P‐wave velocity distribution in basalt flows of the Enni Formation in the Faroe Islands from refraction seismic analysis

The main objective of this work is to establish the applicability of shallow surface‐seismic traveltime tomography in basalt‐covered areas. A densely sampled ～1300‐m long surface seismic profile, acquired as part of the SeiFaBa project in 2003 ( Japsen et al. 2006 ) at Glyvursnes in the Faroe Islands, served as the basis to evaluate the performance of the tomographic method in basalt‐covered areas. The profile is centred at a ～700‐m deep well. V_P, V_S and density logs, a zero‐offset VSP, downhole‐geophone recordings and geological mapping in the area provided good means of control. The inversion was performed with facilities of the Wide Angle Reflection/Refraction Profiling program package ( Ditmar et al. 1999 ). We tested many inversion sequences while varying the inversion parameters. Modelled traveltimes were verified by full‐waveform modelling. Typically an inversion sequence consists in several iterations that proceed until a satisfactory solution is reached. However, in the present case with high velocity contrasts in the subsurface we obtained the best result with two iterations: first obtaining a smooth starting model with small traveltime residuals by inverting with a high smoothing constraint and then inverting with the lowest possible smoothing constraint to allow the inversion to have the full benefit of the traveltime residuals. The tomogram gives usable velocity information for the near‐surface geology in the area but fails to reproduce the expected velocity distribution of the layered basalt flows. Based on the analysis of the tomogram and geological mapping in the area, a model was defined that correctly models first arrivals from both surface seismic data and downhole‐geophone data.     

Tomographic velocity inversion for ADCIGs in areas with a rugged surface

Pre-stack depth migration velocity analysis is one of the key techniques influencing image quality. As for areas with a rugged surface and complex subsurface, conventional prestack depth migration velocity analysis corrects the rugged surface to a known datum or designed surface velocity model on which to perform migration and update the velocity. We propose a rugged surface tomographic velocity inversion method based on angle-domain common image gathers by which the velocity field can be updated directly from the rugged surface without static correction for pre-stack data and improve inversion precision and efficiency. First, we introduce a method to acquire angle-domain common image gathers (ADCIGs) in rugged surface areas and then perform rugged surface tomographic velocity inversion. Tests with model and field data prove the method to be correct and effective.     

数据域特征波反射走时反演

地震波的运动学信息(走时、斜率等)通常用于宏观速度建模.针对走时反演方法,一个基本问题是走时拾取或反射时差的估计.对于成像域反演方法,可以通过成像道集的剩余深度差近似计算反射波时差.在数据域中,反射地震观测数据是有限频带信号,如果不能准确地确定子波的起跳时间,难以精确地确定反射波的到达时间.另一方面,如果缺乏关于模型的先验信息,则很难精确测量自地下同一个反射界面的观测数据同相轴和模拟数据同相轴之间的时差.针对走时定义及时差测量问题,首先从叠前地震数据的稀疏表达出发,利用特征波场分解方法,提取反射子波并估计局部平面波的入射和出射射线参数.进一步,为了实现自动和稳定的走时拾取,用震相的包络极值对应的时间定义反射波的到达时,实现了立体数据中间的自动生成.理论上讲,利用包络极值定义的走时大于真实的反射波走时,除非观测信号具有无限带宽(即delta脉冲).然而,走时反演的目的是估计中-大尺度的背景速度结构,因此走时误差导致的速度误差仍然在可以接受的误差范围内.利用局部化传播算子及特征波聚焦成像条件将特征波数据直接投影到地下虚拟反射点,提出了一种新的反射时差估计方法.既避免了周期跳跃现象以及串层等可能性,又消除了振幅因素对时差测量的影响.最后,在上述工作基础之上,提出了一种基于特征波场分解的新型全自动反射走时反演方法(CWRTI).通过对泛函梯度的线性化近似,并用全变差正则化方法提取梯度的低波数部分,实现了背景速度迭代反演.在理论上,无需长偏移距观测数据或低频信息、对初始模型依赖性低且计算效率高,可以为后续的全波形反演提供可靠的初始速度模型.理论和实际资料的测试结果证明了本文方法的有效性.     

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.     

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.     

Wave equation tomographic velocity inversion method based on the Born/Rytov approximation

This paper discusses Born/Rytov approximation tomographic velocity inversion methods constrained by the Fresnel zone. Calculations of the sensitivity kernel function and traveltime residuals are critical in tomographic velocity inversion. Based on the Born/Rytov approximation of the frequency-domain wave equation, we derive the traveltime sensitivity kernels of the wave equation on the band-limited wave field and simultaneously obtain the traveltime residuals based on the Rytov approximation. In contrast to single-ray tomography, the modified velocity inversion method improves the inversion stability. Tests of the near-surface velocity model and field data prove that the proposed method has higher accuracy and Computational efficiency than ray theory tomography and full waveform inversion methods.     

3D adaptive tomography using Delaunay triangles and Voronoi polygons

The solutions of traveltime inversion problems are often not unique because of the poor match between the raypath distribution and the tomographic grid. However, by adapting the local resolution iteratively, by means of a singular value analysis of the tomographic matrix, we can reduce or eliminate the null space influence on our earth image: in this way, we get a much more reliable estimate of the velocity field of seismic waves. We describe an algorithm for an automatic regridding, able to fit the local resolution to the available raypaths, which is based on Delaunay triangulation and Voronoi tessellation. It increases the local pixel density where the null space energy is low or the velocity gradient is large, and reduces it elsewhere. Consequently, the tomographic image can reveal the boundaries of complex objects, but is not affected by the ambiguities that occur when the grid resolution is not adequately supported by the available raypaths.     

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.     

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。      

Observation of shear‐wave splitting in the multicomponent node data from Atlantis field,Gulf of Mexico

In 2005, a multicomponent ocean bottom node data set was collected by BP and BHP Billiton in the Atlantis field in the Gulf of Mexico. Our results are based on data from a few sparse nodes with millions of shots that were analysed as common receiver azimuthal gathers. A first‐order look at P‐wave arrivals on a common receiver gather at a constant offset reveals variation of P‐wave arrival time as a function of azimuth indicating the presence of azimuthal anisotropy at the top few layers. This prompted us to investigate shear arrivals on the horizontal component data. After preliminary processing, including a static correction, the data were optimally rotated to radial (R) and transverse (T) components. The R component shows azimuthal variation of traveltime indicating variation of velocity with azimuth; the corresponding T component shows azimuthal variation of amplitude and phase (polarity reversal). The observed shear‐wave (S‐wave) splitting, previously observed azimuthal P‐wave velocity variation and azimuthal P‐wave amplitude variation, all indicate the occurrence of anisotropy in the shallow (just below the seafloor) subsea sediment in the area. From the radial component azimuthal gather, we analysed the PP‐ and PS‐wave amplitude variation for the first few layers and determined corresponding anisotropy parameter and V_P/V_S values. Since fracture at this depth is not likely to occur, we attribute the observed azimuthal anisotropy to the presence of microcracks and grain boundary orientation due to stress. The evidence of anisotropy is ubiquitous in this data set and thus it argues strongly in favour of considering anisotropy in depth imaging for obtaining realistic subsurface images, at the least.     

Ray tracing in elliptical anisotropic media using the linear traveltime interpolation (LTI) method applied to traveltime seismic tomography

The linear traveltime interpolation (LTI) method is a suitable ray‐tracing technique for modelling first‐arrival times in isotropic media. LTI is extended to elliptical anisotropic media and applied to a tomographic inversion procedure. A theoretical formulation is first derived and then LTI implementation is discussed in terms of source–receiver arrays and cell size. The method is then combined with the tomographic inversion procedure adopted. The matching of the ray tracing with inversion in elliptical anisotropic media posed a double non‐linear problem. Thus two assumptions were made: the velocity in each cell is uniform and the main directions of anisotropy are known. To take into account the geometrical characteristics of the area under investigation (depth and velocity of the weathering, and thickness of the inner media), cells of varying size were considered. No hypothesis was made on anisotropy weakness.
The algorithm was first tested on synthetic models and then applied to a field survey. On comparing the results of the synthetic models and the field survey with those obtained with a linear raypath approximation, it was found that there were fewer data misfits.     

初至波相位走时层析

近地表速度结构通常是利用射线走时层析或菲涅尔体走时层析等反演方法得到的,但它们的目标函数仍利用射线走时残差构建,导致反演精度不高.为此,本文提出了基于散射积分算法的初至波相位走时层析成像方法.该方法的核心是:(1)提出了依赖于频率的相位走时概念;(2)利用依赖于频率的相位走时信息,而非单一的无限频率射线走时;(3)发展了一种改进的相位展开方法,即通过监测相位不连续性和2π周期判定来消除相位折叠现象;(4)考虑了地震波传播的有限频特征,即基于波动理论而非传统的射线路径或有限空间的菲涅尔体构建核函数.通过利用Overthrust模型的数值实验及与传统射线走时层析和菲涅尔体走时层析的对比表明:本文提出的方法是一种有效的初至波走时反演方法.同时,基于Overthrust模型的数值试验还证明了下列结论,即通过挖掘更多的走时信息的确可以获得更高的反演精度和分辨率.     

三维复杂地形近地表速度估算及地震层析静校正

在地表一致性模型的基础上提出一种可适用于宽线剖面、弯曲测线、传统的二维和目前广泛使用的三维地震观测.在地形及近地表低降速带地质结构复杂的探区，低降速带厚度及速度估算的精度是静校正处理的关键.本研究根据三维地震观测的初至走时数据，利用最小平方与QR分解相结合的算法，在三维空间重建近地表低降速带速度模型，根据重建速度模型实现了静校正长波长分量与短波长分量的同步计算.分析了复杂的近地表低降速带模型初至波的性质，在观测值的自动拾取以及理论值的计算中充分考虑了可能成为初至波的直达波、折射波和反射波的利用，提高了低降速带速度模型反演的精度.在初至走时观测数据的拾取中，本研究采用分形算法克服了初至波波形差异以及折射波相位反转导致的拾取误差，实现了三维初至拾取的大规模全自动化运算.在射线路径与初至波理论走时的计算中，本研究采用一种计算量与模型复杂程度无关的三维射线追踪方法，该方法以最小走时射线路径保证了与观测数据有同等意义的初至波的射线追踪及理论走时的计算.野外实际资料的处理结果表明了方法的有效性.     

微测井约束分步层析静校正技术在古峰庄地区的应用

针对地表剧烈起伏,速度纵、横向变化大的复杂区,层析静校正较以往的折射波静校正方法有明显的优势,但是受初至时间拾取精度、炮检距的选择、近地表模型约束等问题的影响,层析反演的精度还不能满足低幅度构造预测的需求,为此提出微测井约束分步层析的静校正方法,即将浅层速度模型与最终近地表模型分步进行层析反演,并应用微测井信息约束浅层速度模型层析反演,有效地提高了近地表速度模型反演的精度,通过在古峰庄地区的应用较好地解决了复杂地表条件下的静校正问题,低幅度构造预测精度得到提高.     

模拟退火方法在三维速度模型地震波走时反演中的应用

采用块状建模以及三角形拼接的界面描述方式,并通过立方体速度网格线性插值获得块体内部的速度分布。正演过程中采用逐段迭代射线追踪方法计算三维复杂地质模型中的射线走时,并采用模拟退火方法进行了三维模型中的地震波走时反演研究。模型测试结果表明,使用的射线追踪和走时反演算法有效。     

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.     

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.     

Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting

We develop a two‐dimensional full waveform inversion approach for the simultaneous determination of S‐wave velocity and density models from SH ‐ and Love‐wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near‐surface dataset, recorded in the village ?achtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH‐profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signal‐to‐noise ratio well suited for full waveform inversion. Using the Wiechert–Herglotz method, we determined a one‐dimensional gradient velocity model as a starting model for full waveform inversion. The two‐dimensional waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low‐pass filtered field data. This mitigates the non‐linearity of the multi‐parameter inverse problem. Test computations show that the influence of visco‐elastic effects on the waveform inversion result is rather small. Further tests using a mono‐parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S‐wave velocity and density models show a prominent low‐velocity weathering layer. Below this layer, the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love‐wavelength. The results demonstrate the ability of two‐dimensional SH waveform inversion to image shallow small‐scale soil structure. However, they do not show any evidence of foundation walls.     

Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times

Traditional traveltime inversion for anisotropic medium is, in general, based on a “weak” assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both “weak” and “strong”) anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including “strong”) anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.     

Velocity model estimation for depth imaging: Comparison of three tomography methods on a 2D real data set

The estimation of velocity models is still crucial in seismic reflection imaging as it controls the quality of the depth‐migrated image, which is the basis of geological interpretation. Among the numerous existing methods for velocity determination, tomographic methods are very attractive for their efficiency and ability to retrieve heterogeneities of the medium. We present three tomographic methods in order to estimate heterogeneous velocity models from 2D prestack PP reflection data: a traveltime tomography in the time‐migrated domain, a traveltime and slope tomography in the non‐migrated time domain, and a slope tomography in the depth‐migrated domain. The first method (traveltime tomography in the time domain) is based on continuous picked events, whereas the two slope tomographic methods, one in the time domain and the other in the depth domain, are based on locally coherent events, with no assumptions about reflector geometry or the unknown velocity field. The purpose of this paper is not to describe in detail the theoretical basis and implementation of the methods, but to apply and compare their output using the same marine real data set. Based on the estimated velocity models, the migrated images and the common‐image gathers from the three processing routes, the relative strengths and weaknesses of the methods are discussed. Finally, similarities are indicated and potential alternative approaches are proposed.