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- Volume 58, Issue 4, 2010
Geophysical Prospecting - Volume 58, Issue 4, 2010
Volume 58, Issue 4, 2010
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Reflection point sideslip and smear in imaging below dipping anisotropic media
Authors Rob Vestrum and Don LawtonABSTRACTDipping anisotropic clastic strata are ubiquitous in fold and thrust belts. Geological structures below these strata will be mispositioned laterally and vertically on seismic images if we do not properly correct for seismic anisotropy during migration. The magnitude of this lateral mispositioning of a target structure varies with source‐receiver offset, so reflection points will be smeared in the final stacked image. Raytracing demonstrates the lateral‐position and smear phenomena when imaging structures below tilted transversely isotropic media. Analysis of the raytracing results predicts the quantity of lateral‐position error and reflection‐point smear on a seismic image. We created numerical‐model seismic data to show reflection‐point smear on synthetic seismic images and to evaluate the accuracy of the predictions from raytracing.
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On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis
Authors Yuriy Roganov and Alexey StovasABSTRACTThe presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi‐valued and the geometrical spreading correction factor tends to zero due to energy focusing.
We analyse the conditions for the qSV‐wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV‐wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two‐layer vertical symmetry axis model.
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Non‐uniqueness with refraction inversion – the Mt Bulga shear zone
More LessABSTRACTThe tau‐p inversion algorithm is widely employed to generate starting models with many computer programs that implement refraction tomography. However, this algorithm can frequently fail to detect even major lateral variations in seismic velocities, such as a 50 m wide shear zone, which is the subject of this study.
By contrast, the shear zone is successfully defined with the inversion algorithms of the generalized reciprocal method. The shear zone is confirmed with a 2D analysis of the head wave amplitudes, a spectral analysis of the refraction convolution section and with numerous closely spaced orthogonal seismic profiles recorded for a later 3D refraction investigation.
Further improvements in resolution, which facilitate the recognition of additional zones with moderate reductions in seismic velocity, are achieved with a novel application of the Hilbert transform to the refractor velocity analysis algorithm. However, the improved resolution also requires the use of a lower average vertical seismic velocity, which accommodates a velocity reversal in the weathering. The lower seismic velocity is derived with the generalized reciprocal method, whereas most refraction tomography programs assume vertical velocity gradients as the default.
Although all of the tomograms are consistent with the traveltime data, the resolution of each tomogram is comparable only with that of the starting model. Therefore, it is essential to employ inversion algorithms that can generate detailed starting models, where detailed lateral resolution is the objective.
Non‐uniqueness can often be readily resolved with head wave amplitudes, attribute processing of the refraction convolution section and additional seismic traverses, prior to the acquisition of any borehole data. It is concluded that, unless specific measures are taken to address non‐uniqueness, the production of a single refraction tomogram that fits the traveltime data to sufficient accuracy does not necessarily demonstrate that the result is either correct, or even the most probable.
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Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part I: 1D ray propagation‡
Authors Igor Ravve and Zvi KorenABSTRACTAnisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing.
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Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part II: effective model‡
Authors Zvi Koren, Igor Ravve and Ronit LevyABSTRACTWe use residual moveouts measured along continuous full azimuth reflection angle gathers, in order to obtain effective horizontal transversely isotropic model parameters. The angle gathers are generated through a special angle domain imaging system, for a wide range of reflection angles and full range of phase velocity azimuths. The estimation of the effective model parameters is performed in two stages. First, the background horizontal transversely isotropic (HTI)/vertical transversely isotropic (VTI) layered model is used, along with the values of reflection angles, for converting the measured residual moveouts (or traveltime errors) into azimuthally dependent normal moveout (NMO) velocities. Then we apply a digital Fourier transform to convert the NMO velocities into azimuthal wavenumber domain, in order to obtain the effective HTI model parameters: vertical time, vertical compression velocity, Thomsen parameter delta and the azimuth of the medium axis of symmetry. The method also provides a reliability criterion of the HTI assumption. The criterion shows whether the medium possesses the HTI type of symmetry, or whether the azimuthal dependence of the residual traveltime indicates to a more complex azimuthal anisotropy. The effective model used in this approach is defined for a 1D structure with a set of HTI, VTI and isotropic layers (with at least one HTI layer). We describe and analyse the reduction of a multi‐layer structure into an equivalent effective HTI model. The equivalent model yields the same NMO velocity and the same offset azimuth on the Earth's surface as the original layered structure, for any azimuth of the phase velocity. The effective model approximates the kinematics of an HTI/VTI layered structure using only a few parameters. Under the hyperbolic approximation, the proposed effective model is exact.
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Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity‡
Authors Vadim Lisitsa and Dmitriy VishnevskiyABSTRACTThis paper presents a Lebedev finite difference scheme on staggered grids for the numerical simulation of wave propagation in an arbitrary 3D anisotropic elastic media. The main concept of the scheme is the definition of all the components of each tensor (vector) appearing in the elastic wave equation at the corresponding grid points, i.e., all of the stresses are stored in one set of nodes while all of the velocity components are stored in another. Meanwhile, the derivatives with respect to the spatial directions are approximated to the second order on two‐point stencils. The second‐order scheme is presented for the sake of simplicity and it is easy to expand to a higher order.
Another approach, widely‐known as the rotated staggered grid scheme, is based on the same concept; therefore, this paper contains a detailed comparative analysis of the two schemes. It is shown that the dispersion condition of the Lebedev scheme is less restrictive than that of the rotated staggered grid scheme, while the stability criteria lead to approximately equal time stepping for the two approaches. The main advantage of the proposed scheme is its reduced computational memory requirements. Due to a less restrictive dispersion condition and the way the media parameters are stored, the Lebedev scheme requires only one‐third to two‐thirds of the computer memory required by the rotated staggered grid scheme. At the same time, the number of floating point operations performed by the Lebedev scheme is higher than that for the rotated staggered grid scheme.
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Generalized anisotropy parameters and approximations of attenuations and velocities in viscoelastic media of arbitrary anisotropy type – theoretical and experimental aspects*
More LessABSTRACTSeismic anisotropy in geological media is now widely accepted. Parametrizations and explicit approximations for the velocities in such media, considered as purely elastic and moderately anisotropic, are now standards and have even been extended to arbitrary types of anisotropy. In the case of attenuating media, some authors have also recently published different parametrizations and velocity and attenuation approximations in viscoelastic anisotropic media of particular symmetry type (e.g., transversely isotropic or orthorhombic). This paper extends such work to media of arbitrary anisotropy type, that is to say to triclinic media. In the case of homogeneous waves and using the so‐called ‘correspondence principle’, it is shown that the viscoelastic equations (for the phase velocities, phase slownesses, moduli, wavenumbers, etc.) are formally identical to the corresponding purely elastic equations available in the literature provided that all the corresponding quantities are complex (except the unit vector in the propagation direction that remains real). In contrast to previous work, the new parametrization uses complex anisotropy parameters and constitutes a simple extension to viscoelastic media of previous work dealing with non‐attenuating elastic media of arbitrary anisotropy type. We make the link between these new complex anisotropy parameters and measurable parameters, as well as with previously published anisotropy parameters, demonstrating the usefulness of the new parametrization. We compute the explicit complete directional dependence of the exact and of the approximate (first and higher‐order perturbation) complex phase velocities of the three body waves (qP, qS1 and qS2). The exact equations are successfully compared with the ultrasonic phase velocities and phase attenuations of the three body waves measured in a strongly attenuating water‐saturated sample of Vosges sandstone exhibiting moderate velocity anisotropy but very strong attenuation anisotropy. The approximate formulas are checked on experimental data. Compared to the exact solutions, the errors observed on the first‐order approximate velocities are small (<1%) for qP‐waves and moderate (<10%) for qS‐waves. The corresponding errors on the quality factor Q are moderate (<6%) for qP‐waves but critically large (up to 160%) for the qS‐waves. The use of higher‐order approximations substantially improves the accuracy, for instance typical maximum relative errors do not exceed 0.06% on all the velocities and 0.6% on all the quality factors Q, for third‐order approximations. All the results obtained on other rock samples confirm the results obtained on this rock. The simplicity of the derivations and the generality of the results are striking and particularly convenient for practical applications.
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Relating 4D seismics to reservoir geomechanical changes using a discrete element approach
Authors Haitham Alassi, Rune Holt and Martin LandrøABSTRACTA modified discrete element method is briefly introduced and used for modelling reservoir geomechanical response during fluid injection and depletion. The modified approach works as a continuum method until some local failure is initiated, after which it behaves like a discrete element method on a polygonal lattice. The method is advantageous for modelling fracture developments in rocks. It is applied here to synthetic models of two reservoirs taken from the North Sea (Gullfaks and Elgin‐Franklin). For Gullfaks, two cases of water injection were modelled, one with low horizontal effective stress and the other with low vertical effective stress. Vertical fractures are developed in the first case, whereas horizontal fractures are developed in the second case. This would not have been seen using traditional methods. Based on 4D seismics data for the Gullfaks field, one may envision that horizontal fractures could have been formed. The Elgin‐Franklin synthetic model is used to study various scenarios of changing stress field around the depleting reservoir. Based on 4D seismics data from this field, one may see changes that could be interpreted in terms of possible fault reactivation.
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Continuous wavelet transform, theoretical aspects and application to aeromagnetic data at the Huanghua Depression, Dagang Oilfield, China
Authors Yushan Yang, Yuanyuan Li and Tianyou LiuABSTRACTWe use the continuous wavelet transform based on complex Morlet wavelets, which has been developed to estimate the source distribution of potential fields. For magnetic anomalies of adjacent sources, they always superimpose upon each other in space and wavenumber, making the identification of magnetic sources problematic. Therefore, a scale normalization factor, a−n, is introduced on the wavelet coefficients to improve resolution in the scalogram. By theoretical modelling, we set up an approximate linear relationship between the pseudo‐wavenumber and source depth. The influences of background field, random noise and magnetization inclination on the continuous wavelet transform of magnetic anomalies are also discussed and compared with the short‐time Fourier transform results.
Synthetic examples indicate that the regional trend has little effect on our method, while the influence of random noise is mainly imposed on shallower sources with higher wavenumbers. The source horizontal position will be affected by the change of magnetization direction, whereas the source depth remains unchanged. After discussing the performance of our method by showing the results of various synthetic tests, we use this method on the aeromagnetic data of the Huanghua depression in central China to define the distribution of volcanic rocks. The spectrum slices in different scales are used to determine horizontal positions of volcanic rocks and their source depths are estimated from the modulus maxima of complex coefficients, which is in good accordance with drilling results.
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Electrical resistivity and seismic refraction tomography to detect buried cavities
Authors Ettore Cardarelli, Michele Cercato, Antonio Cerreto and Gerardina Di FilippoABSTRACTNear‐surface cavities can pose serious hazards to human safety, especially in highly urbanized town centres. The location of subsurface voids, the estimation of their size and the evaluation of the overburden thickness are necessary to assess the risk of collapse.
In this study, electrical resistivity tomography (ERT) and seismic refraction tomography data are integrated in a joint interpretation process for cavity location in the city of Rome.
ERT is a well established and widely employed method for cavity detection. However, additional information provided by seismic refraction tomography is capable of eliminating some potential pitfalls in resistivity data interpretation. We propose that the structure of the cavities defined by ERT can be used as a base to optimize seismic refraction tomography investigations within the framework of a joint interpretation process.
Data integration and the insertion of a priori information are key issues for reducing the uncertainties associated with the inversion process and for optimizing both acquisition procedures and computation time.
Herein, the two geophysical methods are tested on both synthetic and real data and the integration of the results is found to be successful in detecting isolated cavities and in assessing their geometrical characteristics. The cavity location inferred by geophysical non‐invasive methods has been subsequently confirmed by direct inspection.
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Implicit structural inversion of gravity data using linear programming, a validation study*
Authors Arnout Tim Van Zon and Kabir Roy ChowdhuryABSTRACTIn this study, a regional scale gravity data set has been inverted to infer the structure (topography) of the top of the basement underlying sub‐horizontal strata. We apply our method to this real data set for further proof of concept, validation and benchmarking against results from an earlier forward modelling done elsewhere.
Our aim is to carry out implicit structural inversion, i.e., to obtain a geologically reasonable model, without specifically solving for structure. The 2.5D volume of interest is parametrized with homogeneous horizontal prisms and a two‐lithology medium is assumed. A possible regional linear trend and a general floating reference are also inverted for. Using a gridded parametrization, linear programming is used to minimize the L1‐norm of the data misfit, relative to a floating reference.
Given a known density contrast between the lithologies, an inversion using linear programming has the intrinsic advantage that a relatively sharp image of the sub‐surface is retrieved instead of a smooth one. The model recovered is almost bi‐modal and its general features seem to be robust with respect to several parametrization scenarios investigated. The floating reference and a linear trend in the data were also retrieved simultaneously. The inversion results, indicating two depressions in the basement, are robust and agree with those obtained earlier based upon detailed 2D forward modelling using many narrow, near‐vertical prisms.
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Wavenumber of the guided wave supported by a thin resistive layer in marine controlled‐source electromagnetics
Authors F.N. Kong, S.E. Johnstad and J. ParkABSTRACTThis paper discusses the asymptotic behaviour of the electromagnetic fields received on the sea‐bed (target response), as well as the fields distributed inside a thin resistive target, generated by a horizontal electric dipole above the sea‐bed in marine controlled‐source electromagnetics for hydrocarbon exploration. It is found that the guided wave supported by a thin resistive target can be expressed as a single‐mode exponential function. A simple closed‐form expression is derived to relate the single‐mode wavenumber of the guided wave to the model parameters: the resistivity and thickness of the target layer, the sea‐bed resistivity and the frequency. When the air‐wave is removed, the guided wave is dominant among the fields received on the sea‐bed at far offset. Hence the wavenumber of the guided wave can be calculated from the fields measured on the sea‐bed. The closed‐form expression can then be used to invert the target property from the calculated wavenumber and hence, can be considered as a hydrocarbon indicator.
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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