P-SV反射转换波的倾角时差校正（DMO）方法研究

倾角时差校正（ＤＭＯ）方法对于复杂地质构造条件下的纵波反射波（Ｐ－Ｐ）的多次覆盖地震数据的叠加具有显著的提高信噪比的效果．对于转换反射波（Ｐ－ＳＶ）来说，进行倾角时差校正（ＤＭＯ）处理就更需要．本文首先对Ｐ－ＳＶ波的倾角时差校正（ＤＭＯ）的几何原理进行了分析，然后重点研究用波动方程进行ＤＭＯ的方法，即Ｐ－ＳＶ转换反射波的叠前部分偏移的波动方程法．这种方法也适用于Ｐ－Ｐ反射波的叠前部分偏移处理．研究结果表明，波动方程ＤＭＯ方法在振幅保真方面比几何原理的ＤＭＯ方法有显著改善．     

三维倾斜界面PS转换波CMP道集时距及参数估计

在PS转换波资料处理过程中,往往需要联合P波资料提供相应的模型.在实际应用中存在P波和PS转换波层位对比困难.本文仅利用PS转换波数据,通过三维倾斜界面PS转换波CMP道集精确时距关系推导了近似时距解析表达式;分析了PS波的精确与近似时距关系随测线方位、界面倾角与倾向的变化规律及其拟合误差;并讨论了近似时距关系的三个时距参数随方位的变化特征;理论上给出描述时距的三维倾斜界面倾角、倾向、深度、纵波速度和横波速度这5个独立参数的估计方法,并通过理论模拟数据证明了该方法的可行性.     

一种倾角时差校正和叠前成象方法

本文从测量射线参数出发进行反向射线追踪,导出倾角时差校正（DMO）的公式。经过DMO后,可以从一组等炮检距剖面得出共分角线点道集。用于对这些道集进行叠加的速度值与界面倾角无关。对经过DMO的资料的等时切片进行叠前成象（PSI）,就可以把分布在圆上的绕射能量沿圆弧加起来,并放在圆弧上对应于最大炮检距的位置。经过这两种处理,再应用标准的速度分析和叠加方法,就可得出偏移后的剖面。这两种处理均与速度无关。最后用物理模型试验说明了DMO和PSI的效果是好的。     

A SIMPLE EFFICIENT METHOD OF DIP-MOVEOUT CORRECTION1

Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack. In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.     

OFFSET CONTINUATION IN THEORY AND PRACTICE*

Offset continuation is a technique that was recently proposed for the dip moveout correction. This correction can be carried out in the time-wavenumber domain using a proper partial differential equation that links sections with different offset. It has been shown that a single spike in a common-offset section—corresponds to a semi-elliptically shaped reflector with foci located at the source and receiver in the section migrated after dip moveout correction. The sections that result after offset continuation, stack, and migration are thus a superposition not only of semicircles, but also of semi-ellipses with different lengths of axes. This effect smears the migration alias-noise which, without offset continuation, would appear as migration circles not close enough together to interfere destructively. Offset continuation can improve the quality of seismic sections in several ways: —the velocity analyses are more readable, less dispersed and dip independent; diffraction tails arrive with the same normal moveout velocity as the apex and thus diffraction-noise can be “stacked out”; —noise produced by aliasing in the migrated section is reduced. In this paper we give a practical and conceptual interpretation of the offset continuation method, with a generalization to three-dimensional volumes of data. A critical examination of several synthetic and field data examples shows the actual possibilities and advantages of offset continuation.     

APPLICATION OF THE PARTIAL KARHUNEN-LOÈVE TRANSFORM TO SUPPRESS RANDOM NOISE IN SEISMIC SECTIONS1

The Karhunen-Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero-lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K-L transform.     

三维地震勘探数据的剩余静校正方法研究与软件实现

剩余静校正的目的是消除地震道中由近地表因素造成的静态剩余时差的影响,通常以时差的四因子分解模型为基础建立剩余静校正方程组,并采用迭代求解方法获得剩余静校正量。但实际上,由于地层的倾斜,时差中还应包含横向和纵向倾角项,因此本文首先对剩余校正的理论模型进行了改进,提出了以扩展面元为计算单元的时差分解六因子模型。又由于地层的走向具有局部线性性,因此剩余动校正项,横向及纵向倾角项系数仅在一些给定的面元上计     

VTI介质长偏移距非双曲动校正公式优化

常规Alkhalifah动校正公式精度低,不能精确描述各向异性介质长偏移距地震反射同相轴的时距关系.本文以提高VTI介质长偏移距地震资料动校正公式的精度为目标,在分析VTI介质常规动校正方程的基础上,根据误差最小原理建立优化校正系数图版,实现对常规动校正公式大偏移距误差的修正,建立最优化校正Alkhalifah动校正方程,实现了对VTI介质长偏移距地震资料常规动校正方程的改进.之后由Fomel群速度公式导出高精度VTI模型长偏移距时距函数,提出了高精度VTI介质长偏移距地震资料动校正方程.将以上的动校正方程用于各向异性参数反演,模型计算表明最优化校正Alkhalifah动校正方程的反演精度是常规长偏移距动校正方程反演精度的2～4倍,高精度动校正方程的反演精度是常规动校正方程反演精度的2～8倍.     

多层倾斜层状介质P-SV转换波转换点计算的最佳角度搜索法

转换波转换点的位置对转换波道集的抽取和叠加都非常重要.目前对于单一倾斜反射界面或水平层状介质模型,已经能较好地计算转换波转换点的位置.本文针对多层倾斜层状介质,提出最佳角度搜索法求取P-SV转换波转换点的位置,此方法是通过搜索最符合Snell定律的入射角和反射角来确定最佳的P-SV转换波转换点的位置.在搜索最佳转换点位...     

Perturbation‐based moveout approximations in anisotropic media

The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations.     

DIRECTIONAL DECONVOLUTION OF MARINE SEISMIC REFLECTION DATA: NORTH SEA EXAMPLE1

Directional deconvolution of the signature from a marine seismic source array may be achieved in combination with prestack migration or dip moveout (DMO) processing. The benefit is demonstrated using an example profile from the southern North Sea. In particular, shallow, dipping reflectors have improved continuity and frequency content. The method could be extended to 3D data to remove both in-line and cross-line directivity effects.     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

PLANE-WAVE CONSTRAINTS IN 2D FILTER DESIGN1

A method is presented for developing and/or evaluating 2D filters applied to seismic data. The approach used is to express linear 2D filtering operations in the space-frequency (x–ω) domain. Correction filters are then determined using plane-wave constraints. For example, requiring a vertically propagating plane wave to be unaffected by migration necessitates application of a half-derivative correction in Kirchhoff migration. The same approach allows determination of the region of time-offset space where half-derivative corrections are correct in x–t domain dip moveout. Finally, an x–ω domain dip filter is derived using the constraint that a plane wave be attenuated as its dip increases. This filter has the advantage that it is significantly faster than f–k domain dip filtering and can be used on irregularly spaced data. This latter property also allows the filter to be used for interpolation of irregular data onto a regular grid.     

OFFSET CONTINUATION OF SEISMIC SECTIONS*

Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data.     

Synthetic Experiments Dealing with Anisotropic Model Building

It has been shown in the past that the interval-NMO velocity and the non-ellipticity parameter largely control the P-wave reflection time moveout of VTI media. To invert for these two parameters, one needs either reasonably large offsets, or some structure in the subsurface in combination with relatively mild lateral velocity variation.This paper deals with a simulation of an inversion approach, building on the assumption that accurately measured V _NMO, as defined by small offset asymptotics for a particular reflector, were available. Instead of such measurements we take synthetically computed data. First, an isotropic model is constructed which explains these V _NMO. Subsequently, residual moveout in common image gathers is modelled by ray tracing (replacing real data), along with its sensitivity for changes in the interval-NMO velocity and the non-ellipticity parameter under the constraint that V _NMO is preserved. This enables iterative updating of the non-ellipticity parameter and the interval-NMO velocity in a layer that can be laterally inhomogeneous.This approach is successfully applied for a mildly dipping reflector at the bottom of a layer with laterally varying medium parameters. With the exact V _NMO assumed to be given, lateral inhomogeneity and anisotropy can be distinguished for such a situation. However, for another example with a homogeneous VTI layer overlying a curved reflector with dip up to 30°, there appears to be an ambiguity which can be understood by theoretical analysis. Consistently with existing theory using the NMO-ellipse, the presented approach is successfully applied to the latter example if V _NMO in the strike direction is combined with residual moveout in dip direction.     

Migration to multiple offset and velocity analysis1

The stacking velocity best characterizes the normal moveout curves in a common-mid-point gather, while the migration velocity characterizes the diffraction curves in a zero-offset section as well as in a common-midpoint gather. For horizontally layered media, the two velocity types coincide due to the conformance of the normal and the image ray. In the case of dipping subsurface structures, stacking velocities depend on the dip of the reflector and relate to normal rays, but with a dip-dependent lateral smear of the reflection point. After dip-moveout correction, the stacking velocities are reduced while the reflection-point smear vanishes, focusing the rays on the common reflection points. For homogeneous media the dip-moveout correction is independent of the actual velocity and can be applied as a dip-moveout correction to multiple offset before velocity analysis. Migration to multiple offset is a prestack, time-migration technique, which presents data sets which mimic high-fold, bin-centre adjusted, common-midpoint gathers. This method is independent of velocity and can migrate any 2D or 3D data set with arbitrary acquisition geometry. The gathers generated can be analysed for normal-moveout velocities using traditional methods such as the interpretation of multivelocity-function stacks. These stacks, however, are equivalent to multi-velocity-function time migrations and the derived velocities are migration velocities.     

PRACTICAL ASPECTS OF THE DETERMINATION OF 3-D STACKING VELOCITIES*

Proper stacking of three-dimensional seismic CDP-data generally requires the knowledge of normal moveout velocities in all source-receiver directions contributing to a CDP-gather. The azimuthal variation of the stacking velocities mainly depends on the dip of the seismic interfaces. For a single dipping plane a simple relation exists between the dip and the azimuthal variation of NMO-velocity. Varying strike and dip of subsequent reflectors, however, result in a complex dependency of the seismic parameters. Reliable information on the spatial distribution of the normal moveout (NMO)-velocity can be derived from a wavefront curvature estimation using a 3-D ray-tracing technique. These procedures require additional information, e.g. reflection time gradients or depth maps to show interval velocities between leading interfaces. Moreover, their application to an extended 3-D data volume is restricted by high costs. The need for a routine 3-D procedure resulted in a special data selection to create pseudo 2-D profiles and to apply existing velocity estimation routines to these profiles. At least three estimates in different directions are necessary to derive the full azimuthal velocity variation, characterized by the large and the small main axis and the orientation of the velocity ellipse. Errors are estimated by means of computer models. Stacking velocities obtained by mathematical routines (least-squares fit) and by seismic standard routines (NMO-correction and correlation) are compared. Finally, a general 3-D velocity procedure using cross-correlation of preliminarily NMO-corrected traces is proposed.     

Velocity model updating in prestack Kirchhoff time migration for PS converted waves: Part I – Theory

A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted‐wave velocity only, and the other factor depending on all parameters. The velocity‐dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non‐hyperbolic behaviour of the moveout. This non‐hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal‐moveout common‐image‐point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio (V_P/V_S) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration.     

Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media*

Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.