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.     

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.     

基于一阶速度-应力方程的多震源最小二乘逆时偏移

最小二乘逆时偏移(Least-Square Reverse Time Migration,LSRTM)相比于常规偏移具有更高的成像分辨率、振幅保幅性及均衡性等优势,是当前研究的热点之一.然而,目前LSRTM算法大多是基于二阶常密度标量声波方程建立的,忽略了密度变化对振幅的影响,因而基于振幅匹配策略的常规LSRTM很难在变密度介质下取得保真的成像结果.一阶速度-应力方程能够很好地处理变密度介质,但简单地将一阶速度-应力方程应用到LSRTM中缺乏理论基础.为此,本文从LSRTM的正问题入手,提出了基于交错网格的一阶速度-应力方程LSRTM理论方法.首先将一阶波动方程线性化,建立了一阶方程LSRTM的目标泛函,随后推导其伴随方程,并借助伴随状态法给出了迭代更新流程,最终建立了基于一阶速度-应力方程LSRTM的理论框架.进一步,通过在相位编码LSRTM中引入随机最优化思想,极大地减小了计算量、提高了计算效率.最后,通过模型试算验证了本算法的正确性和有效性.     

表面多次波最小二乘逆时偏移成像

使用相同的炮记录,多次波偏移能提供比反射波偏移更广的地下照明和更多的地下覆盖但是同时产生很多的串声噪声.相比传统逆时偏移,最小二乘逆时偏移反演的反射波成像结果具有更高的分辨率和更均衡的振幅.我们主要利用最小二乘逆时偏移压制多次波偏移产生的串声噪声.多次波最小二乘逆时偏移通常需要一定的迭代次数以较好地消除串声噪声.若提前将一阶多次波从所有阶数的多次波中过滤出来,使用相同的迭代次数,一阶多次波的最小二乘逆时偏移能够得到具有更高信噪比的成像剖面,而且能够提供与多次波最小二乘逆时偏移相似的有效地下结构成像.     

基于一阶速度-应力方程的VTI介质最小二乘逆时偏移

地下地层普遍存在各向异性,忽略介质各向异性会导致速度估计不准确,成像精度下降.基于二阶声波方程的最小二乘逆时偏移忽略了介质各向异性及密度变化的影响,致使模拟地震数据与实际观测数据不匹配,影响收敛速度和反演成像质量.VTI介质一阶速度-应力方程能较好适应各向异性变密度情况,为此,本文首先从VTI介质一阶速度-应力方程出发,进行波动方程线性化;其次推导了相应的扰动方程和伴随方程,并通过伴随状态法得到梯度更新公式;最终形成基于一阶方程的LSRTM算法理论及实现流程.在实现算法的基础上,通过数值试算及成像结果对比,验证了本文算法在处理变密度和VTI介质时的有效性和优越性.偏移速度以及各向异性Thomsen参数误差的敏感性测试及误差收敛曲线对比结果进一步表明:速度及Thomsen参数对成像结果存在明显影响,其中速度敏感性最强,参数epsilon次之,参数delta的敏感性最弱.     

最小二乘逆时偏移中黏弹性和各向异性的校正:以渤海湾地区地震数据为例

地下介质中存在黏弹性和各向异性,在应用最小二乘逆时偏移时,如果没有对黏弹性和各向异性的影响进行校正,在观测数据和模拟数据的匹配过程中就会发生错误,最终使得最小二乘逆时偏移无法得到准确的成像结果.因此,本论文首先对最小二乘逆时偏移的黏弹性和各向异性进行分别校正,然后对两种影响进行同时校正.在实际资料试算部分,通过对渤海湾数据进行测试,分别采用常规声波最小二乘逆时偏移、补偿黏弹性的最小二乘逆时偏移、校正各向异性的最小二乘逆时偏移及同时校正两种性质的最小二乘逆时偏移进行比较测试,证明了在同时校正了黏弹性和各向异性影响之后,最小二乘逆时偏移得到了更高质量的成像结果,具体表现在低频噪音压制、震源效应压制、深部能量改善、分辨率提升、目的层刻画等方面都明显优于其他三种最小二乘逆时偏移的成像结果,同时也证明了同时校正黏弹性和各向异性最小二乘逆时偏移方法的正确性及在实际资料处理中的适用性.     

基于平面波加速的VTI介质最小二乘逆时偏移

地震各向异性集中表现为速度各向异性,势必影响地震波运动学特征.传统声波逆时偏移(RTM)和最小二乘逆时偏移(LSRTM)没有考虑介质各向异性特征,导致反射波不能正确归位、同相轴出现扭曲及寻优速度慢或不收敛等,VTI介质逆时偏移(VTI-RTM)矫正了声波成像的不足,但仍存在低频干扰严重、中深部成像不佳、振幅保持差等缺陷.为此,本文首先实现了VTI介质最小二乘逆时偏移(VTI-LSRTM)方法,为了节省I/O及内存需求并提高效率,进一步引入平面波编码技术,提出了一种基于平面波加速的VTI介质最小二乘逆时偏移(VTI-PLSRTM)策略.在此基础上开展了简单模型及复杂Marmousi模型成像试验,并与标准逆时偏移剖面对比表明:本方法能够校正各向异性造成的相位畸变,且在迭代中自动压制串扰及低频噪声、补偿中深部能量,是一种兼具质量与效率的保幅成像策略;对速度误差的敏感性测试说明该方法需要相对正确的偏移速度及Thomsen参数模型.     

基于Student′s t分布的不依赖子波最小二乘逆时偏移

最小二乘逆时偏移(Least-Squares Reverse Time Migration,LSRTM)与常规偏移相比具有更高的成像分辨率、振幅保真性及均衡性等优势,是当前研究的热点之一.震源子波的估计直接影响LSRTM结果的好坏,在实际情况下考虑到震源子波的空变特性,其估计十分困难.为了消除子波对LSRTM结果的影响,本文发展了基于卷积目标泛函的不依赖子波LSRTM算法.目标泛函由观测记录卷积模拟记录的参考道以及模拟记录卷积观测记录的参考道组成,由于观测子波和模拟子波在目标泛函的两项中同时存在,从而消除了子波的影响.此外,常用的基于L2范数拟合的LSRTM算法对噪声非常敏感,尤其是当地震数据中含有异常值时,常规LSRTM无法得到满意的结果.Student′s t分布相比L2范数具有更好的稳健性,本文将其推广到不依赖子波LSRTM中,提升了算法的稳健性,最后通过理论模型及实际资料试算验证了算法的有效性和对复杂模型的适应性.     

去均值归一化互相关最小二乘逆时偏移及其应用

最小二乘逆时偏移相对于常规逆时偏移具有更高的成像分辨率、振幅保幅性及均衡性等优势,在一定程度上可满足岩性油气藏勘探的需求,是目前研究的热点之一.然而由于实际地下介质的黏滞性和变密度,以及无法准确地估计震源子波等,基于振幅匹配的常规最小二乘逆时偏移算法很难在实际资料处理中取得好的效果.此外,实际数据常包含大量噪声,进一步限制了常规算法的应用.为此,本文通过修改目标泛函,提出了去均值归一化的互相关最小二乘逆时偏移算法,并给出了陆上资料的应用实例.研究表明,归一化策略减弱了算法对子波能量的苛求;互相关算法强调相位匹配,进一步弱化了子波的影响,提升了算法的稳定性和可靠性;去均值思想在处理低信噪比资料方面有较大优势.理论模型和陆上实际资料处理都验证了本算法的有效性和对复杂模型的适应性.     

基于逆散射成像条件的最小二乘逆时偏移

最小二乘逆时偏移（LSRTM）相对于常规逆时偏移（RTM）具有分辨率更高、振幅更准确、噪音更少等优势,可以对复杂的地质构造进行有效的成像.这种迭代更新反演成像方法十分依赖目标函数的梯度质量和计算效率.当地质模型中存在强反射界面或者记录中存在折射波时,基于常规互相关成像条件（CCC）的最小二乘逆时偏移梯度会包含很强的低频噪音,从而使反演的收敛速度和成像质量降低.为此,本文在最小二乘逆时偏移的梯度中引进了逆散射成像条件来压制这种低频噪音,并以此提出基于逆散射成像条件（ISC）的最小二乘逆时偏移方法.数值模拟结果表明,两者计算耗时基本一致,但逆散射成像条件能高效压制梯度中的低频噪音,从而使反演过程中收敛加速,成像质量得到显著提高.     

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.     

Acquisition design for direct reflectivity and velocity estimation from blended and irregularly sampled data

Blended acquisition along with efficient spatial sampling is capable of providing high-quality seismic data in a cost-effective and productive manner. While deblending and data reconstruction conventionally accompany this way of data acquisition, the recorded data can be processed directly to estimate subsurface properties. We establish a workflow to design survey parameters that account for the source blending as well as the spatial sampling of sources and detectors. The proposed method involves an iterative scheme to derive the survey design leading to optimum reflectivity and velocity estimation via joint migration inversion. In the workflow, we extend the standard implementation of joint migration inversion to cope with the data acquired in a blended fashion along with irregular detector and source geometries. This makes a direct estimation of reflectivity and velocity models feasible without the need of deblending or data reconstruction. During the iterations, the errors in reflectivity and velocity estimates are used to update the survey parameters by integrating a genetic algorithm and a convolutional neural network. Bio-inspired operators enable the simultaneous update of the blending and sampling operators. To relate the choice of survey parameters to the performance of joint migration inversion, we utilize a convolutional neural network. The applied network architecture discards suboptimal solutions among newly generated ones. Conversely, it carries optimal ones to the subsequent step, which improves the efficiency of the proposed approach. The resultant acquisition scenario yields a notable enhancement in both reflectivity and velocity estimation attributable to the choice of survey parameters.     

AN EXTENSION OF THE BORN INVERSION METHOD TO A DEPTH DEPENDENT REFERENCE PROFILE*

An extension of the multidimensional Born inversion technique for acoustic waves is described. In earlier work, a perturbation in reference sound velocity was determined by assuming that the reference velocity was constant. In this extension, we allow the reference velocity to be a function of the depth variable z. The output of this method is a high-frequency bandlimited reflectivity function of the subsurface. The reflectivity function is an array of bandlimited singular functions scaled by the normal reflection strength. Each singular function is a Dirac delta function of a scalar argument which measures distance normal to a reflecting interface. Thus, the reflectivity function is an indicator map of subsurface reflectors equivalent to the map produced by migration. In addition to the assumption of small perturbation, the method requires that the reflection data reside in the high frequency regime in a well-defined sense. The method is based on the derivation of an integral equation for the perturbation in sound velocity from a known reference velocity. When the reference velocity is constant, the integral equation admits an analytic solution as a multifold integral of the reflection data. Further high frequency asymptotic analysis simplifies this integral considerably and leads to an extremely efficient numerical algorithm for computing the reflectivity function. The development of a computer code to implement this constant-reference-velocity solution is published elsewhere. For a reference velocity c(z) we can no longer invert the integral equation exactly. However, we can write down an asymptotic high-frequency approximation for the kernal of the integral equation and an asymptotic solution for the perturbation. The computer implementation of this result is designed along the same lines as the code for constant background velocity. In tests the total processing time for this algorithm with depth-dependent background velocity is usually considerably less than that required by a standard Kirchhoff migration algorithm. The method is implemented as a migration technique and compared with alternative migration algorithms on the flanks of the salt dome.     

基于最小二乘逆时偏移的场声反射成像测井模拟?

近年来,声反射成像测井技术（ARILT）在井旁裂缝、孔洞性储层评价中成为研究热点。常规ARILT的探测深度一般在20m以内,且对复杂构造边界刻画能力不足。本文基于测井观测系统及采集参数,将最小二乘逆时偏移（LSRTM）地震成像技术引入ARILT中,以提高井旁区域有效成像范围和成像精度。本文在实现偏移算法及处理流程基础上,将算法用于典型模型和实际资料,重点分析不同频率、深度和偏移方法成像效果的差异。成像结果对比发现:①偏移算法影响ARILT成像精度,LSRTM具有较高分辨率,并能揭示构造体横向变化特征;②激发源频率也影响成像分辨率,提高频率会改善分辨率,但会降低探测深度;③在给定的测井观测参数下,LSRTM能有效探测23m范围内的井旁构造。      

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.     

Super-resolution least-squares prestack Kirchhoff depth migration using the <Emphasis Type="Italic">L</Emphasis><Subscript>0</Subscript>-norm

Least-squares migration (LSM) is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L₂-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L₀-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.     

A nonlinear method for multiparameter inversion of pre‐stack seismic data based on anisotropic Markov random field

Multiparameter inversion for pre‐stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non‐unique results and unstable nature of the processing; the pre‐stack seismic inversion problem is ill‐posed and band‐limited. Combining the full Zoeppritz equation and additional assumptions with edge‐preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge‐preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity R_PP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S‐ and P‐wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P‐wave velocity, the fitting deviation of S‐wave velocity, and the density were inverted instead of the P‐wave velocity, the S‐wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two‐dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high‐order anisotropic Markov random field neighbourhoods at early stages and low‐order anisotropic Markov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.     

Least-squares reverse time migration method using the factorization of the Hessian matrix

Least-squares reverse time migration (LSRTM) can eliminate imaging artifacts in an iterative way based on the concept of inversion, and it can restore imaging a...