基于时空局域化dreamlet单程波算子的观测系统沉降法偏移

Dreamlet偏移成像目的是探索一类能够对地震波场和单程波传播算子同时分解和压缩的理论和方法,也即实现在压缩域的传播与成像、地震数据在时间和空间的非平稳性质,决定了要实现地震数据的有效稀疏表示,分解方法必须在时间和空间上同时具有局域化性质.Dreamlet由时间和空间局部分解原子的张量积构成,可以看作一种脉冲-小波束形式的波场分解原子.时空局域化的dreamlet单程波传播算子在对波场沿深度方向延拓时,地震数据在时间轴上总是向同一方向流动.随着深度的增加,部分用于成像浅层结构的数据归位至其空间位置后被dreamlet算子丢弃,波场的有效记录时间变短,每一步用于波场延拓的计算量也相应下降.为了充分发挥这一优势,本文介绍dreamlet传播算子与观测系统沉降法偏移相结合的理论与方法.观测系统沉降法偏移每一步都将记录到的所有数据向下延拓,沉降后的波场等效于把源和检波器都放置在目标深度所能接收的反射数据.Dreamlet观测系统沉降过程只保留用于成像观测系统下部地质结构的有效数据,自动丢弃已经用于成像观测系统上部而对下部成像没有贡献的信号.本文通过二维SEG/EAGE叠后和Marmousi叠前数据算例展示了dreamlet传播算子应用于观测系统沉降法偏移的这一特点.数值算例结果显示,在不影响成像质量的前提下,该偏移方法能够有效减少传播数据量,为发展一种快速高效的偏移方法提供了新的思路.     

时-空局域化地震波传播方法:Dreamlet叠前深度偏移

提出了一种在时间和空间上完全局域化的波场分解和传播算法─dreamlet偏移方法.Dreamlet是一种脉冲-小波束形式的波场分解原子,它利用多维局部分解变换,把时空域波场映射到局部时间-频率-空间-波数相空间,并用局部相空间的传播算子(dreamlet算子)沿深度延拓.本文利用多维局部余弦变换实现dreamlet算法,分解后的波场系数和传播算子不仅有很好的稀疏性,且均为实数,也即波的传播和成像过程完全在实数域实现.文中推导了局部余弦基dreamlet波场分解和传播算子理论公式并将其应用于叠前深度偏移.在dreamlet相空间波的传播过程为稀疏矩阵相乘,而且延拓后的地表数据波场的有效时间长度随深度的增加不断减小,从而可以减少需要传播的波场系数.二维SEG/EAGE盐丘和SIGSBEE模型算例验证了理论推导的正确性,成像结果显示该方法在横向速度变化剧烈情况下有很好的精度.     

基于局部余弦基小波束的观测系统沉降法叠前深度偏移

将局部余弦基小波束波场分解、传播与观测系统沉降法叠前深度偏移相结合,推导了源-检波器观测系统沉降法传播算子.本算法中,先对频率域的共点源和共点检波器道集做局部余弦小波束分解,然后分别沿共小波束源和共小波束检波器在深度方向延拓得到下一层波场.每个深度的波场,都等效于把源和检波器放在该层后所能接收到的地震记录,每点的像值由炮点和检波点重合时的零时刻波场值给出.通过二维SEG/EAGE盐丘模型和Marmousi模型的偏移成像结果验证该方法理论推导的正确性.另外,结果显示该方法继承了小波束域波场延拓在速度扰动较大情况下波传播及成像精度高的优点.     

Gabor‐frame‐based Gaussian packet migration

We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.     

低信噪比海底多分量地震数据波场分离方法

以多分量地震观测为基础,联合纵波和转换横波数据能更有效地估计地下介质的弹性和物性参数,提升地质构造成像与油气储层描述的精度.在海底多分量地震数据处理过程中,观测记录的上-下行波分解和P/S波分离可压制水层鸣震以及P与S波之间的串扰,对偏移成像和纵横波速度建模至关重要.但受海底环境、仪器与观测因素共同影响,许多海底多分量地震资料都无法基于现有的海底波场分离方法与流程取得合理的结果.本文以海底声波场与弹性波场分离基本原理为基础,通过对方法流程的修正,摆脱常规流程对中小偏移距直达波信号的依赖性.借助模拟数据实验讨论了波场分离对海底介质参数、噪声的敏感性.结合东海YQ探区海底多分量地震资料上-下行P/S波分离及其叠前深度偏移处理,验证了本文方法流程的可行性.     

Source location using time‐reverse imaging

We present the chain of time‐reverse modeling, image space wavefield decomposition and several imaging conditions as a migration‐like algorithm called time‐reverse imaging. The algorithm locates subsurface sources in passive seismic data and diffractors in active data. We use elastic propagators to capitalize on the full waveforms available in multicomponent data, although an acoustic example is presented as well. For the elastic case, we perform wavefield decomposition in the image domain with spatial derivatives to calculate P and S potentials. To locate sources, the time axis is collapsed by extracting the zero‐lag of auto and cross‐correlations to return images in physical space. The impulse response of the algorithm is very dependent on acquisition geometry and needs to be evaluated with point sources before processing field data. Band‐limited data processed with these techniques image the radiation pattern of the source rather than just the location. We present several imaging conditions but we imagine others could be designed to investigate specific hypotheses concerning the nature of the source mechanism. We illustrate the flexible technique with synthetic 2D passive data examples and surface acquisition geometry specifically designed to investigate tremor type signals that are not easily identified or interpreted in the time domain.     

利用矩阵分解理论的双程波方程叠前深度偏移方法

叠前深度偏移理论及方法一直是地震数据成像中研究的热点问题.业界对单程波叠前深度偏移方法和逆时深度偏移开展了深入的研究,但对双程波方程波场深度延拓理论及成像方法的研究还鲜有报道.本文以地表记录的波场值为基础,利用单程波传播算子估计波场对深度的偏导数,为在深度域求解双程波方程提供充分的边界条件,并提出利用矩阵分解理论实现双程波方程的波场深度外推.通过对强速度变化介质中传播波场的计算,与传统的单程波偏移方法相比,本文提出的偏移方法计算的波场与常规有限差分技术计算的波场相一致,证明了本方法计算的准确性.通过对SEAM模型的成像,在相同的成像参数下,与传统的单程波偏移算法和逆时深度偏移算法方法相比,本文提出的偏移方法能够提供更少的虚假成像和更清晰的成像结果.本文所提偏移算法具有深度偏移和双程波偏移的双重特色,推动和发展了双程波叠前深度偏移的理论和实践.     

Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration

The key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.     

Increasing resolution of reverse‐time migration using time‐shift gathers

Reverse‐time migration has become an industry standard for imaging in complex geological areas. We present an approach for increasing its imaging resolution by employing time‐shift gathers. The method consists of two steps: (i) migrating seismic data with the extended imaging condition to get time‐shift gathers and (ii) accumulating the information from time‐shift gathers after they are transformed to zero‐lag time‐shift by a post‐stack depth migration on a finer grid. The final image is generated on a grid, which is denser than that of the original image, thus improving the resolution of the migrated images. Our method is based on the observation that non‐zero‐lag time‐shift images recorded on the regular computing grid contain the information of zero‐lag time‐shift image on a denser grid, and such information can be continued to zero‐lag time‐shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero‐offset migration and is almost negligible compared with the cost of pre‐stack shot‐record reverse‐time migration. Numerical tests on synthetic models demonstrate that the method can effectively improve reverse‐time migration resolution. It can also be regarded as an approach to improve the efficiency of reverse‐time migration by performing wavefield extrapolation on a coarse grid and by generating the final image on the desired fine grid.     

Acoustic directional snapshot wavefield decomposition

Up–down wavefield decomposition is effectuated by a scaled addition or subtraction of the pressure and vertical particle velocity, generally on horizontal or vertical surfaces, and works well for data given on such surfaces. The method, however, is not applicable to decomposing a wavefield when it is given at one instance in time, i.e. on snapshots. Such situations occur when a wavefield is modelled with methods like finite-difference techniques, for the purpose of, for example, reverse time migration, where the entire wavefield is determined per time instance. We present an alternative decomposition method that is exact when working on snapshots of an acoustic wavefield in a homogeneous medium, but can easily be approximated to heterogeneous media, and allows the wavefield to be decomposed in arbitrary directions. Such a directional snapshot wavefield decomposition is achieved by recasting the acoustic system in terms of the time derivative of the pressure and the vertical particle velocity, as opposed to the vertical derivative in up–down decomposition for data given on a horizontal surface. As in up–down decomposition of data given at a horizontal surface, the system can be eigenvalue decomposed and the inverse of the eigenvector matrix decomposes the wavefield snapshot into fields of opposite directions, including up–down decomposition. As the vertical particle velocity can be rotated at will, this allows for decomposition of the wavefield into any spatial direction; even spatially varying directions are possible. We show the power and effectiveness of the method by synthetic examples and models of increasing complexity.     

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries + multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two‐way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal‐to‐noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed‐loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).     

Migration velocity analysis and waveform inversion

Least‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.     

基于波场垂向和水平方向外推的高陡构造偏移

常规的单程波波动方程偏移成像方法对大角度的高陡构造偏移成像存在内在的限制.根据波动方程在各个空间方向的数学特性和高陡构造反射地震波的传播特征,通过把地震波分解为垂向的上下行波、水平方向的前后行波和左右行波,提出基于波场垂向外推和水平方向外推相结合的单程波波动方程高陡构造偏移成像方法,即用波场垂向外推的单程波波动方程偏移成像方法解决中低角度平缓构造的偏移成像,用波场水平方向外推的单程波波动方程偏移成像方法解决中高角度陡倾构造的偏移成像.这种基于波场垂向和水平方向外推相结合的高陡构造偏移成像方法是常规单程波波动方程叠前深度偏移成像方法的补充和改进,它相对基于全波方程的逆时偏移具有计算效率上的优势.     

三维VSP数据高效偏移成像的超道集方法

当前的三维VSP地震数据偏移成像实现都是在共炮点道集或共检波点道集中逐个道集循环进行的,计算效率相对较低.根据三维VSP观测系统中炮点和检波点布置的特殊性和地震波场满足线性叠加的特性,本文提出了一种三维VSP数据的高效偏移成像方法,即首先通过对三维VSP共接收点道集进行地震数据的广义合成得到一种超道集,然后在共接收点道集的波场深度外推过程中逐步应用多震源波场对超道集进行偏移成像,即利用一次波场深度外推循环完成对所有共检波点道集数据的偏移成像.通过三维VSP模型数据与实际地震数据的偏移成像试验验证了这种高效的超道集偏移成像方法可取得与常规共检波点道集相当的偏移成像效果,还具有极高的计算效率,其计算量与单个共检波点道集的偏移成像计算量相当.     

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods.     

Reverse time migration of ground-penetrating radar with full wavefield decomposition based on the Hilbert transform

The conventional reverse time migration of ground-penetrating radar data is implemented with the two-way wave equation. The cross-correlation result contains low-frequency noise and false images caused by improper wave paths. To eliminate low-frequency noise and improve the quality of the migration image, we propose to separate the left-up-going, left-down-going, right-up-going and right-down-going wavefield components in the forward- and backward-propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground-penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground-penetrating radar data of a tilt-interface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground-penetrating radar data, low-frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.     

非零偏VSP弹性波叠前逆时深度偏移技术探讨

非零偏VSP地震资料是一种多分量资料,处理非零偏VSP资料,弹性波叠前逆时深度偏移技术无疑是最适合的处理技术.本文从二维各向同性介质的弹性波波动方程出发,研究了对非零偏VSP资料进行叠前逆时深度偏移的偏移算法,讨论了逆时传播过程中的边值问题和数值频散问题及其相应的解决方案;采用求解程函方程计算得到地下各点的地震波初至时间作为成像时间,实现了非零偏VSP资料的叠前逆时深度偏移.最后进行了模型试算和非零偏VSP地震资料的试处理,结果表明该方法不受地层倾角限制,较适用于高陡构造地区或介质横向速度变化较大地区的非零偏VSP地震资料处理.     

The design of visco‐acoustic weighted L1‐error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L ₁ ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L ₁ ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L ₄ ‐norm and L_∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L ₁ ‐error method enhances the resolution and results in practically stable images.     

The utilization of the double focal transformation for sparse data representation and data reconstruction

In many cases, seismic measurements are coarsely sampled in at least one dimension. This leads to aliasing artefacts and therefore to problems in the subsequent processing steps. To avoid this, seismic data reconstruction can be applied in advance. The success and reliability of reconstruction methods are dependent on the assumptions they make on the data. In many cases, wavefields are assumed to (locally) have a linear space–time behaviour. However, field data are usually complex, with strongly curved events. Therefore, in this paper, we propose the double focal transformation as an efficient way for complex data reconstruction. Hereby, wavefield propagation is formulated as a transformation, where one‐way propagation operators are used as its basis functions. These wavefield operators can be based on a macro velocity model, which allows our method to use prior information in order to make the data decomposition more effective. The basic principle of the double focal transformation is to focus seismic energy along source and receiver coordinates simultaneously. The seismic data are represented by a number of localized events in the focal domain, whereas aliasing noise spreads out. By imposing a sparse solution in the focal domain, aliasing noise is suppressed, and data reconstruction beyond aliasing is achieved. To facilitate the process, only a few effective depth levels need to be included, preferably along the major boundaries in the data, from which the propagation operators can be calculated. Results on 2D and 3D synthetic data illustrate the method's virtues. Furthermore, seismic data reconstruction on a 2D field dataset with gaps and aliased source spacing demonstrates the strength of the double focal transformation, particularly for near‐offset reflections with strong curvature and for diffractions.