NATURAL SMOOTHNESS CONSTRAINTS IN CROSS-HOLE SEISMIC TOMOGRAPHY1

Tomographic inversion problems are ill-posed and therefore solutions must be either damped or regularized to produce results that are geologically reasonable. We introduce a priori information in terms of parameter covariances to constrain the solution. We use slowness logs to determine the appropriate parameter covariances for the inversion of traveltime data collected for a cross-hole geometry. We find that the logs exhibit power spectra proportional to a power α of the frequency. The value of α controls the smoothness of the inversion solution. For α < 0, the solution smoothness is maximized. Thus, knowing the correct value of α, which can be found from well logs, we can specify the appropriate amount of smoothing, rather than using some arbitrary level. Inversions were carried out on synthetic data for the case of α= 0 and α=?1. The use of α= 0 implies uncorrelated model parameters and is equivalent to standard damped least-squares methods. We find that solutions for α= 0 show greater complexity than for α=?1 but this level of resolution can be illusory. An example from the Midale field, Saskatchewan, Canada, is inverted using both α= 0 and α=?2, given by the observed parameter covariances. The solution for α= 0 exhibits spurious detail which must be smoothed away. For α=?2, the solution smoothness is maximized and we recover only that structure which is required to fit the data.     

RESOLUTION OF RESISTIVITY TOMOGRAPHY INFERRED FROM NUMERICAL SIMULATION1

Some factors affecting the resolution and accuracy of resistivity tomography are examined using numerical simulation. The inversion method used is based on smoothness-constrained least-squares and finite-element methods. An appropriate block discretization is obtained by dividing the target region into square blocks of size equal to half the minimum electrode spacing. While the effect of the damping factor on the resolution is significant, the resolution is not very sensitive to Gaussian noise as long as the damping factor is properly chosen, according to the noise level. The issue of choosing an optimum electrode array should be considered at the planning stage of a survey. When the instrumental accuracy is high, the dipole-dipole array is more suitable for resolving complex structures than the pole-pole array. The pole-dipole array gives somewhat less resolution than the dipole-dipole array but yields greater signal strength; thus, the pole-dipole array may be a good compromise between resolution and signal strength. The effect of an inhomogeneity located outside the target region may be very small if block discretization is done so as to represent the resistivity variations in both the target and outside regions.     

SYNTHETIC APERTURE RADAR:A NEW APPLICATION FOR WAVE EQUATION TECHNIQUES1

The techniques of downward continuation and imaging invented for seismic waves can be applied to other types of waves. We show how they can be applied to electromagnetic surveys conducted with Synthetic Aperture Radar (SAR). The algorithms used closely follow those used for seismic waves. Differences are induced by alternate wavelengths, wave velocities, distances between sources and reflectors, etc. We analyse in detail a survey carried out using a satellite; difficulties arise from because the orbit of the satellite cannot be approximated by a simple straight line if the spatial resolution of the survey is high. We determine appropriate techniques for the correction of the distortion induced by the latter and we delimit the resolution of the observed data, as seen from a satellite. Finally we show examples of the application of the technique of seismic migration to satellite data that were irradiated to Earth during the short but productive life of Seasat .     

TOMOGRAPHIC INVERSION OF NORMALIZED DATA: DOUBLE-TRACE TOMOGRAPHY ALGORITHMS1

Tomography is widely used in geophysics as a technique for imaging geological structures by means of data that are line integrals of physical characteristics. In some transmission measurements, due to various kinds of normalization, the measured data are related to two (the current and the reference) raypaths and can be expressed as a function of differences between line integrals. This is the case, for example, in seismo-acoustic emission measurements, when (since the exact start time is unknown) only the differences between traveltimes (differences between line integrals of the slowness) can be determined. Similarly the use of normalized Fourier amplitudes results in data dependent upon the difference between line integrals of the absorption coefficient (computed along the actual and the reference raypaths). In order to invert these data the ordinary tomography algorithms should be modified. Some generalizations are presented for series expansion tomography methods in order to make them applicable to reconstruction problems in which the input data are differences between two line integrals. The conjugate gradient and the simultaneous iterative reconstruction technique (SIRT) methods were adapted and tested. It is shown that the modified tomography algorithms are stable and sufficiently accurate for practical use. In the reconstruction of noise-free difference data, the conjugate gradient algorithm is found to be faster and more accurate while, in the case of noisy difference data, the modified SIRT algorithm is more stable and insensitive to noise.     

P波偏振层析成像

论述了Ｐ波偏振层析成像方法。这是一个利用Ｐ波远震偏振资料去反演速度结构的方法,与走时层析成像相比,它有几个显著的优点：不受震源定位和发震时刻误差的影响;对深地幔速度结构不敏感而对接收器附近的速度结构和速度梯度最敏感,在这一意义上它与时反演是互补的。如果联合使用走时和偏振资料可以改善层析成像的结果。走时的变化对应于速度的变化,而偏振的变化则与速度梯度的变化相对应,因昆,要确定速度异常的边界,用偏振数     

ANISOTROPIC TRAVELTIME TOMOGRAPHY

Velocity estimation technique using seismic data is often based on time/distance equations which are independent of direction, and even though we now know that many rocks are quite anisotropic, useful results have been obtained over the years from these isotropic estimates. Nevertheless, if velocities are significantly direction-dependent, then the isotropic assumption may lead to serious structural interpretation errors. Additionally, information on angle-dependence may lead to a better understanding of the lithology of the rocks under measurement. VSP and cross-well data may each lack the necessary aperture to estimate more than two velocity parameters for each wave type, and if the data straddle a symmetry axis, then these may be usefully chosen to be the direct velocities (from time-and-distance measurements along the axis) and NMO velocities (from differential time-offset measurements). These sets of two parameters define ellipses, and provide intermediate models for the variation of velocity with angle which can later be assembled and translated into estimates of the elastic moduli of the rocks under scrutiny. If the aperture of the measurements is large enough e.g. we have access to both VSP and cross-well data, we divide the procedure into two independent steps, first fitting best ellipses around one symmetry axis and then fitting another set around the orthogonal axis. These sets of four elliptical parameters are then combined into a new, double elliptical approximation. This approximation keeps the useful properties of elliptical anisotropy, in particular the simple relation between group and phase velocities which simplifies the route from the traveltimes measurements to the elastic constants of the medium. The inversion proposed in this paper is a simple extension of well-known isotropic schemes and it is conceptually identical for all wave types. Examples are shown to illustrate the application of the technique to cross-well synthetic and field P-wave data. The examples demonstrate three important points: (a) When velocity anisotropy is estimated by iterative techniques such as conjugate gradients, early termination of the iterations may produce artificial anisotropy. (b) Different components of the velocity are subject to different type of artifacts because of differences in ray coverage, (c) Even though most rocks do not have elliptical dispersion relations, our elliptical schemes represent a useful intermediate step in the full characterization of the elastic properties.     

STOCHASTIC INVERSION BY RAY CONTINUATION: APPLICATION TO SEISMIC TOMOGRAPHY1

The conventional tomographic inversion consists in minimizing residuals between measured and modelled traveltimes. The process tends to be unstable and some additional constraints are required to stabilize it. The stochastic formulation generalizes the technique and sets it on firmer theoretical bases. The Stochastic Inversion by Ray Continuation (Sirc ) is a probabilistic approach, which takes a priori geological information into account and uses probability distributions to characterize data correlations and errors. It makes it possible to tie uncertainties to the results. The estimated parameters are interval velocities and B -spline coefficients used to represent smoothed interfaces. Ray tracing is done by a continuation technique between source and receivers. The ray coordinates are computed from one path to the next by solving a linear system derived from Fermat's principle. The main advantages are fast computations, accurate traveltimes and derivatives. The seismic traces are gathered in CMPs. For a particular CMP, several reflecting elements are characterized by their time gradient measured on the stacked section, and related to a mean emergence direction. The program capabilities are tested on a synthetic example as well as on a field example. The strategy consists in inverting the parameters for one layer, then for the next one down. An inversion step is divided in two parts. First the parameters for the layer concerned are inverted, while the parameters for the upper layers remain fixed. Then all the parameters are reinverted. The velocity-depth section computed by the program together with the corresponding errors can be used directly for the interpretation, as an initial model for depth migration or for the complete inversion program under development.     

四川地区的地震层析成像

由四川地震台网的P波数据所进行的层析成像研究得到了该区地壳及上地幔速度图像的新信息(结果表明:1.20^-km深度处的速度图像与地表构造特征密切有关,反映了地壳的岩性分布,呈现为断块结构;龙门山、鲜水河主要断裂及南北构造带和四川盆地清晰地成像在图上.一直被认为是隐伏存在的华蓥山断裂则鲜明地展现在20-85km深度的速度图像上.2.50±km深度处的速度图像则反映了该区的莫霍面深度明显起伏;四川盆地、徽（县）成（县）盆地和汉中盆地的地壳厚度小于50km,上地幔顶部速度约8.1km/s.龙门山以104°E为界,北段地壳厚度与四川盆地一样,中南段与川西相近.康滇地轴为四川地区地壳由东向西增厚的过渡地带.3.岩石层厚度显著变化,扬子准地台为比较活动的褶皱区,具有较厚的岩石层.4.速度结构与地震活动性存在一定的联系,该区1930年以来M≥6.0的强震震中在20^-km深度（上地壳）上的投影大都分布在速度梯度带上,成条带分布.考虑到强震的余震区大都偏高速体一侧,似乎表明,高速体有高于周围介质的剪切强度,它可能起沿断裂带凹凸体的作用.强震震中在50⁺km深度（上地幔顶部）上的投影几乎都分布在低速区及其边缘,那里壳幔间速度呈过渡关系,是软流层顶部较浅地区.     

四川地区的地震层析成像

由四川地震台网的P波数据所进行的层析成像研究得到了该区地壳及上地幔速度图像的新信息(结果表明:1.20-km深度处的速度图像与地表构造特征密切有关,反映了地壳的岩性分布,呈现为断块结构;龙门山、鲜水河主要断裂及南北构造带和四川盆地清晰地成像在图上.一直被认为是隐伏存在的华蓥山断裂则鲜明地展现在20—85km深度的速度图像上.2.50±km深度处的速度图像则反映了该区的莫霍面深度明显起伏;四川盆地、徽（县）成（县）盆地和汉中盆地的地壳厚度小于50km,上地幔顶部速度约8.1km/s.龙门山以104°E为界,北段地壳厚度与四川盆地一样,中南段与川西相近.康滇地轴为四川地区地壳由东向西增厚的过渡地带.3.岩石层厚度显著变化,扬子准地台为比较活动的褶皱区,具有较厚的岩石层.4.速度结构与地震活动性存在一定的联系,该区1930年以来M≥6.0的强震震中在20-km深度（上地壳）上的投影大都分布在速度梯度带上,成条带分布.考虑到强震的余震区大都偏高速体一侧,似乎表明,高速体有高于周围介质的剪切强度,它可能起沿断裂带凹凸体的作用.强震震中在50+km深度（上地幔顶部）上的投影几乎都分布在低速区及其边缘,那里壳幔间速度呈过渡关系,是软流层顶部较浅地区.     

地震层析成像软件

GABWIT是应用地震体波走时资料、遗传算法反演地壳三维速度结构的软件,本介绍了该地震层析成像软件的主要功能以及技术特点,软件界面友好,功能齐全,适用性强,易于推广。     

STUDY OF TRAVELTIME AND AMPLITUDE TIME-LAPSE TOMOGRAPHY USING PHYSICAL MODEL DATA1

In seismic tomography the observed traveltimes or amplitudes of direct waves are inverted to obtain an estimate of seismic velocity or absorption of the section surveyed. There has been much recent interest in using cross-well traveltime tomography to observe the progress of fluids injected into the reservoir rocks during enhanced oil recovery (EOR) processes. If repeated surveys are carried out, then EOR processes may be monitored over a period of time. This paper describes the results of a simulated time-lapse tomography experiment to image the flood zone in an EOR process. Two physical models were made out of epoxy resins to simulate an essentially plane-layered sedimentary sequence containing a reservoir layer and simple geological structure. The models differed only in the reservoir layer, which was uniform in the ‘pre-flood’ model and contained a flood zone of known geometry in the ‘post-flood’ model. Data sets were acquired from each model using a cross-well survey geometry. Traveltime and amplitude tomographic imaging techniques have been applied to these data in an attempt to locate the extent of the flood zone. Traveltime tomography locates the flood zone quite accurately. Amplitude tomography shows the flood zone as a region of higher absorption, but does not image its boundaries as precisely. This is primarily because of multipathing and diffraction effects, which are not accounted for by the ray-based techniques for inverting seismic amplitudes. Nevertheless, absorption tomograms could complement velocity tomograms in real, heterogeneous reservoirs because absorption and velocity respond differently to changes in liquid/gas saturations for reservoir rocks.     

论华北地区的均衡状态(一)——方法和局部补偿

根据经典均衡的原理,本文重点分析了五种局部均衡补偿模式.在计算方法上利用频域三维重力场的理论公式,快速求得均衡校正值,据此计算了66个模型的均衡重力异常场,注意到对这许多不同参量的模型而言,它们的均衡异常场在形态与分布特征上基本一致,其中计入了地表和上下地壳密度差异分布的 Airy 模型具有最佳的补偿效果,它的均衡面在莫霍界面以下的上地幔中,标准深度50km.从整体上看,华北地台处于亚均衡状态,均衡异常的均值为1810-5m/s2.均衡重力异常的分布表现出明显的块体特征,正均衡异常区主要分布在东部胶辽地块和冀中平原北缘,在汾渭裂谷区存在负异常.模型对比表明,以莫霍界面作为均衡补偿面的模型是不可取的;Airy 模型比 Pratt 模型的补偿效果略好,这同地壳构造以层状为主而侧向变化有限的特征相符.有关复合补偿、均衡重力异常的基本特征和深部构造的关系等结果,将在文章的第二部分发表.      

VELOCITY ANALYSIS FOR WIDE APERTURE SEISMIC DATA*

Common midpoint data are now being collected with ever increasing source-receiver offsets. For wide aperture seismic data classical methods of interpretation fail, since velocity analyses and signal-to-noise enhancement methods based on hyperbolic traveltime curves are no longer appropriate. Therefore, the goals of increased velocity resolution and signal enhancement, which motivate the increase in offset, are not achieved. Approximate methods, involving higher order traveltime curves or extrapolations, have been developed for velocity analysis but these are ineffective in the presence of refracted arrivals, and lack a physical basis. These problems can be minimized by transforming the observational data to the domain of intercept or vertical delay time τ and horizontal ray parameter p. In this domain headwave refractions are collapsed into points and both near vertical and wide angle reflections can be analyzed simultaneously to derive velocity-depth information, even in the presence of velocity gradients or low velocity zones.     

采用射线寻迹的井间层析成像

本文采用二维井间观测走时反演地震波速,用迭代射线寻迹走时成像方法进行层析成像.作者导出三次多项式插值基函数计算离散网格内的折射率分布,还给出了具有自己特点的二步扫描法,不但加快了正演计算时间,同时方便地建立走时残差与模型修正量的关系.考虑到实际应用时,震源与接收器常不位于同一平面,为此进行了校正,并给出了校正方法,提高了重建精度. 数值的与实际应用的结果表明,本文给出的层析成像算法是快速的、稳定的、适用的.     

采用射线寻迹的井间层析成像

本文采用二维井间观测走时反演地震波速,用迭代射线寻迹走时成像方法进行层析成像.作者导出三次多项式插值基函数计算离散网格内的折射率分布,还给出了具有自己特点的二步扫描法,不但加快了正演计算时间,同时方便地建立走时残差与模型修正量的关系.考虑到实际应用时,震源与接收器常不位于同一平面,为此进行了校正,并给出了校正方法,提高了重建精度. 数值的与实际应用的结果表明,本文给出的层析成像算法是快速的、稳定的、适用的.     

地震面波频散的层析成像

本文较详细地介绍了群速度频散测定的多重滤波法,以及ＬＳＱＲ反演方法运用于网格频散反演和地球内部结构反演的地震面波频散的层析成像方法。给出了计算程序框图及数值模拟结果     

采用射线寻迹的井间层析成像

本文采用二维井间观测走时反演地震波速,用迭代射线寻迹走时成像方法进行层析成像.作者导出三次多项式插值基函数计算离散网格内的折射率分布,还给出了具有自己特点的二步扫描法,不但加快了正演计算时间,同时方便地建立走时残差与模型修正量的关系.考虑到实际应用时,震源与接收器常不位于同一平面,为此进行了校正,并给出了校正方法,提高了重建精度. 数值的与实际应用的结果表明,本文给出的层析成像算法是快速的、稳定的、适用的.     

地震监测中的电阻率层析技术

将电阻率层析技术应用于地震监测,由视电阻率值重建出介质的真电阻率图像,取得了较好效果.在宝坻台和昌黎台设立的两个试验点上于1998年4月14日ML5.0和ML4.4唐山两次地震前的6天左右层析图像出现了明显的异常变化:宝坻台的电阻率图像一改通常的在平稳背景上叠加小量随机变化的特点,出现了一种有序性特征的新图样;昌黎台也出现了反差加大、高低阻区集中分布的有序性特征.上述异常图样均在震后消失.层析图像在震前出现的熵值降低可能是这次地震活动的前兆.地层导电结构和孔隙度的变化,是引起电阻率异常的直接原因.研究表明,常规的单一极距的视电阻率测量之所以对真电阻率的变化不敏感且丧失空间分辨能力,是由于该物理量同时具有积分值和位函数这两个固有特征所决定的.在地震监测中,改造现行观测系统,引入层析成像,是发展技术的方向.     

地震监测中的电阻率层析技术

将电阻率层析技术应用于地震监测,由视电阻率值重建出介质的真电阻率图像,取得了较好效果.在宝坻台和昌黎台设立的两个试验点上于1998年4月14日ML5.0和ML4.4唐山两次地震前的6天左右层析图像出现了明显的异常变化:宝坻台的电阻率图像一改通常的在平稳背景上叠加小量随机变化的特点,出现了一种有序性特征的新图样;昌黎台也出现了反差加大、高低阻区集中分布的有序性特征.上述异常图样均在震后消失.层析图像在震前出现的熵值降低可能是这次地震活动的前兆.地层导电结构和孔隙度的变化,是引起电阻率异常的直接原因.研究表明,常规的单一极距的视电阻率测量之所以对真电阻率的变化不敏感且丧失空间分辨能力,是由于该物理量同时具有积分值和位函数这两个固有特征所决定的.在地震监测中,改造现行观测系统,引入层析成像,是发展技术的方向.     

地震层析成像研究方法综述

国际上对地震层析成像的研究始于上世纪70年代末,经过30多年的发展,地震层析成像方法逐渐成熟,并越来越广泛地被运用到地球物理各个领域中.以地震层析成像方法的发展作为主线,主要介绍了地震层析成像方法和所用地震数据的发展.