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1.
Velocity model updating in prestack Kirchhoff time migration for PS converted waves: Part I – Theory
A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted‐wave velocity only, and the other factor depending on all parameters. The velocity‐dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non‐hyperbolic behaviour of the moveout. This non‐hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal‐moveout common‐image‐point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio (VP/VS) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration. 相似文献
2.
在偏移后成像空间中的共成像点道集中可以对多次波进行衰减,对于给定的偏移速度模型,一次波与多次波在叠前偏移后的共成像点道集中具有不同的动校时差,这样我们就可以使用类似于偏移前衰减多次波的方法将一次波和多次波进行分离.本文在成像空间中应用抛物Radon变换分离多次波和有效波,由于每个共成像点道集都包含了复杂三维波场传播效应,所以本文方法具有处理三维数据和复杂地下构造的能力.相比于SRME以及传统Radon变换衰减多次波方法,本文方法能够在保持较小的计算量的同时,保证了衰减多次波的准确性.通过对模型数据试算和对实际数据的处理验证了本文方法在叠前时间偏移后衰减多次波的能力,并取得了很好的成像效果. 相似文献
3.
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
4.
Multiples have longer propagation paths and smaller reflection angles than primaries for the same source–receiver combination, so they cover a larger illumination area. Therefore, multiples can be used to image shadow zones of primaries. Least-squares reverse-time migration of multiples can produce high-quality images with fewer artefacts, high resolution and balanced amplitudes. However, viscoelasticity exists widely in the earth, especially in the deep-sea environment, and the influence of Q attenuation on multiples is much more serious than primaries due to multiples have longer paths. To compensate for Q attenuation of multiples, Q-compensated least-squares reverse-time migration of different-order multiples is proposed by deriving viscoacoustic Born modelling operators, adjoint operators and demigration operators for different-order multiples. Based on inversion theory, this method compensates for Q attenuation along all the propagation paths of multiples. Examples of a simple four-layer model, a modified attenuating Sigsbee2B model and a field data set suggest that the proposed method can produce better imaging results than Q-compensated least-squares reverse-time migration of primaries and regular least-squares reverse-time migration of multiples. 相似文献
5.
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
6.
The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing. The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data. The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented. 相似文献
7.
8.
Anisotropy 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. 相似文献
9.
Generalized non‐hyperbolic approximation for qP‐wave relative geometrical spreading in a layered transversely isotropic medium with a vertical symmetry axis 
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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
10.
H.
ZDEM
IR 《Geophysical Prospecting》1982,30(3):292-317
Wavenumber aliasing is the main limitation of conventional optimum least-squares linear moveout filters: it prevents adequate reject domain weighting for efficient coherent noise rejection. A general frequency domain multichannel filter design technique based on a one-to-one mapping method between two-dimensional (2D) space and one-dimensional (1D) space is presented. The 2D desired response is mapped to the 1D frequency axis after a suitable sorting of the coefficients. A min-max or Tchebycheff approximation to the desired response is obtained in the 1D frequency domain and mapped back to the 2D frequency domain. The algorithm is suitable for multiband 2D filter design. No aliasing damage is inherent in the linear moveout filters designed using this technique because the approximation is done in the frequency-wavenumber (f, k)-domain. Linear moveout filters designed by using the present coefficient mapping technique achieve better pass domain approximations than the corresponding conventional least-squares filters. Compatible reject domain approximations can be obtained from suitable mappings of the origin coefficient of the desired (f k)-response to the 1D frequency axis. The (fk)-responses of linear moveout filters designed by using the new technique show equi-ripple behavior. Synthetic and real data applications show that the present technique is superior to the optimum least-squares filters and straight stacking in recovering and enhancing the signal events with relatively high residual statics. Their outputs also show higher resolution than those of the optimum least-squares filters. 相似文献
11.
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
12.
提出一种基于Radon 变换和正交多项式变换的多方向正交多项式变换压制多次波方法.抛物Radon变换对不同曲率方向的同相轴叠加,根据速度差异区分一次波和多次波,但Radon反变换会损伤振幅特性,不利于AVO分析.多方向正交多项式变换在Radon变换(某一曲率方向的零阶特性)的基础上,利用正交多项式变换进一步分析同相轴的高阶多项式分布特性,用正交多项式谱表征同相轴AVO特性;根据一次波和多次波速度差异和同相轴能量分布特征实现多次波压制.该方法的优点是仅用一个曲率参数就可描述同相轴剩余时差参数,提高了一次波和多次波的剩余时差分辨率.实验结果表明,该方法可以有效压制多次波并保留一次波AVO特性. 相似文献
13.
将多次波转换成反射波并按传统反射波偏移算法成像,是多次波成像的一种方法.聚焦变换能准确的将多次波转换为纵向分辨率更高的新波场记录,其中一阶多次波转换为反射波.本文对聚焦变换提出了两点改进:1)提出局部聚焦变换,以减小存储量和计算量,增强该方法对检波点随炮点移动的采集数据的适应性;2)引入加权矩阵,理论上证明原始记录的炮点比检波点稀疏时,共检波点道集域的局部聚焦变换可以将多次波准确转换成炮点与检波点有相同采样频率的新波场记录.本文在第一个数值实验中对比了对包含反射波与多次波的原始记录做局部聚焦变换和直接对预测的多次波做局部聚焦变换两种方案,验证了第二种方案转换得到的波场记录信噪比更高且避免了第一个方案中切聚焦点这项比较繁杂的工作.第二个数值实验表明:在炮点采样较为稀疏时,该方法能有效的将一阶多次波转换成反射波;转换的反射波能提供更丰富的波场信息,成像结果更均衡、在局部有更高的信噪比,以及较高的纵向分辨率. 相似文献
14.
动校正拉伸是地震资料处理的一个基本问题，解决拉伸问题的处理方法是切除.现代地震数据大多为长排列采集，动校正拉伸更为严重.依据褶积模型和Fourier变换的基本性质，本文给出频谱代换无拉伸动校正方法.算法实现就是将CMP道集变换到频率域，取参考道的相位谱替换其它偏移距道的相位，同时保持其振幅谱不变，再做Fourier反变换就得到动校正后的地震剖面.通过其实现过程可知该方法不需要地下介质的速度信息，算法可完全自动实现，且具有较高的计算效率.频谱代换无拉伸动校正可适用于任何偏移距的地震资料，而且还可有效保持地震资料的AVO效应.理论模拟数据及其叠加结果显示频谱代换法的有效性和实用性，同时该方法具有较强的抗随机噪音能力. 相似文献
15.
The filter for wave-equation-based water-layer multiple suppression, developed by the authors in the x-t, the linear τ-p, and the f-k domains, is extended to the parabolic τ-2 domain. The multiple reject areas are determined automatically by comparing the energy on traces of the multiple model (which are generated by a wave-extrapolation method from the original data) and the original input data (multiples + primaries) in τ-p space. The advantage of applying the data-adaptive 2D demultiple filter in the parabolic τ-p domain is that the waves are well separated in this domain. The numerical examples demonstrate the effectiveness of such a dereverberation procedure. Filtering of multiples in the parabolic τ-p domain works on both the far-offset and the near-offset traces, while the filtering of multiples in the f-k domain is effective only for the far-offset traces. Tests on a synthetic common-shot-point (CSP) gather show that the demultiple filter is relatively immune to slight errors in the water velocity and water depth which cause arrival time errors of the multiples in the multiple model traces of less than the time dimension (about one quarter of the wavelet length) of the energy summation window of the filter. The multiples in the predicted multiple model traces do not have to be exact replicas of the multiples in the input data, in both a wavelet-shape and traveltime sense. The demultiple filter also works reasonably well for input data contaminated by up to 25% of random noise. A shallow water CSP seismic gather, acquired on the North West Shelf of Australia, demonstrates the effectiveness of the technique on real data. 相似文献
16.
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
17.
A simple and accurate traveltime approximation is important in many applications in seismic data processing, inversion and modelling stages. Generalized moveout approximation is an explicit equation that approximates reflection traveltimes in general two-dimensional models. Definition of its five parameters can be done from properties of finite offset rays, for general models, or by explicit calculation from model properties, for specific models. Two versions of classical finite-offset parameterization for this approximation use traveltime and traveltime derivatives of two rays to define five parameters, which makes them asymmetrical. Using a third ray, we propose a balance between the number of rays and the order of traveltime derivatives. Our tests using different models also show the higher accuracy of the proposed method. For acoustic transversely isotropic media with a vertical symmetry axis, we calculate a new moveout approximation in the generalized moveout approximation functional form, which is explicitly defined by three independent parameters of zero-offset two-way time, normal moveout velocity and anellipticity parameter. Our test shows that the maximum error of the proposed transversely isotropic moveout approximation is about 1/6 to 1/8 of that of the moveout approximation that had been reported as the most accurate approximation in these media. The higher accuracy is the result of a novel parameterization that do not add any computational complexity. We show a simple example of its application on synthetic seismic data. 相似文献
18.
Amplitude versus offset concepts can be used to generate weighted stacking schemes (here called geo-stack) which can be used in an otherwise standard seismic data processing sequence to display information about rock properties. The Zoeppritz equations can be simplified and several different approximations appear in the literature. They describe the variation of P-wave reflection coefficients with the angle of incidence of a P-wave as a function of the P-wave velocities, the S-wave velocities and the densities above and below an interface. Using a smooth, representative interval velocity model (from boreholes or velocity analyses) and assuming no dip, the angle of incidence can be found as a function of time and offset by iterative ray tracing. In particular, the angle of incidence can be computed for each sample in a normal moveout corrected CMP gather. The approximated Zoeppritz equation can then be fitted to the amplitudes of all the traces at each time sample of the gather, and certain rock properties can be estimated. The estimation of the rock properties is achieved by the application of time- and offset-variant weights to the data samples before stacking. The properties which can be displayed by geo-stack are: P-wave reflectivity (or true zero-offset reflectivity), S-wave reflectivity, and the reflectivity of P-wave velocity divided by S-wave velocity (or ‘pseudo-Poisson's ratio reflectivity’). If assumptions are made about the relation between P-wave velocity and S-wave velocity for water-bearing clastic silicate rocks, then it is possible to create a display which highlights the presence of gas. 相似文献
19.
B. BUTTKUS 《Geophysical Prospecting》1979,27(1):29-39
Long leg multiples can be suppressed by a method which provides an alternative to weighted common-depth-point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time-dependent weighting factor decreases as the semblance of the multiple reflections increases. The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented. For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water-bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions. During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non-linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low-pass filtering. Among the various applications available, only the suppression of long leg water-bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common-depth-point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the multiple suppression. 相似文献
20.
Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data. 相似文献