利用qP波慢度和偏振矢量计算 弱各向异性介质参数

提出了一种使用慢度矢量分量和偏振矢量计算变井源距垂直地震剖面(walkaway VSP)钻孔中接收点附近介质弱各向异性(WA)参数的方法. 假定介质是任意弱各向异性介质, 从一般公式中得到了只有一条观测剖面情况下的反演公式. 如果知道了慢度矢量的垂直分量和偏振矢量, 可以通过反演得到与剖面和钻孔所在平面相关的WA参数, 反演过程不用进行射线追踪, 与上覆介质无关. 用合成数据检验了公式和方法的正确性, 并把它们应用于在爪哇海地区得到的一条变井源距垂直地震剖面的弱各向异性参数反演中.      

变井源距垂直地震剖面各向异性参数反演

利用微扰理论推导了弱各向异性(WA)介质参数正反演计算的基本公式;给出了在已知慢度矢量的一个分量和偏振矢量情况下确定WA参数的方法.如果这一方法被用于单一的变井源距垂直地震剖面(walkawayVSP)资料,可以获得9个WA参数.这9个WA参数完全决定了qP波和两个qS波在由剖面和钻井所决定的平面内传播的特性.对单条walkawayVSP观测系统数据的产生和WA参数的反演进行了数值模拟计算,对所能确定的WA参数及其可靠性进行了详细的讨论.     

Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

We apply the inversion scheme of Zheng and Peník (2002) to the walkaway VSP data of Horne and Leaney (2000) collected in the Java Sea region. The goal is a local determination of parameters of the medium surrounding the borehole receiver array. The inversion scheme is based on linearized equations expressing qP-wave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. It thus represents an alternative approach to Horne and Leaney (2000), who based their procedure on inversion of the Christoffel equation using a global optimization method. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. The inverson formula is local, and has therefore potential to separate effects of anisotropy from effects of inhomogeneity. The data used are components of the slowness vector along the receiver array and polarization vectors. The inversion is performed without any assumptions concerning the remaining components of the slowness vector. The inversion is made (a) assuming arbitrary anisotropy, i.e., without any assumptions about symmetry of the medium, (b) assuming transverse isotropy with a vertical axis of symmetry and (c) assuming isotropy of the medium. Inverted are the raw data as well as data, in which weighting is used to reduce the effect of outliers. It is found that the WA parameters _z, ₁₅ and ₃₅ are considerably more stable than the parameters _x and _x. The latter two parameters are also found to be strongly correlated. Weaker correlation is also found between the mentioned two parameters and _z. The results of inversion show clearly that the studied medium is not isotropic. They also seem to indicate that the studied medium does not possess the VTI symmetry.     

多测线变偏移距VSP地震各向异性反演

本文从一般弱各向异性介质参数反演中得到了使用两条相互正交的变偏VSP测线计算弱各向异性(WA)参数的反演公式. 如果仅仅使用qP波, 则可以确定9个独立的WA参数, 这9个WA参数可以完全地描述井中接收点在两个剖面内介质的各向异性性质. 通过对走时曲线进行最小二乘条件下的三次样条光滑, 可以获得慢度矢量的垂直分量和水平分量. 如果介质是横向非均匀介质, 则水平分量仅仅被用作反演时的约束条件. 为了获得偏振矢量, 本文引入质心计算方法, 该方法计算简单、 稳定, 而且不存在解的奇异问题. 在寻找与一般各向异性介质最接近的高对称性正交各向异性介质和TTI各向异性介质时, 使用qP波各向异性坐标变换方法和最小二乘求解方法, 得到了与一般各向异性介质最接近的正交各向异性和TTI各向异性参数及其对称轴方向参数的计算公式. 使用这些方法, 对瓜哇海地区布设的两条相互正交的变偏VSP测线数据进行各向异性反演, 获得了井中10个接收点处介质的WA参数. 数值计算和实际资料反演表明, 本文所使用的反演方法能够准确地得到VSP井中接收点处介质的WA参数, 这是地震勘探中研究地壳介质各向异性性质最直接和最可靠的方法.      

The Use of Wave-field Directivity for Velocity Estimation: Moving Source Profiling (MSP) Experiments at KTB

—Within the "Integrated Seismics Oberpfalz 1989 (ISO89)" a three-component Moving Source Profiling (MSP) experiment, also named walk-away VSP, was carried out at the drilling site of the "Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland (KTB)" in Germany. Analysis of transmitted waves traveling from the source locations at the surface down to the receiver array in the borehole reveals velocity information about the illuminated part of the subsurface. Complementary to the widely used evaluation of travel-time perturbations to locate velocity inhomogeneities we suggest the use of the directivity of transmitted wave types down in the borehole. To determine the wave-field directivity we focus on transmitted arrivals by employing principles of "Controlled Directional Reception (CDR)." We calculate local slant-stacks for three different depth positions as a function of the source offset, thus obtaining the variation of the vertical slowness (vertical ray parameter) of incident waves along the horizontal source profile and the vertical receiver array. The slowness data combined with travel times are interpreted by forward modeling taking into account geological information of the survey area. Our findings confirm results from gravity measurements which suggest the existence of large amphibolite/metabasite complexes in the vicinity of the borehole. The described method is also used to identify P-to-S converted energy originating from fracture zones above the receiver array and to locate the region in which conversion occurs.     

ANISOTROPY DETECTED IN SHALLOW CLAYS USING SHEAR-WAVE SPLITTING IN A VSP SURVEY1

Shear waves can provide valuable information about seismic anisotropy. On entering an anisotropic medium, a shear wave generally splits (shear-wave splitting) into a fast and a slow quasi-shear wave with polarizations fixed by the elastic properties of the medium and direction of travel. If the medium contains planar discontinuities with common normals, the fast shear wave will be suitably propagated if its polarization lies in the plane of the discontinuities. Measuring this polarization, using a VSP geometry with oriented three-component geophones in the borehole, offers the possibility of monitoring the orientation and density of the discontinuities as a function of depth. Such a shear-wave VSP was carried out in an uncased 0.3 m diameter borehole drilled to a depth of 120 m in the north of The Netherlands. The upper 80 m of the sequence, consisting of a glacial till and sands and clays of Pleistocene age, was studied. The clays in this sequence have been subjected to glacial deformation and as a result are overconsolidated and locally fissured. In our shallow VSP experiment, shear-wave splitting and therefore anisotropy was identified at various geophone depths for one source offset. Hodograms showed a consistent polarization of the fast shear-wave component over a large depth interval. Under the assumption that the anisotropy was caused by planar discontinuities with common normals, this polarization direction gives the strike of the fissures in this interval. The polarization direction of the fast S-wave did not correspond exactly with the strike which was obtained from geological information on the fissures. The geological information was from undisturbed oriented 70 mm core samples taken at 3 m intervals in the borehole. The discrepancy, however, could be explained in terms of dipping fissures, and such a dip was confirmed by the geological and geotechnical information. The orientation of fissures is an important factor in the directional deformation and strength characteristics of clays as far as geotechnical behaviour is concerned. This study thus illustrates a practical application of shear-wave splitting observed in shallow shear-wave VSP for geology and geotechnical engineering.     

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。     

CDP mapping and image reconstruction by using offset VSP data

Because zero-offset VSP (Vertical Seismic Profile) data can only provide the information of rock properties and structure in the area around the Fresnel zone within the well, the scheme of VSP with offset was developed to acquire the reflection information away from the borehole in order to widen the range of VSP survey and to improve the precision of imaging.In this paper, we present a new CDP (Common Depth Point) mapping approach to image the reflecting structure by using offset VSP data. For the processing of offset VSP data, we firstly separated the up-going and down-going wave-fields from VSP data by means of F-K filtering technique, and we can calculate the mapping conditions (position and reflecting traveltime for CDP point) in homogeneous media, and then reconstruct the inner structure of the earth.This method is tested by using the offset VSP data which are used to simulate the case of super-deep borehole by means of finite-difference method. The imaged structure matches the real model very well. The results show that the method present here could accurately image the inner structure of the earth if the deviation of initial velocity model from the true model is less than 10%. Finally, we presented the imaged results for the real offset data by using this method.     

REFLECTION AND POLARIZATION OF TUBE WAVES AS SEEN IN VSP DATA1

P-wave and S-wave data acquired with vertical seismic profiling (VSP) often include tube waves propagating in the borehole, although considerable efforts are generally made to ensure that these waves are not recorded. However, several theoretical studies have indicated that tube waves could provide important information about the rock formation and thus should not be considered as pure noise. In order to study some of these aspects experimentally, tube waves were acquired by VSP in a well in the Paris Basin both before and after casing. A sparker was used as source inside the borehole, which ensured that the data recorded contained high-amplitude tube waves. It is shown that the casing is an obstacle which prevents the study of formation parameters, and thus further tube-wave acquisitions should be carried out in open holes only. The before-casing tube-wave reflection log is compared to a synthetic log computed from the sonic log. The high resolution of the tube waves is of particular interest, revealing layers that are too thin to be detected in body-wave surveys. It has recently been suggested that the projection of the tube-wave polarization in the horizontal plane can be used to determine directions of stress-induced anisotropy in the rock formation. Strong polarization anomalies are observed in the data sets but are attributed to tool problems rather than any rock-formation feature.     

VERTICAL SEISMIC PROFILING—SEPARATION OF P- AND S-WAVES*

In vertical seismic profile's (VSP's) shot with a large source offset, rays from shot to receiver can have large angles of incidence. Shear waves generated by the source and by conversions at interfaces are likely to be recorded by both the vertical and the horizontal geophones. Varying angles of incidence may give strong variations in the recorded amplitudes. Separation of P- and SV-waves and recovery of their full amplitudes are important for proper processing and interpretation of the data. A P-S separation filter for three-component offset VSP data is presented which performs this operation. The separation filter is applied in the k-f domain and needs an estimate of the P- and S-velocities along the borehole as input. Implementation and stability aspects of the filter are considered. The filter was tested on an 1800 m offset VSP and appeared to be robust. Large velocity variations along the borehole could be handled and results were superior to those obtained by velocity filtering.     

Shear Wave Splitting Analysis to Estimate Fracture Orientation and Frequency Dependent Anisotropy

Shear wave splitting is a well-known method for indication of orientation, radius, and length of fractures in subsurface layers. In this paper, a three component near offset VSP data acquired from a fractured sandstone reservoir in southern part of Iran was used to analyse shear wave splitting and frequency-dependent anisotropy assessment. Polarization angle obtained by performing rotation on radial and transverse components of VSP data was used to determine the direction of polarization of fast shear wave which corresponds to direction of fractures. It was shown that correct implementation of shear wave splitting analysis can be used for determination of fracture direction. During frequencydependent anisotropy analysis, it was found that the time delays in shearwaves decrease as the frequency increases. It was clearly demonstrated throughout this study that anisotropy may have an inverse relationship with frequency. The analysis presented in this paper complements the studied conducted by other researchers in this field of research.     

A shear experiment over the Natih field in Oman: pilot seismic and borehole data

An experimental multicomponent three-dimensional (3D) seismic survey has been carried out over the Natih field in Oman. This paper describes the small-scale two-dimensional experiment carried out beforehand, and how the results obtained from this pilot were used to assess the feasibility of a nine-component three-dimensional (9C3D) operation as well as to determine the field parameters for the field-scale 3D survey. It also describes the two VSPs and a wireline shear log, acquired in conjunction with the pilot experiment, and the importance of such borehole data for establishing the correct time-to-depth relationship for the seismic data and for providing an independent check on the seismic interpretation. The observation of cusps in the offset VSP indicated the strong anisotropy of the Fiqa shales overlying the Natih reservoir.     

Nonlinear ray perturbation theory with its applications to ray tracing and inversion in anisotropic media

A comprehensive approach, based on the general nonlinear ray perturbation theory (Druzhinin, 1991), is proposed for both a fast and accurate uniform asymptotic solution of forward and inverse kinematic problems in anisotropic media. It has been developed to modify the standard ray linearization procedures when they become inconsistent, by providing a predictable truncation error of ray perturbation series. The theoretical background consists in a set of recurrent expressions for the perturbations of all orders for calculating approximately the body wave phase and group velocities, polarization, travel times, ray trajectories, paraxial rays and also the slowness vectors or reflected/transmitted waves in terms of elastic tensor perturbations. We assume that any elastic medium can be used as an unperturbed medium. A total 2-D numerical testing of these expressions has been established within the transverse isotropy to verify the accuracy and convergence of perturbation series when the elastic constants are perturbed. Seismological applications to determine crack-induced anisotropy parameters on VSP travel times for the different wave types in homogeneous and horizontally layered, transversally isotropic and orthorhombic structures are also presented. A number of numerical tests shows that this method is in general stable with respect to the choice of the reference model and the errors in the input data. A proof of uniqueness is provided by an interactive analysis of the sensitivity functions, which are also used for choosing optimum source/receiver locations. Finally, software has been developed for a desktop computer and applied to interpreting specific real VSP observations as well as explaining the results of physical modelling for a 3-D crack model with the estimation of crack parameters.     

P-wave Tomography in Inhomogeneous Orthorhombic Media

— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry.     

Approximate Relation Between the Ray Vector and the Wave Normal in Weakly Anisotropic Media

Determination of the ray vector (the unit vector specifying the direction of the group velocity vector) corresponding to a given wave normal (the unit vector parallel to the phase velocity vector or slowness vector) in an arbitrary anisotropic medium can be performed using the exact formula following from the ray tracing equations. The determination of the wave normal from the ray vector is, generally, a more complicated task, which is usually solved iteratively. We present a first-order perturbation formula for the approximate determination of the ray vector from a given wave normal and vice versa. The formula is applicable to qP as well as qS waves in directions, in which the waves can be dealt with separately (i.e. outside singular directions of qS waves). Performance of the approximate formulae is illustrated on models of transversely isotropic and orthorhombic symmetry. We show that the formula for the determination of the ray vector from the wave normal yields rather accurate results even for strong anisotropy. The formula for the determination of the wave normal from the ray vector works reasonably well in directions, in which the considered waves have convex slowness surfaces. Otherwise, it can yield, especially for stronger anisotropy, rather distorted results.     

Interpreting non-orthogonal split shear waves for seismic anisotropy in multicomponent VSPS

There are two main sources of non-orthogonality in multicomponent shear-wave seismics: inherent non-orthogonal split shear waves arising from substantial ray deviation in off-symmetry planes due to strong anisotropy or complex overburden, and apparent non-orthogonal split shear waves in the horizontal plane due to variation of the angle of incidence even if the two shear waves along the raypath are orthogonal. Many techniques for processing shear-wave splitting in VSP data ignore these kinds of non-orthogonality of the split shear waves. Assuming inherent non-orthogonality in zero-offset VSPs, and apparent non-orthogonality in offset VSPs, we derive equations for the four-component data matrix. These can be solved by extending the linear-transform technique (LTT) to determine the shear-wave polarizations in zero-offset and offset VSPs. Both full-wave synthetic and field data are used to evaluate the technique and to examine the effects of non-orthogonal polarized split shear waves. If orthogonality is incorrectly assumed, errors in polarization measurements increase with the degree of non-orthogonality, which introduces a consistent decreasing trend in the polarization measurements. However, the effect of non-orthogonality on the estimation of geophone orientation and time delays of the two split shear waves is small and negligible in most realistic cases. Furthermore, for most cases of weak anisotropy (less than 5% shear-wave anisotropy) apparent non-orthogonality is more significant than inherent non-orthogonality. Nevertheless, for strong anisotropy (more than 10% shear-wave anisotropy) with complicated structure (tilted or inclined symmetry axis), inherent non-orthogonality may no longer be negligible. Applications to both synthetic and real data show that the extended linear-transform techniques permit accurate recovery of polarization measurements in the presence of both significant inherent and apparent non-orthogonality where orthogonal techniques often fail.     

Weak Contrast PP Wave Displacement R/T Coefficients in Weakly Anisotropic Elastic Media

—Approximate PP plane wave displacement coefficients of reflection and transmission for weak contrast interfaces separating weakly but arbitrarily anisotropic elastic media are presented. The PP reflection coefficient for such an interface has been derived recently by Vavry?uk and P?en?ík (1997). The PP transmission coefficient presented in this paper was derived by the same approach. The coefficients are given as a sum of the coefficient for the weak contrast interface separating two nearby isotropic media and a term depending linearly on contrasts of the so-called weak anisotropy (WA) parameters (parameters specifying deviation of properties of the medium from isotropy), across the interface. While the reflection coefficient depends only on 8 of the complete set of the WA parameters describing P-wave phase velocity in weakly anisotropic media, the transmission coefficient depends on their complete set. The PP reflection coefficient depends on "shear-wave splitting parameter" γ. Tests of accuracy of the approximate formulae are presented on several models.     

Traveltime inversion and error analysis for layered anisotropy

While tilted transverse isotropy (TTI) is a good approximation of the velocity structure for many dipping and fractured strata, it is still challenging to estimate anisotropic depth models even when the tilted angle is known. With the assumption of weak anisotropy, we present a TTI traveltime inversion approach for models consisting of several thickness-varying layers where the anisotropic parameters are constant for each layer. For each model layer the inversion variables consist of the anisotropic parameters ε and δ, the tilted angle φ of its symmetry axis, layer velocity along the symmetry axis, and thickness variation of the layer. Using this method and synthetic data, we evaluate the effects of errors in some of the model parameters on the inverted values of the other parameters in crosswell and Vertical Seismic Profile (VSP) acquisition geometry. The analyses show that the errors in the layer symmetry axes sensitively affect the inverted values of other parameters, especially δ. However, the impact of errors in δ on the inversion of other parameters is much less than the impact on δ from the errors in other parameters. Hence, a practical strategy is first to invert for the most error-tolerant parameter layer velocity, then progressively invert for ε in crosswell geometry or δ in VSP geometry.