共查询到20条相似文献，搜索用时 985 毫秒
1.
We 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. 相似文献
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We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi‐compressional, quasi‐shear, and converted waves in one‐dimensional multi‐layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface‐offset azimuth and applying our derived relationship between the surface‐offset azimuth and phase‐velocity azimuth, we obtain the normal moveout velocity versus the phase‐velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time‐domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local‐angle‐domain common image gathers. The angle and azimuth parameters of the local‐angle‐domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψphs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi‐layer structure is based on the fact that, for a one‐dimensional model assumption, the horizontal slowness and the azimuth of the phase velocity ψphs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface‐offset azimuth and phase‐velocity azimuth domains. 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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对Christoffel公式进行Bond变换得到EDA介质的Christoffel方程,并由其非零解推导出EDA介质中视横波(qSV)、横波(SH)、视纵波(qP)的相速度、群速度、偏振向量(质点的振动方向)的三维计算公式.通过模型计算分析了具有水平对称轴的各向异性(HTI)介质和EDA介质中介质对称轴的极角和方位角对相速度、群速度及偏振向量的影响,对其随极角、方位角的变化特征进行了分析,并采用Matlab进行了数值计算,对其特征采用三维显示.通过取极角或方位角为零简化得到HTI介质和具有垂直对称轴的各向异性(VTI)介质中地震波的相速度、群速度,对EDA介质中的三维计算结果进行退化验证. 通过数值计算进一步验证了地震波相速度与EDA介质对称轴的相互关系. 结果表明,通过广角地震勘探可探明地下介质的裂隙走向及密度,从而确定灾害体产状. 相似文献
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It has been shown in the past that the interval-NMO velocity and the non-ellipticity parameter largely control the P-wave reflection time moveout of VTI media. To invert for these two parameters, one needs either reasonably large offsets, or some structure in the subsurface in combination with relatively mild lateral velocity variation.This paper deals with a simulation of an inversion approach, building on the assumption that accurately measured V
NMO, as defined by small offset asymptotics for a particular reflector, were available. Instead of such measurements we take synthetically computed data. First, an isotropic model is constructed which explains these V
NMO. Subsequently, residual moveout in common image gathers is modelled by ray tracing (replacing real data), along with its sensitivity for changes in the interval-NMO velocity and the non-ellipticity parameter under the constraint that V
NMO is preserved. This enables iterative updating of the non-ellipticity parameter and the interval-NMO velocity in a layer that can be laterally inhomogeneous.This approach is successfully applied for a mildly dipping reflector at the bottom of a layer with laterally varying medium parameters. With the exact V
NMO assumed to be given, lateral inhomogeneity and anisotropy can be distinguished for such a situation. However, for another example with a homogeneous VTI layer overlying a curved reflector with dip up to 30°, there appears to be an ambiguity which can be understood by theoretical analysis. Consistently with existing theory using the NMO-ellipse, the presented approach is successfully applied to the latter example if V
NMO in the strike direction is combined with residual moveout in dip direction. 相似文献
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Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media 
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下载免费PDF全文 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. 相似文献
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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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Generalized non‐hyperbolic approximation for qP‐wave relative geometrical spreading in a layered transversely isotropic medium with a vertical symmetry axis 下载免费PDF全文
下载免费PDF全文 Compensation for geometrical spreading along the ray‐path is important in amplitude variation with offset analysis especially for not strongly attenuative media since it contributes to the seismic amplitude preservation. The P‐wave geometrical spreading factor is described by a non‐hyperbolic moveout approximation using the traveltime parameters that can be estimated from the velocity analysis. We extend the P‐wave relative geometrical spreading approximation from the rational form to the generalized non‐hyperbolic form in a transversely isotropic medium with a vertical symmetry axis. The acoustic approximation is used to reduce the number of parameters. The proposed generalized non‐hyperbolic approximation is developed with parameters defined by two rays: vertical and a reference rays. For numerical examples, we consider two choices for parameter selection by using two specific orientations for reference ray. We observe from the numerical tests that the proposed generalized non‐hyperbolic approximation gives more accurate results in both homogeneous and multi‐layered models than the rational counterpart. 相似文献
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Guiting Chen Zhenli Wang Oluwatosin John Rotimi Suyang Zhang 《Geophysical Prospecting》2020,68(4):1314-1327
Conventional Kirchhoff prestack time migration based on the hyperbolic moveout can cause ambiguity in laterally inhomogeneous media, because the root mean square velocity corresponds to a one-dimensional model under the horizontal layer assumption; it does not include the lateral variations. The shot/receiver configuration with different offsets and azimuths should adopt different migration velocities as they contribute to a single image point. Therefore, we propose to use an offset-vector to describe the lateral variations through an offset-dependent velocity corresponding to the difference in offset from surface points to the image point. The offset-vector is decomposed into orthogonal directions along the in-line and cross-line directions so that the single velocity can be expressed as a series of actual velocities. We use a simple Snell's law-based ray tracing to calculate the travel time recorded at the image point and convert the travel time to an equivalent velocity corresponding to a pseudo-straight ray. The double-square-root equation using such an equivalent velocity in the offset-vector domain is non-hyperbolic and asymmetrical, which improves the accuracy of the migration. Numerical examples using the Marmousi model and a wide azimuth field data show that the proposed method can achieve reasonable accuracy and significantly enhances the imaging of complex structures. 相似文献
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Tariq Alkhalifah 《Geophysical Prospecting》2004,52(1):39-48
The azimuth moveout (AMO) operator in homogeneous transversely isotropic media with a vertical symmetry axis (VTI), as in isotropic media, has an overall skewed saddle shape. However, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even in weaker anisotropies, with the anisotropy parameter η= 0.1 (10% anisotropy), the AMO operator is considerably different from the isotropic operator, although free of triplications. The structure of the operator in VTI media (positive η) is stretched (has a wider aperture) compared with operators in isotropic media, with the amount of stretch being dependent on the strength of anisotropy. If the medium is both vertically inhomogeneous, i.e. the vertical velocity is a function of depth (v(z)), and anisotropic, which is a common combination in practical problems, the shape of the operator again differs from that for isotropic media. However, the difference in the AMO operator between the homogeneous and the v(z) cases, even for anisotropic media, is small. Stated simply, anisotropy influences the shape and aperture of the AMO operator far more than vertical inhomogeneity does. 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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The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ? of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ?. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ?, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ? reveals that travel times are more sensitive to η than to the symmetry axis azimuth ?. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ? differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ?, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values. 相似文献
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Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities. 相似文献
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Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalised seismic data interpolation as a basis pursuit problem and proposed an iteration framework for recovering missing data. The method is based on non‐linear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimisation problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalised velocity‐dependent formulation of the seislet transform as an effective sparse transform, in which the non‐hyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parametres in the common‐midpoint domain. It can also be reduced to the traditional velocity‐dependent seislet if special heterogeneity parametre is selected. The generalised velocity‐dependent seislet transform predicts prestack reflection data in offset coordinates, which provides a high compression of reflection events. The method was applied to synthetic and field data examples, and the results show that the generalised velocity‐dependent seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for non‐hyperbolic reflections under complex conditions, such as vertical transverse isotropic (VTI) media or aliasing. 相似文献
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Three‐dimensional residual moveout analysis is the basic step in velocity model refinement. The analysis is generally carried out using horizontal and/or vertical semblances defined on a sparse set of in‐lines or cross‐lines with densely sampled source–receiver offsets. An alternative approach, which we call dense residual moveout analysis (DRMA), is to use all the bins of a three‐dimensional survey but sparsely sampled offsets. The proposed technique is very fast and provides unbiased and statistically efficient estimates of the residual moveout. Indeed, for the sparsest possible offset distribution, when only near‐ and far‐angle stacks are used, the variance of the residual moveout estimate is only 1.4 times larger than the variance of the least‐squares estimate obtained using all offsets. The high performance of DRMA makes it a useful tool for many applications, of which azimuthal velocity analysis is considered here. For a horizontal transverse isotropy (HTI) model, a deterministic procedure is proposed to define, at every point of residual moveout estimation, the azimuthal angle of the HTI axis of symmetry, the Thomsen anisotropy coefficients, and the interval (or root‐mean‐square) velocities in both the HTI isotropy and symmetry planes. The procedure is not restricted by DRMA assumptions; for example, it is also applicable to semblance‐based residual moveout estimates. The high resolution of the technique is illustrated by azimuthal velocity analysis over an oilfield in West Siberia. 相似文献
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利用横波响应进行裂缝性各向异性介质的检测在实际应用中取得了很好的效果,但技术复杂、成本较高使该方法的广泛使用受到限制,而纵波资料采集和处理技术的精细有效保持了纵波的各种属性,这为直接利用纵波资料进行裂缝检测创造了条件.地下垂直定向裂缝通常用HTI介质模型来描述,为此,本文利用射线追踪和反射率法计算了层状各向同性介质背景下的HTI介质顶、底界面的反射纵波旅行时和反射系数,并分析了这些属性随观测方位的变化规律.研究表明,HTI介质底界面反射纵波旅行时和HTI介质顶界面反射系数表现出了明显的方位各向异性;旅行时、振幅和AVO梯度属性均在0°观测方位和90°观测方位上存在最大差异,可以用多种属性联合来精确判定裂缝的发育方向. 相似文献
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Imaging diffracted waves can provide useful information about complex subsurface geology and fracture networks. Separation of diffractions from typically more intensive reflected events can be done based on specularity, which measures deviation from Snell’s law. Here, we analyze two formulations of specularity and their applicability to diffraction processing in the presence of anisotropy. We show that the most common definition of specularity, originally introduced for pure modes in isotropic media, remains valid for both pure and converted waves in arbitrarily anisotropic models. The other formulation operates directly with the difference between the slowness projections onto the reflector for the incident and reflected waves. Testing on a VTI (transversely isotropic with a vertical symmetry axis) diffraction ramp model demonstrates that both formulations produce satisfactory results for anisotropic media with appropriate tapering of the specularity gathers. Then separation and imaging of diffractions is performed for the structurally complex VTI Marmousi model. We also analyze the sensitivity of diffractions in the specularity gathers to errors in the symmetry-direction velocity and anellipticity parameter η. 相似文献