PARABOLIC AND HYPERBOLIC PARAXIAL TWO-POINT TRAVELTIMES IN 3D MEDIA1

The 4 × 4 T -propagator matrix of a 3D central ray determines, among other important seismic quantities, second-order (parabolic or hyperbolic) two-point traveltime approximations of certain paraxial rays in the vicinity of the known central ray through a 3D medium consisting of inhomogeneous isotropic velocity layers. These rays result from perturbing the start and endpoints of the central ray on smoothly curved anterior and posterior surfaces. The perturbation of each ray endpoint is described only by a two-component vector. Here, we provide parabolic and hyperbolic paraxial two-point traveltime approximations using the T -propagator to feature a number of useful 3D seismic models, putting particular emphasis on expressing the traveltimes for paraxial primary reflected rays in terms of hyperbolic approximations. These are of use in solving several forward and inverse seismic problems. Our results simplify those in which the perturbation of the ray endpoints upon a curved interface is described by a three-component vector. In order to emphasize the importance of the hyperbolic expression, we show that the hyperbolic paraxial-ray traveltime (in terms of four independent variables) is exact for the case of a primary ray reflected from a planar dipping interface below a homogeneous velocity medium.     

A three-dimensional model of the Baltic Shield crust from data of deep seismic studies

A 3-D velocity structure of the crust has been constructed for almost the entire Baltic Shield area from data of extensive deep seismic studies on the shield. The construction involved a revision of all primary data (record sections and observed traveltime curves) obtained in this region over 50 years of research. Comparative analysis of wave fields revealed that three reference reflectors traceable throughout the shield area are K1 (a boundary velocity of 6.4–6.5 km/s), K2 (～6.8 km/s), and the mantle surface M (8.0–8.2 km/s). The resulting 3-D velocity structure is represented in the form of structural maps of these surfaces and a velocity distribution scheme in the upper crust. Using this general basic model, seismic cross sections are constructed by means of mathematical modeling along all profiles. They showed that, in addition to the main layers and reflectors above the K1 boundary, a lower velocity layer is traceable almost everywhere and the majority of deep faults flatten out toward this layer. On the whole, lateral variations in the velocity structure of the crust are small up to a depth of 40 km. The variations are most significant in the M topography: its average depth being 40–45 km, two deep (down to 50–60 km) depressions exist in southern Finland and the Baltic region. The origin of this depression filled with high velocity (7.2–7.4 km/s) rocks remains unclear.     

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。     

DETERMINATION OF LATERAL INHOMOGENEITIES IN REFLECTION SEISMICS BY INVERSION OF TRAVELTIME RESIDUALS*

Lateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed. The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account. In this paper the method and its application to data obtained with two-dimensional models are described.     

台湾西南海域地震数据处理及天然气水合物地震属性

对台湾西南海域增生楔部位长排列多道地震数据进行地震成像、速度分析、AVO分析、AVO反演处理,获得了天然气水合物多属性地震特征.在偏移剖面上,BSR与海底近似平行,极性与海底相反,穿越沉积层.AVO分析显示,强BSR振幅部位,BSR振幅随偏移距增大而增大.精细速度分析表明强BSR振幅下方存在纵波低速层.对应于强BSR振幅部位,AVO反演的P波、G波为相对高负值区,位于P、G交会图的第三象限,该部位泊松比变化率为负值,横波反射系数接近于零.以上多属性地震特征均预示着该区域可能存在天然气水合物层,且天然气水合物层下方可能存在游离甲烷气层.     

COMPUTING FIELD STATICS WITH THE HELP OF SEISMIC TOMOGRAPHY*

Field static corrections in general need be applied to all onshore seismic reflection data to eliminate the disturbing effects a weathering layer or near-surface low velocity zone has on the continuity of deep seismic reflections. The traveltimes of waves refracted at the bottom of the low velocity zone (or intermediate refracting interfaces) can often be observed as first breaks on shot records and used to develop a laterally inhomogeneous velocity model for this layer, from which the field static corrections can then be obtained. A simple method is described for computing accurate field statics from first breaks. It is based on a linearization principal for traveltimes and leads to the algorithms that are widely and successfully applied within the framework of seismic tomography. We refine an initial model for the low velocity layer (estimated by a standard traveltime inversion technique) by minimizing the errors between the observed first arrivals on field records and those computed by ray theory through an initial model of the low velocity layer. Thus, one can include more lateral velocity variations within the low velocity layers, which are important to obtain good field static corrections. Traditional first break traveltime inversion methods cannot, in general, provide such refined velocity values. The technique is successfully applied to seismic data from the Amazon Basin. It is based on a simple model for the low velocity layer that consists of an undulating earth surface and one planar horizontal refractor overlain by a laterally changing velocity field.     

The influence of sea water velocity variation on seismic traveltimes, ray paths, and amplitude

The main factors affecting seismic exploration is the propagation velocity of seismic waves in the medium. In the past, during marine seismic data processing, the propagation velocity of sea water was generally taken as a constant 1500 m/s. However, for deep water exploration, the sound velocity varies with the season, time, location, water depth, ocean currents, and etc.. It also results in a layered velocity distribution, so there is a difference of seismic traveltime, ray paths, and amplitude, which affect the migration imaging results if sea water propagation velocity is still taken as constant for the propagation wavefield. In this paper, we will start from an empirical equation of seismic wave velocity in seawater with changes of temperature, salinity, and depth, consider the variation of their values, build a seawater velocity model, and quantitatively analyze the impact of seawater velocity variation on seismic traveltime, ray paths, and amplitude in the seawater velocity model.     

鄂尔多斯盆地上地壳速度分布与沉积建造和结晶基底起伏的构造研究

基于在鄂尔多斯盆地与其北部造山带地域,即沿延川—包头—满都拉地带进行的地震宽角反射和折射波场探测,取得了高分辨率的Pg波震相.通过走时差分层析成像方法进行Pg波波场走时反演,给出了沿剖面辖区的上地壳速度分布,求得了沉积建造和结晶基底折射界面的起伏变化,并给予了解释.研究结果表明,鄂尔多斯盆地上地壳为双层结构,上下层之间存在明显的折射界面,上层速度低,纵向变化梯度大;下层速度高,变化较为均匀.基于沿剖面辖区上地壳的速度分布特征提出自南向北应分为：榆林南凹陷、榆林—刀兔隆起、刀兔北至鄂尔多斯北缘断裂为箕形凹陷及其内部的次级构造、呼包凹陷以及伴随的断裂等沉积建造和结晶基底的起伏变化.阴山造山带上地壳速度明显比两侧地区高,速度呈纵向条带状展布,故呈现出结晶基底结构的分布特征和乌拉山、色尔腾山、和教岩体及白云鄂博群陆壳拼合及增生现象.内蒙造山带上地壳亦为双层结构,但基底折射界面不如鄂尔多斯块体明显.本文基于对该区沉积建造和结晶基底的起伏,讨论了沿剖面各有关凹陷的沉积特征与油气前景.     

Influence of background heterogeneity on traveltime shifts for compacting reservoirs

Compaction induced by pore‐pressure decrease inside a reservoir can be monitored by measuring traveltime shifts of reflection events on time‐lapse seismic data. Recently we introduced a perturbation‐based formalism to describe traveltime shifts caused by the 3D stress‐induced velocity field around a compacting reservoir. Application of this method to homogeneous background models showed that the offset variation of traveltime shifts is controlled primarily by the anisotropic velocity perturbations and can provide valuable information about the shear and deviatoric stresses. Here, we model and analyse traveltime shifts for compacting reservoirs whose elastic properties are different from those of the surrounding medium. For such models, the excess stress is influenced primarily by the contrast in the rigidity modulus μ across the reservoir boundaries. Synthetic examples demonstrate that a significant (25% or more) contrast in μ enhances the isotropic velocity perturbations outside the reservoir. Nevertheless, the influence of background heterogeneity is mostly confined to the reservoir and its immediate vicinity and the anisotropic velocity changes are still largely responsible for the offset dependence of traveltime shifts. If the reservoir is stiffer than the host rock, the background heterogeneity reduces anisotropic velocity perturbations inside the reservoir but increases them in the overburden. As a result, in this case, the magnitude of the offset variation of traveltime shifts is generally higher for reflections from interfaces above the reservoir. We also study compaction‐induced stress/strain and traveltime shifts for a stiff reservoir embedded in a softer layered model based on velocity profiles from the Valhall Field in the North Sea. Despite producing discontinuities in strain across medium interfaces, horizontal layering does not substantially alter the overall behaviour of traveltime shifts. The most pronounced offset variation of traveltime shifts is observed for overburden events recorded at common midpoints close to the reservoir edges. On the whole, prestack analysis of traveltime shifts should help better constrain compaction‐induced velocity perturbations in the presence of realistic background heterogeneity.     

2D inversion of refraction traveltime curves using homogeneous functions

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.     

起伏地形下的高精度反射波走时层析成像方法

全球造山带及中国大陆中西部普遍具有强烈起伏的地形条件.复杂地形条件下的地壳结构成像问题像一面旗帜引领了当前矿产资源勘探和地球动力学研究的一个重要方向.深地震测深记录中反射波的有效探测深度可达全地壳乃至上地幔顶部,而初至波通常仅能探测上地壳浅部.为克服和弥补初至波探测深度的不足,本文基于前人对复杂地形条件下初至波成像的已有研究成果,采用数学变换手段将笛卡尔坐标系的不规则模型映射到曲线坐标系的规则模型,并将快速扫描方法与分区多步技术相结合,发展了反射波走时计算和射线追踪的方法.进而利用反射波走时反演,实现起伏地形下高精度的速度结构成像,从而为起伏地形下利用反射波数据高精度重建全地壳速度结构提供了一种全新方案.数值算例从正演计算精度、反演中初始模型依赖性、反演精度、纵横向分辨率以及抗噪性等方面验证了算法的正确性和可靠性.     

干涉走时微地震震源定位方法

本文基于地震波场干涉原理,建立了干涉走时微地震震源定位方法.该方法将两个接收点相对于一个微地震事件的走时差(称为干涉走时)的扰动作为残差函数,通过迭代求解最小残差函数,最终获得震源的空间位置.干涉走时震源定位方法利用两个接收点的到时差消除发震时刻未知和速度模型误差的影响,简化了震源定位算法.数值计算表明,本文提出的干涉走时定位方法在速度模型有误差的情况下仍然可以获得准确的微地震震源定位.     

Sub-basalt imaging problems and the application of Artificial Neural Networks

In many areas of the world, the presence of shallow high velocity, highly heterogeneous layers complicate seismic imaging of deeper reflectors. Of particular economic interest are areas where potentially hydrocarbon-bearing strata are obscured by layers of basalt. Basalt layers are highly reflective and heterogeneous. Using reflection seismic, top basalt is typified by a high-amplitude, coherent reflector with poor resolution of reflectors below the basalt, and even bottom basalt. Here, we present a new approach to the imaging problem using the pattern recognition abilities of a back-propagation Artificial Neural Network (ANN). ANNs are computational systems that attempt to mimic natural biological neural networks. They have the ability to recognize patterns and develop their own generalizations about a given data set. Back-propagation neural networks are trained on data sets for which the solution is known and tested on the data that are not previously presented to the ANN in order to validate the network result. We show that Artificial Neural Networks, due to their pattern recognition capabilities, can invert the medium statistics based on the seismic character. We produce statistically defined models involving a basalt analogous layer, and calculate full wavefield finite difference synthetic seismograms. We vary basalt layer thickness and source frequency to generate a synthetic model that produces seismic that is similar to real sub-basalt seismic, i.e. high amplitude top basalt reflector and the absence of base basalt and sub-basalt events. Using synthetic shot gathers, generated in a synthetic representation of the sub-basalt case, we can invert the velocity medium standard deviation by using an ANN. By inverting the velocity medium standard deviation, we successfully identified the transition from basalt to sub-basalt on the synthetic shot gathers. We also show that ANNs are capable of identifying the basalt to sub-basalt transition in the presence of incoherent noise. This is important for any future applications of this technique to the real-world seismic data, as this data is never completely noise-free. There is always a certain level of residual (noise remaining after initial noise filtering) environmental/ambient noise present on the recorded seismics, hence, neural network training with noise-free synthetic seismic is less than optimal.     

VTI介质P波非双曲时差分析

具有垂直对称轴的横向各向同性介质模型(VTI)是目前各向异性理论研究和多波多分量地震资料叠前成像处理中最常用的一种各向异性模型.VTI介质中反射 P波时距曲线一般不再是双曲线.基于不同的相速度近似公式会得到不同的时距关系式.文中对几种典型的非双曲时距曲线与射线追踪得到的准确时距曲线在不同各向异性强度下进行了对比，结果表明Muir等和Stovas等提出的非双曲时距公式由于过高地考虑了横波垂直速度的影响与精确的时距曲线有很大偏差；Tsvankin等提出的弱各向异性非双曲时距公式在ε-δ<0时误差增大；Alkhalifah等提出的非双曲时距公式在大炮检距任意各向异性强度下都具有较高的精度，适于在实际资料处理中应用.     

海洋拖缆地震资料初至波走时层析反演

初至波走时层析反演技术作为建立近地表速度模型的重要手段,是解决陆地资料复杂静校正问题的关键技术。而折射波广泛发育的海洋地震资料,对折射波信息的关注与运用并没有得到广泛的重视。本文首次将层析反演方法应用于海洋拖缆地震数据的近海底速度模型的建立。本文方法与陆地资料层析反演的主要区别在于:①在震源信号的最小相位化处理后进行初至时间的拾取,避免了混合相位子波初至拾取不准带来的误差;②以海水深度与海水速度作为反演约束条件,减小了迭代误差。实测二维资料的层析反演结果表明,本文方法可反演出较为精确的海洋地层速度结构。      

Estimation of geological dip and reflector curvature from zero-offset seismic reflections in heterogeneous anisotropic media

Depth conversion of selected seismic reflections is a valuable procedure to position key reflectors in depth in a process of constructing or refining a depth-velocity model. The most widespread example of such procedure is the so-called map migration, in which normal-incidence, zero-offset (stacked) seismic data are employed. Since the late seventies and early eighties, under the assumption of an isotropic velocity model, map migration algorithms have been devised to convert traveltime and its first and second derivatives into reflector position, dip and curvatures in depth. In this work we revisit map migration to improve the existing algorithms in the following accounts: (a) We allow for fully anisotropic media; (b) In contrast to simple planar measurement surface, arbitrary topography is allowed, thus enlarging the algorithms applicability and (c) Derivations and results are much simplified upon the use of the methodology of surface-to-surface paraxial matrices.     

Depth migration anisotropy analysis in the time domain

In areas of complex geology such as the Canadian Foothills, the effects of anisotropy are apparent in seismic data and estimation of anisotropic parameters for use in seismic imaging is not a trivial task. Here we explore the applicability of common‐focus point (CFP)‐based velocity analysis to estimate anisotropic parameters for the variably tilted shale thrust sheet in the Canadian Foothills model. To avoid the inherent velocity‐depth ambiguity, we assume that the elastic properties of thrust‐sheet with respect to transverse isotropy symmetry axis are homogeneous, the reflector below the thrust‐sheet is flat, and that the anisotropy is weak. In our CFP approach to velocity analysis, for a poorly imaged reflection point, a traveltime residual is obtained as the time difference between the focusing operator for an assumed subsurface velocity model and the corresponding CFP response obtained from the reflection data. We assume that this residual is due to unknown values for anisotropy, and we perform an iterative linear inversion to obtain new model parameters that minimize the residuals. Migration of the data using parameters obtained from our inversion results in a correctly positioned and better focused reflector below the thrust sheet. For traveltime computation we use a brute force mapping scheme that takes into account weakly tilted transverse isotropy media. For inversion, the problem is set up as a generalized Newton's equation where traveltime error (differential time shift) is linearly dependent on the parameter updates. The iterative updates of parameters are obtained by a least‐squares solution of Newton's equations. The significance of this work lies in its applicability to areas where transverse isotropy layers are heterogeneous laterally, and where transverse isotropy layers are overlain by complex structures that preclude a moveout curve fitting.     

中美洲鹦鹉湾气旋涡的亚中尺度结构特征

海洋中普遍存在的涡旋对全球海洋热、盐通量有重要贡献.一条于2000年6月在中美洲鹦鹉湾采集的地震剖面L115捕获到了一个海水次表层透镜状反射结构.透镜状反射的宽度约150 km,厚度约500 m,深度从100 m延伸到约600 m,核心深约200 m.结合和地震采集时间近同步的再分析数据中的流速和海水温度数据以及计算的Rossby数和Okubo-Weiss参数,将其解释为气旋涡,且可能是亚中尺度相干涡(SCV).由于地震剖面并未穿过涡旋核心水,涡旋顶底与核心水外层水团的双扩散作用使得剖面上的气旋涡中心表现为上下相邻的强反射双核结构.同航次采集的与L115大致正交的其他几条地震剖面也捕捉到了这个气旋涡.这些剖面整体的反射特征一致性较好,但和L115差异较大,涡旋内部普遍表现为近水平的中等强度反射.涡旋上边界为倾斜的强反射,这是气旋涡的等温线上凸引起的,这里也是亚中尺度锋面的发育区.这些地震剖面的涡旋反射特征的差异表明了该气旋涡空间结构的不对称性和时间演化特征.     

各向异性TI介质qP反射波走时层析成像

地震走时层析成像是反演地层各向异性参数分布的有效方法,但是关于地震各向异性介质走时层析成像的研究并不多,其技术远远没有达到成熟的阶段.在野外数据采集时,地表反射波观测方式相对井间和垂直地震剖面观测方式的成本更低,利用qP反射波走时反演各向异性参数具有更加广泛的实用价值.本文实现的TI介质地震走时层析成像方法结合了TI介质反射波射线追踪算法、走时扰动方程和非线性共轭梯度算法,它可以对任意强度的TI介质模型进行反演,文中尝试利用qP反射波走时重建TI介质模型的参数图像.利用qP反射波对层状介质模型和块状异常体模型进行走时反演,由于qP波相速度对弹性模量参数和Thomsen参数的偏微分不同,所以可以分别反演弹性模量参数和Thomsen参数.数值模拟结果表明:利用qP反射波可以反演出TI介质模型的弹性模量参数与Thomsen参数,不同模型的走时迭代反演达到了较好的收敛效果,与各向同性介质走时反演结果相比较,各向异性介质走时反演结果具有较好的识别能力.     

DETECTION AND RESOLUTION OF THIN LAYERS: A MODEL SEISMIC STUDY1

The detection and resolution of a thin layer closely situated above a high-impedance basement are predominantly determined by both the frequency content of the incident seismic wavelet and the existence of the nearby high-impedance bedrock. The separation of the thin layer and the basement arrivals is investigated depending on the low-frequency content of the wavelet. The high-frequency content of the wavelet is kept constant. The initial wavelet spectrum with low frequencies has a rectangular shape. All wavelets used have zero-phase characteristics. Numerical and analogue seismic modelling techniques are used. The study is based on the geology of the Pachangchi Sandstone in West Taiwan. Firstly the resolution of a thin layer between two half-spaces is examined by applying the Ricker and De Voogd-Den Rooijen criteria. The lack of low-frequency components of the incident seismic wavelet reduces the shortest true two-way traveltime by about 20%. In addition, low-frequency components of the wavelet diminish the deviation between true and apparent two-way traveltime by about 65% for layer thicknesses in the transition from a thick to a thin layer. The second step deals with the influence of a high-impedance basement just below a thin layer on the detection and resolution of that thin layer. Reflected signal energies and apparent two-way traveltimes are considered. The reflected signal energy depends on the low-frequency content of the incident wavelet, the layer's thickness and the distance between the basement and the layer. This applies only to layers with thicknesses less than or equal to one-third of the mean wavelength in the layer, and a distance to basement in the range of one to one-half of the mean wavelength in the rock material between layer and basement. The minimum thin-layer thickness resolvable decreases with increasing distance to the basement; i.e. for a layer thickness of one-third of the mean wavelength in the layer the relative error of the two-way traveltime increases from 5% to 30%, if the distance is reduced from one to one-half of the mean wavelength in the material between the basement and the thin layer. Finally, a combination of vertical seismic profiling and downward-continuation techniques is presented as a preprocessing procedure to prepare realistic data for the detection and resolution investigation.