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1.
In this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost. 相似文献
2.
Wave equation–based migration velocity analysis techniques aim to construct a kinematically accurate velocity model for imaging or as an initial model for full waveform inversion applications. The most popular wave equation–based migration velocity analysis method is differential semblance optimization, where the velocity model is iteratively updated by minimizing the unfocused energy in an extended image volume. However, differential semblance optimization suffers from artefacts, courtesy of the adjoint operator used in imaging, leading to poor convergence. Recent findings show that true amplitude imaging plays a significant role in enhancing the differential semblance optimization's gradient and reducing the artefacts. Here, we focus on a pseudo-inverse operator to the horizontally extended Born as a true amplitude imaging operator. For laterally inhomogeneous models, the operator required a derivative with respect to a vertical shift. Extending the image vertically to evaluate such a derivative is costly and impractical. The inverse operator can be simplified in laterally homogeneous models. We derive an extension of the approach to apply the full inverse formula and evaluate the derivative efficiently. We simplified the implementation by applying the derivative to the imaging condition and utilize the relationship between the source and receiver wavefields and the vertical shift. Specifically, we verify the effectiveness of the approach using the Marmousi model and show that the term required for the lateral inhomogeneity treatment has a relatively small impact on the results for many cases. We then apply the operator in differential semblance optimization and invert for an accurate macro-velocity model, which can serve as an initial velocity model for full waveform inversion. 相似文献
3.
Paul Sava 《Geophysical Prospecting》2015,63(5):1050-1069
Imaging the change in physical parameters in the subsurface requires an estimate of the long wavelength components of the same parameters in order to reconstruct the kinematics of the waves propagating in the subsurface. One can reconstruct the model by matching the recorded data with modeled waveforms extrapolated in a trial model of the medium. Alternatively, assuming a trial model, one can obtain a set of images of the reflectors from a number of seismic experiments and match the locations of the imaged interfaces. Apparent displacements between migrated images contain information about the velocity model and can be used for velocity analysis. A number of methods are available to characterize the displacement between images; in this paper, we compare shot‐domain differential semblance (image difference), penalized local correlations, and image‐warping. We show that the image‐warping vector field is a more reliable tool for estimating displacements between migrated images and leads to a more robust velocity analysis procedure. By using image‐warping, we can redefine the differential semblance optimization problem with an objective function that is more robust against cycle‐skipping than the direct image difference. We propose an approach that has straightforward implementation and reduced computational cost compared with the conventional adjoint‐state method calculations. We also discuss the weakness of migration velocity analysis in the migrated‐shot domain in the case of highly refractive media, when the Born modelling operator is far from being unitary and thus its adjoint (migration) operator poorly approximates the inverse. 相似文献
4.
Moshe Reshef 《Geophysical Prospecting》2014,62(6):1453-1467
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
5.
Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre‐stack wavefield (the double‐square‐root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre‐stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach. 相似文献
6.
A technique for automatic cross-well tomography based on semblance and differential semblance optimization is presented. Given a background velocity, the recorded seismic data traces are back-propagated towards the source, i.e. shifted towards time zero using the modelled traveltime between the source and the receiver and corrected for the geometrical spreading. Therefore each back-propagated trace should be a pulse, close to time zero. The mismatches between the back-propagated traces indicate an error in the velocity model. This error can be measured by stacking the back-propagated traces (semblance optimization) or by computing the norm of the difference between adjacent traces (differential semblance optimization).
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross-well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross-well tomography is based on the high-frequency approximation to wave propagation. The wavefronts are constructed using a ray-tracing algorithm. The gradient of the cost function is computed by the adjoint-state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross-well data. The method is applied to a synthetic data set to demonstrate its efficacy. 相似文献
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross-well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross-well tomography is based on the high-frequency approximation to wave propagation. The wavefronts are constructed using a ray-tracing algorithm. The gradient of the cost function is computed by the adjoint-state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross-well data. The method is applied to a synthetic data set to demonstrate its efficacy. 相似文献
7.
Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis 
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下载免费PDF全文 Mark Noble 《Geophysical Prospecting》2015,63(2):391-404
Migration velocity analysis aims at determining the background velocity model. Classical artefacts, such as migration smiles, are observed on subsurface offset common image gathers, due to spatial and frequency data limitations. We analyse their impact on the differential semblance functional and on its gradient with respect to the model. In particular, the differential semblance functional is not necessarily minimum at the expected value. Tapers are classically applied on common image gathers to partly reduce these artefacts. Here, we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data‐domain. For an automatic and more robust formulation, we introduce a weight in the original data‐domain objective function. The weight is determined such that the Hessian resembles a Dirac function. In that way, we extend quantitative migration to the subsurface‐offset domain. This is an automatic way to compensate for illumination. We analyse the modified scheme on a very simple 2D case and on a more complex velocity model to show how migration velocity analysis becomes more robust. 相似文献
8.
苏北大陆科学钻探靶区深反射地震的叠前深度偏移 总被引：4，自引：2，他引：2
由于深反射地震数据具有信噪比低和记录长度长等特点,叠前深度偏移方法的应用有许多困难．为此,我们研究了一种适合于深反射地震的叠前深度偏移方法;包括：用逆风有限差分方法计算程函方程;在常规速度扫描的基础上,用协方差控制提高速度分析精度;用联合反演算法计算层速度,再插值后得到初始速度模型;用Ｋｉｒｃｈｈｏｆｆ法作为偏移速度分析工具,求得最终的速度模型;最终的速度模型作为有限差分深度偏移的输入,求得最终的偏移结果．用该方法对“中国大陆科学深钻工程”东海二维深反射地震数据ＤＨ－４线进行了叠前深度偏移,取得了良好的效果。 相似文献
9.
断层识别是断块型油气田勘探开发的重要研究内容,尤其是在复杂断块油气田的勘探开发中,准确合理的断层识别是落实油气田构造和确定注采井网的关键因素.方差体、相干体、曲率属性等常规方法在断层识别中发挥着重要作用,但在复杂断裂发育区地震资料品质较差,常规方法分辨率较低从而无法准确识别断层组合关系.基于相似系数改进的似然属性在已知断层倾向和倾角时可以精确表征断层,但由于断层的倾向和倾角是未知的,因此可以采用断层倾向和倾角扫描的方法计算最大似然属性来表征断层.本文对比分析了相似系数和最大似然属性的原理;并将最大似然属性应用于模型正演数据和实际地震数据进行断层识别分析,结果表明,最大似然属性在剖面上更符合断层展布特征,在平面上断层组合关系更加清晰,在断层识别上具有较好的应用效果. 相似文献
10.
Multicomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single component recordings are not independent, the processing should be performed jointly for all the components. A way to achieve this goal is to exploit quaternions, hyper‐complex numbers that due to their very nature are apt to represent multidimensional data. In fact, quaternion algebra allows us to extend coherence functionals used for scalar observations to multicomponent data. Therefore by means of quaternions we implement semblance and other methods based on matched filtering and on the data covariance properties. As an application we show the results from a quaternion velocity analysis carried out combining information from the geophones and from the hydrophones of an ocean bottom cable (OBC) survey, and thus recognizing the true vectorial nature of the incoming wavefield. This also allows one to relax, at least partially, vector fidelity constraints. We demonstrate that quaternion velocity analysis yields an improved resolution with respect to the single component velocity analysis for any coherence functional chosen and that it simultaneously evidences velocity trends pertaining to different wave modes. This facilitates the interpreter in the estimation of interval Vp/Vs by means of event correlation, and in making use of a priori information from VSP and well logs. It also speeds up the velocity picking that can be performed in a single pass on a multicomponent velocity panel, rather than once for each single component velocity panel. 相似文献
11.
Seismograms predicted from acoustic or elastic earth models depend very non-linearly on the long wavelength components of velocity. This sensitive dependence demands the use of special variational principles in waveform-based inversion algorithms. The differential semblance variational principle is well-suited to velocity inversion by gradient methods, since its objective function is smooth and convex over a large range of velocity models. An extension of the adjoint state technique yields an accurate estimate of the differential semblance gradient. Non-linear conjugate gradient iteration is quite successful in locating the global differential semblance minimum, which is near the ordinary least-squares global minimum when coherent data noise is small. Several examples, based on the 2D primaries-only acoustic model, illustrate features of the method and its performance. 相似文献
12.
是否能够正确地建立深度域三维速度模型是三维叠前深度偏移成败的关键 .本文根据Deregowski循环 ,利用叠前深度域地震成像对速度模型变化的敏感性 ,采用偏移迭代逐次逼近最佳成像速度 ,研究开发了一套快捷有效的三维叠前深度偏移深度域速度模型建立技术 .借鉴时间域CDP(共深度点 )道集上常规叠加速度分析的策略 ,在深度域CRP(共反射点 )道集上 ,提出剩余慢度平方谱的概念并建立相应的实现技术 .导出深度域中均方根速度与层速度之间的关系 ;按照串级偏移原理确定偏移循环过程中初始速度、剩余速度及修改后速度之间的关系 ;采用蒙特卡洛非线性优化算法实现从剩余慢度平方谱中自动拾取层速度 ,讨论了其地质速度约束条件和蒙特卡洛非线性优化的收敛准则 ,使得所拾取的层速度模型具有合理的地质意义并获得最佳偏移成像效果 .SEG EAGE理论模型数值试算验证了方法的有效性 ,在海拉尔盆地霍多莫尔工区 ,5 8km2 三维资料的速度模型建立并获得满意的三维叠前深度偏移成像 . 相似文献
13.
Seismic velocity analysis in the scattering-angle/azimuth domain 总被引：2，自引：0，他引：2
Migration velocity analysis is carried out by analysing the residual moveout and amplitude variations in common image point gathers (CIGs) parametrized by scattering angle and azimuth. The misfit criterion in the analysis is of the differential-semblance type. By using angles to parametrize the imaging we are able to handle and exploit data with multiple arrivals, although artefacts may occur in the CIGs and need to be suppressed. The CIGs are generated by angle migration, an approach based on the generalized Radon transform (GRT) inversion, and they provide multiple images of reflectors in the subsurface for a range of scattering angles and azimuths. Within the differential semblance applied to these CIGs, we compensate for amplitude versus angle (AVA) effects. Thus, using a correct background velocity model, the CIGs should have no residual moveout nor amplitude variation with angles, and the differential semblance should vanish. If the velocity model is incorrect, however, the events in the CIGs will appear at different depths for different angles and the amplitude along the events will be non-uniform. A standard, gradient-based optimization scheme is employed to develop a velocity updating procedure. The model update is formed by backprojecting the differential semblance misfits through ray perturbation kernels, within a GRT inverse. The GRT inverse acts on the data, subject to a shift in accordance with ray perturbation theory. The performance of our algorithm is demonstrated with two synthetic data examples using isotropic elastic models. The first one allows velocity variation with depth only. In the second one, we reconstruct a low-velocity lens in the model that gives rise to multipathing. The velocity model parametrization is based upon the eigentensor decomposition of the stiffness tensor and makes use of B-splines. 相似文献
14.
Anders U. Waldeland Tiago A. Coimbra Jorge H. Faccipieri Anne H. Schistad Solberg Leiv-J. Gelius 《Geophysical Prospecting》2019,67(5):1163-1183
We present a method for fast estimation of finite offset common reflection surface parameters. Firstly, the derivatives with respect to offset are derived from the velocity guide. Secondly, we apply structure tensors to extract the derivatives with respect to midpoint from stacked common offset sections. Finally, the mixed derivative is estimated using a one-parametric semblance search. The proposed method is compared to the global five-parametric semblance search and the pragmatic sequential two-parametric semblance search on one synthetic and one real data set. The experiments show that the proposed method is more robust against noise than the pragmatic search and have comparable robustness with the global search. The proposed method smoothes parameter estimates in a local window, and the window size is set to give the best trade-off between detail and robustness. Since the proposed method is dependent on a velocity guide, the quality of the other parameter estimates may be influenced by any inaccuracies in the guide. The main advantage of the proposed method is the computational efficiency. When compared with a gridded implementation of the semblance search, the proposed method is 10 and 400 times faster than the pragmatic and global search. Alternative search strategies significantly reduce the computational cost of the global search. However, since more than 99% of the computational cost of the proposed method comes from the semblance search to estimate the mixed derivative, it is expected that such techniques also reduce the computational cost for the proposed method. 相似文献
15.
According to the actual observation conditions of the Yangtze River valley from Anqing city to Maanshan city, we designed the 3D acquisition geometry, and applied the multi-scale checkerboard semblance analysis to assess the preliminary resolution of the designed observation. The checkerboard semblance tests use the refraction and reflection travel-time simultaneous inversion algorithm to quantitatively provide both resolution assessment of velocity structure and Moho topography. The multi-scale checkerboard semblance recovery results show that while the checkerboard semblance threshold value is 0.5, the preliminary resolution of the designed acquisition geometry is better than 10 km in the upper crust (the depth is less than 10 km), around 15 km in the mid-crust (the depth is 10?25 km), and better than 20 km in the lower crust (the depth is 25?33 km). The preliminary tomographic resolution for the Moho topography is about 20 km in the ray-path coverage area beneath the acquisition geometry. While the checkerboard semblance threshold value is 0.75, the preliminary resolution is 20 km in the upper crust, around 20?25 km in the mid-crust and 25 km in the lower crust. And the preliminary tomographic resolution for the Moho topography is better than 30 km in the ray-path coverage area beneath the acquisition geometry. These non-linear checkerboard tests reveal that the designed acquisition geometry is suitable to image the crustal velocity structure of the Yangtze River valley in the Anhui province. 相似文献
16.
Migration velocity analysis and waveform inversion 总被引：3，自引：0，他引：3
William W. Symes 《Geophysical Prospecting》2008,56(6):765-790
Least‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting. 相似文献
17.
叠加速度分析技术是常规地震资料处理中的重要环节,也是经典的时间域速度建模方法.叠加速度分析技术主要包括速度谱计算和拾取两个步骤.至今为止,多数研究工作通过提高速度谱的分辨率以及抗噪声能力,获得高质量的速度谱从而有利于拾取.本文的目标是将叠加速度分析技术转为一个全自动化的处理流程.从参数估计的角度出发,将叠加速度估计转化为稀疏反演框架下的模型参数估计问题,并通过稀疏反演算法自动反演叠加速度,进而提高叠加速度建模的效率.为实现这一目标,首先给出了正问题的定义,即层状介质中CMP道集的预测模型,利用叠加速度、垂向双程走时(t_0)以及反射子波以及CMP道集时距关系(如双曲时距关系)可以预测CMP道集.接着,速度分析反问题可以描述为已知观测的CMP道集,估计模型参数(叠加速度及t_0时间等).利用模型参数的稀疏性作为约束条件并用L_0范数作为模型稀疏性的度量准则,叠加速度分析可以转化为L_0范数约束下的稀疏反演问题.本文提出了一种基于预测校正思想的匹配追踪算法求解上述反问题,实现了自动叠加速度建模并为后续的高精度速度反演方法提供较好的初始模型.理论和实际资料的测试结果证明了本文方法的有效性. 相似文献
18.
Tadashi Kito Takuo ShibutaniKazuro Hirahara 《Physics of the Earth and Planetary Interiors》2003,138(1):55-69
Precursor and coda portions of short-period PcP waves (reflected P wave from the core-mantle boundary, CMB) recorded at J-array stations in Japan were analyzed in order to extract weak scattered signals originating from small-scale heterogeneities in the lowermost mantle beneath northeastern China. Two nuclear explosions at Lop Nor in China detonated on 21 May 1992 (Mb=6.5) and 8 June 1996 (Mb=5.9) were used for our analysis.Three-dimensional grids above the CMB were defined in the area around the PcP bounce points beneath northeastern China to calculate theoretical travel times of scattered waves which propagate from the sources to each grid point and arrive at each station based on the IASP91 model. Subsequently the waveforms were aligned with respect to the theoretical travel times and the semblance (an amplitude dependent measure of coherency) was calculated for each grid point. In order to obtain a more accurate travel time correction, we applied a cross correlation method to PcP waveforms in order to reduce picking error of the PcP onset time. A cross convolution method was also applied so that the two events could be analyzed simultaneously without using unstable deconvolutions.We could identify regions with relative high semblance values in semblance contour maps at about 200 and 375 km above the CMB. Stacking waveforms with respect to the theoretical travel times for the grid points with relative high semblance values indicate coherent wavelets originating at those grid points, that is, they correspond to scattered waves originating from small-scale heterogeneities in the lowermost mantle. Our results indicate the existence of small-scale scattering objects in the D″ layer, especially in the depth range of 200 and 375 km above the CMB beneath northeastern China. Considering recent tomographic images of high velocity anomalies in this area, these scattering objects could be fragments of old oceanic crusts which have subducted through the lower mantle and have accumulated in the D″ layer beneath northeastern China. 相似文献
19.
M. Corciulo A. Zollo M. Vassallo P. Dell'Aversana S. Morandi 《Geophysical Prospecting》2008,56(4):541-553
In order to retrieve a 2D background velocity model and to retrieve the geometry and depth of shallow crustal reflectors in the Southern Apennines thrust belt a separate inversion of first arrival traveltimes and reflected waveforms was performed. Data were collected during an active seismic experiment in 1999 by Enterprise Oil Italiana and Eni-Agip using a global offset acquisition geometry. A total of 284 on-land shots were recorded by 201 receivers deployed on an 18 km line oriented SW–NE in the Val D'Agri region (Southern Apennines, Italy).
The two-step procedure allows for the retrieval of a reliable velocity model by using a non-linear tomographic inversion and reflected waveform semblance data inversion. The tomographic model shows that the P wave velocity field varies vertically from approximately 3 km/s to 6 km/s within 4 km from the Earth's surface. Moreover, at a distance of approximately 11 km along the profile, there is an abrupt increase in the velocity field. In this zone indeed, an ascent from 2 km depth to 0 km above sea level of the 5.2 km/s iso-velocity contour can be noted. The retrieved velocity can be associated with Plio-Pleistocene clastic deposits outcropping in the basin zone and with Mesozoic limestone deposits. The inversion of waveform semblance data shows that a P-to-P reflector is retrieved at a depth of approximately 2 km. This interface is deeper in the north-eastern part of the profile, where it reaches 3 km depth and can be associated with a limestone horizon. 相似文献
The two-step procedure allows for the retrieval of a reliable velocity model by using a non-linear tomographic inversion and reflected waveform semblance data inversion. The tomographic model shows that the P wave velocity field varies vertically from approximately 3 km/s to 6 km/s within 4 km from the Earth's surface. Moreover, at a distance of approximately 11 km along the profile, there is an abrupt increase in the velocity field. In this zone indeed, an ascent from 2 km depth to 0 km above sea level of the 5.2 km/s iso-velocity contour can be noted. The retrieved velocity can be associated with Plio-Pleistocene clastic deposits outcropping in the basin zone and with Mesozoic limestone deposits. The inversion of waveform semblance data shows that a P-to-P reflector is retrieved at a depth of approximately 2 km. This interface is deeper in the north-eastern part of the profile, where it reaches 3 km depth and can be associated with a limestone horizon. 相似文献
20.
Reiter , E.C., Toksoz , M.N. and Purdy , G.M. 1992. A semblance-guided median filter. Geophysical Prospecting 41 , 15–41. A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user-specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well-known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance. This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal-to-noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal. We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large-offset ocean bottom hydrophone data to enhance weak refracted and post-critically reflected energy. 相似文献