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Effective parameters and seismic velocites for azimuthally anisotropic media
By I. TsvankinAnalytic description of seismic signatures in azimuthally anisotropic media is of utmost importance in seismic investigations of fractured reservoirs. Since many fractured formations in sedimentary basins are believed to have orthorhombic symmetry (e.g., Wild and Crampin, 1991), azimuthally-dependent seismic wavefields are governed by nine stiffness coefficients. A new notation introduced in this work is designed to make seismic treatment of orthorhombic media more practical by reducing the number of independent parameters and simplifying the description of seismic velocities and amplitudes. For the transversely isotropic model with a horizontal symmetry axis, which can be considered as a special case of orthorhombic media, the formalism developed here makes it possible to use P-wave reflection moveout to estimate the shear-wave splitting parameter and the crack density.
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About the relation between the effective model of layered fluid-solid medium and transversely isotropic biot model
Authors L. Molotkov and A. BakulinInvestigation of wave propagation in porous and fractured media is usually carried out on basis of effective models because it is impossible to solve the wave diffraction problem on one or several pores of arbitrary shape. One of such model is effective model of layered solid-fluid medium.
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Stacking analysis in transversely isotropic media
Authors M. Le Bougeant and R. G. PrattMany seismic data processing algorithms are based on a number of simplifying assumptions. As larger offset data are now more commonly acquired, it makes sense to examine and possibly overcome these assumptions. One such assumption is that a small-offset, isotropic approximation can be used to define the moveout of reflected arrivals. At finite offsets in 1D media, especially in anisotropic media, the travel time-offset relationship (the moveout) becomes non hyperbolic. This non-hyperbolic behaviour causes degradation of standard velocity analysis, causes a degradation of the stack, and causes a bias to appear in the velocity values.
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Velocity analysis using nonhyperbolic move out in transversely isotropic media
More LessP-wave reflections from horizontal interfaces in transversely isotropic (TI) media have nonhyperbolic moveout.
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Anisotropic seismic data processing
Authors O. Uzcategui, D. Mujica and V. CelisIt is known that in areas with significant shale content, the isotropic assumption in seismic data processing is not correct, and this can lead to misfocusing of dipping events and wrong depth positioning if not properly accounted for.
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Poststack time remigration
Authors M. S. Jaya, J. Schleicher and P. HubralCommon-mid-point (CMP) stack sections can be transformed by a so-called image-wave equation into a panel of time-migrated record sections for a continuum of (constant) migration velocities. The derivation of this image-wave equation as well as its kinematic and dynamic aspects will be presented. The resulting panels of time-migrated sections will be shown for selected examples.
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Different simulations of the kinematics of time migration - A Review
More LessThere are many applications that require simulation of the kinematics of time-migration. Time-demigration, for example, is an important step in map migration and stacking velocity/traveltime inversion. Mapping of well trajectories from the depth domain into the time-migrated block is another [4]. We compare the simplistic techniques of vertical stretch and image ray mapping with more sophisticated methods that accurately simulate the time-migration operator used. We simulate Kirchhoff-type time-migration analytically and finite difference time-migration by anisotropic ray tracing in the time-migrated domain.
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Accurate 3D time migration focusing in regions of lateral velocity gradients
By C. HarrisMany 3D zero offset time migration algorithms allow lateral velocity variations. However, these methods are generally derived by employing simplifying assumptions about the medium velocity. It should not be expected that, if the derivation is based on a constant velocity or v(z) medium, the resulting algorithm will be accurate in regions with lateral gradients. It is well known that time migration mispositions events relative to their true subsurface position whenever lateral gradients are present. Here, I address only the issue of focusing. Insight into this aspect of the problem may be gained by analyzing the scalar wave equation in the natural coordinates of the time migration output space: image ray surface location and two-way traveltime.
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Accurate migration using offset-checkshot surveys
Authors J. R. Krebs, D. R. Fara and A. E. BerlinAccurate seismic migration, particularly of steeply dipping or overturned reflectors, requires an accurate velocity model (Lamer, Beasley et al . 1989). Recent research has focused on the notion that the migration velocity model must include velocity anisotropy (Alkhalifah and Lamer 1994; Larner and Cohen 1993; Lynn, Gonzalez et al. 1991). While it is true that most migration algorithms require accurate velocity models, Kirchhoff migration is an exception to this rule. Unlike most migration methods, Kirchhoff migration does not require a velocity model as input. Rather, all that is required is a table listing the seismic traveltime from subsurface imaging points to points in the surface migration aperture (Gray and May 1994). Thus, in the case of Kirchhoff migration, accurate traveltime tables would ensure a kinematically accurate image.
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