三维起伏地表条件下地震波走时计算的不等距迎风差分法

三维起伏地表条件下的地震波走时计算技术是研究三维起伏地表地区很多地震数据处理技术的基础性工具.为了获得适应于任意三维起伏地表且计算精度高的走时算法,提出三维不等距迎风差分法.该方法采用不等距网格剖分三维起伏地表模型,通过在迎风差分格式中引入不等距差分格式、Huygens原理及Fermat原理来建立地表附近的局部走时计算公式,并通过在窄带技术中设定新的网格节点类型来获得三维起伏地表条件下算法的整体实现步骤.精度及算例分析表明:三维不等距迎风差分法具有很高的计算精度且能够适应于任意三维起伏地表模型.     

一种用于走时层析成像的改进算法

走时层析成像是根据首波走时重建声波、地震波或电磁波波速的层析技术，其所用到的射线路径依赖于波速分布。本文提出了一个依据费马原理寻找射线路径的新方法。费马原理指出，从发射点到接点的射线首波的走时极小，因此寻找射线路径的问题是一个最优化问题。     

Geostatistical traveltime tomography in elliptically anisotropic media

In geological materials, anisotropy may arise due to different mechanisms and can be found at different scales. Neglecting anisotropy in traveltime tomographic reconstruction leads to artefacts that can obscure important subsurface features. In this paper, a geostatistical tomography algorithm to invert cross‐hole traveltime data in elliptically anisotropic media is presented. The advantages of geostatistical tomography are that the solution is regularized by the covariance of the model parameters, that known model parameters can be used as constraints and fitted exactly or within a prescribed variance and that stochastic simulations can be performed to appraise the variability of the solution space. The benefits of the algorithm to image anisotropic media are illustrated by two examples using synthetic georadar data and real seismic data. The first example confirms suspected electromagnetic anisotropy in the vadose zone caused by relatively rapid water content variations with respect to wavelength at georadar frequencies. The second presents how sonic log data can be used to constrain the inversion of cross‐well seismic data and how geostatistical simulations can be used to infer parameter uncertainty. Results of both examples show that considering anisotropy yields a better fit to the data at high ray angles and reduces reconstruction artefacts.     

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.     

Accounting for velocity anisotropy in seismic traveltime tomography: a case study from the investigation of the foundations of a Byzantine monumental building

We estimate velocity anisotropy factors from seismic traveltime tomographic data and apply a correction for anisotropy in the inversion procedure to test possible improvements on the traveltime fit and the quality of the resulting tomographic images. We applied the anisotropy correction on a traveltime data set obtained from the investigation of the foundation structure of a monumental building: a Byzantine church from the 11th century AD, in Athens, Greece. Vertical transverse isotropy is represented by one axis of symmetry and one anisotropy magnitude for the entire tomographic inversion grid. We choose the vertical direction for the symmetry axis by analysing the available data set and taking into account information on the character of the foundations of the church from the literature and past excavations. The anisotropy magnitude is determined by testing a series of values of anisotropy and examining their effect on the tomographic inversion results. The best traveltime fit and image quality are obtained with an anisotropy value (V_max/V_min) of 1.6, restricted to the high velocity structures in the subsurface. We believe that this anisotropy value, which is significantly higher than the usual values reported for near‐surface geological material, is related to the fabric of the church foundations, due to the shape of the individual stone blocks and the layout of the stonework. Inversion results obtained with the correction for anisotropy indicate that both the traveltime fit and the image quality are improved, providing an enhanced reconstruction of the velocity field, especially for the high‐velocity features. Based on this enhanced and more reliable reconstruction of velocity distribution, an improved image of the subsurface material character was made possible. In particular, the pattern and state of the church foundations and possible weak ground material areas were revealed more clearly. This improved subsurface knowledge may assist in a better design of restoration measures for monumental buildings such as Byzantine churches.     

First‐arrival traveltime tomography with modified total‐variation regularization

First‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L₂ total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.     

Amplitude Preserving Kirchhoff Migration: A Traveltime Based Strategy

Amplitude versus offset information is a key feature to seismic reservoir characterization. Therefore amplitude preserving migration was developed to obtain this information from seismic reflection data. For complex 3-D media, however, this process is computationally expensive. In this paper we present an efficient traveltime based strategy for amplitude preserving migration of the Kirchhoff type. Its foundations are the generation of traveltime tables using a wavefront-oriented ray-tracing technique, and a generalized moveout relation for 3-D heterogeneous media. All required quantities for the amplitude preserving migration are computed from coarsely gridded traveltime tables. The migration includes the interpolation from the coarsely gridded input traveltimes onto the fine migration grid, the computation of amplitude preserving weight functions, and, optionally, the evaluation of an optimized migration aperture. Since ray tracing is employed for the traveltime computation the input velocity model needs to be smooth, i.e. velocity variations of spatial dimensions below the wavelength of the considered reflection signals are removed. Numerical examples on simple generic models validate the technique and an application to the Marmousi model demonstrates its potential to complex media. The major advantage of the traveltime based strategy consists of its computational efficiency by maintaining sufficient accuracy. Considerable savings in storage space (10⁵ and more for 3-D data with respect to no interpolation at all) can be achieved. The computational time for the stack can be substantially reduced (up to 90% in 3-D) with the optimized migration aperture since only those traces are stacked which really contribute to the image point under consideration.     

On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis

The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi‐valued and the geometrical spreading correction factor tends to zero due to energy focusing. We analyse the conditions for the qSV‐wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV‐wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two‐layer vertical symmetry axis model.     

基于波射线路径偏移压制多次波

波射线路径压制多次波的反射波成像是在偏移过程去除多次波同时仅对反射波成像.通过在共炮道集和共检波点道集分别计算炮点射线的入射角和检波点射线的出射角计算射线的路径.从炮点入射的射线与从检波点出射的射线的交点形成的走时,若等于观测走时,可以判断此条射线是反射波;反之,若不相等,则是多次波.数值实验表明此方法可以有效地去掉由于多次波能量产生的假成像点和压制多次波,因此界面可以正确归位,同时去掉由于多次波引起的假成像位置.     

复杂地表条件下基于线性插值和窄带技术的地震波走时计算

为了在复杂地表条件下实现地震波走时计算,提出了一种基于线性插值和窄带技术的走时计算新方法.其中,线性插值用于局部走时计算,窄带技术用于局部波前捕获和追踪.为了逼近起伏地表,采用三角网和矩形网相结合的方法对速度模型进行剖分.为了得到局部走时计算公式,利用费马（Fermat）原理和关于入射点位置的限定条件.有关编程实践和数值试验表明：新方法不仅可以有效、灵活地处理地表高程的剧烈变化,而且还具有很好的适应性和稳定性,得到的计算结果满足波前传播规律.     

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.     

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.     

A new parameterization for generalized moveout approximation,based on three rays

A simple and accurate traveltime approximation is important in many applications in seismic data processing, inversion and modelling stages. Generalized moveout approximation is an explicit equation that approximates reflection traveltimes in general two-dimensional models. Definition of its five parameters can be done from properties of finite offset rays, for general models, or by explicit calculation from model properties, for specific models. Two versions of classical finite-offset parameterization for this approximation use traveltime and traveltime derivatives of two rays to define five parameters, which makes them asymmetrical. Using a third ray, we propose a balance between the number of rays and the order of traveltime derivatives. Our tests using different models also show the higher accuracy of the proposed method. For acoustic transversely isotropic media with a vertical symmetry axis, we calculate a new moveout approximation in the generalized moveout approximation functional form, which is explicitly defined by three independent parameters of zero-offset two-way time, normal moveout velocity and anellipticity parameter. Our test shows that the maximum error of the proposed transversely isotropic moveout approximation is about 1/6 to 1/8 of that of the moveout approximation that had been reported as the most accurate approximation in these media. The higher accuracy is the result of a novel parameterization that do not add any computational complexity. We show a simple example of its application on synthetic seismic data.     

Transmission + reflection anisotropic wave-equation traveltime and waveform inversion

A transmission + reflection wave-equation traveltime and waveform inversion method is presented that inverts the seismic data for the anisotropic parameters in a vertical transverse isotropic medium. The simultaneous inversion of anisotropic parameters and ε is initially performed using transmission wave-equation traveltime inversion method. Transmission wave-equation traveltime only provides the low-intermediate wavenumbers for the shallow part of the anisotropic model; in contrast, reflection wave-equation traveltime estimates the anisotropic parameters in the deeper section of the model. By incorporating a layer-stripping method with reflection wave-equation traveltime, the ambiguity between the background-velocity model and the depths of reflectors can be greatly mitigated. In the final step, multi-scale full-waveform inversion is performed to recover the high-wavenumber component of the model.  We use a synthetic model to illustrate the local minima problem of full-waveform inversion and how transmission and reflection wave-equation traveltime can mitigate this problem. We demonstrate the efficacy of our new method using field data from the Gulf of Mexico.     

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。      

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。     

Traveltime parameters in a tilted elliptical anisotropic medium‡

In this paper, we derive analytical expressions for one‐way and two‐way kinematical parameters in elliptical tilted transverse isotropy media. We show that the homogeneous elliptical tilted transverse isotropy models result in hyperbolic moveout with a reflection point sideslip x₀, which can be considered as an additional traveltime parameter for one‐way wave propagation. For homogeneous elliptical tilted transverse isotropy models we show that the inversion of one‐way traveltime parameters suffers from the ambiguity for large tilts. It is shown that the accuracy of the inversion is sensitive to the error in x₀. We also derive and invert the traveltime parameters for a vertically heterogeneous elliptical tilted transverse isotropy model with a tilt gradually changing with depth. The a priori knowledge of parameter δ is very important for inversion. The wrong choise of this parameter results in significant errors in inverted model parameters.     

几种CT图像重建算法的研究和比较

本文研究了滤波反投影算法（FBP），局部重建算法（LocalRA)，修正的代数重建算法（MART）。用特别设计的仿真数据和实采数据，分别对这三种算法进行了成像数值试验，分析和比较了各算法的重建速度，空间分辨率，密度分辨率，及其优缺点和适用范围。     

Non‐uniqueness with refraction inversion – a syncline model study

Non‐uniqueness occurs with the 1D parametrization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of non‐uniqueness is the inversion algorithm used to generate the starting model. This study applies 1D, 1.5D and 2D inversion algorithms to traveltime data for a syncline (2D) model, in order to generate starting models for wave path eikonal traveltime tomography. The 1D tau‐p algorithm produced a tomogram with an anticline rather than a syncline and an artefact with a high seismic velocity. The 2D generalized reciprocal method generated tomograms that accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than the true seismic velocities as well as the true values. It is concluded that 2D inversion algorithms, which explicitly identify forward and reverse traveltime data, are required to generate useful starting models in the near‐surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non‐uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non‐uniqueness is a fundamental reality with the inversion of all near‐surface seismic refraction data. Unless specific measures are taken to explicitly address non‐uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ‘correct’ or the most probable.     

THE INTERPRETATION OF TRAVELTIME FIELDS IN REFRACTION SEISMOLOGY*

We consider multiply covered traveltimes of first or later arrivals which are gathered along a refraction seismic profile. The two-dimensional distribution of these traveltimes above a coordinate frame generated by the shotpoint axis and the geophone axis or by the common midpoint axis and the offset axis is named a traveltime field. The application of the principle of reciprocity to the traveltime field implies that for each traveltime value with a negative offset there is a corresponding equal value with positive offset. In appendix A procedures are demonstrated which minimize the observational errors of traveltimes inherent in particular traveltime branches or complete common shotpoint sections. The application of the principle of parallelism to an area of the traveltime field associated with a particular refractor can be formulated as a partial differential equation corresponding to the type of the vibrating string. The solution of this equation signifies that the two-dimensional distribution of these traveltimes may be generated by the sum of two one-dimensional functions which depend on the shotpoint coordinate and the geophone coordinate. Physically, these two functions may be interpreted as the mean traveltime branches of the reverse and the normal shot. In appendix B procedures are described which compute these two functions from real traveltime observations by a least-squares fit. The application of these regressed traveltime field data to known time-to-depth conversion methods is straightforward and more accurate and flexible than the use of individual traveltime branches. The wavefront method, the plus-minus method, the generalized reciprocal method and a ray tracing method are considered in detail. A field example demonstrates the adjustment of regressed traveltime fields to observed traveltime data. A time-to-depth conversion is also demonstrated applying a ray tracing method.