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1.
We present a new method for producing a ‘brute’ velocity image rapidly and automatically from traveltimes picked from densely sampled refraction data. The procedure involves imaging by data transformation from the time–offset domain into the tau–p (intercept–slope) domain, and does not include conventional modelling steps. Differences in apparent velocity and tau along reciprocal paths in the up- and downdip directions allow the estimation of the true velocity and geometrical position of the ray turning points. The tau–velocity–turningpoint (τ–ν–x) map distributes phases automatically on the basis of geometry and velocity to give a two-dimensional representation of subsurface structure. This map may be converted simply to depth and two-way-time images. Such images have potential for direct geological interpretation, for use as a starting model for seismic inversion, for superimposition on to conventional reflection images, or for input into prestack depth migration and other processing routines. 相似文献
2.
2D multiscale non-linear velocity inversion 总被引：2，自引：0，他引：2
An efficient and robust non-linear inversion method for velocity optimization combining a global random search followed by a simplex technique is presented. The background velocity field is estimated at different spatial scales by analysing image gathers after iterative prestack depth migrations. First, the global random search is used to determine the main features/trends of the velocity model (large-scale component). Then, the simplex technique improves the resolution of the velocity field by estimating smaller-scale features. A measure of the quality of the velocity model (objective function) is based on flattening offset events in depth-migrated image gathers. To help constrain the solution, the algorithm can incorporate a priori information about the model and a smoothness condition. This 2D velocity estimation offers the benefit of being semi-automatic (requiring minimal human intervention) as well as providing a global and objective solution (which is a useful approach to an interpretation-derived velocity-estimation technique). The method is applied to a real data set where AVO analysis is carried out after prestack depth migration, as structural effects are non-negligible. It is demonstrated that the method can successfully estimate a laterally inhomogeneous velocity model at a computational cost modest compared with an interpretation-based iterative prestack depth velocity-analysis technique. 相似文献
3.
Reflection and refraction data are normally processed with tools designed to deal specifically with either near- or far-offset data. Furthermore, the refraction data normally require the picking of traveltimes prior to analysis. Here, an automatic processing algorithm has been developed to analyse wide-angle multichannel streamer data without resorting to manual picking or traveltime tomography. Time–offset gathers are transformed to the tau–p domain and the resulting wavefield is downward continued to the depth–p domain from which a velocity model and stacked section are obtained. The algorithm inputs common-depth-point (CDP) gathers and produces a depth-converted stacked section that includes velocity information. The inclusion of long-offset multichannel streamer data within the tau–p transformation enhances the signal from high-velocity refracted basalt arrivals. Downward continuation of the tau–p transformed wavefield to the depth–p domain allows the reflection and refraction components of the wavefield to be treated simultaneously. The high-slowness depth–p wavefield provides the velocity model and the low-slowness depth–p wavefield may be stacked to give structural information. The method is applied to data from the Faeroe Basin from which sub-basalt velocity images are obtained that correlate with an independently derived P-wave model from the line. 相似文献
4.
The effect of wave-equation migration on amplitudes is determined. This effect is derived for zero-offset traces and for second-order approximations of the traveltimes. Three steps are followed: firstly, the amplitudes of zero-offset traces are established; secondly minus half the traveltimes are used as input for downward continuation in migration (forward in space and time); thirdly, the amplitudes of the migrated events are determined by downward continuation (at zero-traveltimes). Layered models (piles of homogeneous layers) with smooth interfaces are used. The determinants of the 2 × 2 matrices B 0 obtained for these models are responsible for the main effect on migration. The migration result primarily depends on the overburden as the inverse of det ( B 0). Drastic effects can occur over small distances. For weakly reflecting media, it is confirmed that wave-equation migration gives “correct” results (but the input data must be multiplied by V0T0), i.e. amplitudes proportional to the reflection coefficient. For any velocity changes, the inverse of det ( B 0) will, in general, give inaccurate migration amplitudes and inaccurate lithological interpretations. In a simple step, true amplitude migration, or exact migration, is derived from our results. It is assumed that no focus phenomena are present. The effect of buried foci is discussed briefly. 相似文献
5.
6.
A three-dimensional (3-D) kinematic migration algorithm for media in which migration velocity varies linearly with depth is developed, implemented and tested. The algorithm is based on the concept that a single reflection or diffraction in a (zero- or finite-offset) trace may have originated at any point on a constant traveltime surface within the Earth defined by the observed two-way traveltime. The envelope of all such constant time surfaces, for all observed reflections and diffractions produced by one reflector, is the desired migrated 3-D image. The optimal envelope position in depth is determined, beneath each point on a regular grid, by a statistical imaging condition; an incremental function of depth containing the number of constant time surfaces passing through that depth increment is cross-correlated with a Gaussian function whose width is chosen to correspond to the vertical scale of the features of interest. The numerical procedures are based on the observation that, in a medium in which velocity varies linearly with depth, ray segments are circular so traveltimes can be computed analytically. Also, traveltimes are independent of azimuth so the 3-D problem can be collapsed into an equivalent 2-D problem. The algorithm is illustrated and tested by application to synthetic data and to scale-model data from the Seismic Acoustics Laboratory at the University of Houston. 相似文献
7.
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
8.
研究与实践表明,对于长偏移距、宽方位地震数据,忽略各向异性会明显降低成像质量,影响储层预测与描述的精度.针对典型的横向各向同性(TI)介质,本文面向深度域构造成像与偏移速度分析的需要,研究基于射线理论的局部角度域叠前深度偏移成像方法.它除了像传统Kirchhoff叠前深度偏移那样输出成像剖面和炮检距域的共成像点道集,还遵循地震波在成像点处的局部方向特征、基于扩展的脉冲响应叠加原理获得入射角度域和照明角度域的成像结果.为了方便快捷地实现TI介质射线走时与局部角度信息的计算,文中讨论和对比了两种改进的射线追踪方法:一种采用从经典各向异性介质射线方程演变而来的由相速度表征的简便形式;另一种采用由对称轴垂直的TI(即VTI)介质声学近似qP波波动方程推导出来的射线方程.文中通过坐标旋转将其扩展到了对称轴倾斜的TI(即TTI)介质.国际上通用的理论模型合成数据偏移试验表明,本文方法既适用于复杂构造成像,又可为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
9.
Although it is widely recognized that anisotropy can have a significant influence on the focusing and positioning of migrated reflection events, conventional depth imaging methods still operate with isotropic velocity fields. Here, we present an application of a 2D migration velocity analysis (MVA) algorithm, designed for factorized v(x, z) VTI (transversely isotropic with a vertical symmetry axis) media, to an offshore data set from West Africa. By approximating the subsurface with factorized VTI blocks, it is possible to decouple the spatial variations in the vertical velocity from the anisotropic parameters with minimal a priori information. Since our method accounts for lateral velocity variation, it produces more accurate estimates of the anisotropic parameters than those previously obtained with time‐domain techniques. The values of the anellipticity parameter η found for the massive shales exceed 0.2, which confirms that ignoring anisotropy in the study area can lead to substantial imaging distortions, such as mis‐stacking and mispositioning of dipping events. While some of these distortions can be removed by using anisotropic time processing, further marked improvement in image quality is achieved by prestack depth migration with the estimated factorized VTI model. In particular, many fault planes, including antithetic faults in the shallow part of the section, are better focused by the anisotropic depth‐migration algorithm and appear more continuous. Anisotropic depth migration facilitates structural interpretation by eliminating false dips at the bottom of the section and improving the images of a number of gently dipping features. One of the main difficulties in anisotropic MVA is the need to use a priori information for constraining the vertical velocity. In this case study, we successfully reconstructed the time–depth curve from reflection data by assuming that the vertical velocity is a continuous function of depth and estimating the vertical and lateral velocity gradients in each factorized block. If the subsurface contains strong boundaries with jumps in velocity, knowledge of the vertical velocity at a single point in a layer is sufficient for our algorithm to determine all relevant layer parameters. 相似文献
10.
First-arrival traveltimes from a multi-offset vertical seismic profile (VSP) were used to estimate velocity anisotropy in the presence of a vertical velocity gradient. A numerical model consisting of two layers with vertical velocity gradients of 3.1 and 1.2 s−1, respectively, and global anisotropy parameters of =0.12±0.02 and δ=0.30±0.06 yielded first-arrival traveltimes that matched the observed traveltimes well. Shallow receivers were found to be crucial for constraining the vertical velocity field and for determining the parameters of anisotropy at depth. 相似文献
11.
CDP mapping in tilted transversely isotropic (TTI) media. Part II: Velocity analysis by combining CDP mapping with a genetic algorithm 总被引：1，自引：0，他引：1
This paper presents a method for velocity analysis in tilted transversely isotropic (TTI) media by combining CDP mapping with a genetic algorithm. CDP mapping is a velocity analysis method for determining anisotropic velocity but has difficulties due to the following factors: (i) it involves a non-linear and multimodal objective function; (ii) it is prohibitively expensive in the evaluation of candidate solutions, which often involves the calculation of images in the depth domain; (iii) there is often a very large parameter space. Recognizing the global and multimodal nature of the problem, a genetic algorithm is employed to search for the optimal velocity model. The efficiency of the method contributes to two critical processes: rapid model evaluation, achieved by generating CDP mapping only in the neighbourhood of specific reflectors, and fast computation, based on Fermat's principle, of the CDP points and traveltimes in TTI media. The method produces subsurface structure images in the depth domain, and can also solve for Thomsen's anisotropic parameters (ɛ and δ), the vertical velocity and the dip of the symmetry axis in the model space, simultaneously. 相似文献
12.
We propose a two-dimensional, non-linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source-to-receiver acquisition lay-out. This method uses a scheme of non-linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite-difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best-fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities. 相似文献
13.
Alvin K. Benson 《Geophysical Prospecting》1995,43(6):729-741
A migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase-shift migration by using a variable-length spatial transform. This process significantly reduces the number of lateral wave-numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0. 相似文献
14.
M. J. KUHN 《Geophysical Prospecting》1979,27(1):62-77
The first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interface z=z1, abruptly terminated at x= o. The amplitude and phase responses are computed in the plane z=z0= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source-receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔR between two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx > λ/4. The muting curves are symmetrical about the line x= 0 and their angular opening depends on spatial separation Δx, depth z, and wavelength λ (which may vary with depth). The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three-dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data. The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weights (including muting). 相似文献
15.
The authors present a method for estimation of interval velocities using the downward continuation of the wavefield to perform
layer-stripping migration velocity analysis. The generalized, phase-shift migration MG(F-K) in wavenumber-frequency domain
was used for fulltime downward extrapolation of the wavefield. Such downward depth extrapolation accounts for strong changes
of velocity in lateral and vertical directions and helps in correct positioning of the wavefield image in complex structures.
Determination of velocity is the recursive process which means that the wavefield on depth level z
n−1 (n = 0, 1, ...) is an input data-set for determination of velocity on level z
n
. The velocity ν [x, z
n
− z
n−1] can be thus treated as interval velocity in Δz
n
= z
n
− z
n−1 step. This method was tested on synthetic Marmousi data-set and showed satisfactory results for complex, inhomogeneous media. 相似文献
16.
Amplitude versus offset information is a key feature to seismic reservoir characterization. Therefore amplitude preserving migration was developed to obtain this information from seismic reflection data. For complex 3-D media, however, this process is computationally expensive. In this paper we present an efficient traveltime based strategy for amplitude preserving migration of the Kirchhoff type. Its foundations are the generation of traveltime tables using a wavefront-oriented ray-tracing technique, and a generalized moveout relation for 3-D heterogeneous media. All required quantities for the amplitude preserving migration are computed from coarsely gridded traveltime tables. The migration includes the interpolation from the coarsely gridded input traveltimes onto the fine migration grid, the computation of amplitude preserving weight functions, and, optionally, the evaluation of an optimized migration aperture. Since ray tracing is employed for the traveltime computation the input velocity model needs to be smooth, i.e. velocity variations of spatial dimensions below the wavelength of the considered reflection signals are removed. Numerical examples on simple generic models validate the technique and an application to the Marmousi model demonstrates its potential to complex media. The major advantage of the traveltime based strategy consists of its computational efficiency by maintaining sufficient accuracy. Considerable savings in storage space (105 and more for 3-D data with respect to no interpolation at all) can be achieved. The computational time for the stack can be substantially reduced (up to 90% in 3-D) with the optimized migration aperture since only those traces are stacked which really contribute to the image point under consideration. 相似文献
17.
A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity VP0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces. 相似文献
18.
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
19.
Tiago A. Coimbra Jorge H. Faccipieri Dany S. Rueda Martin Tygel 《Studia Geophysica et Geodaetica》2016,60(3):500-530
Since the early days of seismic processing, time migration has proven to be a valuable tool for a number of imaging purposes. Main motivations for its widespread use include robustness with respect to velocity errors, as well as fast turnaround and low computation costs. In areas of complex geology, in which it has well-known limitations, time migration can still be of value by providing first images and also attributes, which can be of much help in further, more comprehensive depth migration. Time migration is a very close process to common-midpoint (CMP) stacking and, more recently, to zero-offset commonreflection- surface (CRS) stacking. In fact, Kirchhoff time migration operators can be readily formulated in terms of CRS parameters. In the nineties, several studies have shown advantages in the use of common-reflection-point (CRP) traveltimes to replace conventional CMP traveltimes for a number of stacking and migration purposes. In this paper, we follow that trend and introduce a Kirchhoff-type prestack time migration and velocity analysis algorithm, referred to as CRP time migration. The algorithm is based on a CRP operator together with optimal apertures, both computed with the help of CRS parameters. A field-data example indicates the potential of the proposed technique. 相似文献
20.
The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots. The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section. Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming. The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data. 相似文献