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1.
Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (VP0 and VS0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves. 相似文献
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We rederive and generalize hyperbolic moveout formulae for the common-midpoint (CMP) gather and for the zero-offset (ZO) section that can be efficiently used for macro-model-independent reflection imaging in two-dimensional media. The hyperbolic moveout formulae for the common-midpoint gather are obtained from different Taylor series expansions of a particular parametric moveout surface defined in the multicoverage data space. Such a moveout surface involves three kinematic wave-field attributes of two hypothetical waves, which have to be determined by a coherency analysis. By using hyperbolic moveout curves in the CMP gather and in the ZO section one can determine these attributes in two steps. The relationships between the local shapes of the interfaces and the attributes of the hypothetical wave-fields attributes are considered by means of geometrical optics. The determination of these attributes allows to perform a macro-model-independent ZO simulation and a subsequent inversion. 相似文献
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J.F.B. Bolte 《Geophysical Prospecting》2004,52(6):523-534
The common focal point (CFP) method and the common reflection surface (CRS) stack method are compared. The CRS method is a fast, highly automated procedure that provides high S/N ratio simulation of zero‐offset (ZO) images by combining, per image point, the reflection energy of an arc segment that is tangential to the reflector. It uses smooth parametrized two‐way stacking operators, based on a data‐driven triplet of attributes in 2D (eight parameters in 3D). As a spin‐off, the attributes can be used for several applications, such as the determination of the geometrical spreading factor, multiple prediction, and tomographic inversion into a smooth background velocity model. The CFP method aims at decomposing two‐way seismic reflection data into two full‐aperture one‐way propagation operators. By applying an iterative updating procedure in a half‐migrated domain, it provides non‐smooth focusing operators for prestack imaging using only the energy from one focal point at the reflector. The data‐driven operators inhibit all propagation effects of the overburden. The CFP method provides several spin‐offs, amongst which is the CFP matrix related to one focal point, which displays the reflection amplitudes as measured at the surface for each source–receiver pair. The CFP matrix can be used to determine the specular reflection source–receiver pairs and the Fresnel zone at the surface for reflection in one single focal point. Other spin‐offs are the prediction of internal multiples, the determination of reflectivity effects, velocity‐independent redatuming and tomographic inversion to obtain a velocity–depth model. The CFP method is less fast and less automated than the CRS method. From a pointwise comparison of features it is concluded that one method is not a subset of the other, but that both methods can be regarded as being to some extent complementary. 相似文献
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The method of common reflection surface (CRS) extends conventional stacking of seismic traces over offset to multidimensional stacking over offset‐midpoint surfaces. We propose a new form of the stacking surface, derived from the analytical solution for reflection traveltime from a hyperbolic reflector. Both analytical comparisons and numerical tests show that the new approximation can be significantly more accurate than the conventional CRS approximation at large offsets or at large midpoint separations while using essentially the same parameters. 相似文献
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In areas of complex geology such as the Canadian Foothills, the effects of anisotropy are apparent in seismic data and estimation of anisotropic parameters for use in seismic imaging is not a trivial task. Here we explore the applicability of common‐focus point (CFP)‐based velocity analysis to estimate anisotropic parameters for the variably tilted shale thrust sheet in the Canadian Foothills model. To avoid the inherent velocity‐depth ambiguity, we assume that the elastic properties of thrust‐sheet with respect to transverse isotropy symmetry axis are homogeneous, the reflector below the thrust‐sheet is flat, and that the anisotropy is weak. In our CFP approach to velocity analysis, for a poorly imaged reflection point, a traveltime residual is obtained as the time difference between the focusing operator for an assumed subsurface velocity model and the corresponding CFP response obtained from the reflection data. We assume that this residual is due to unknown values for anisotropy, and we perform an iterative linear inversion to obtain new model parameters that minimize the residuals. Migration of the data using parameters obtained from our inversion results in a correctly positioned and better focused reflector below the thrust sheet. For traveltime computation we use a brute force mapping scheme that takes into account weakly tilted transverse isotropy media. For inversion, the problem is set up as a generalized Newton's equation where traveltime error (differential time shift) is linearly dependent on the parameter updates. The iterative updates of parameters are obtained by a least‐squares solution of Newton's equations. The significance of this work lies in its applicability to areas where transverse isotropy layers are heterogeneous laterally, and where transverse isotropy layers are overlain by complex structures that preclude a moveout curve fitting. 相似文献
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The multifocus moveout of Gelchinsky et al. [Gelchinsky, B., Berkovitch, A., Keydar, S., 1997. Multifocusing homeomorphic imaging: Parts I and II: Course Notes, Special Course on Homeomorphic Imaging. Seeheim, Germany] is a powerful tool for stacking multicoverage data in arbitrary configurations. Based on general ray theoretical assumptions and on attractively simple geometrical considerations, the multifocus moveout is designed to express the traveltimes of neighbouring rays arbitrarily located around a fixed central, primary reflected or even diffracted, ray. In this work, the basic derivations and results concerning the multifocus approach are reviewed. A higher-order multifocus moveout expression that generalizes the corresponding one of Gelchinsky is obtained from slight modifications of the original derivation. An alternative form of the obtained multifocus expression that is best suited for numerical implementation is also provided. By means of a simple numerical experiment, we also comment on the accuracy of the multifocus traveltime approximations. 相似文献
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Ralf Ferber 《Geophysical Prospecting》2000,48(6):995-1008
'Coverage' or 'fold' is defined as the multiplicity of common-midpoint (CMP) data. For CMP stacking the coverage is consistent with the number of traces sharing a common reflection point on flat subsurface reflectors. This relationship is not true for dipping reflectors. The deficiencies of CMP stacking with respect to imaging dipping events have long been overcome by the introduction of the dip-moveout (DMO) correction. However, the concept of coverage has not yet satisfactorily been updated to a 'DMO coverage' consistent with DMO stacking. A definition of constant-velocity DMO coverage will be proposed here. A subsurface reflector will be illuminated from a given source and receiver location if the time difference between the reflector zero-offset traveltime and the NMO- and DMO-corrected traveltime of the reflection event is less than half a dominant wavelength. Due to the fact that a subsurface reflector location is determined by its zero-offset traveltime, its strike and its dip, the DMO coverage also depends on these three parameters. For every surface location, the proposed DMO coverage consists of a 3D fold distribution over reflector strike, dip and zero-offset traveltime. 相似文献
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The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging. 相似文献
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共反射面元（CRS）叠加是目前认为最好的生成零炮检距剖面的方式. 共反射面元 意指地下某一反射点邻近的一个反射弧段,该弧段在时空域内的走时响应称为CRS叠加面,该 叠加面可视为反射弧段上各共反射点（CRP）的时空域内走时响应的组合. 在一般的共反射 点走时关系基础上,引入两种特征波——Normal波和Normal Incidence Point波,就可以在 傍轴近似假设下,将CRP走时关系推广到反射点邻近的各反射点,将这些反射点的CRP走时关系 加以组合就得到了关于该反射点的共反射面元的走时关系. 考察从共反射点（CRP）到共反 射面元(CRS)的过渡,这一过程提供了CRS叠加的应用理论基础. 相似文献
11.
Emil Blias 《Geophysical Prospecting》2013,61(3):574-581
I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations. 相似文献
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Decomposing seismic data in local slopes is the basic idea behind velocity‐independent imaging. Using accurate moveout approximations enables computing moveout attributes such as normal moveout velocity and nonhyperbolic parameters as functions of zero‐offset travel time. Mapping of moveout attributes is performed from the pre‐stack seismic data domain into the time‐migrated image domain. The different moveout attributes have different accuracy for a given moveout approximation that depends on the corresponding order of travel‐time derivative. The most accurate attribute is the zero‐offset travel time, and the nonhyperbolic parameter has the worst accuracy, regardless of the moveout approximation. Typically, the mapping of moveout attributes is performed using a point‐to‐point procedure, whereas the generalized moveout approximation requires two point‐to‐point mappings. Testing the attribute mapping on the different models shows that the accuracy of mapped attributes is model dependent, whereas the generalized moveout approximation gives practically exact results. 相似文献
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The common-reflection-surface (CRS) stack can be viewed as a physically justified extension of the classical common-midpoint (CMP) stack, utilizing redundant information not only in a single, but in several neighboring CMP gathers. The zero-offset CRS moveout is parameterized in terms of kinematic attributes, which utilize reciprocity and raypath symmetries to describe the two-way process of the actual wave propagation in active seismic experiments by the propagation of auxiliary one-way wavefronts. For the diffraction case, only the attributes of a single one-way wavefront, originating from the diffractor are sufficient to explain the traveltime differences observed at the surface. While paraxial ray theory gives rise to a second-order approximation of the CRS traveltime, many higher-order approximations were subsequently introduced either by squaring the second-order expression or by employing principles of optics and geometry. It was recently discovered that all of these higher-order operators can be formulated either for the optical projection or in an auxiliary medium of a constant effective velocity. Utilizing this duality and the one-way nature of the CRS parameters, we present a simple data-driven stacking scheme that allows for the estimation of the a priori unknown excitation time of a passive seismic source. In addition, we demonstrate with a simple data example that the output of the suggested workflow can directly be used for subsequent focusing-based normal-incidence-point (NIP) tomography, leading to a reliable localization in depth. 相似文献
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A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity VP0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces. 相似文献
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In an acoustic transversely isotropic medium, there are two waves that propagate. One is the P-wave and another one is the S-wave (also known as S-wave artefact). This paper is devoted to analyse the S-wave in two-dimensional acoustic transversely isotropic media with a tilted symmetry axis. We derive the S-wave slowness surface and traveltime function in a homogeneous acoustic transversely isotropic medium with a tilted symmetry axis. The S-wave traveltime approximations in acoustic transversely isotropic media with a tilted symmetry axis can be mapped from the counterparts for acoustic transversely isotropic media with a vertical symmetry axis. We consider a layered two-dimensional acoustic transversely isotropic medium with a tilted symmetry axis to analyse the S-wave moveout. We also illustrate the behaviour of the moveout for reflected S-wave and converted waves. 相似文献
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Common-reflection-surface (CRS) stack for common offset 总被引：8，自引：0，他引：8
We provide a data-driven macro-model-independent stacking technique that migrates 2D prestack multicoverage data into a common-offset (CO) section. We call this new process the CO common-reflection-surface (CRS) stack. It can be viewed as the generalization of the zero-offset (ZO) CRS stack, by which 2D multicoverage data are stacked into a well-simulated ZO section. The CO CRS stack formula can be tailored to stack P-P, S-S reflections as well as P-S or S-P converted reflections. We point out some potential applications of the five kinematic data-derived attributes obtained by the CO CRS stack for each stack value. These include (i) the determination of the geometrical spreading factor for reflections, which plays an important role in the construction of the true-amplitude CO section, and (ii) the separation of the diffractions from reflection events. As a by-product of formulating the CO CRS stack formula, we have also derived a formula to perform a data-driven prestack time migration. 相似文献
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We describe an integrated method for solving the complex near‐surface problem in land seismic imaging. This solution is based on an imaging approach and is obtained without deriving a complex near‐surface velocity model. We start by obtaining from the data the kinematics of the one‐way focusing operators (i.e. time‐reversed Green's functions) that describe propagation between the acquisition surface and a chosen datum reflector using the common‐focus‐point technology. The conventional statics solutions obtained from prior information about the near surface are integrated in the initial estimates of the focusing operators. The focusing operators are updated iteratively until the imaging principle of equal traveltime is fulfilled for each subsurface gridpoint of the datum reflector. Therefore, the seismic data is left intact without any application of time shifts, which makes this method an uncommitted statics solution. The focusing operators can be used directly for wave‐equation redatuming to the respective reflector or for prestack imaging if determined for multiple reflecting boundaries. The underlying velocity model is determined by tomographic inversion of the focusing operators while also integrating any hard prior information (e.g. well information). This velocity model can be used to perform prestack depth imaging or to calculate the depth of the new datum level. We demonstrate this approach on 2D seismic data acquired in Saudi Arabia in an area characterized by rugged topography and complex near‐surface geology. 相似文献