Velocity model updating using image gathers1

For successful prestack depth migration an accurate velocity model is needed. One method for model updating is based on image gather analysis. In an image gather all reflectors line up horizontally if the correct velocities are used for the depth migration. This is also true for dipping reflectors, as all traces of an image gather belong to the same surface coordinate. The images of the reflector in an image gather curve upwards if the velocity used for the migration is too low, or downwards if the velocity is too high. This deviation can be used for model updating. Curves which depend on depth, offset and a parameter which relates the estimated to the true model are fitted to the image. By calculating the coherence along the deviation curves, this parameter can be estimated and hence an update can be calculated. Formulae are derived for the deviation curves and the update of the velocity depth model for a multilayered model for both shot and common-offset migrated data, with and without gradients. The method is tested on synthetic data with satisfactory results.     

不同参数对地震干涉实现VSP向SWP波场重构的影响

地震干涉是近几年勘探地球物理领域研究的一个热点方向,它是波场重构的有力工具.然而,地震干涉往往引入虚假同相轴,影响波场重构的质量.为进一步分析虚假同相轴产生的原因并改善波场重构的质量,本文基于稳相分析,详细探讨子波主频、激发炮数、检波器埋深、检波器间距和地层倾角五个因素对波场重构的影响.模型结果表明,震检排列方式和地层倾角等因素通过改变有限震检范围内稳相点的位置来影响波场重构的质量.将垂直地震剖面VSP中的下行直达波与下行反射波进行地震干涉处理,可有效重构来自高陡反射面的下行反射波,将传统的VSP转化为单井地震剖面SWP.直接利用重构SWP波场进行成像,不仅扩大传统VSP的成像范围,而且避免常规勘探面临的静校正和近地表速度建模问题,为高陡构造成像提供一种新方法.     

Dreamlet source‐receiver survey sinking prestack depth migration

Survey sinking migration downward continues the entire surface observed multi‐shot data to the subsurface step by step recursively. Reflected energy from reflectors at current depth appear at zero time and zero offset in the extrapolated wavefield. The data (seismic records) of t > 0 at this depth are equivalent to the data acquired by a survey system deployed at this depth. This is the reason to name the process ‘survey sinking’. The records of negative time need not to be further propagated since they carry no information to image structures beneath the new survey system. In this paper, we combine survey sinking with dreamlet migration. The dreamlet migration method decomposes the seismic wavefield and one‐way wave propagator by complete time‐space localized bases. The localization on time gives flexibility on time‐varying operations during depth extrapolation. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sunk survey system and gets rid of the data already used to image structures above it. The deeper the depth is, the shorter is the valid time records of the remaining data and less computation is needed for one depth step continuation. For data decomposition, in addition to time axis, dreamlet survey sinking also decomposes the data for source and receiver gathers, which is a fully localized decomposition of prestack seismic data. A three‐scatter model is first used to demonstrate the computational feature and principle of this method. Tests on the two‐dimensional SEG/EAGE salt model show that with reduced data sets the proposed method can still obtain good imaging quality on complex geology structures and a strong velocity contrast environment.     

基于波场传播方向的波动方程偏移有效去噪方法(英文)

本文研究分析了双程波波动方程偏移成像中广泛存在的三种主要噪声,特别是针对过去研究中没能很好解决的存在于高速盐丘悬垂边界附近的射线状噪声,提出了基于优化成像条件的有效去噪方法。射线状噪声主要来自于震源一侧波场的下行透射波分量和接收阵列一侧波场的上行散射波互相关成像。这一部分能量具有较强的互相关性,但并不携带真实的反射面信息。它广泛存在叠前偏移成像中,与信号在强度上同量级。多数情况下偏移成像中的相关噪声由方向性传播的波场能量产生。利用波场梯度得到的波场传播角度,可以分离出噪声对应的波场能量,并在成像条件中减去。采用这一方法可以有效地去除多种噪声,包括直达波噪声、散射波噪声和射线状噪声。该去噪方法不依赖波场外推算子,在需要时可以方便地运用到几乎所有的波动方程偏移中去。并且该去噪方法针对噪声的物理根源,对信号的损害很小。对去噪后的偏移成像结果额外地进行波数域滤波处理,可以进一步提高叠加图像的质量。这一去噪方法在超广角单程波偏移成像中取得良好效果,我们同时期待其在其他双程波波动方程偏移特别是逆时偏移(RTM)中的成功运用。     

角度域剩余深度对剩余速度的敏感性分析

本文针对地震勘探深度域偏移速度建模研究,利用角度域共成像点道集(ADCIGS)建立了以剩余速度为自变量,剩余深度为目标函数的关系式,及目标函数的梯度公式.利用导出的两个公式分别对剩余深度与剩余速度的关系进行了定量分析.通过理论分析和模型试算证明初始速度模型的误差具有方向敏感性,即正误差较负误差对速度建模迭代收敛更敏感.利用此结论进行深度域速度建模既可以提高计算效率也可以提高建模精度.     

2D multiscale non-linear velocity inversion

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.     

Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration

The key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.     

Singularity-free Green’s function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green’s functions for an electromagnetic (EM) transmitting source embedded in a homogeneous stratified medium. A virtual interface parallel to layer interfaces is introduced through the source location. The potentials for Green’s function are derived by decomposing the partial wave solutions to Helmholtz’s equations into upward and downward within boundaries. The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level. The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface. Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters, whereas the kernel connected with the stratified media stays unchanged. Hence, the present method can be easily applied to EM transmitting sources with little modification. The application of the proposed method to the marine controlled-source electromagnetic method (MCSEM) demonstrates its simplicity and flexibility.     

MIGRATION OF VSP DATA BY RAY EQUATION EXTRAPOLATION IN 2-D VARIABLE VELOCITY MEDIA*

The standard Kirchhoff algorithm can be generalized for migration of pre-stack finite-offset data from variable-velocity media. The concentric ellipses over which the data are spread in constant velocity media become significantly distorted (even multi-valued) in the variable velocity case. The specific shapes can be explicitly defined by kinematic extrapolation of the source and recorded wave fields with the ray equation. The use of Kirchhoff migration with a surface source and a subsurface recorder requires that two sets of Kirchhoff loci be superimposed. For each trace, the first set of loci is computed with the source and the actual recorder position as foci; the second set is computed with the source and the virtual recorder position as foci. This dual procedure explicitly incorporates the primary diffracted energy and the free-surface reflections, respectively. Implementation involves the construction of a virtual medium, lying above the free surface, with a velocity distribution that is the mirror image of the actual distribution below the free surface. Ray-equation extrapolation is performed through the real/virtual boundary. The resulting image is produced in a split form, with all the contributions of the primary reflected and diffracted energy lying in the lower ‘real’ half and all the contributions of the energy that was reflected at the free surface lying in the upper ‘virtual’ half. The final image is produced by folding the split image about the free surface and adding the two halves. A practical advantage is that the origin of various contributions (and artifacts) can be more readily identified (for interpretation or removal) in the split images. The ray-equation pre-stack migration algorithm is very general. It is applicable to all source-recorder geometries and variable velocity media and reduces exactly to the standard Kirchhoff algorithm when applied to zero or finite-offset surface survey data. The algorithm is illustrated by application to VSP data. For the VSP geometry, the algorithm does not require any specific trace spacing (in depth) and can be used for data from deviated as well as vertical holes.     

Scour Downstream of Grade Control Structures under the Influence of Upward Seepage

The installation of free falling jet grade control structures has become a popular choice for river bed stabilization. However, the formation and development of scour downstream of the structure may lead to failure of the structure itself. The current approaches to scour depth prediction are generally based on studies conducted with the absence of upward seepage. In the present study, the effects of upward seepage on the scour depth were investigated. A total of 78 tests without and with the application of upward seepage were carried out using three different sediment sizes, three different tailwater depths, four different flow discharges, and four different upward seepage flow discharge rates. In some tests, the three-dimensional components of the flow velocity within the scour hole were measured for both the cases with and without upward seepage. The scour depth measured for the no-seepage results compared well with the most accurate relationship found in the literature. It was found that generally the upward seepage reduced the downward velocity components near the bed, which led to a decrease in the maximum scour depth. A maximum scour depth reduction of 49% was found for a minimum tailwater depth, small sediment size, and high flow discharge. A decay of the downward velocity vector within the jet impingement was found due to the upward seepage flow velocity. The well known equation of D’Agostino and Ferro was modified to account for the effect of upward seepage, which satisfactorily predicted the experimental scour depth, with a reasonable average error of 10.7%.     

Velocity modelling and prestack depth imaging below complex salt structures: a case history from on-shore Germany

In recent years, the advances in velocity model building and depth imaging have provided a better understanding of complex subsalt plays. The tomographic approach to subsurface velocity modelling, using interpretive processes, has led to significant progress in solving subsalt imaging problems, which were once considered to be impenetrable barriers. We show how gravity data, as an alternative data source, can be integrated into iterative velocity–depth model building to constrain the overburden velocity model and delineate the shape of the salt body above the target reflector. In this way, a structurally accurate image of subsalt reflectors is achieved.     

RADON DEPTH MIGRATION1

A depth migration method is presented that uses Radon-transformed common-source seismograms as input. It is shown that the Radon depth migration method can be extended to spatially varying velocity depth models by using asymptotic ray theory (ART) to construct wavefield continuation operators. These operators downward continue an incident receiver-array plane wave and an assumed point-source wavefield into the subsurface. The migration velocity model is constrained to have longer characteristic wavelengths than the dominant source wavelength such that the ART approximations for the continuation operators are valid. This method is used successfully to migrate two synthetic data examples:

• 1 a point diffractor, and
• 2 a dipping layer and syncline interface model.

It is shown that the Radon migration method has a computational advantage over the standard Kirchhoff migration method in that fewer rays are computed in a main memory implementation.     

SEISMIC MIGRATION IN ELLIPTICALLY ANISOTROPIC MEDIA1

The study of wave propagation in media with elliptical velocity anisotropy shows that seismic energy is focused according to the horizontal component of the velocity field while the vertical component controls the time-to-depth relation. This implies that the vertical component cannot be determined from surface seismic velocity analysis but must be obtained using borehole or regional geological information. Both components of the velocity field are required to produce a correctly focused depth image. A paraxial wave equation is developed for elliptical anisotropic wave propagation which can be used for modelling or migration. This equation is then transformed by a change of variable to a second paraxial equation which only depends on one effective velocity field. A complete anisotropic depth migration using this transformed equation involves an imaging step followed by a depth stretching operation. This allows an approximate separation or splitting of the focusing and depth conversion steps of depth migration allowing a different velocity model to be used for each step. This split anisotropic depth migration produces a more accurate result than that obtained by a time migration using the horizontal velocity field followed by an image-ray depth conversion using the vertical velocity field. The results are also more accurate than isotropic depth migration and yield accurate imaging in depth as long as the lateral variations in the anisotropy are slow.     

近震震源深度测定精度的理论误差分析

震源深度是地震学中最难准确测定的参数之一,各种方法对于震源深度的估计都具相当程度的不确定性,影响着人们对震源过程的认识。各种因素对震源深度的影响是非线性的,本文从近震走时公式入手,分析了震中距、到时残差和速度模型(地壳模型)对震源深度的影响。当地震波传播速度一定时,震源深度的误差随着震中距或台站距离的增大和走时残差的增大而增大。走时残差一定时,震源深度误差随着震中距的增大和地震波速度的增大而增大。研究也表明,当速度已知,走时残差一定时,越浅的地震,定位误差可能越大。定位精度产生的水平误差随着震中距、走时误差和地震波速度的增大而增大,震源深度误差也将增大。另外,震源深度的误差会导致发震时刻的变化,随之而来的结果都会因此而改变。     

Determining friction coefficients for interrill flows: the significance of flow filaments and backwater effects

Friction coefficients in overland flows are customarily estimated from mean flow properties (depth, velocity, slope) that subsume spatial variations in flow arising from two major causes: microtopography and obstacles. This paper uses laboratory experiments in shallow flumes to examine the extent of non‐uniformity in flow conditions associated with each cause. Randomly placed emergent obstacles in a flume with a shallow axial channel generally yielded higher hydraulic roughness than the same pattern of obstacles on a planar flume, as well as greater variation in roughness as the obstacle locations were altered. In both flumes, hydraulic roughness fell with increasing Reynolds number for 10% obstacle cover, showed a flattening trend at 20% cover, and exhibited a convex‐downward trend at 30% obstacle cover. These results indicate the progressive onset of flow controls at narrow gaps in the obstacle field. In such flows, the use of mean flow properties conceals the existence of two main subdivisions of flow: flow filaments and backwater flows. In the experiments, flow filaments involved velocities more than twice the overall mean, whereas backwater flows were much slower than the mean. The existence of fast‐moving flow filaments may be significant in understanding soil transport in surface runoff, and backwater depths may modify splash detachment. Similarly, friction coefficients that fail to reflect these important non‐uniform flow components may not be optimal for hydraulic calculations or in erosion models. It is concluded that new approaches to observing and processing flow data may be required, in order to avoid the loss of important flow detail that is entailed in assuming uniform flow conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

用天然地震探测青藏高原中部地壳、上地幔结构

从西藏南部的定日、嘎拉至青海铜铁山的天然地震探测剖面，实际路线长约２０００ｋｍ，布设了约１１０台便携地震仪，记录了数百次远震和近震事件，采用多种方法进行了资料处理与解释．依据ＳＫＳ，ＰＫＳ，ｐｓ等横波分裂特征计算的青藏高原中部上地幔的地震各向异性表明：研究区各构造单元内的地震各向异性有明显变化，发现上地幔各向异性快速波的偏振方向与造山带的走向不完全一致．在雅江缝合线、崩错－嘉黎、唐古拉山口、昆仑山口几条断裂带处南、北各向异性出现显著的差异，而金沙江缝合线和班公－怒江缝合线的南、北则没有明显的各向异性变化．由Ｐ波走时残差，利用层析技术反演了４００ｋｍ深度内的速度图像，可以看出近地表１００ｋｍ范围内速度的不均匀变化与地表划分的构造单元很吻合，进一步佐证了青藏高原是由不同时期的微板块拼合而成的认识．在青藏高原中部１５０ｋｍ深度以下发现了多处低速区．在金沙江缝合带下方约２００ｋｍ深度处有一长２５０ｋｍ以上、延伸１５０ｋｍ的低速体，推测可能是一地幔柱．利用ＰＳ转换波划分的界面，显示出青藏高原北部具有低速层和高速层交替出现的地壳结构．     

Tomographic velocity inversion for ADCIGs in areas with a rugged surface

Pre-stack depth migration velocity analysis is one of the key techniques influencing image quality. As for areas with a rugged surface and complex subsurface, conventional prestack depth migration velocity analysis corrects the rugged surface to a known datum or designed surface velocity model on which to perform migration and update the velocity. We propose a rugged surface tomographic velocity inversion method based on angle-domain common image gathers by which the velocity field can be updated directly from the rugged surface without static correction for pre-stack data and improve inversion precision and efficiency. First, we introduce a method to acquire angle-domain common image gathers (ADCIGs) in rugged surface areas and then perform rugged surface tomographic velocity inversion. Tests with model and field data prove the method to be correct and effective.     

Accuracy of crowdsourced streamflow and stream level class estimates

ABSTRACT

Streamflow data are important for river management and the calibration of hydrological models. However, such data are only available for gauged catchments. Citizen science offers an alternative data source, and can be used to estimate streamflow at ungauged sites. We evaluated the accuracy of crowdsourced streamflow estimates for 10 streams in Switzerland by asking citizens to estimate streamflow either directly, or based on the estimated width, depth and velocity of the stream. Additionally, we asked them to estimate the stream level class by comparing the current stream level with a picture that included a virtual staff gauge. To compare the different estimates, the stream level class estimates were converted into streamflow. The results indicate that stream level classes were estimated more accurately than streamflow, and more accurately represented high and low flow conditions. Based on this result, we suggest that citizen science projects focus on stream level class estimates instead of streamflow estimates.     

Wavefield downward extrapolation for migration velocity analysis on Marmousi data-set

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.     

Extended imaging conditions for wave‐equation migration

Wavefield‐based migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in common‐image gathers that represent reflectivity as a function of depth and extensions, e.g., reflection angles. We introduce extended common‐image point (CIP) gathers constructed only as a function of the space‐ and time‐lag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIP's constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIP's also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIP's remove the depth bias of common‐image gathers constructed as a function of the depth axis. An interpretation of the CIP's using the scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIP's are characterized by focused energy at the origin of the space‐ and time‐lag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefield‐based tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinate‐independent CIP's can be a decomposed as a function of the angles of incidence.