Modelling and migration with orthogonal isochron rays

For increasing time values, isochrons can be regarded as expanding wavefronts and their perpendicular lines as the associated orthogonal isochron rays. The speed of the isochron movement depends on the medium velocity and the source-receiver position. We introduce the term equivalent-velocity to refer to the speed of isochron movement. In the particular case of zero-offset data, the equivalent velocity is half of the medium velocity. We use the concepts of orthogonal isochron-rays and equivalent velocity to extend the application of the exploding reflector model to non-zero offset imaging problems. In particular, we employ these concepts to extend the use of zero-offset wave-equation algorithms for modelling and imaging common-offset sections. In our imaging approach, the common-offset migration is implemented as a trace-by-trace algorithm in three steps: equivalent velocity computation, data conditioning for zero-offset migration and zero-offset wave-equation migration. We apply this methodology for modelling and imaging synthetic common-offset sections using two kinds of algorithms: finite-difference and split-step wavefield extrapolation. We also illustrate the isochron-ray imaging methodology with a field-data example and compare the results with conventional common-offset Kirchhoff migration. This methodology is attractive because it permits depth migration of common-offset sections or just pieces of that by using wave-equation algorithms, it extends the use of robust zero-offset algorithms, it presents favourable features for parallel processing, it permits the creation of hybrid migration algorithms and it is appropriate for migration velocity analysis.     

Cost-effective 3D one-pass depth migration1

A crucial point in the processing of 3D seismic data is the migration step, both because of its 3D nature and the computational cost involved. The efficiency and accuracy of 3D migration are determined by the wavefield extrapolation technique employed. Wavefield extrapolation based on second-order differential operators of variable-length is very efficient and accurate at the same time. Compared to migration based on the McClellan transform and operator splitting, the use of variable-length second-order differential operators offers significant advantages. The 3D migration operator has an almost perfect circular symmetry. No positioning errors in the 45° azimuth between the in-line and cross-line directions are evident. The method is, in practice, only limited by spatial aliasing and does not require expensive interpolation of data to reduce numerical artifacts. This reduces the computational cost of 3D one-pass depth migration by a large factor.     

MIGRATION BY EXTRAPOLATION OF TIME-DEPENDENT BOUNDARY VALUES*

Migration of an observed zero-offset wavefield can be performed as the solution of a boundary value problem in which the data are extrapolated backward in time. This concept is implemented through a finite-difference solution of the two-dimensional acoustic wave equation. All depths are imaged simultaneously at time 0 (the imaging condition), and all dips (right up to vertical) are correctly migrated. Numerical examples illustrate this technique in both constant and variable velocity media.     

利用联合反演技术进行反射地震的波速成象

本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C（x,z）具有间断性,除利用走时数据T（x,t）外,在地层比较水平的情况下,还利用了均方根速度V（x,t）和统计子波W（t）的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。     

Imaging seismic data in complex structures by introducing the partial diffraction surface stack method

The common reflection surface (CRS) stack method is known as a generalized stacking velocity analysis tool and was originally introduced as a data-driven method to simulate zero-offset sections. However, this method has some difficulties in imaging complex structures and low-quality data. The problem of conflicting dips is one of the drawbacks of the CRS method addressed in many studies. The common diffraction surface (CDS) method was explicitly introduced to overcome this problem. In one study, the problem was resolved by combination of the CDS method and the common offset CRS method. The method was called the common offset CDS method showed successful application on improving image quality in semi-complex media. In this study, we combined the partial CRS with the CDS to derive the partial CDS for more efficient resolve of the conflicting dips problem. In the partial CDS, thresholds in the angle spectrum were removed for full contribution of all possible dips to have volume of operators for a sample point. The aperture definition in the partial CDS is the same as in the partial CRS, where an offset and time variant aperture is used. The new method was applied on a simple synthetic data set with much diffraction points imbedded in the model. Then it was applied to a semicomplex data set to enhance the body of mud volcanoes and faults. For better comparison, it was applied to two more real data sets from a complex overthrust zone to improve the seismic quality and remove the geological ambiguities in the interpretation. In the synthetic data example, more conflicting dips were resolved than in the other methods. In all real data examples, the enhanced partial CDS data were depth-migrated to compare them with the pre-stack depth migration of partial CRS gathers. More details of the geological structures can be observed in the new results.     

AN INVESTIGATION OF THE RELATIVE ACCURACY OF THE MOST COMMON NORMAL-MOVEOUT EXPRESSIONS IN VELOCITY ANALYSES*

Three common expressions for the normal moveout of recorded seismic events are investigated by numerical simulation procedures for accuracy in predicting the root-mean-squared (RMS) or mean, as the case may be, subsurface velocity function from seismic data. The principal investigation, for which detailed error curves are shown, was derived for a stochastic subsurface model composed of strata with thicknesses ranging up to 91.4 m (300 ft) and boundary velocity contrasts ranging up to 45.7 m/sec (150 ft/sec); there was a 95 percent chance of velocity increase with increased depth. The effects of changes in the basic statistical subsurface model are discussed. The results appear to confirm the judiciousness of the choices of to and (x/z') as plotting parameters to be used with the respective percent errors in the three expressions, where are, respectively, the zero-offset arrival time of, the offset distance of, and the mean-squared velocity encountered by a seismic ray. Out of the three normal-moveout expressions examined, the “straight-raypath” expression with the RMS velocity substituted as its velocity term proved to be the most accurate in the determination of velocities.     

A FREQUENCY DOMAIN APPROACH TO TWO-DIMENSIONAL MIGRATION *

The problem of the propagation of acoustic waves in a two-dimensional layered medium can be easily solved in the frequency domain if the Dix approximation is used, i.e. when only the primary reflections are considered. The migrated data at a depth z are obtained by convolving the time section with a proper two-dimensional operator dependent on z. The same result can be obtained by multiplying their two-dimensional spectra and summing for all the values of the temporal frequency. The aspect of the operator in the time-space domain has the classic hyperbolic structure together with the prescribed temporal and spatial decay. The main advantages of the frequency domain approach consist in the noticeable computer time savings and in the better approximation. On the other hand lateral velocity variations are very difficult to be taken into account. This can be done if a space variant filter is used in the time-space domain. To reduce computer time, this filter has to be recursive; the problem has been solved by Claerbout by transforming the hyperbolic partial differential equation into a parabolic one, and using the latter to generate the recursion operator. In the presentation a method is given for the generation of recursive filters with a better phase characteristics that have a pulse response with the requested hyperbolic shape instead of the parabocli one. This allows a better migration of steeper dips.     

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.     

First-Order Perturbation Theory for Seismic Isochrons

A first-order perturbation theory for seismic isochrons is presented in a model independent form. Two ray concepts are fundamental in this theory, the isochron ray and the velocity ray, for which I obtain first-order approximations to position vectors and slowness vectors. Furthermore, isochron points are connected to a shot and receiver by conventional ray fields. Based on independent perturbation of the shot and receiver ray I obtain first-order approximations to velocity rays. The theory is applicable for 3D inhomogeneous anisotropic media, given that the shot and receiver rays, as well as their perturbations, can be generated with such model generality. The theory has applications in sensitivity analysis of prestack depth migration and in velocity model updating. Numerical examples of isochron and velocity rays are shown for a 2D homogeneous VTI model. The general impression is that the first-order approximation is, with some exceptions, sufficiently accurate for practical applications using an anisotropic velocity model.     

Regularized inversion of amplitude-versus-incidence angle (AVA) based on a piecewise-smooth model

Different from the stacked seismic data, pre-stack data includes abundant information about shear wave and density. Through inversing the shear wave and density information from the pre-stack data, we can determine oil-bearing properties from different incident angles. The state-of-the-art inversion methods obtain either low vertical resolution or lateral discontinuities. However, the practical reservoir generally has sharp discontinuities between different layers in vertically direction and is horizontally smooth. Towards obtaining the practical model, we present an inversion method based on the regularized amplitude-versus-incidence angle (AVA) data to estimate the piecewise-smooth model from pre-stack seismic data. This method considers subsurface stratum as a combination of two parts: a piecewise smooth part and a constant part. To fix the ill-posedness in the inversion, we adopt four terms to define the AVA inversion misfit function: the data misfit itself, a total variation regularization term acting as a sparsing operator for the piecewise constant part, a Tikhonov regularization term acting as a smoothing operator for the smooth part, and the last term to smoothly incorporate a priori information for constraining the magnitude of the estimated model. The proposed method not only can incorporate structure information and a priori model constraint, but also is able to derive into a convex objective function that can be easily minimized using iterative approach. Compared with inversion results of TV and Tikhonov regularization methods, the inverted P-wave velocity, S-wave velocity and density of the proposed method can better delineate the piecewise-smooth characteristic of strata.     

Common reflection surface stack using dip decomposition for rugged surface topography

We present an extension of the Common Reflection Surface （CRS） stack that provides support for an arbitrary top surface topography. CRS stacking can be applied to the original prestack data without the need for any elevation statics. The CRS-stacked zero- offset section can be corrected （redatumed） to a given planar level by kinematic wave field attributes. The seismic processing results indicate that the CRS stacked section for rugged surface topography is better than the conventional stacked section for S/N ratio and better continuity of reflection events. Considering the multiple paths of zero-offset rays, the method deals with reflection information coming from different dips and performs the stack using the method of dip decomposition, which improves the kinematic and dynamic character of CRS stacked sections.     

零偏移距VSP资料层Q反演及其应用研究(英文)

地层品质因子Q的可用于地震资料高分辨率处理,而从VSP资料下行直达波更容易获取准确的地层品质因子。通过对零偏移距VSP资料的监控子波和下行初至波的频谱进行综合分析,仿照Ricker子波频谱的表达式,本文提出了震源子波频谱新的表达式。在震源子波频谱新的表达式基础上,我们介绍了改进的频谱拟合法和改进的谱比法的层Q值反演方法及相应的处理流程。基于本文提出的层Q值反演方法,利用实际的零偏移距VSP资料的下行直达波,反演稳定的层Q值,并用于零偏移距VSP资料及井旁地面地震资料的反Q滤波振幅补偿处理,提高了地震资料的分辨率。     

STEEP DIP FINITE-DIFFERENCE MIGRATION*

A method is presented to derive approximate versions of the wave equation which allow finite-difference migration for very steep dips (> 50°). It is shown that for conventional finite-difference schemes, in addition to the dip limitation, the maximum acceptable frequency should be specified. A finite-difference migration technique is proposed in the frequency domain. It is derived that finite-difference wave field extrapolation in the frequency domain consists of a space-variant convolution procedure for each frequency component, the space-variance being defined by the lateral variation in the velocity. Finally it is shown that with finite-difference migration, particle velocity data can be easily obtained from pressure data.     

Look-ahead vertical seismic profiling inversion approach for density and compressional wave velocity in Bayesian framework

To reduce drilling uncertainties, zero-offset vertical seismic profiles can be inverted to quantify acoustic properties ahead of the bit. In this work, we propose an approach to invert vertical seismic profile corridor stacks in Bayesian framework for look-ahead prediction. The implemented approach helps to successfully predict density and compressional wave velocity using prior knowledge from drilled interval. Hence, this information can be used to monitor reservoir depth as well as quantifying high-pressure zones, which enables taking the correct decision during drilling. The inversion algorithm uses Gauss–Newton as an optimization tool, which requires the calculation of the sensitivity matrix of trace samples with respect to model parameters. Gauss–Newton has quadratic rate of convergence, which can speed up the inversion process. Moreover, geo-statistical analysis has been used to efficiently utilize prior information supplied to the inversion process. The algorithm has been tested on synthetic and field cases. For the field case, a zero-offset vertical seismic profile data taken from an offshore well were used as input to the inversion algorithm. Well logs acquired after drilling the prediction section was used to validate the inversion results. The results from the synthetic case applications were encouraging to accurately predict compressional wave velocity and density from just a constant prior model. The field case application shows the strength of our proposed approach in inverting vertical seismic profile data to obtain density and compressional wave velocity ahead of a bit with reasonable accuracy. Unlike the commonly used vertical seismic profile inversion approach for acoustic impedance using simple error to represent the prior covariance matrix, this work shows the importance of inverting for both density and compressional wave velocity using geo-statistical knowledge of density and compressional wave velocity from the drilled section to quantify the prior covariance matrix required during Bayesian inversion.     

A NOVEL HIGH-SPEED ALGORITHM FOR SUMMATIONAL TYPE SEISMIC VELOCITY ANALYSES*

Velocity analysis of reflection seismic data has increased in popularity with petroleum exploration personnel to such an extent that it now constitutes a significant tool in the routine digital processing program. One drawback to such an analysis is its computational cost, resulting from the numerous mathematical calculations required by a digital computer to extract comprehensive velocity information. The subject algorithm affords a computational cost saving of approximately one order of magnitude over a straightforward summational type velocity analysis with little sacrifice in accuracy. The utility of the algorithm is demonstrated on some Offshore Louisiana seismic data and a comparison of the results reveals that they are almost identical with a conventional velocity analysis. The algorithm is based on the concept that a normal-moveout pattern of time shifts may be accurately applied over a considerable span of zero-offset times to a CDP trace gather, rather than only at a single zero-offset time. With each application however, the rms-velocity associated with the moveout pattern is different. A specific relationship which associates an rms-velocity with a zero-offset time for the same moveout time delay pattern is approximated by numerical simulation studies on a digital computer.     

陆上纵波源VSP资料中的纯横波

常规陆上VSP(Vertical Seismic Profiling)勘探普遍采用纵波震源激发,三分量检波器接收,主要利用的是纵波和转换横波信息。已有的研究表明,炸药震源在井下激发、可控震源在地面垂向振动,均会产生较强的纯纵波和一定强度的纯横波;泊松比差别较大的分界面有利于形成较强的透射转换横波。本文通过对激发形成的纯横波和下行转换形成的横波进行对比分析,认为纯横波的主频往往低于纯纵波的主频,而下行转换横波的主频通常接近纵波的主频。本文分别对两个陆上纵波源零偏和非零偏VSP资料进行分析,结果表明这些资料中普遍存在纯横波,只是横波的强弱存在不同程度的变化。利用纵波源零偏VSP资料,可以获得横波速度信。最后对VSP纵波和横波联合应用前景进行了分析,应该充分利用纵波源VSP资料中的横波信息。     

MODEL-BASED STACK: A METHOD FOR CONSTRUCTING AN ACCURATE ZERO-OFFSET SECTION FOR COMPLEX OVERBURDENS1

The interpretation of stacked time sections can produce a correct geological image of the earth in cases when the stack represents a true zero-offset section. This assumption is not valid in the presence of conflicting dips or strong lateral velocity variations. We present a method for constructing a relatively accurate zero-offset section. We refer to this method as model-based stack (MBS), and it is based on the idea of stacking traces within CMP gathers along actual traveltime curves, and not along hyperbolic trajectories as it is done in a conventional stacking process. These theoretical curves are calculated for each CMP gather by tracing rays through a velocity-depth model. The last can be obtained using one of the methods for macromodel estimation. In this study we use the coherence inversion method for the estimation of the macromodel since it has the advantage of not requiring prestack traveltime picking. The MBS represents an accurate zero-offset section in cases where the estimated macromodel is correct. Using the velocity–depth macromodel, the structural inversion can be completed by post-stack depth migration of the MBS.     

Kinematical characteristics of the factorized velocity model

The factorized velocity model that incorporates both vertical heterogeneity and constant anisotropy is one of the complicated analytical models used in seismic data processing and interpretation. In this paper, I derive the analytic equations for offset, traveltime and relative geometrical spreading for the quasi‐compressional (qP‐) waves that can be used for modelling and inversion of the traveltime parameters. I show that the presence of anelliptic anisotropy usually dominates over the vertical heterogeneity with respect to the non‐hyperbolicity of the factorized velocity model.     

Moveout analysis for tranversely isotropic media with a tilted symmetry axis

The transversely isotropic (TI) model with a tilted axis of symmetry may be typical, for instance, for sediments near the flanks of salt domes. This work is devoted to an analysis of reflection moveout from horizontal and dipping reflectors in the symmetry plane of TI media that contains the symmetry axis. While for vertical and horizontal transverse isotropy zero-offset reflections exist for the full range of dips up to 90°, this is no longer the case for intermediate axis orientations. For typical homogeneous models with a symmetry axis tilted towards the reflector, wavefront distortions make it impossible to generate specular zero-offset reflected rays from steep interfaces. The ‘missing’ dipping planes can be imaged only in vertically inhomogeneous media by using turning waves. These unusual phenomena may have serious implications in salt imaging. In non-elliptical TI media, the tilt of the symmetry axis may have a drastic influence on normal-moveout (NMO) velocity from horizontal reflectors, as well as on the dependence of NMO velocity on the ray parameter p (the ‘dip-moveout (DMO) signature’). The DMO signature retains the same character as for vertical transverse isotropy only for near-vertical and near-horizontal orientation of the symmetry axis. The behaviour of NMO velocity rapidly changes if the symmetry axis is tilted away from the vertical, with a tilt of ±20° being almost sufficient to eliminate the influence of the anisotropy on the DMO signature. For larger tilt angles and typical positive values of the difference between the anisotropic parameters ε and δ, the NMO velocity increases with p more slowly than in homogeneous isotropic media; a dependence usually caused by a vertical velocity gradient. Dip-moveout processing for a wide range of tilt angles requires application of anisotropic DMO algorithms. The strong influence of the tilt angle on P-wave moveout can be used to constrain the tilt using P-wave NMO velocity in the plane that includes the symmetry axis. However, if the azimuth of the axis is unknown, the inversion for the axis orientation cannot be performed without a 3D analysis of reflection traveltimes on lines with different azimuthal directions.     

地震波频散效应与反Q滤波相位补偿

本文以Futterman提出的地震波振幅衰减和相速度频散表达式为基础,从井震匹配的角度出发,推导了不进行反Q滤波、仅反Q滤波振幅补偿、仅反Q滤波相位补偿,以及反Q滤波相位与振幅同时补偿四种情况下,地震波速度频散与相速度及地震记录振幅谱间的表达式,并从理论上说明了反Q滤波相位补偿的必要性.通过相同观测系统,炸药震源和可控震源分别激发采集的零偏移距VSP资料实例,验证了本文所推导的速度频散表达式的合理性;通过井震标定实例,进一步说明了反Q滤波相位补偿,可有效消除地震子波速度频散,提升地面地震资料与零偏移距VSP走廊叠加剖面的匹配度,最终提高地震资料成果的可信度.