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1.
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
2.
The design of reflection traveltime approximations for optimal stacking and inversion has always been a subject of much interest
in seismic processing. A most prominent role is played by quadratic normal moveouts, namely reflection traveltimes around
zero-offset computed as second-order Taylor expansions in midpoint and offset coordinates. Quadratic normal moveouts are best
employed to model symmetric reflections, for which the ray code in the downgoing direction coincides with the ray code in
the upgoing direction in reverse order. Besides pure (non-converted) primaries, many multiply reflected and converted waves
give rise to symmetric reflections. We show that the quadratic normal moveout of a symmetric reflection admits a natural decomposition
into a midpoint term and an offset term. These, in turn, can be be formulated as the traveltimes of the one-way normal (N)
and normal-incidence-point (NIP) waves, respectively. With the help of this decomposition, which is valid for propagation
in isotropic and anisotropic elastic media, we are able to derive, in a simple and didactic way, a unified expression for
the quadratic normal moveout of a symmetric reflection in its most general form in 3D. The obtained expression allows for
a direct interpretation of its various terms and fully encompasses the effects of velocity gradients and Earth surface topography. 相似文献
3.
The homeomorphic imaging (HI) approach is a generalization of the common mid-point (CMP) stack to media of arbitrary structures with the following key properties: it collects and enhances useful waves; no knowledge about the velocity structure of the overburden is required for correlation and stacking; and neither the resolution of nor the information about the target objects is degraded by stacking the data. The so-called common reflecting element (CRE) method, which has all three properties, was proposed by Gelchinsky [Gelchinsky, B., 1988. Common reflecting element (CRE) method. Explor. Geophys. 19, 71–75]. However, the CRE method did not only provide a generalization of the CMP method with the key properties; it also has a topological feature that led to the creation of the HI approach. Today, HI can be regarded as a system of methods and schemes for the study of seismic structures that are based on asymptotic wave theory and on fundamental topological ideas. HI is based on a single supposition: it assumes that a target wave exists on the chosen central trace. The next step makes use of the ensemble of all possible wave fronts that can be formed in the vicinity of the central ray corresponding to the chosen central trace. This approach is applicable to a medium of arbitrary structure without the assumption of a seismic model or its parameters. 相似文献
4.
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
5.
Non‐hyperbolic generalised moveout approximation is a powerful tool to approximate the travel‐time function by using information obtained from two rays. The standard approach for parameter selection is using three parameters defined from zero‐offset ray and two parameters obtained from a reference ray. These parameters include the travel time and travel‐time derivatives of different order. The original parameter selection implies more fit at zero offset compared with offset from a reference ray. We propose an alternative approach for parameter selection within the frame of generalised moveout approximation by transferring more fit from the zero offset to a reference ray by changing in parameter selection. The modified approximation is tested against the original one in few analytical model examples, including the multi‐layered model. 相似文献
6.
7.
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
8.
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
9.
本文从测量射线参数出发进行反向射线追踪,导出倾角时差校正（DMO）的公式。经过DMO后,可以从一组等炮检距剖面得出共分角线点道集。用于对这些道集进行叠加的速度值与界面倾角无关。对经过DMO的资料的等时切片进行叠前成象（PSI）,就可以把分布在圆上的绕射能量沿圆弧加起来,并放在圆弧上对应于最大炮检距的位置。经过这两种处理,再应用标准的速度分析和叠加方法,就可得出偏移后的剖面。这两种处理均与速度无关。最后用物理模型试验说明了DMO和PSI的效果是好的。 相似文献
10.
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
11.
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
12.
W.J. VETTER 《Geophysical Prospecting》1987,35(6):700-717
Since the important contributions of Dürbaum and Dix, 30 years ago, velocity profile estimation procedures on horizontally layered and vertically heterogeneous media from seismic probing data have been based largely on hyperbolic moveout models and RMS and stacking velocity concepts. Re-examination of the fundamentals reveals that quantitative velocity heterogeneity and canonical valocity profiles have been implicit factors for moveout modelling and for profile inversion in the use of the Dix procedure. Heterogeneity h is the ratio (and vRMS the geometric or harmonic mean) of the path-average and time-average velocities for a raypath or, in a more restricted sense, for the normal ray belonging to a velocity profile. The canonical profile for a given velocity profile or profile segment is a moveout-equivalent monotonically increasing ramp-like profile. The ramp or constant gradient in depth is the simplest velocity profile approximator which can explicitly accommodate velocity heterogeneity. A ramp model structure is detailed which facilitates moveout simulation and model parameter estimation, and the parametric effects are explored. The horizontal offset range is quantified for which this model can give good moveout approximations. 相似文献
13.
Paulo E. M. Melo Milton J. Porsani Michelângelo G. Silva 《Geophysical Prospecting》2009,57(3):343-353
We present a new filtering method for the attenuation of ground-roll. The method is based on the application of a bi-dimensional filter for obtaining the time-derivative of the seismograms. Before convolving the filter with the input data matrix, the normal moveout correction is applied to the seismograms with the purpose of flattening the reflections. The method can locally attenuate the amplitude of data of low frequency (in the ground-roll and stretch normal moveout region) and enhance flat events (reflections). The filtered seismograms can reveal horizontal or sub-horizontal reflections while vertical or sub-vertical events, associated with ground-roll, are attenuated. A regular set of samples around each neighbourhood data sample of the seismogram is used to estimate the time-derivative. A numerical approximation of the derivative is computed by taking the difference between the interpolated values calculated in both the positive and the negative neighbourhood of the desired position. The coefficients of the 2D time-derivative filter are obtained by taking the difference between two filters that interpolate at positive and negative times. Numerical results that use real seismic data show that the proposed method is effective and can reveal reflections masked by the ground-roll. Another benefit of the method is that the stretch mute, normally applied after the normal moveout correction, is unnecessary. The new filtering approach provides results of outstanding quality when compared to results obtained from the conventional FK filtering method. 相似文献
14.
15.
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
16.
Yanghua Wang 《Geophysical Prospecting》2002,50(6):665-672
The delay‐time Radon transform parametrizes coherent events in a seismic gather by the far‐offset trace delay time, instead of the conventional parabolic curvature or ray parameter. The reformulation may give a different physical insight into the aliasing effect in the Radon transformation and may also lead to a different algorithm. The delay‐time parametrization enables modelling of a seismic gather as the sum of coherent events with any form of moveout curve. For example, a parabolic curve can be used for traces within a moderate offset range and a linear moveout for far‐offset traces. When using this delay‐time Radon transform, it is the number of traces, rather than the spatial sampling, of the input gather that directly controls aliasing in the Radon transform image. A preconditioning operator that implicitly increases the number of input traces by spatial reconstruction (without physically performing the spatial resampling) may minimize aliasing noise in the Radon transform image. 相似文献
17.
同类反射波（非转换波）走时偏离双曲,称为非双曲或四次时差,在长排列各向异性地震资料处理中需要校正．本文基于我们导出的水平界面任意空间取向TI (ATI)介质中同类反射波四次时差系数(A4)的精确解析解,数值计算研究P波四次时差系数特征．正演结果表明,ATI条件下A4系数随CMP测线方位变化的特征不仅与TI介质的各向异性参数有关,而且与TI对称轴的空间取向密切相关; TI介质的各向异性参数和TI对称轴的倾角决定了A4变化特征,而且TI对称轴的方位决定了A4随测线方位变化的对称性．此研究结果将对各向异性解释及参数反演有参考意义． 相似文献
18.
We review the multifocusing method for traveltime moveout approximation of multicoverage seismic data. Multifocusing constructs the moveout based on two notional spherical waves at each source and receiver point, respectively. These two waves are mutually related by a focusing quantity. We clarify the role of this focusing quantity and emphasize that it is a function of the source and receiver location, rather than a fixed parameter for a given multicoverage gather. The focusing function can be designed to make the traveltime moveout exact in certain generic cases that have practical importance in seismic processing and interpretation. The case of a plane dipping reflector (planar multifocusing) has been the subject of all publications so far. We show that the focusing function can be generalized to other surfaces, most importantly to the spherical reflector (spherical multifocusing). At the same time, the generalization implies a simplification of the multifocusing method. The exact traveltime moveout on spherical surfaces is a very versatile and robust formula, which is valid for a wide range of offsets and locations of source and receiver, even on rugged topography. In two‐dimensional surveys, it depends on the same three parameters that are commonly used in planar multifocusing and the common‐reflection surface (CRS) stack method: the radii of curvature of the normal and normal‐incidence‐point waves and the emergence angle. In three dimensions the exact traveltime moveout on spherical surfaces depends on only one additional parameter, the inclination of the plane containing the source, receiver and reflection point. Comparison of the planar and spherical multifocusing with the CRS moveout expression for a range of reflectors with increasing curvature shows that the planar multifocusing can be remarkably accurate but the CRS becomes increasingly inaccurate. This can be attributed to the fact that the CRS formula is based on a Taylor expansion, whereas the multifocusing formulae are double‐square root formulae. As a result, planar and spherical multifocusing are better suited to model the moveout of diffracted waves. 相似文献
19.
The objective of moveout parameter inversion is to derive sets of parameter models that can be used for moveout correction and stacking at each common midpoint location to increase the signal-to-noise ratio of the data and to provide insights into the kinematic characteristics of the data amongst other things. In this paper, we introduce a data-driven user-constrained optimization scheme that utilizes manual picks at a point on each reflector within a common midpoint gather to constrain the search space in which an optimization procedure can search for the optimal parameter sets at each reflection. The picks are used to create boundary curves which can be derived approximately via an optimization technique or analytically via the derivation of an analytical bounds function. In this paper, we derive analytical forms of bounds functions for four different moveout cases. These are normal moveout, non-hyperbolic moveout, azimuthally dependent normal moveout and azimuthally dependent non-hyperbolic moveout. The optimization procedure utilized here to search for the optimal moveout parameters is the particle swarm optimization technique. However, any metaheuristic optimization procedure could be modified to account for the constraints introduced in this paper. The technique is tested on two-layer synthetic models based on three of the four moveout cases discussed in this paper. It is also applied to an elastic forward modelled synthetic model called the HESS model, and finally to real 2D land data from Alaska. The resultant stacks show a marked improvement in the signal-to-noise ratio compared to the raw stacks. The results for the normal moveout, non-hyperbolic moveout and azimuthally dependent normal moveout tests suggest that the method is viable for said models. Results demonstrate that our method offers potential as an alternative to conventional parameter picking and inversion schemes, particularly for some cases where the number of parameters in the moveout approximation is 2 or greater. 相似文献
20.
Determination of a shallow velocity–depth model from seismic refraction data by coherence inversion1
Seismic refractions have different applications in seismic prospecting. The travel- times of refracted waves can be observed as first breaks on shot records and used for field static calculation. A new method for constructing a near-surface model from refraction events is described. It does not require event picking on prestack records and is not based on any approximation of arrival times. It consists of the maximization of the semblance coherence measure computed using shot gathers in a time window along refraction traveltimes. Time curves are generated by ray tracing through the model. The initial model for the inversion was constructed by the intercept-time method. Apparent velocities and intercept times were taken from a refraction stacked section. Such a section can be obtained by appling linea moveout corrections to common-shot records. The technique is tested successfully on synthetic and real data. An important application of the proposed method for solving the statics problem is demonstrated. 相似文献