共查询到20条相似文献，搜索用时 46 毫秒
1.
Daniel Trad 《Geophysical Prospecting》2020,68(3):802-814
Least squares migration uses the assumption that, if we have an operator that can create data from a reflectivity function, the optimal image will predict the actual recorded data with minimum square error. For this assumption to be true, it is also required that: (a) the prediction operator must be error-free, (b) model elements not seen by the operator should be constrained by other means and (c) data weakly predicted by the operator should make limited contribution to the solution. Under these conditions, least squares migration has the advantage over simple migration of being able to remove interference between different model components. Least squares migration does that by de-convolving or inverting the so-called Hessian operator. The Hessian is the cascade of forward modelling and migration; for each image point, it computes the effects of interference from other image points (point-spread function) given the actual recording geometry and the subsurface velocity model. Because the Hessian contains illumination information (along its diagonal), and information about the model cross-correlation produced by non-orthogonality of basis functions, its inversion produces illumination compensation and increases resolution. In addition, sampling deficiencies in the recording geometry map to the Hessian (both diagonal and non-diagonal elements), so least squares migration has the potential to remove sampling artefacts as well. These (illumination compensation, resolution and mitigating recording deficiencies) are the three main goals of least squares migration, although the first one can be achieved by cheaper techniques. To invert the Hessian, least squares migration relies on the residual errors during iterations. Iterative algorithms, like conjugate gradient and others, use the residuals to calculate the direction and amplitudes (gradient and step size) of the necessary corrections to the reflectivity function or model. Failure of conditions (a), (b) or (c) leads the inversion to calculate incorrect model updates, which translate to noise in the final image. In this paper, we will discuss these conditions for Kirchhoff migration and reverse time migration. 相似文献
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Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media 
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下载免费PDF全文 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. 相似文献
4.
Jia-Jia Yang Xi-Wu Luan Bing-Shou He Gang Fang Jun Pan Wei-Min Ran Tao Jiang 《应用地球物理》2017,14(4):492-504
Angle-domain common-image gathers (ADCIGs) transformed from the shotdomain common-offset gathers are input to migration velocity analysis (MVA) and prestack inversion. ADCIGs are non-illusion prestack inversion gathers, and thus, accurate. We studied the extraction of elastic-wave ADCIGs based on amplitude-preserving elastic-wave reversetime migration for calculating the incidence angle of P-and S-waves at each image point and for different source locations. The P-and S-waves share the same incident angle, namely the incident angle of the source P-waves. The angle of incidence of the source P-wavefield was the difference between the source P-wave propagation angle and the reflector dips. The propagation angle of the source P-waves was obtained from the polarization vector of the decomposed P-waves. The reflectors’ normal direction angle was obtained using the complex wavenumber of the stacked reverse-time migration (RTM) images. The ADCIGs of P-and S-waves were obtained by rearranging the common-shot migration gathers based on the incident angle. We used a horizontally layered model, the graben medium model, and part of the Marmousi-II elastic model and field data to test the proposed algorithm. The results suggested that the proposed method can efficiently extract the P-and S-wave ADCIGs of the elastic-wave reverse-time migration, the P-and S-wave incident angle, and the angle-gather amplitude fidelity, and improve the MVA and prestack inversion. 相似文献
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Liangguo Dong Zhongyi Fan Hongzhi Wang Benxin Chi Yuzhu Liu 《Geophysical Prospecting》2018,66(8):1503-1520
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. 相似文献
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We present preserved‐amplitude downward continuation migration formulas in the aperture angle domain. Our approach is based on shot‐receiver wavefield continuation. Since source and receiver points are close to the image point, a local homogeneous reference velocity can be approximated after redatuming. We analyse this approach in the framework of linearized inversion of Kirchhoff and Born approximations. From our analysis, preserved‐amplitude Kirchhoff and Born inverse formulas can be derived for the 2D case. They involve slant stacks of filtered subsurface offset domain common image gathers followed by the application of the appropriate weighting factors. For the numerical implementation of these formulas, we develop an algorithm based on the true amplitude version of the one‐way paraxial approximation. Finally, we demonstrate the relevance of our approach with a set of applications on synthetic datasets and compare our results with those obtained on the Marmousi model by multi‐arrival ray‐based preserved‐amplitude migration. While results are similar, we observe that our results are less affected by artefacts. 相似文献
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提出三维Kirchhoff叠前时间偏移角度域共像点道集的改进算法,克服传统角度求取算法局限,可计算相对倾斜地层法线入射角;与Kirchhoff直射线叠前时间偏移求角度算法相比,本文方法考虑射线弯曲效应,包含层速度,角度范围加大,更接近真实入射角;计算走时采取弯曲射线或者适应线性横向变速介质的非对称走时等算法,角度道集在大角度处得到拉平;采用相对保幅的权因子以及覆盖次数校正技术,有利于叠前AVA反演.模型测试结果表明：叠前时间偏移角度道集,相对CMP、CRP所转化角度道集,更准确反应AVA效应;实际三维数据测试表明本文方法可以提供品质优良的角度道集,适用于AVA分析、反演,提高叠前反演分辨率. 相似文献
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三维电阻率探测的线性反演和非线性反演中均存在着多解性的固有难题.电阻率线性反演方法的效率较高,但反演结果对初始模型的依赖性较强,易陷入局部极小;而非线性反演方法不依赖初始模型,但搜索效率极低,尚未见到关于三维电阻率非线性反演的文献.针对上述问题,融合线性与非线性反演方法的互补优势,提出了最小二乘法(线性方法)与改进遗传算法(非线性方法)相结合的混合反演方法的概念和思想.首先,提出了将介质电阻率变化范围作为不等式约束引入反演方程的思路,以实现压制多解性、提高可靠性的目标.提出了宽松不等式约束和基于钻孔推断的局部严格不等式约束的获取及定义方法.在此基础上,分别提出了基于不等式约束的最小二乘线性反演方法和遗传算法非线性反演方法.其次,对于遗传算法在变异搜索方向控制、初始群体产生等方面进行了改进,优化了其搜索方向和初始群体多样性.然后,提出了混合反演方法及其实现方案,利用改进遗传算法进行第一阶段反演,发挥其对初始模型的依赖程度低的优势,搜索到最优解附近的空间,输出当前最优个体;利用最小二乘法进行第二阶段反演,将遗传算法得到的当前最优个体作为初始模型,在最优解附近空间执行高效率的局部线性搜索,最终实现地电结构的三维成像.最后,开展了合成数据与实际工程算例验证,与传统最小二乘方法进行了对比,发现混合反演方法在压制多解性、摆脱初始模型依赖和提高反演效果方面有较好效果. 相似文献
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总结了牛顿类地震反演方法中Hessian算子的作用,对其在地震反演成像中的数学物理含义进行了分析.Hessian算子是误差泛函对模型参数的二阶导数,反映了误差泛函对模型变化的二次型特征.分析声波方程下的Hessian算子的格林函数表达形式,发现其表达了整个观测系统和子波频带等因素对地震数据空间到模型空间投影过程的影响.提出了两种分别适用于最小二乘偏移和全波形反演的Hessian算子简化格式.平面波Hessian算子应用于最小二乘偏移能够得到相对保真的成像结果,改善了地震偏移成像的精度.地下偏移距Hessian算子应用于全波形反演能够加快反演迭代的计算效率.最后,对Hessian算子在地震反演成像中的价值进行了讨论和评价. 相似文献
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We propose a method based on the Poynting vector that combines angle-domain imaging and image amplitude correction to overcome the shortcomings of reverse-time migration that cannot handle different angles during wave propagation. First, the local image matrix (LIM) and local illumination matrix are constructed, and the wavefield propagation directions are decomposed. The angle-domain imaging conditions are established in the local imaging matrix to remove low-wavenumber artifacts. Next, the angle-domain common image gathers are extracted and the dip angle is calculated, and the amplitude-corrected factors in the dip angle domain are calculated. The partial images are corrected by factors corresponding to the different angles and then are superimposed to perform the amplitude correction of the final image. Angle-domain imaging based on the Poynting vector improves the computation efficiency compared with local plane-wave decomposition. Finally, numerical simulations based on the SEG/EAGE velocity model are used to validate the proposed method. 相似文献
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本文详细地给出了基于非均匀介质的体散射广义散射层析成像反演的基本理论.广义散射层析成像反演可以描述为波场的反向传播和对成像场进行局部波数域滤波的过程.在数值算例中,利用背景速度沿深度方向均匀变化的v（z）介质中的简单的方块作为速度异常体的模型,通过对该模型产生的低频的Born数据和声波的正演数据的测试,在对采集系统进行有限频率带宽和空间孔径的校正来进行局部成像矩阵谱的恢复中,可以看出模型中各点的谱在恢复后的质量无论从覆盖的面积范围还是幅值的均一性上都有着明显的提高;在对速度模型的重建中,广义散射层析成像反演能够很好地恢复速度模型的低频分量,即便是方块速度异常体相对于背景速度的平均速度扰动是23%也能很好地重建模型中的速度,且对于不同的背景速度模型基本上都能很好地恢复Marmousi速度模型的低频分量.所以该方法将基于Born模型的层析成像反演适应范围进行了一定程度的扩展. 相似文献
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研究与实践表明,对于长偏移距、宽方位地震数据,忽略各向异性会明显降低成像质量,影响储层预测与描述的精度.针对典型的横向各向同性(TI)介质,本文面向深度域构造成像与偏移速度分析的需要,研究基于射线理论的局部角度域叠前深度偏移成像方法.它除了像传统Kirchhoff叠前深度偏移那样输出成像剖面和炮检距域的共成像点道集,还遵循地震波在成像点处的局部方向特征、基于扩展的脉冲响应叠加原理获得入射角度域和照明角度域的成像结果.为了方便快捷地实现TI介质射线走时与局部角度信息的计算,文中讨论和对比了两种改进的射线追踪方法:一种采用从经典各向异性介质射线方程演变而来的由相速度表征的简便形式;另一种采用由对称轴垂直的TI(即VTI)介质声学近似qP波波动方程推导出来的射线方程.文中通过坐标旋转将其扩展到了对称轴倾斜的TI(即TTI)介质.国际上通用的理论模型合成数据偏移试验表明,本文方法既适用于复杂构造成像,又可为TI介质深度域偏移速度分析与模型建立提供高效的偏移引擎. 相似文献
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叠前深度偏移已成为近年来地震偏移成像领域广泛应用的技术之一,其中复杂盐丘下方目标区域结构的成像始终是偏移成像中较难解决的问题.局部角度域波场分解可以提供在空间和方向上的双重局部化信息,因而这一技术被广泛地应用在方向照明分析、成像振幅校正等方面.本文在采用局部指数标架小波束进行角度域方向照明分析的基础上,研究采集系统对复杂盐丘下部层状结构成像质量的影响;同时通过分析目标区对应于相对地表采集系统分布的照明能量,确定叠前炮集数据中对盐下目标区成像起重要贡献的部分,并将这些数据用来对目标区成像,从而达到提高盐下结构成像质量的目的.本文将二维SEG-EAGE盐丘模型中盐下反射体作为目标区,分别计算其照明分析和由照明能量分布确定的炮集数据对目标区的偏移成像结果,同时通过与成像振幅校正前后的成像结果对比,说明了该方法对提高目标区结构成像质量的有效性. 相似文献
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Wave-equation migration velocity analysis. I. Theory 总被引：2，自引：0，他引：2
We present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle‐domain common‐image gathers (ADCIGs) over the aperture‐angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray‐based tomography, we invert ‘image perturbations’ using a linearized wave‐equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs. Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first‐order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction. We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies. 相似文献
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双程波方程逆时深度偏移是复杂介质高精度成像的有效技术,但其结果中通常包含成像方法引起的噪音和假象,一般的滤波方法会破坏成像剖面上的振幅,其中的假象也会给后续地质解释带来困扰.将波场进行方向分解然后实现入射波与反射波的相关成像能够有效地消除这类成像噪音,并提高逆时偏移成像质量.波传播方向的分解通常在频率波数域实现,它会占用大量的存储和计算资源,不便于在沿时间外推的逆时深度偏移中应用.本文提出解析时间波场外推方法,可以在时间外推的每个时间片上实现波传播方向的显式分解,逆时深度偏移中利用分解后的炮检波场进行对应的相关运算,实现成像噪音和成像信号的分离.在模型和实际数据上的测试表明,相比于常规互相关逆时偏移成像结果,本文方法能够有效地消除低频成像噪音和特殊地质构造导致的成像假象. 相似文献
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Unequal illumination of the subsurface highly impacts the quality of seismic imaging. Different image points receive different folds of reflection‐angle illumination, which can be caused by irregular acquisition or by wave propagation in complex media. Illumination problems can deteriorate amplitudes in migrated images. To address this problem, we present a method of stacking angle‐domain common‐image gathers, in which we use local similarity with soft thresholding to determine the folds of local illumination. Normalization by local similarity regularizes local illumination of reflection angles for each image point of the subsurface model. This approach compensates for irregular illumination by selective stacking in the image space, regardless of the cause of acquisition or propagation irregularities. Additional migration is not required because the methodology is implemented in the reflection angle domain after migration. We use two synthetic examples to demonstrate that our method can normalize migration amplitudes and effectively suppress migration artefacts. 相似文献
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This paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful. 相似文献
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Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis 下载免费PDF全文
下载免费PDF全文 Mark Noble 《Geophysical Prospecting》2015,63(2):391-404
Migration velocity analysis aims at determining the background velocity model. Classical artefacts, such as migration smiles, are observed on subsurface offset common image gathers, due to spatial and frequency data limitations. We analyse their impact on the differential semblance functional and on its gradient with respect to the model. In particular, the differential semblance functional is not necessarily minimum at the expected value. Tapers are classically applied on common image gathers to partly reduce these artefacts. Here, we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data‐domain. For an automatic and more robust formulation, we introduce a weight in the original data‐domain objective function. The weight is determined such that the Hessian resembles a Dirac function. In that way, we extend quantitative migration to the subsurface‐offset domain. This is an automatic way to compensate for illumination. We analyse the modified scheme on a very simple 2D case and on a more complex velocity model to show how migration velocity analysis becomes more robust. 相似文献
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3D地震数据不规则采样缺失重建是地震勘探数据处理流程中的重要问题.本文提出了一种基于具有保幅特性的非均匀高阶抛物Radon变换（NHOPRT）地震数据重建方法.在最小二乘反演方程中引入Delaunay三角网格剖分来计算空间不规则加权系数,从而获得最接近完整规则数据的高阶抛物Radon变换域系数.在用SVD求解反演方程过程中,利用高阶抛物Radon变换算子在频率域为指数函数,具有线性可分解特性,将二维空间的高阶抛物Radon变换算子分解为两个独立的一维空间变换算子,减小了变换算子的矩阵大小,从而很大程度地提高了计算效率.理论模型和实际地震数据重建测试证明了本文方法的有效性以及实用性. 相似文献
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探地雷达（GPR）时间域全波形反演计算量巨大,内存要求高,在微机上计算难度大.本文中作者基于GPU并行加速的维度提升反演策略,采用优化的共轭梯度法,避免了Hessian矩阵的计算,在普通微机上实现了时间域全波形二维GPR双参数（介电常数和电导率）快速反演.论文首先推导了二维TM波的时域有限差分法（FDTD）的交错网格离散差分格式及波场更新策略.然后,基于Lagrange乘数法,将约束问题转化为无约束最小问题,构建了共轭梯度法反演目标函数,采用Fletcher-Reeves公式与非精确线搜索Wolfe准则,确保了梯度方向修正因子及迭代步长选取的合理性.而GPU并行计算及维度提升反演策略的应用,数倍地提升了反演速度.最后,开展了3个模型的合成数据的反演实验,分别从观测方式、梯度优化及天线频率等方面,分析了这些因素对雷达全波形反演的影响,说明双参数的反演较单一的介电常数反演,能提供更丰富的信息约束,有效提高模型重建的精度. 相似文献