Wave equation least square imaging using the local angular Hessian for amplitude correction

Local angular Hessian can be used to improve wave equation least square migration images. By decomposing the original Hessian operator into the local wavenumber domain or the local angle domain, the least square migration image is obtained as the solution of a linearized least‐squares inversion in the frequency and local angle domains. The local angular Hessian contains information about the acquisition geometry and the propagation effects based on the given velocity model. The inversion scheme based on the local angular Hessian avoids huge computation on the exact inverse Hessian matrix. To reduce the instability in the inversion, damping factors are introduced into the deconvolution filter in the local wavenumber domain and the local angle domain. The algorithms are tested using the SEG/EAGE salt2D model and the Sigsbee2A model. Results show improved image quality and amplitudes.     

地震数据的反射波动方程最小二乘偏移

基于反射波动方程,本文提出了一种估计地下反射率分布的地震数据最小二乘偏移方法.高频近似下,非齐次的一次反射波动方程的源项是由反射率与入射波场的时间一阶导数相互作用产生的.根据反射波动方程,利用线性最小二乘反演方法由地震反射数据重建出地下产生反射波的反射源,再结合波场正演计算出的地下入射波场,得到地下反射率分布的估计.在地下反射源的线性最小二乘反演重建中,我们采用迭代求解方法,并以地震波的检波器单向地下照明强度作为最小二乘优化问题中Hessian矩阵的近似.     

基于平面波照明的偏移成像补偿

受地下复杂构造和地震数据采集系统的影响,地震波对地下目标的照明出现不均匀,在地震数据的偏移成像中出现成像阴影.根据地震数据最小二乘偏移/反演理论,和把地震波场照明结果作为最小二乘偏移/反演中的Hessian矩阵的近似对偏移成像进行补偿的原理,提出一种应用平面波照明结果对平面波偏移成像结果进行补偿以消除偏移成像阴影的方法.这种基于平面波照明的偏移成像补偿方法相对于局部角度域的照明偏移成像补偿方法具有计算效率上的优势.     

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.     

地震反演成像中的Hessian算子研究

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.     

利用偏移进行视反射率估计的初步研究

视反射率估计是地震数据处理解释中的一项重要内容,通常采用反演的方法得到.本文以地震偏移和地震线性反演理论相结合为基础,并利用保幅单程波传播算子和保幅波动方程叠前偏移算法以及成像空间中的角度域波动方程偏移成像和照明补偿等方法技术,提出了一种利用单程波波动方程偏移进行地下反射面视反射率估计方法,并进行了理论模型的数值试验.这种估计方法得到的视反射率估计是一种近法向入射的小角度反射率.     

Iterative resolution estimation in least‐squares Kirchhoff migration

We apply iterative resolution estimation to least‐squares Kirchhoff migration. Reviewing the theory of iterative optimization uncovers the common origin of different optimization methods. This allows us to reformulate the pseudo‐inverse, model resolution and data resolution operators in terms of effective iterative estimates. When applied to Kirchhoff migration, plots of the diagonal of the model resolution matrix reveal low illumination areas on seismic images and provide information about image uncertainties. Synthetic and real data examples illustrate the proposed technique and confirm the theoretical expectations.     

Least‐squares reverse‐time migration in a matrix‐based formulation

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.     

Simultaneous joint migration inversion for high-resolution imaging/inversion of time-lapse seismic datasets

The current time-lapse practice is to exactly repeat well-sampled acquisition geometries to mitigate acquisition effects on the time-lapse differences. In order to relax the rigid requirements on acquisition effects, we propose simultaneous joint migration inversion as an effective time-lapse tool for reservoir monitoring, which combines a joint time-lapse data processing strategy with the joint migration inversion method. Joint migration inversion is a full-wavefield inversion method that explains the measured reflection data using a parameterization in terms of reflectivity and propagation velocity. Both the inversion process inside the imaging/inversion scheme and the extra illumination provided by including multiples in joint migration inversion makes the obtained velocity and reflectivity operator largely independent of the utilized acquisition geometry and, thereby, relaxes the strong requirement of non-repeatability during the monitoring. Because simultaneous joint migration inversion inverts for all datasets simultaneously and utilizes various constraints on the estimated reflectivities and velocity, the obtained time-lapse differences have much higher accuracy compared to inverting each dataset separately. It allows the baseline and monitor parameters to communicate with each other dynamically during inversion via a user-defined spatial weighting operator. In order to get more localized time-lapse velocity differences, we further extend the regular simultaneous joint migration inversion to a robust high-resolution simultaneous joint migration inversion process using the time-lapse reflectivity difference as an extra constraint for the velocity estimation during inversion. This constraint makes a link between the reflectivity- and the velocity difference by exploiting the relationship between them. We demonstrate the feasibility of the proposed method with a highly realistic synthetic model based on the Grane field offshore Norway and a time-lapse field dataset from the Troll Field.     

Avoiding pitfalls of least‐squares inversion by using the energy‐flux error criterion

Seismic inversion by modelling and data fitting depends on the criterion chosen to measure the misfit between observed and modelled data. The popular least‐squares error criterion has an important drawback: it is sensitive both to the shape of the recording surface and to velocity variations along this surface. Tests on synthetic seismic reflection data show that least‐squares inversion may work surprisingly poorly in situations where (i) the range of angles between reflected rays and the acquisition surface is large, (ii) the velocity varies significantly along this surface, or (iii) a compensation for the effects of dissipation is applied to the gradients. In these situations, the gradients may contain important artefacts and have incorrect amplitudes. The outgoing flux of energy of the residual wavefield across the acquisition surface provides an alternative measure of the data misfit which is independent of the recording surface, provided this surface is closed, and which is only sensitive to the aperture in the practical situation of an open surface or line of receivers. Energy‐flux inversion presents a strong resemblance to reverse‐time migration, but with the additional possibility of iteratively improving the images. In all the tests, energy‐flux inversion provided better images than least‐squares inversion.     

Efficient amplitude encoding least‐squares reverse time migration using cosine basis

Least‐squares reverse time migration provides better imaging result than conventional reverse time migration by reducing the migration artefacts, improving the resolution of the image and balancing the amplitudes of the reflectors. However, it is computationally intensive. To reduce its computational cost, we propose an efficient amplitude encoding least‐squares reverse time migration scheme in the time domain. Although the encoding scheme is effective in increasing the computational efficiency, it also introduces the well‐known crosstalk noise in the gradient that degrades the quality of the imaging result. We analyse the cause of the crosstalk noise using an encoding correlation matrix and then develop two numerical schemes to suppress the crosstalk noise during the inversion process. We test the proposed method with synthetic and field data. Numerical examples show that the proposed scheme can provide better imaging result than reverse time migration, and it also generates images comparable with those from common shot least‐squares reverse time migration but with less computational cost.     

基于照明补偿的单程波最小二乘偏移

最小二乘偏移是一种基于反射地震数据与地下反射率间线性关系而建立起来的地震数据线性反演方法,相比常规偏移成像具有更好的保幅性能.本文提出了一种基于照明补偿的单程波最小二乘偏移方法,首先利用单程波方程的稳定Born近似广义屏波场传播算子构建反射地震数据与地下反射率间的线性算子,然后再应用线性最优化方法求解最小二乘偏移所对应的线性反问题.在迭代求解最优化问题的过程中,以地震波场的地下照明强度作为迭代反演的预条件算子加快迭代的收敛速度.单程波传播过程中考虑了速度分界面产生的透射效应,并用单极震源代替常规偏移中的偶极震源.把本文提出的方法应用于层状理论模型和Marmosi模型地震数据的数值试验中均取得了理想的结果.     

目标函数叠前保幅偏移方法与应用

将理论反射率与偏移反射率的差作为目标函数,给出一种迭代振幅补偿保幅偏移方法.把偏移看作一个反问题,寻找反问题中的最优解.偏移算子是正演算子的伴随共轭,其伴随矩阵非对角占优.通过预条件优化伴随矩阵,使Hessian矩阵准对角化.依据地震波传播稳定相位理论,计算反射点,以反射点为中心、菲涅耳带为半径偏移.考虑振幅几何扩散补偿、散射角度补偿,在迭代反演过程求出最优解,即保幅偏移解.本文给出了一个保幅数值模拟结果和一个实际地震数据实例.     

一种新的针对反射波的逆时偏移真振幅成像条件

真振幅成像是一种代表性的定量估计模型参数扰动高波数部分的地震波成像方法.经典的真振幅成像方法在高频近似和理想照明假设条件下求取显式对角Hessian逆矩阵作为偏移振幅加权算子,用以校正波传播过程中的几何扩散效应,得到模型参数扰动的带限估计.真振幅保真成像方法在利用逆时偏移（RTM）框架实现时会产生低波数噪声,影响对高波数参数估计的精度.本文给出了一种新的基于RTM框架的真振幅保真成像条件,该成像条件针对反射波数据,在高频近似下散射模式对应正问题及Bayes反问题框架下导出.与传统基于高频渐进反演的波动方程成像方法类似,利用本文提出RTM成像条件能够保证计算结果与高频近似下反演结果的一致性.同时,利用本文提出RTM真振幅成像条件能够在成像过程中自动保真的消除传统真振幅RTM算法中存在低波数噪声,模型数值实验结果验证了本文方法的正确性和有效性.     

基于短算子设计的黏性介质叠前时间偏移

为了提高频域黏性介质叠前时间偏移的计算效率,本文采用加权最小平方方法设计高精度的、最优时域褶积短算子,发展了一套表驱动的时域黏性介质叠前时间偏移方法.该方法将大量的逐频率补偿运算转化为少量的时域褶积运算,并将走时,振幅表和补偿褶积短算子系数表的计算过程与补偿成像过程相剥离,提高了时域算法的计算效率;通过控制最大的补偿因...     

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.     

Least squares reverse-time migration in the pseudodepth domain and reservoir exploration

Least squares reverse-time migration (LSRTM) is an inversion method that removes artificial images and preserves the amplitude of reflectivity sections. LSRTM has been used in reservoir exploration and processing of 4D seismic data. LSRTM is, however, a computationally costly and memory-intensive method. In this study, LSRTM in the pseudodepth domain was combined with the conjugate gradient method to reduce the computational cost while maintaining precision. The velocity field in the depth domain was transformed to the velocity field in the pseudodepth domain; thus, the total number of vertical sampling points was reduced and oversampling was avoided. Synthetic and field data were used to validate the proposed method. LSRTM in the pseudodepth domain in conjunction with the conjugate gradient method shows potential in treating field data.     

同时震源数据的加权结构增强最小二乘逆时偏移

同时震源（Simultaneous-source,SS）地震采集技术能有效地提高地震数据采集效率,但直接对SS混合数据偏移成像会在最后的成像剖面中引入很强的串扰噪声.将SS数据偏移成像看作一个反演问题,利用最小二乘（Least-squares,LS）求解是压制SS直接成像中串扰噪声的一种有效尝试.构造增强滤波（Structure-enhancing filter,SE）约束的最小二乘逆时偏移（LSRTM）方法可以有效地压制SS数据成像中的串扰噪声,但SE实质为低通滤波,会将成像中的陡倾角等细节信息平滑涂抹,降低成像分辨率.本文在利用SE对LSRTM约束的基础上,提出了基于加权构造增强约束的LSRTM方法（WSE-LSRTM）并应用于SS数据的反演成像中.该方法不仅能够有效地压制串扰噪声（cross-talk）、保留结构信息,而且可以保护成像中的陡倾角结构不被过度平滑而破坏.在对简单模型和复杂Marmousi模型的数值测试中,该方法都取得了良好的效果.     

Acoustic Reverse-time Migration using Optimal Staggered-grid Finite-difference Operator Based on Least Squares

Reverse-time migration (RTM) directly solves the two-way wave equation for wavefield propagation; therefore, how to solve the wave equation accurately and quickly is very important for RTM. The conventional staggered-grid finite-difference (SFD) operators are usually based on the Taylor-series expansion theory. If they are used to solve wave equation on a larger frequency content, a strong dispersion will occur, which directly affects the seismic image quality. In this paper, we propose an optimal SFD operator based on least squares to solve acoustic wave equation for prestack RTM, and obtain a new antidispersion RTM algorithm that can use short spatial difference operators. The synthetic and real data tests demonstrate that the least squares SFD (LSSFD) operator can mitigate the numerical dispersion, and the acoustic RTM using the LSSFD operator can effectively improve image quality comparing with that using the Taylor-series expansion SFD (TESFD) operator. Moreover, the LSSFD method can adopt a shorter spatial difference operator to reduce the computing cost.