Seismic velocity analysis in the scattering-angle/azimuth domain

Migration velocity analysis is carried out by analysing the residual moveout and amplitude variations in common image point gathers (CIGs) parametrized by scattering angle and azimuth. The misfit criterion in the analysis is of the differential-semblance type. By using angles to parametrize the imaging we are able to handle and exploit data with multiple arrivals, although artefacts may occur in the CIGs and need to be suppressed. The CIGs are generated by angle migration, an approach based on the generalized Radon transform (GRT) inversion, and they provide multiple images of reflectors in the subsurface for a range of scattering angles and azimuths. Within the differential semblance applied to these CIGs, we compensate for amplitude versus angle (AVA) effects. Thus, using a correct background velocity model, the CIGs should have no residual moveout nor amplitude variation with angles, and the differential semblance should vanish. If the velocity model is incorrect, however, the events in the CIGs will appear at different depths for different angles and the amplitude along the events will be non-uniform. A standard, gradient-based optimization scheme is employed to develop a velocity updating procedure. The model update is formed by backprojecting the differential semblance misfits through ray perturbation kernels, within a GRT inverse. The GRT inverse acts on the data, subject to a shift in accordance with ray perturbation theory. The performance of our algorithm is demonstrated with two synthetic data examples using isotropic elastic models. The first one allows velocity variation with depth only. In the second one, we reconstruct a low-velocity lens in the model that gives rise to multipathing. The velocity model parametrization is based upon the eigentensor decomposition of the stiffness tensor and makes use of B-splines.     

Velocity model building from seismic reflection data by full‐waveform inversion

Full‐waveform inversion is re‐emerging as a powerful data‐fitting procedure for quantitative seismic imaging of the subsurface from wide‐azimuth seismic data. This method is suitable to build high‐resolution velocity models provided that the targeted area is sampled by both diving waves and reflected waves. However, the conventional formulation of full‐waveform inversion prevents the reconstruction of the small wavenumber components of the velocity model when the subsurface is sampled by reflected waves only. This typically occurs as the depth becomes significant with respect to the length of the receiver array. This study first aims to highlight the limits of the conventional form of full‐waveform inversion when applied to seismic reflection data, through a simple canonical example of seismic imaging and to propose a new inversion workflow that overcomes these limitations. The governing idea is to decompose the subsurface model as a background part, which we seek to update and a singular part that corresponds to some prior knowledge of the reflectivity. Forcing this scale uncoupling in the full‐waveform inversion formalism brings out the transmitted wavepaths that connect the sources and receivers to the reflectors in the sensitivity kernel of the full‐waveform inversion, which is otherwise dominated by the migration impulse responses formed by the correlation of the downgoing direct wavefields coming from the shot and receiver positions. This transmission regime makes full‐waveform inversion amenable to the update of the long‐to‐intermediate wavelengths of the background model from the wide scattering‐angle information. However, we show that this prior knowledge of the reflectivity does not prevent the use of a suitable misfit measurement based on cross‐correlation, to avoid cycle‐skipping issues as well as a suitable inversion domain as the pseudo‐depth domain that allows us to preserve the invariant property of the zero‐offset time. This latter feature is useful to avoid updating the reflectivity information at each non‐linear iteration of the full‐waveform inversion, hence considerably reducing the computational cost of the entire workflow. Prior information of the reflectivity in the full‐waveform inversion formalism, a robust misfit function that prevents cycle‐skipping issues and a suitable inversion domain that preserves the seismic invariant are the three key ingredients that should ensure well‐posedness and computational efficiency of full‐waveform inversion algorithms for seismic reflection data.     

Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures

Full waveform inversion is a powerful tool for quantitative seismic imaging from wide‐azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the solution of a large‐scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artefacts generated by energetic multiple reflections. Conventional minimization methods (nonlinear conjugate gradient, quasi‐Newton methods) only roughly approximate the effect of this operator. In this study, we are interested in the truncated Newton minimization method. These methods are based on the computation of the model update through a matrix‐free conjugate gradient solution of the Newton linear system. We present a feasible implementation of this method for the full waveform inversion problem, based on a second‐order adjoint state formulation for the computation of Hessian‐vector products. We compare this method with conventional methods within the context of 2D acoustic frequency full waveform inversion for the reconstruction of P‐wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data‐set from the Valhall oil field in North sea. Although, from a computational cost point of view, the truncated Newton method appears to be more expensive than conventional optimization algorithms, the results emphasize its increased robustness. A better reconstruction of the P‐wave velocity model is provided when energetic multiple reflections make it difficult to interpret the seismic data. A better trade‐off between regularization and resolution is obtained when noise contamination of the data requires one to regularize the solution of the inverse problem.     

反射地震数据的逐层波形反演

本文针对层状介质并结合梯度法波形反演,提出逐层波形反演的方法. 首先给出介质扰动响应的概念,并在此基础上分析了梯度法波形反演方法. 波形反演实质上是将实测地震记录和预测地震记录的波形残差信息转化为实际地质模型和预测地质模型的模型残差信息. 波形反演的优点是利用大量振幅相位信息得到高分辨率的反演结果, 其缺点是运行耗时大;当初始模型和实际模型相差较大时,迭代算法容易陷入局部极小点,这是因为目标函数和初始模型同实际模型间的差异是非线性的关系. 逐层波形反演方法是使自上而下每一层的目标函数最小,这样总的目标函数也是最小的. 利用二分法速度扫描确定每一层速度不仅提高了运算速度也避免了迭代算法陷入局部极小点的问题. 结合介质扰动响应和目标函数值变化可以更为准确迅速地确定每一层速度和该层界面位置.     

Source-independent wave-equation based microseismic source location using traveltime inversion

A new source location method using wave-equation based traveltime inversion is proposed to locate microseismic events accurately. With a sourceindependent strategy, microseismic events can be located independently regardless of the accuracy of the source signature and the origin time. The traveltime-residuals-based misfit function has robust performance when the velocity model is inaccurate. The new Fréchet derivatives of the misfit function with respect to source location are derived directly based on the acoustic wave equation, accounting for the influence of geometrical perturbation and spatial velocity variation. Unlike the mostly used traveltime inversion methods, no traveltime picking or ray tracing is needed.Additionally, the improved scattering-integral method is applied to reduce the computational cost. Numerical tests show the validity of the proposed method.     

不依赖子波、基于包络的FWI初始模型建立方法研究

地震全波形反演(FWI)从理论走向实际面临着诸多难题,其中之一就是需要一个较高精度的初始模型,另一个难题就是需要一个较为精确的震源子波,初始模型和震源子波的准确程度严重影响着全波形反演的最终结果.为此,本文提出了不依赖子波、基于包络的FWI初始模型建立的方法,建立了相应的目标函数,推导出了反演的梯度,给出了伴随震源的表达式,理论上分析了不依赖子波FWI的可行性.在数值试验中,讨论了参考道的选取方式,通过分析归一化目标函数收敛速率,认为近偏移距参考道优于远偏移距参考道,在地震数据含干扰噪音时,平均道作为参考道要优于最小偏移距参考道.通过包络、包络对数、包络平方三种目标函数反演结果的比较,发现包络对数目标函数对深层的反演效果最好.通过不同子波的试验进一步验证了本方法的正确性.     

基于面波频散的三维横波速度方位各向异性层析成像方法

地震各向异性是反映地球内部介质特性的重要指针之一。常用的横波分裂法和二维面波方位各向异性层析成像方法很难准确反映各向异性随深度的变化。将与周期相关的区域化面波方位各向异性转换成与深度相关的一维横波速度方位各向异性可以弥补深度信息不足的缺陷。现有三维横波速度各向异性研究多是通过两步方法来实现的,即逐个周期二维面波方位各向异性层析成像以及逐个格点一维横波速度方位各向异性反演。这种分步反演的方式既不利于三维先验约束的引入,也不利于利用原始观测拟合误差对三维模型进行直接评估。因此本文开发了基于面波频散曲线的三维横波速度方位各向异性层析成像方法,并编制了相关正演和反演程序。为了检测方法和程序的有效性,我们对规律分布的三维检测板模型进行了模拟测试。测试结果显示:该方法可以很好地恢复各向同性波速异常、各向异性相对强度和快波方向等三维结构信息;而且反演模型相对于参考模型明显改善了对观测数据的拟合,降低了对观测数据的均方根误差。但对各向同性理论模型进行各向异性反演时,在波速均匀区可产生小于0.5%的假各向异性幅值,在波速非均匀区该假的各向异性幅值会更大,浅部可达3.5%。因此在实际应用中需要谨慎解释（浅部）非均匀区的各向异性结果。      

Wave‐equation migration velocity analysis with time‐shift imaging

Wave‐equation migration velocity analysis is a technique designed to extract and update velocity information from migrated images. The velocity model is updated through the process of optimizing the coherence of images migrated with the known background velocity model. The capacity for handling multi‐pathing of the technique makes it appropriate in complex subsurface regions characterized by strong velocity variation. Wave‐equation migration velocity analysis operates by establishing a linear relation between a slowness perturbation and a corresponding image perturbation. The linear relationship and the corresponding linearized operator are derived from conventional extrapolation operators and the linearized operator inherits the main properties of frequency‐domain wavefield extrapolation. A key step in the implementation is to design an appropriate procedure for constructing an image perturbation relative to a reference image that represents the difference between the current image and a true, or more correct image of the subsurface geology. The target of the inversion is to minimize such an image perturbation by optimizing the velocity model. Using time‐shift common‐image gathers, one can characterize the imperfections of migrated images by defining the focusing error as the shift of the focus of reflections along the time‐shift axis. The focusing error is then transformed into an image perturbation by focusing analysis under the linear approximation. As the focusing error is caused by the incorrect velocity model, the resulting image perturbation can be considered as a mapping of the velocity model error in the image space. Such an approach for constructing the image perturbation is computationally efficient and simple to implement. The technique also provides a new alternative for using focusing information in wavefield‐based velocity model building. Synthetic examples demonstrate the successful application of our method to a layered model and a subsalt velocity update problem.     

Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

Full waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.     

Joint Inversion of Body-Wave Arrival Times and Surface-Wave Dispersion for Three-Dimensional Seismic Structure Around SAFOD

We incorporate body-wave arrival time and surface-wave dispersion data into a joint inversion for three-dimensional P-wave and S-wave velocity structure of the crust surrounding the site of the San Andreas Fault Observatory at Depth. The contributions of the two data types to the inversion are controlled by the relative weighting of the respective equations. We find that the trade-off between fitting the two data types, controlled by the weighting, defines a clear optimal solution. Varying the weighting away from the optimal point leads to sharp increases in misfit for one data type with only modest reduction in misfit for the other data type. All the acceptable solutions yield structures with similar primary features, but the smaller-scale features change substantially. When there is a lower relative weight on the surface-wave data, it appears that the solution over-fits the body-wave data, leading to a relatively rough V _s model, whereas for the optimal weighting, we obtain a relatively smooth model that is able to fit both the body-wave and surface-wave observations adequately.     

基于宽范围岩石物性约束的大地电磁和地震联合反演

岩石物性约束是地球物理联合反演重要的实现方式.在以往联合反演研究中,这种约束通常以点对点的映射方式出现,要求经验性的岩石物性关联是相对精确的,无形中提高了岩石物性约束应用于联合反演的条件.基于此,本文结合全局寻优的模拟退火算法,提出了宽范围岩石物性约束技术.该技术将岩石物性约束与模拟退火模型扰动、模型接受准则相结合,实现了空间对空间的映射,将电阻率和速度耦合在一起.文章以MT和地震正则化同步联合反演为例,检验了不同的先验信息条件下的宽范围岩石物性约束技术的适用性.模型试验表明:新技术容易实现,容错性高,可降低"不精确"岩石物性关联信息引入带来的风险,提高岩石物性约束应用的灵活性.     

Misfit functionals in Laplace‐Fourier domain waveform inversion,with application to wide‐angle ocean bottom seismograph data

In seismic waveform inversion, non‐linearity and non‐uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace‐Fourier domain waveform inversion: i) subtraction of complex‐valued observed data from complex‐valued predicted data (the ‘conventional phase‐amplitude’ residual), ii) a ‘conventional phase‐only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase‐amplitude’ residual and finally iv) a ‘logarithmic phase‐only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide‐angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase‐amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase‐amplitude inversions starting from the logarithmic phase‐only inversion result. The resulting velocity updates are prominent only in the high‐wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near‐offset traces, the conventional phase‐amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase‐only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models.     

Regularized inversion of amplitude-versus-incidence angle (AVA) based on a piecewise-smooth model

Different from the stacked seismic data, pre-stack data includes abundant information about shear wave and density. Through inversing the shear wave and density information from the pre-stack data, we can determine oil-bearing properties from different incident angles. The state-of-the-art inversion methods obtain either low vertical resolution or lateral discontinuities. However, the practical reservoir generally has sharp discontinuities between different layers in vertically direction and is horizontally smooth. Towards obtaining the practical model, we present an inversion method based on the regularized amplitude-versus-incidence angle (AVA) data to estimate the piecewise-smooth model from pre-stack seismic data. This method considers subsurface stratum as a combination of two parts: a piecewise smooth part and a constant part. To fix the ill-posedness in the inversion, we adopt four terms to define the AVA inversion misfit function: the data misfit itself, a total variation regularization term acting as a sparsing operator for the piecewise constant part, a Tikhonov regularization term acting as a smoothing operator for the smooth part, and the last term to smoothly incorporate a priori information for constraining the magnitude of the estimated model. The proposed method not only can incorporate structure information and a priori model constraint, but also is able to derive into a convex objective function that can be easily minimized using iterative approach. Compared with inversion results of TV and Tikhonov regularization methods, the inverted P-wave velocity, S-wave velocity and density of the proposed method can better delineate the piecewise-smooth characteristic of strata.     

时间二阶积分波场的全波形反演

通过对波场的时间二阶积分运算以增强地震数据中的低频成分,提出了一种可有效减小对初始速度模型依赖性的地震数据全波形反演方法—时间二阶积分波场的全波形反演方法.根据散射理论中的散射波场传播方程,推导出时间二阶积分散射波场的传播方程,再利用一阶Born近似对时间二阶积分散射波场传播方程进行线性化.在时间二阶积分散射波场传播方程的基础上,利用散射波场反演地下散射源分布,再利用波场模拟的方法构建地下入射波场,然后根据时间二阶积分散射波场线性传播方程中散射波场与入射波场、速度扰动间的线性关系,应用类似偏移成像的公式得到速度扰动的估计,以此建立时间二阶积分波场的全波形迭代反演方法.最后把时间二阶积分波场的全波形反演结果作为常规全波形反演的初始模型可有效地减小地震波场全波形反演对初始模型的依赖性.应用于Marmousi模型的全频带合成数据和缺失4Hz以下频谱成分的缺低频合成数据验证所提出的全波形反演方法的正确性和有效性,数值试验显示缺失4Hz以下频谱成分数据的反演结果与全频带数据的反演结果没有明显差异.     

扩展成像条件下的最小二乘逆时偏移

逆时偏移(RTM)是复杂介质条件下地震成像的重要手段.因受观测系统限制、上覆地层影响以及波场带宽有限等因素的影响,现行的常规RTM所采用的互相关成像条件通常对地下构造进行模糊成像.最小二乘逆时偏移(LSRTM)通过最小化线性Born近似正演数据和采集数据之间的波形差异,采用梯度类反演算法优化反射系数模型,获得的成像结果具有更高的分辨率和更可靠的振幅保真度.然而,基于波形拟合的LSRTM对背景速度模型的依赖性很强.误差太大的速度模型容易产生周波跳跃现象,导致LSRTM难以获得全局最优解.为了克服这一问题,本文基于扩展模型的思想,在线性Born近似下,推导得到RTM扩展成像条件.并基于最小二乘反演理论,提出扩展成像条件下的LSRTM方法.理论模型试算表明,本文方法不仅可以提供分辨率更高、振幅属性更为可靠的成像结果,而且能够在一定程度上消除速度误差对反演成像的影响.     

Correlation‐based reflection waveform inversion by one‐way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.     

基于新的惩罚因子算法的波场重构反演

全波形反演是一种高精度的反演方法,其目标函数是一个强非线性函数,易受局部极值影响,而且反演过程计算量较大.波场重构反演是近几年提出的一种改进的全波形反演理论.该反演方法通过将波动方程作为惩罚项引入到目标函数中,通过拓宽解的寻找空间减弱了局部极小值的影响,而且反演过程不需要计算伴随波场,提高了计算效率.但该反演方法一直缺少准确的惩罚因子算法,直接影响到该方法的准确度.本文将波场重构反演拓展到时间域并利用梯度法进行波场重构.频率域的惩罚因子用来加强波动方程的约束,而时间域惩罚因子表现为调节模拟波场和实际波场的权重因子.为此,我们根据约束优化理论,在波动方程准确以及重构波场与反演参数解耦的假设下,提出以波动方程为目标函数的新的惩罚因子算法.根据波形反演在应用时普遍存在的噪音干扰、子波错误和低频信息缺失的情况下,应用部分Sigsbee2A模型合成数据对本文提出的算法进行实验.数值实验结果表明：基于新的惩罚因子算法,在其他信息不准确的情况下,波场重构反演可以给出高精度的反演结果.     

二阶精度广义非线性全局最优的偏移速度反演方法(英文)

如何快速、精确地利用叠前深度偏移进行偏移速度分析是勘探地震学的一项重要研究内容,针对该问题,本文提出一种二阶精度广义非线性全局最优的偏移速度反演方法。我们将首先去掉速度模型修正量与成象深度差呈线性关系的假设,推导出具有二阶精度的速度模型修正量计算公式,使每一次迭代得到的速度模型尽可能地接近实际模型;然后采用广义非线性反演方法反演获得对所有道集的全局最优的速度模型修正量,不仅极大地加快了收敛速度,而且反演过程中陷入局部极小的可能性也减小了。理论模型和Marmousi模型的处理结果表明:本方法精度高、处理速度快,提高了偏移速度分析方法的实用性和对复杂构造成像的准确性。     

地震与大地电磁测深数据的自适应正则化同步联合反演

在传统的联合反演研究中,地球物理学者往往更多地关注数据拟合,很少涉及正则化理论.本文在电阻率和速度随机分布的大地电磁测深(MT)与地震联合反演研究的基础之上,将正则化思想引入到同步联合反演中,加入先验信息进行模型约束,选取最小模型为稳定泛函,并首次采用自适应正则化算法来确定联合反演的正则化因子.根据以往研究成果,采用非...     

遗传算法中的光滑约束反演及其在青藏高原面波研究中的应用

光滑约束技术在线性反演中具有重要的作用，但在遗传算法的反演中则很难直接施加于模型参数，其原因是采用光滑处理后的模型参与迭代后，模型的多样性受到很强的压制，并在少量的迭代过程中使种群的各个模型趋向一致，从而得不到满足条件的最优解．本文给出了一种可用于遗传算法反演的间接光滑约束方法．该方法将遗传算法迭代过程中产生的模型经处理后得到的光滑模型，作为误差函数计算的输入模型．迭代过程仍采用原模型，避免了模型的多样性损失，在面波反演和接收函数反演的试验中取得了良好的效果．我们利用该方法对青藏高原地区的瑞利波相速度资料进行了反演，揭示了青藏高原中部地区S波速度结构的横向变化特征．结果表明，青藏高原北部地区地壳Ｓ波速度较南部地区低；大多数路径在15～40ｋｍ 深度范围内，存在12～25ｋｍ 厚的地壳低速层；上地幔低速层位于100ｋｍ 深度以下，厚度主要在40～80ｋｍ 范围内变化，个别路径可达100ｋｍ 以上．安多台以北、玛沁和玉树以西之间，在上地幔90～230ｋｍ 深度范围存在明显的低速层，最低速度约4.2～ 4.3km／s．根据不同路径的S波速度结构和前人的资料，我们认为印度板块的俯冲可能以雅鲁藏布缝合带附近为界．