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1.
Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy. 相似文献
2.
Ali A. Nowroozi 《Pure and Applied Geophysics》1990,133(1):103-115
In reflection surveys and velocity analysis, calculations of interval velocities and layer-thicknesses of a multilayered horizontal structure are often based on Dix's equation which requires the travel times at zero offsets and a prior estimate of the root mean squared velocities.In this paper a method is presented which requires only the reflection travel-time data. A set of equations are derived which relate the interval velocity and thickness of a layer to the reflection travel time from the top and the bottom of that layer, the offset distances and the ray parameter. It is shown that the difference of the offset distances and the difference of the picked travel times of any reflected rays with the same value of ray parameter from the top and the bottom of a horizontal layer can be used to calculate the interval velocity and thickness of that layer. 相似文献
3.
Emil Blias 《Geophysical Prospecting》2012,60(6):1054-1067
This paper presents a new explicit method for the estimation of layered vertical transverse isotropic (VTI) anisotropic parameters from walkaway VSP data. This method is based on Dix‐type normal moveout (NMO) inversion. To estimate interval anisotropic parameters above a receiver array, the method uses time arrivals of surface‐related double‐reflected downgoing waves. A three‐term NMO approximation function is used to estimate NMO velocity and a non‐hyperbolic parameter. Assuming the vertical velocity is known from zero‐offset VSP data, Dix‐type inversion is applied to estimate the layered Thomsen anisotropic parameters ?, δ above the receivers array. Model results show reasonable accuracy for estimates through Dix‐type inversion. Results also show that in many cases we can neglect the influence of the velocity gradient on anisotropy estimates. First breaks are used to estimate anisotropic parameters within the walkaway receiver interval. Analytical uncertainty analysis is performed to NMO parameter estimates. Its conclusions are confirmed by modelling. 相似文献
4.
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
5.
Proper stacking of three-dimensional seismic CDP-data generally requires the knowledge of normal moveout velocities in all source-receiver directions contributing to a CDP-gather. The azimuthal variation of the stacking velocities mainly depends on the dip of the seismic interfaces. For a single dipping plane a simple relation exists between the dip and the azimuthal variation of NMO-velocity. Varying strike and dip of subsequent reflectors, however, result in a complex dependency of the seismic parameters. Reliable information on the spatial distribution of the normal moveout (NMO)-velocity can be derived from a wavefront curvature estimation using a 3-D ray-tracing technique. These procedures require additional information, e.g. reflection time gradients or depth maps to show interval velocities between leading interfaces. Moreover, their application to an extended 3-D data volume is restricted by high costs. The need for a routine 3-D procedure resulted in a special data selection to create pseudo 2-D profiles and to apply existing velocity estimation routines to these profiles. At least three estimates in different directions are necessary to derive the full azimuthal velocity variation, characterized by the large and the small main axis and the orientation of the velocity ellipse. Errors are estimated by means of computer models. Stacking velocities obtained by mathematical routines (least-squares fit) and by seismic standard routines (NMO-correction and correlation) are compared. Finally, a general 3-D velocity procedure using cross-correlation of preliminarily NMO-corrected traces is proposed. 相似文献
6.
Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε(1,2), δ(1,2,3) and γ(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε(1,2), δ(1,2) and γ(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x1 and x2 (i.e. in the shear-wave polarization directions). The remaining coefficient δ(3) is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ(1,2,3) which control the rotation of the P-, S1- and S2-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S1- and S2-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS1- and PS2-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium. 相似文献
7.
推导了各向异性介质中由弹性系数表示的方位动校NMO速度的具体表达式,表明各向异性介质中方位NMO速度程椭圆形状,并分别对具水平对称轴的横向各向同性介质(HTI)、正交介质和单斜各向异性介质及在不同的裂隙填充物的性质下方位NMO速度进行了计算,结果表明裂隙的存在对NMO速度的影响不仅与裂隙密度有关,还取决于裂隙填充物的性质.同时,研究表明对于裂隙型单斜各向异性介质,其方位NMO速度椭圆轴向并不象HTI介质和正交介质中的那样与自然坐标系的坐标轴一致,而是发生了一定角度的偏离,其大小与裂隙填充物的性质、两组裂隙密度的比值及裂隙间的夹角等因素有关,研究结果为进一步区分裂隙介质的类型及裂隙填充物的性质提供依据. 相似文献
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R. MARSCHALL 《Geophysical Prospecting》1972,20(3):700-711
From seismic surveys zero offset reflection times and root-mean-square velocities are obtained. By use of Dix-Krey's formula, the interval velocities can be calculated. If no well velocity survey exists, the interval velocities and T(o) times are the only available information. The suggested way to get a regionally valid velocity distribution is to select N“leading horizons”, where a major change in the velocity parameters occurs and to compute the parameters of the selected velocity depth function (in most cases linear increase with depth) by a special approximation for the interval between two adjacent “leading horizons”. Herewith all reflection horizons within the interval are taken into account. 相似文献
10.
传统二阶动校正方法基于较小最大偏移距与目标层深度比和地震波沿直线传播假设,进行长偏移距地震资料处理时,这些假设不再成立.高阶项动校正公式能提高长偏移动校正精度,文中对几种典型的高阶项动校正方法进行了比较,并提出了优化四阶、优化六阶动校正方法.模型计算表明,高阶项动校正方法能取得较常规动校正方法好的动校正结果,但并非阶数越高动校正精度就越高;在纵向速度变化剧烈时,高阶动校正或优化高阶动校正方法一般不能适用于最大偏移距与目标层深度大于3.5的地震反射同相轴,优化四阶和优化六阶动校正公式由于考虑了无穷大偏移距的影响,具有更稳定、更加精确动校正效果,适合于实际的各向同性长偏移距地震资料处理. 相似文献
11.
The multifold acquisition principle was applied to a borehole radar survey, performed in a granitic site (Grimsel Test Site, Switzerland). Two multifold coverage acquisitions (40-fold and 20-fold) were carried out in a subhorizontal borehole. Instrumental drifts (transmission time and sampling frequency fluctuations) were corrected in order to remove shifts observed on CMP gathers and to optimize velocity analysis and trace stacking. Computation of velocity spectra was adapted in order to take into account the features of the medium investigated (homogeneous velocity, various reflector orientations). The NMO velocities were then interpreted as angles between reflectors and the survey line. The processing, based on the computation of several constant velocity stacked sections performed with different NMO velocities, leads to better results than the standard DMO + NMO processing. The signal-to-noise ratio of the stacked profile is improved in comparison with the single-fold section, which results from a standard acquisition. From a practical point of view, the implementation of a multifold radar survey within a borehole is difficult but a greater investigation range is obtained, more reflectors are detected and the mapping of geological discontinuities is improved. 相似文献
12.
H. JAKUBOWICZ 《Geophysical Prospecting》1990,38(3):221-245
Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack. In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking. 相似文献
13.
Time horizons can be depth-migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973). Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise VNMO velocities at zero offset are known. However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities. A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model. Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust. 相似文献
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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
16.
Abstract The main aim of this study is the experimental investigation of friction velocities and shear stresses in rivers under unsteady flow conditions. Special measurements of mean velocities and other hydraulic parameters were made in two small lowland rivers in central Poland. Four controlled flood waves were released and analysed in the selected reaches. The main hydrometric characteristics and the relationship between water level and discharge were established. Friction velocities were obtained directly from the full St Venant equations of motion, as well as from only the steady momentum equation, and their time-dependent forms were established. Both these approaches provided similar results when the unsteadiness parameter was relatively low. It appeared that real friction velocities were much larger than those obtained from the common uniform flow formula. The passing hydrograph influenced the value of the shear velocity significantly. 相似文献
17.
Liangguo Dong Zhongyi Fan Hongzhi Wang Benxin Chi Yuzhu Liu 《Geophysical Prospecting》2018,66(8):1503-1520
Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model. 相似文献
18.
We introduce a processing technique which minimizes the 'stretching effects' of conventional NMO correction. Unlike conventional NMO, the technique implies constant normal moveout (CNMO) for a finite time interval of a seismic trace. The benefits of the proposed method include preservation of higher frequencies and reduction of spectral distortions at far offsets. The need for severe muting after the correction is reduced, allowing longer spreads for stack, velocity and AVO analysis. The proposed technique has been tested on model and real data. The method may improve the resolution of CMP stack and AVO attribute analysis. The only assumptions for this stretch-free NMO correction are (i) all time samples of a digital reflected wavelet at a particular offset have the same normal moveout, and (ii) reflection records have an interference nature. 相似文献
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