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1.
Explicit equations for the spatial derivatives and perturbation derivatives of amplitude in both isotropic and anisotropic media are derived. The spatial and perturbation derivatives of the logarithm of amplitude can be calculated by numerical quadratures along the rays. The spatial derivatives of amplitude may be useful in calculating the higher-order terms in the ray series, in calculating the higher-order amplitude coefficients of Gaussian beams, in estimating the accuracy of zero-order approximations of both the ray method and Gaussian beams, in estimating the accuracy of the paraxial approximation of individual Gaussian beams, or in estimating the accuracy of the asymptotic summation of paraxial Gaussian beams. The perturbation derivatives of amplitude may be useful in perturbation expansions from elastic to viscoelastic media and in estimating the accuracy of the common-ray approximations of the amplitude in the coupling ray theory.  相似文献   

2.
Localization of fractured areas is of primary interest in the study of oil and gas geology in carbonate environments. Hydrocarbon reservoirs in these environments are embedded within an impenetrable rock matrix but possess a rich system of various microheterogeneities, i.e., cavities, cracks, and fractures. Cavities accumulate oil, but its flow is governed by a system of fractures. A distinctive feature of wave propagation in such media is the excitation of the scattered/diffracted waves by the microheterogeneities. This scattering could be a reliable attribute for characterization of the fine structure of reservoirs, but it has extremely low energy and any standard data processing renders them practically invisible in comparison with images produced by specular reflections. Therefore, any attempts to use these waves for image congestion of microheterogeneities should first have a preliminary separation of the scattering and specular reflections. In this paper, the approach to performing this separation is based on the asymmetric summation. It is implemented by double focusing of Gaussian beams. To do this, the special weights are computed by propagating Gaussian beams from the target area towards the acquisition system separately for sources and receivers. The different mutual positioning of beams in each pair introduces a variety of selective images that are destined to represent some selected singular primitives of the target objects such as fractures, cavities, and edges. In this way, one can construct various wave images of a target reservoir, particularly in scattered/diffracted waves. Additional removal of remnants of specular reflections is done by means of spectral analysis of the scattered/diffracted waves' images to recognize and cancel extended lineaments. Numerical experiments with Sigsbee 2A synthetic seismic data and some typical structures of the Yurubcheno‐Tokhomskoye oil field in East Siberia are presented and discussed.  相似文献   

3.
We present an innovative approach for seismic image enhancement using multi‐parameter angle‐domain characterization of common image gathers. A special subsurface angle‐domain imaging system is used to generate the multi‐parameter common image gathers in a summation‐free image space. The imaged data associated with each common image gathers depth point contain direction‐dependent opening‐angle image contributions from all the available incident and scattered wave‐pairs at this point. Each direction‐dependent opening‐angle data can be differently weighted according to its coherency measure. Once the optimal migration velocity is used, it is assumed that in the actual specular direction, the coherency measure (semblance) along reflection events, from all available opening angles and opening azimuths, is larger than that along non‐specular directions. The computed direction‐dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image. The ability to analyse the structural properties of the image points by the multi‐parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures. The proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples.  相似文献   

4.
近年来,油气勘探的重心正转向具有复杂地表和复杂地质体的双复杂区域.本文发展了一种精确的双复杂条件下基于地表倾角信息的非倾斜叠加束偏移方法,相对于传统束成像方法无需进行三方面处理:(1)高程静校正;(2)相位校正;(3)束中心与接收点之间关于速度和束出射角的近似替换,因而具有更高的成像精度.通过加拿大逆掩断层模型、中原油田断层模型及实际资料的偏移试算,并与传统束偏移及波动方程偏移成像结果对比可知:本文非近似束偏移方法在近地表、高陡倾等构造处的成像精度、反射界面成像振幅等方面优于传统的偏移方法,以此验证了本文非倾斜叠加精确束偏移方法的正确性、优越性及适应性.  相似文献   

5.
We study the stability of source mechanisms inverted from data acquired at surface and near‐surface monitoring arrays. The study is focused on P‐wave data acquired on vertical components, as this is the most common type of acquisition. We apply ray modelling on three models: a fully homogeneous isotropic model, a laterally homogeneous isotropic model and a laterally homogeneous anisotropic model to simulate three commonly used models in inversion. We use geometries of real arrays, one consisting in surface receivers and one consisting in ‘buried’ geophones at the near‐surface. Stability was tested for two of the frequently observed source mechanisms: strike‐slip and dip‐slip and was evaluated by comparing the parameters of correct and inverted mechanisms. We assume these double‐couple source mechanisms and use quantitatively the inversion allowing non‐double‐couple components to measure stability of the inversion. To test the robustness we inverted synthetic amplitudes computed for a laterally homogeneous isotropic model and contaminated with noise using a fully homogeneous model in the inversion. Analogously amplitudes computed in a laterally homogeneous anisotropic model were inverted in all three models. We show that a star‐like surface acquisition array provides very stable inversion up to a very high level of noise in data. Furthermore, we reveal that strike‐slip inversion is more stable than dip‐slip inversion for the receiver geometries considered here. We show that noise and an incorrect velocity model may result in narrow bands of source mechanisms in Hudson's plots.  相似文献   

6.
In order to trace a ray between known source and receiver locations in a perfectly elastic medium, the take-off angle must be determined, or equialently, the ray parameter. In a viscoelastic medium, the initial value of a second angle, the attenuation angle (the angle between the normal to the plane wavefront and the direction of maximum attenuation), must also be determined. There seems to be no agreement in the literature as to how this should be done. In computing anelastic synthetic seismograms, some authors have simply chosen arbitrary numerical values for the initial attenuation angle, resulting in different raypaths for different choices. There exists, however, a procedure in which the arbitrariness is not present, i.e., in which the raypath is uniquely determined. It consists of computing the value of the anelastic ray parameter for which the phase function is stationary (Fermat's principle). This unique value of the ray parameter gives unique values for the take-off and attenuation angles. The coordinates of points on these stationary raypaths are complex numbers. Such rays are known as complex rays. They have been used to study electromagnetic wave propagation in lossy media. However, ray-synthetic seismograms can be computed by this procedure without concern for the details of complex raypath coordinates. To clarify the nature of complex rays, we study two examples involving a ray passing through a vertically inhomogeneous medium. In the first example, the medium consists of a sequence of discrete homogeneous layers. We find that the coordinates of points on the ray are generally complex (other than the source and receiver points which are usually assumed to lie in real space), except for a ray which is symmetric about an axis down its center, in which case the center point of the ray lies in real space. In the second example, the velocity varies continuously and linearly with depth. We show that, in geneneral, the turning point of the ray lies in complex space (unlike the symmetric ray in the discrete layer case), except if the ratio of the velocity gradient to the complex frequency-dependent velocity at the surface is a real number. We also present a numerical example which demonstrates that the differences between parameters, such as arrival time and raypath angles, for the stationary ray and for rays computed by the above-mentioned arbitrary approaches can be substantial.  相似文献   

7.
Synthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P- to S-wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non-vertical incidence on synthetic seismograms is examined in this paper. Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source. Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.  相似文献   

8.
I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.  相似文献   

9.
Refracted arrivals are analysed to estimate the near‐surface anisotropy of marine sediments using a vertical‐cable (VC) configuration. In the presence of dip, the horizontal and vertical ray‐slownesses are obtained from the observed apparent slownesses in the up‐ and downdip directions using a sum or difference at each azimuth. The multiple azimuths generated by a VC geometry permit the ray‐slowness distribution of the marine sediments to be determined. An inversion procedure is developed to provide dip and anisotropy parameters for refractive layers from the measured refraction traveltimes in multilayered azimuthally isotropic and anisotropic media. Two sets of transversely isotropic models are used to analyse the azimuthal variations of apparent and ray slownesses. In the first set, we fix the anisotropic parameters of the models but vary the dip (0°, 5° and 10°) to test the effects of the presence of dip. In the second set, we vary the P‐wave anisotropy strength (5.2%, 10.3%, 15.8% and 22.0%) to examine the sensitivity and accuracy of ray‐slowness approximations which are independent of dip. We test this inversion procedure on synthetic P‐wave VC data calculated for six different models by a finite‐difference method. The results of applications to real VC data acquired from the North Sea are also presented.  相似文献   

10.
TI介质局部角度域高斯束叠前深度偏移成像   总被引：4，自引：4，他引：0       下载免费PDF全文
各向异性射线理论基础上的局部角度域叠前深度偏移方法能够为深度域构造成像与基于角道集的层析反演提供有力支撑,但是对于复杂地质构造而言,高斯度叠前深度偏移在不失高效、灵活等特点的情况下,具有明显的精度优势.为此,本文研究局部角度域理论框架下的高斯束叠前深度偏移方法.为提高算法效率与实用性,文中讨论了一种从经典弹性参数表征的各向异性介质运动学和动力学射线方程演变而来的由相速度表征的简便形式,并提出了一种比较经济的各向异性高斯束近似合成方案.结合地震波局部角度域成像原理,讨论一种适合高斯束偏移的角度参数计算方法.国际上通用的理论模型合成数据试验表明：相比局部角度域Kirchhoff叠前深度偏移成像方法,本文方法具有更高的成像精度与抗噪能力,既适用于复杂构造成像,也可为TI介质深度域偏移速度分析与模型建立提供高效的偏移引擎.  相似文献   

11.
The reflection operator for a simple flat‐lying interface can be thought of as the set of all its plane‐wave reflection coefficients or as the set of virtual surveys with sources and receivers along the interface. When there is dip, however, it is necessary to include the varying effects of propagation between the virtual‐survey level and the interface. Hence, step one in this paper is to derive the reflection operator for a dipping plane interface as observed at a datum level some distance away. The key assumption is that the aperture at the datum level is sufficient to characterize the reflector properties around a particular point. This translates into an assumption that the dip is moderate, though no explicit small‐angle approximation is required. The second step is to find the apparent reflection operator that would relate data that have been extrapolated from the datum towards and possibly beyond the reflector using an assumed migration velocity. This apparent reflection operator is closely related to extended common‐image gathers. The apparent reflection operator may be analysed asymptotically in terms of rays and other signals, shedding light on the structure of extended image gathers. In keeping with the virtual‐survey idea, the results are considered in a subsurface space‐time or slowness‐time domain at various extrapolation levels around the interface. An important distinction is drawn between using subsurface midpoint‐offset coordinates and the wavefield coordinates of the incident and reflected waves. The latter reveal more clearly the effects of dip, because they lead to a more asymmetric apparent reflection operator. Properties such as an up‐dip shift of a traveltime minimum and its associated curvature theoretically provide information about the reflector location and dip and the migration‐velocity error. The space‐time form of the reflection operator can be highly intricate around the offset‐time origin and it was described for a simple flat interface in a background paper. To avoid a layer of mathematics, the reflection‐operator formulas presented here are in the intermediate space‐frequency domain. They are analysed by considering their stationary‐phase and branch‐point high‐frequency contributions. There is no Born‐like assumption of weak reflector contrast and so wide‐angle, total reflection and head‐wave effects are included. Snell’s law is an explicit part of the theory. It is hoped that the work will therefore be a step towards the goal of unifying amplitude‐versus‐offset, imaging and waveform inversion.  相似文献   

12.
Sensitivity of seismic waves to structure   总被引：2，自引：0，他引：2  
We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.  相似文献   

13.
高斯束逆时偏移是一种兼具计算效率和成像精度的深度域成像方法,能够面向目标成像.地下介质中黏滞性普遍存在,利用传统各向同性或完全弹性的成像方法处理黏滞性探区的数据会降低分辨率,并导致成像位置不准确和振幅欠估计等问题.本文在高斯束逆时偏移的基础上,通过对震源点和检波点处的波场进行衰减补偿,并结合高斯束求解时的角度信息,实现了黏声介质角度域高斯束逆时偏移方法.最后通过模型和实际资料试算对本文方法的正确性和适用性进行了验证.试算结果表明:相比于声波高斯束逆时偏移,本文方法能够对黏滞性引起的吸收衰减进行有效补偿,同时提取的角度域共成像点道集(ADCIGs)不仅可以用于分角度叠加成像压制成像噪声,而且能够为后续的偏移速度分析提供支撑.  相似文献   

14.
An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that are ideally diffraction-free and do not diverge when they propagate. They can be described by plane waves with normal vectors along a cone with a fixed angle from the beam propagation direction. X-waves are an example of pulsed beams that propagate in an undistorted fashion. For realizable localized beam solutions, Bessel beams must ultimately be windowed by an aperture, and for a Gaussian tapered window function this results in Bessel-Gauss beams. Bessel-Gauss beams can also be realized by a combination of Gaussian beams propagating along a cone with a fixed opening angle. Depending on the beam parameters, Bessel-Gauss beams can be used to describe a range of beams solutions with Gaussian beams and Bessel beams as end-members. Both Gaussian beams, as well as limited diffraction beams, can be used as building blocks for the modeling and synthesis of other types of wave fields. In seismology and geophysics, limited diffraction beams have the potential of providing improved controllability of the beam solutions and a large depth of focus in the subsurface for seismic imaging.  相似文献   

15.
— In this paper, an overview of the calculation of synthetic seismograms using the Gaussian beam method is presented accompanied by some representative applications and new extensions of the method. Since caustics are a frequent occurrence in seismic wave propagation, modifications to ray theory are often necessary. In the Gaussian beam method, a summation of paraxial Gaussian beams is used to describe the propagation of high-frequency wave fields in smoothly varying inhomogeneous media. Since the beam components are always nonsingular, the method provides stable results over a range of beam parameters. The method has been shown, however, to perform better for some problems when different combinations of beam parameters are used. Nonetheless, with a better understanding of the method as well as new extensions, the summation of Gaussian beams will continue to be a useful tool for the modeling of high-frequency seismic waves in heterogeneous media.  相似文献   

16.
Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated. Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data. Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.  相似文献   

17.
Extracting true amplitude versus angle common image gathers is one of the key objectives in seismic processing and imaging. This is achievable to different degrees using different migration techniques (e.g., Kirchhoff, wavefield extrapolation, and reverse time migration techniques) and is a common tool in exploration, but the costs can vary depending on the selected migration algorithm and the desired accuracy. Here, we investigate the possibility of combining the local‐shift imaging condition, specifically the time‐shift extended imaging condition, for angle gathers with a Kirchhoff migration. The aims are not to replace the more accurate full‐wavefield migration but to offer a cheaper alternative where ray‐based methods are applicable and to use Kirchhoff time‐lag common image gathers to help bridge the gap between the traditional offset common image gathers and reverse time migration angle gathers; finally, given the higher level of summation inside the extended imaging migration, we wish to understand the impact on the amplitude versus angle response. The implementation of the time‐shift imaging condition along with the computational cost is discussed, and results of four different datasets are presented. The four example datasets, two synthetic, one land acquisition, and a marine dataset, have been migrated using a Kirchhoff offset method, a Kirchhoff time‐shift method, and, for comparison, a reverse time migration algorithm. The results show that the time‐shift imaging condition at zero time lag is equivalent to the full offset stack as expected. The output gathers are cleaner and more consistent in the time‐lag‐derived angle gathers, but the conversion from time lag to angle can be considered a post‐processing step. The main difference arises in the amplitude versus offset/angle distribution where the responses are different and dramatically so for the land data. The results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers. The same disadvantages with a ray‐based approach will apply using the extended imaging condition relative to a wave equation angle gather solution. Nevertheless, using this approach allows one to explore the relationship between the velocity model and focusing of the reflected energy, to use the Radon transformation to remove noise and multiples, and to generate consistent products from a ray‐based migration and a full‐wave equation migration, which can then be interchanged depending on the process under study.  相似文献   

18.
复杂地表条件下保幅高斯束偏移   总被引：8，自引：6，他引：2       下载免费PDF全文
高斯束偏移是一种准确、灵活、高效的深度域成像方法,其不但具有接近于波动方程偏移的成像精度,还保留了Kirchhoff偏移灵活、高效的特点以及对复杂地表条件良好的适应性.本文提出了一种适用于复杂地表条件的且具有相对振幅保持特点的高斯束偏移方法.通过考虑地表高程、倾角以及实际的道间距等信息,推导了基于高斯束表示的波场反向延拓公式,并结合反褶积成像条件,得到了复杂地表条件下的共炮域保幅高斯束偏移公式.同原有方法相比,本文方法不但可以直接在起伏的地表面进行局部平面波的分解,具有更高的成像精度,而且可以得到反映地下随角度变化反射系数的成像结果.数值模型的试算验证了上述结论.  相似文献   

19.
The goal of seismic reflection surveys is the derivation of petrophysical subsurface parameters from surface measurements. Today's well established technique in data acquisition, as well as processing terms, is based on the acoustic approximation to the real world's wave propagation. In recent years a lot of work has been done to extend the technique to the elastic approximation. There was especially an important trend towards elastic inversion techniques operating on plane-wave seismograms, called simultaneous P-SV inversion (or short P-SV inversion) within this paper. Being still under investigation, some important aspects of P-SV inversion concerning data acquisition as well as pre-processing, should be pointed out. To fit the assumptions of P-SV inversion schemes, at least a two-dimensional picture of the reflected wavefield with vertical and in-line horizontal receivers has to be recorded. Moreover, the theoretical work done suggests that in addition to a survey with a compressional wave source, a second survey should be done using sources radiating vertically polarized shear waves, is needed. Finally, proper slant stacking must be performed to get plane-wave seismograms. The P/S separated plane-wave seismograms are then well prepared for feeding into the inversion algorithms. P/S separated planewave seismograms are then well prepared for feeding into the inversion algorithm.s In this paper, a tutorial overview of the data acquisition and pre-processing in accordance with the P-SV inversion philosophy is given and illustrated using synthetic seismograms. A judgement on the feasibility of the P-SV inversion philosophy must be left to ongoing research.  相似文献   

20.
Parsimonious post‐stack migration is extended to three dimensions. By tracing single rays back along each incident wave direction (as determined by a local slant stack at the receivers), the ray tracing can be embedded in the migration. This approach significantly reduces the computer time and disk space needed because it is not necessary to build and save image time maps; 3D migration can be performed on a workstation or personal computer rather than using a supercomputer or cluster. The location of a reflector in the output image is defined by tracing a zero‐offset ray to the one‐way traveltime (the image condition); the orientation of the reflector is defined as a surface perpendicular to the raypath. The migration impulse response operator is confined to the first Fresnel zone around the estimated reflection point, which is much smaller than the large isochronic surface in traditional Kirchhoff depth migration. Additional efficiency is obtained by applying an amplitude threshold to reduce the amount of data to be migrated. Tests on synthetic data show that the proposed implementation of parsimonious 3D post‐stack Kirchhoff depth migration is at least two orders of magnitude faster than traditional Kirchhoff migration, at the expense of slightly degraded migration image coherence. The proposed migration is expected to be a useful complement to conventional time migrations for fast initial imaging of subsurface structures and for real‐time imaging of near‐offset sections during data acquisition for quality control.  相似文献   

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