正交各向异性介质P波走时分析及Thomsen参数反演

对于包含有垂向裂缝的横向各向同性地层或含有多组正交裂缝的各向同性地层,正交各向异性介质模型是最简单的与实际地层相符的方位各向异性模型.本文对单层水平反射界面正交各向异性模型采用射线追踪法计算了全方位角变化的P波走时,时距曲线表现出强方位各向异性.采用小生境遗传算法,对三条成一定角度的测线的走时信息进行速度和各向异性参数反演.模型算例表明,此方法可以得到高精度的裂缝方位角、P波垂直速度和较高精度的Thomsen各向异性参数.     

非均匀正交各向异性特征参数地震散射反演方法研究

在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法.

     

Reflection moveout inversion in azimuthally anisotropic media: accuracy, limitations and acquisition

Parameter estimation from the elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently, the source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of an NMO ellipse, in particular the parameter α, is also sensitive to the magnitude of anisotropy. On the other hand, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any magnitude of anisotropy.   To invert for the NMO ellipse parameters at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g. full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates.   In order to maximize quality in the inversion process, it is recommended to design the seismic data acquisition such that it contains small sectors (≤10°) with adequate fold and offset distribution.   Using three NMO-velocity measurements, 60° apart, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might occur for fractured reservoirs) should have a relative thickness (in time) with respect to the total thickness at least equal to the ratio of the error in the NMO (stacking) velocity to the interval anisotropy of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50%, depending on the number of observations (NMO velocities) that enter the inversion procedure.     

Azimuth moveout correction for transversely isotropic media

The azimuth moveout (AMO) operator in homogeneous transversely isotropic media with a vertical symmetry axis (VTI), as in isotropic media, has an overall skewed saddle shape. However, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even in weaker anisotropies, with the anisotropy parameter η= 0.1 (10% anisotropy), the AMO operator is considerably different from the isotropic operator, although free of triplications. The structure of the operator in VTI media (positive η) is stretched (has a wider aperture) compared with operators in isotropic media, with the amount of stretch being dependent on the strength of anisotropy. If the medium is both vertically inhomogeneous, i.e. the vertical velocity is a function of depth (v(z)), and anisotropic, which is a common combination in practical problems, the shape of the operator again differs from that for isotropic media. However, the difference in the AMO operator between the homogeneous and the v(z) cases, even for anisotropic media, is small. Stated simply, anisotropy influences the shape and aperture of the AMO operator far more than vertical inhomogeneity does.     

任意空间取向TI介质中P波四次时差系数特征

同类反射波（非转换波）走时偏离双曲,称为非双曲或四次时差,在长排列各向异性地震资料处理中需要校正．本文基于我们导出的水平界面任意空间取向TI (ATI)介质中同类反射波四次时差系数(A4)的精确解析解,数值计算研究P波四次时差系数特征．正演结果表明,ATI条件下A4系数随CMP测线方位变化的特征不仅与TI介质的各向异性参数有关,而且与TI对称轴的空间取向密切相关; TI介质的各向异性参数和TI对称轴的倾角决定了A4变化特征,而且TI对称轴的方位决定了A4随测线方位变化的对称性．此研究结果将对各向异性解释及参数反演有参考意义．     

VTI介质长偏移距非双曲动校正公式优化

常规Alkhalifah动校正公式精度低,不能精确描述各向异性介质长偏移距地震反射同相轴的时距关系.本文以提高VTI介质长偏移距地震资料动校正公式的精度为目标,在分析VTI介质常规动校正方程的基础上,根据误差最小原理建立优化校正系数图版,实现对常规动校正公式大偏移距误差的修正,建立最优化校正Alkhalifah动校正方程,实现了对VTI介质长偏移距地震资料常规动校正方程的改进.之后由Fomel群速度公式导出高精度VTI模型长偏移距时距函数,提出了高精度VTI介质长偏移距地震资料动校正方程.将以上的动校正方程用于各向异性参数反演,模型计算表明最优化校正Alkhalifah动校正方程的反演精度是常规长偏移距动校正方程反演精度的2～4倍,高精度动校正方程的反演精度是常规动校正方程反演精度的2～8倍.     

3D description and inversion of reflection moveout of PS‐waves in anisotropic media

Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t²(x²) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (V_P0 and V_S0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (V_P0, V_S0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves.     

P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismic monitoring.     

任意空间取向TI介质中长排列非双曲动校正公式优化(英文)

常规长排列非双曲动校正公式是在VTI介质中得到的,它不能满足任意空间取向TI(ATI)条件下的扩展.本文以VTI介质中非双曲动校正公式为基础,基于我们推导得出的ATI介质中精确四次时差系数解析解和NMO速度解析解,给出ATI介质中长排列优化的非双曲动校正公式.通过与各向异性射线追踪方法计算所得出的"精确走时"结果对比,研究表明优化后的非双曲动校正公式能精确地描述任意强弱、ATI介质中随测线方位变化的走时曲线,可以用来替代耗时、多偏移距、多方位的射线追踪方法正演拟合ATI介质中长偏移距反射走时,为利用非双曲时距的各向异性参数反演提供理论基础性认识。     

Normal moveout velocity for pure‐mode and converted waves in layered orthorhombic medium

We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi‐compressional, quasi‐shear, and converted waves in one‐dimensional multi‐layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface‐offset azimuth and applying our derived relationship between the surface‐offset azimuth and phase‐velocity azimuth, we obtain the normal moveout velocity versus the phase‐velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time‐domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local‐angle‐domain common image gathers. The angle and azimuth parameters of the local‐angle‐domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψ_phs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi‐layer structure is based on the fact that, for a one‐dimensional model assumption, the horizontal slowness and the azimuth of the phase velocity ψ_phs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface‐offset azimuth and phase‐velocity azimuth domains.     

3D waveform inversion of downhole microseismic data for transversely isotropic media

3D anisotropic waveform inversion could provide high-resolution velocity models and improved event locations for microseismic surveys. Here we extend our previously developed 2D inversion methodology for microseismic borehole data to 3D transversely isotropic media with a vertical symmetry axis. This extension allows us to invert multicomponent data recorded in multiple boreholes and properly account for vertical and lateral heterogeneity. Synthetic examples illustrate the performance of the algorithm for layer-cake and ‘hydraulically fractured’ (i.e. containing anomalies that simulate hydraulic fractures) models. In both cases, waveform inversion is able to reconstruct the areas which are sufficiently illuminated for the employed source-receiver geometry. In addition, we evaluate the sensitivity of the algorithm to errors in the source locations and to band-limited noise in the input displacements. We also present initial inversion results for a microseismic data set acquired during hydraulic fracturing in a shale reservoir.     

长偏移距地震资料的优化契比雪夫动校正方法

传统的双曲型动校正方法仅适用于偏移距与目标层深度比值较小的情况.对于长偏移距地震资料,须采用非双曲动校正公式才能得到较高的动校正精度.但常规的非双曲方法对于大偏移距仍然有较大的误差.本文提出契比雪夫截断加模拟退火优化的思路:通过沿用高阶项补偿系数的形式以克服对于大偏移距可能存在的不稳定现象,然后对常规的泰勒展开进行契比...     

Estimating the elastic parameters of anisotropic media using a joint inversion of P-wave and SV-wave traveltime error

A method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P‐wave and vertically polarized shear‐wave (SV‐wave) data. This method is a ‘layer‐stripping’ technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ?p) domain, DTSs are traveltimes Δτ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize Δτ with respect to error in the elastic parameters and thickness, and least‐squares inversion is used to update the model. For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode‐converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion.     

Recursive impedance inversion of ground-penetrating radar data in stochastic media

The travel time and amplitude of ground-penetrating radar (GPR) waves are closely related to medium parameters such as water content, porosity, and dielectric permittivity. However, conventional estimation methods, which are mostly based on wave velocity, are not suitable for real complex media because of limited resolution. Impedance inversion uses the reflection coefficient of radar waves to directly calculate GPR impedance and other parameters of subsurface media. We construct a 3D multiscale stochastic medium model and use the mixed Gaussian and exponential autocorrelation function to describe the distribution of parameters in real subsurface media. We introduce an elliptical Gaussian function to describe local random anomalies. The tapering function is also introduced to reduce calculation errors caused by the numerical simulation of discrete grids. We derive the impedance inversion workflow and test the calculation precision in complex media. Finally, we use impedance inversion to process GPR field data in a polluted site in Mongolia. The inversion results were constrained using borehole data and validated by resistivity data.     

Application of the redundant-lifting scheme for ground-roll attenuation in near-surface characterization using full-waveform inversion on P-wave seismic data

Seismic modelling of the shallow subsurface (within the first few metres) is often challenging when the data are dominated by ground-roll and devoid of reflection. We showed that, even when transmission is the only available phase for analysis, fine-scale and interpretable P-wave velocity (V_P) and attenuation (Q_P⁻¹) models can still be prepared using full-waveform inversion, with data being preconditioned for ground-roll. To prove this idea, we suppressed the ground-roll in two different ways before full-waveform inversion modelling: first, through a bottom mute; second, through a novel wavelet transform-based method known as the redundant-lifting scheme. The applicability of full-waveform inversion is tested through imaging two buried targets. These include a pair of utility water pipes with known diameters of 0.8 m and burial depths of 1.5 m, respectively. The second target is the poorly documented backfill, which was the former location of the pipe(s). The data for full-waveform inversion are acquired along a 2D profile using a static array of 24, 40 Hz vertical component geophones and a buried point source. The results show that (a) the redundant-lifting scheme better suppresses the ground roll, which in turn provides better images of the targets in full-waveform inversion; and (b) the V_P and Q_P⁻¹ models from full-waveform inversion of redundant-lifting scheme data could detect the two targets adequately.     

Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics

Based on the long-wavelength approximation, a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study, we propose a reliable method for predicting the Thomsen’s weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen’s weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen’s weak anisotropic parameters and fracture weaknesses. Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth (AVAZ) inversion for Thomsen’s weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares (IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen’s weak anisotropic parameters and fracture weaknesses.     

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.     

频率域海洋可控源电磁垂直各向异性三维反演

地层宏观电性各向异性会对可控源电磁响应产生重要影响.由于海底地层电性结构常表现为电导率各向异性,若仅对海洋可控源电磁(MCSEM)数据进行常规各向同性反演,有可能无法获得准确的反演解释结果,从而削弱MCSEM技术的可靠性.本文实现了电导率垂直各向异性(VTI)条件下频率域海洋可控源电磁数据三维反演算法.其中,三维正演采用基于二次场控制方程的交错网格有限体积法,并利用直接矩阵分解技术来求解离散所得的大型线性方程组,有利于快速计算多场源的响应.反演采用具有近似二次收敛性的高斯牛顿算法对目标函数进行最优化.最后,对具有VTI电性各向异性特征的盐丘构造模型的MCSEM合成数据分别进行了电导率各向同性和垂直各向异性三维反演,结果表明:各向同性三维反演算法无法对受VTI介质影响的MCSEM数据进行正确的反演解释,而垂直各向异性三维反演能够获得更为可靠的地下电阻率结构和异常体分布,展现出对海底电性各向异性结构更为优良的反演解释能力.