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1.
The goal of wave‐mode separation and wave‐vector decomposition is to separate a full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse‐time migration to handle each wave mode independently. Several of the previously proposed methods to accomplish this task require the knowledge of the polarisation vectors of all three wave modes in a given anisotropic medium. We propose a wave‐vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low‐rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low‐symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase‐velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artefacts caused by the local discontinuity of polarisation vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal–noise orthogonalisation. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media.  相似文献   

2.
With the progress in computational power and seismic acquisition, elastic reverse time migration is becoming increasingly feasible and helpful in characterizing the physical properties of subsurface structures. To achieve high-resolution seismic imaging using elastic reverse time migration, it is necessary to separate the compressional (P-wave) and shear (S-wave) waves for both isotropic and anisotropic media. In elastic isotropic media, the conventional method for wave-mode separation is to use the divergence and curl operators. However, in anisotropic media, the polarization direction of P waves is not exactly parallel to the direction of wave propagation. Also, the polarization direction of S-waves is not totally perpendicular to the direction of wave propagation. For this reason, the conventional divergence and curl operators show poor performance in anisotropic media. Moreover, conventional methods only perform well in the space domain of regular grids, and they are not suitable for elastic numerical simulation algorithms based on non-regular grids. Besides, these methods distort the original wavefield by taking spatial derivatives. In this case, a new anisotropic wave-mode separation scheme is developed using Poynting vectors. This scheme can be performed in the angle domain by constructing the relationship between group and polarization angles of different wave modes. Also, it is performed pointwise, independent of adjacent space points, suitable for parallel computing. Moreover, there is no need to correct the changes in phase and amplitude caused by the derivative operators. By using this scheme, the anisotropic elastic reverse time migration is more efficiently performed on the unstructured mesh. The effectiveness of our scheme is verified by several numerical examples.  相似文献   

3.
Seismic data are usually separated into P-waves and S-waves before being put through a scalar (acoustic) migration. The relationship between polarization and moveout is exploited to design filters that extract the desired wavetype. While these filters can always be applied to shot records, they can only be applied to a triaxial common-receiver gather in special cases since the moveout of scattered energy on the receiver gather relates to path differences between the surface shots and the scatterer while the polarization is determined by the path from scatterer to downhole geophone. Without the ability to separate wavefields before migration, a ‘vector scalar’ or an elastic migration becomes a necessity. Here the propagation of the elastic wavefield for a given mode (e.g. P-S) is approximated by two scalar (acoustic) propagation steps in a ‘vector scalar’ migration. ‘Vector’ in that multicomponent data is migrated and 'scalar’ in that each propagation step is based on a scalar wave equation for the appropriate mode. It is assumed that interaction between the wavefields occurs only once in the far-field of both the source and receiver. Extraction of the P, SV and SH wavefields can be achieved within the depth migration (if one assumes isotropy in the neighbourhood of the downhole receiver) by a projection onto the polarization for the desired mode. Since the polarization of scattered energy is only a function of scatterer position and receiver position (and not source position), the projection may be taken outside the migration integral in the special case of the depth migration of a common-receiver gather. The extraction of the desired mode is then performed for each depth migration bin after the separate scalar migration of each receiver gather component. This multicomponent migration of triaxial receiver gathers is conveniently implemented with a hybrid split-step Fourier-excitation-time imaging condition depth migration. The raytracing to get the excitation-time imaging condition also provides the expected polarization for the post-migration projection. The same downward extrapolated wavefield can be used for both the P-P and P-S migrations, providing a flexible and efficient route to the migration of multicomponent data. The technique is illustrated on a synthetic example and a single-level Walk-away Seismic Profile (WSP) from the southern North Sea. The field data produced images showing a P-P reflector below the geophone and localized P-P and P-S scatterers at the level of the geo-phone. These scatterers, which lie outside the zone of specular illumination, are interpreted as faults in the base Zechstein/top Rotliegendes interface.  相似文献   

4.
Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source‐dependent effective velocities for the elliptic medium using kinematic high‐frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high‐frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade‐off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear‐wave artefacts as opposed to the conventional finite‐difference‐based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.  相似文献   

5.
各向异性介质qP波传播描述II:分离纯模式标量波   总被引:1,自引:1,他引:0       下载免费PDF全文
在各向异性地震波场中,qP波与qS波常常是耦合在一起的.多分量地震数据处理中一个关键环节就是波型分离(即模式解耦),以纵波成分为主的常规单分量地震数据的成像则需要合理描述标量qP波的传播算子.本文作者曾构建了在运动学上同弹性波动方程等价,动力学上突出标量qP波的伪纯模式波动方程.为了彻底消除qS波残余,本文根据波矢量与qP波偏振矢量之间的偏差,提出从伪纯模式波场提取纯模式标量qP波的方法.数值分析展示了投影偏差算子在波数域和空间域的特征.基于不同复杂程度理论模型的试验结果表明,联合"伪纯模式传播算子"与"投影偏差校正"可为各向异性介质分离模式波场传播过程提供一种简便的描述工具.  相似文献   

6.
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.  相似文献   

7.
三维VSP资料中,各种不同类型的波混杂一起形成复杂的波场.因此,波场分离是三维VSP数据处理关键的第一步.从不同波场的偏振方向和传播方向之差异着手,提出了一种高保真的VSP波场分离方法.首先通过射线追踪和偏振滤波的结合,把复杂波场(分解为简单波场;然后根据简单波场中不同波的传播方向截然相反的特点,进行方向滤波,达到波场分离的目的.实际数据处理表明,与常规波场分离方法相比,本方法大大降低了混波作用以及由此而生的波形畸变.  相似文献   

8.
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.  相似文献   

9.
波场延拓得到的多分量波场中既包含纵波信息也包含横波信息,能否在全波场中实现纵横波的分离对各向同性和各向异性逆时偏移都有非常重要的意义.传统的散度旋度分离只适应于各向同性介质而对各向异性介质却无效.在非规则、非结构网格的弹性波数值模拟方法的基础上,发展了一种适应于各向异性介质的波场分离方法.该方法通过求解Christoffel方程,得到相角和极化角的关系,再利用群角和相角的关系,直接得到群角和极化角的关系.该方法与现存的各向异性波场分离相比,获得的计算效率改进更显著,而且存储量小.用简单各向异性模型和SEG各向异性Hess模型进行测试,都得到了较好的效果,证明了本文方法的有效性.  相似文献   

10.
Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.  相似文献   

11.
王维红  张伟  石颖  柯璇 《地球物理学报》2017,60(7):2813-2824
尽管叠前逆时偏移成像精度高,但仅针对单一纵波的成像也可能形成地下介质成像盲区,由于基于弹性波方程的逆时偏移成像可形成多波模式的成像数据,因此弹性波逆时偏移成像可提供更为丰富的地下构造信息.本文依据各向同性介质的一阶速度-应力方程组构建震源和检波点矢量波场,再利用Helmholtz分解提取纯纵波和纯横波波场,使用震源归一化的互相关成像条件获得纯波成像,避免了直接使用坐标分量成像而引起的纵横波串扰问题.针对转换波成像的极性反转问题,文中提出一种共炮域极性校正方法.为有效节约存储成本,也提出一种适用于弹性波逆时偏移的震源波场逆时重建方法,在震源波场正传过程中,仅保存PML边界内若干层的速度分量波场,进而逆时重建出所有分量的震源波场.本文分别对地堑模型和Marmousi2模型进行了弹性波逆时偏移成像测试,结果表明:所提出的共炮域极性校正方法正确有效,基于波场分离的弹性波逆时偏移成像的纯波数据能够对复杂地下构造准确成像.  相似文献   

12.
纵横波波场分离是弹性波偏移方法的必要条件,通过纵横波成像的差异可以获取更多地下介质的信息.目前所用的纵横波波场分离方法多采用Helmholtz分解,这样得到的波场不仅物理意义发生了变化,振幅和相位也会发生改变.本文采用纵横波解耦的弹性波方程,将其应用于三维介质,对比分析了纵横波解耦方法相对传统Helmholtz分解方法在相位、振幅上的优势.将该解耦的波场分离方法应用于弹性波逆时偏移,能得到相位、振幅和物理意义不受改变的偏移结果.但是该解耦方法分离得到的纵横波波场均为矢量场,将该波场分离方法用于弹性波逆时偏移,还需要解决矢量场如何得到标量成像结果的问题.本文引入了Poynting矢量,通过Poynting矢量对矢量波场进行标量化,这样就能得到保振幅、相位,且无极性反转的标量PP和PS成像结果.同时针对S波Poynting矢量求取不准确的问题,采用拟S波应力场和S波速度场得到了更加准确的S波Poynting矢量.理论计算证明了本文采用的3D波场解耦的矢量波场分离方法的正确性和引入Poynting矢量对矢量波场进行标量成像的有效性.  相似文献   

13.
Anisotropic reverse-time migration for tilted TI media   总被引:1,自引:0,他引:1  
Seismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop an anisotropic reverse‐time depth migration approach for P‐wave and SV‐wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula and dispersion relationships for weak anisotropy, we derive the wave equation for P‐wave and SV‐wave propagation in tilted transversely isotropic (TTI) media. The accuracy of the P‐wave equation and the SV‐wave equation is analyzed and compared with other acoustic wave equations for TTI media. Using this analysis and the pseudo‐spectral method, we apply reverse‐time migration to numerical and physical‐model data. According to the comparison between the isotropic and anisotropic migration results, the anisotropic reverse‐time depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.  相似文献   

14.
地震波在各向异性介质中以一个准P波(qP)和两个准S波(qS1和qS2)的形式传播.研究三种波的相速度、群速度以及偏振方向等传播性质能够为各向异性介质中的正反演问题提供有效支撑.具有比横向各向同性(TI)介质更一般对称性的正交各向异性介质通常需要9个独立参数对其进行描述,这使得对传播特征的计算更为复杂.当两个准S波速度相近时具有耦合性,从而令慢度的计算产生奇异性.因此,奇异点(慢度面的鞍点和交叉点)附近的反射与透射(R/T)系数的求解不稳定,会导致波场振幅不准确.本文首次通过结合耦合S波射线理论和基于迭代的各向异性相速度与偏振矢量的高阶近似解,得到了适用于正交各向异性介质以qP波入射所产生的二阶R/T系数的计算方法.与基于一阶近似的结果相比,基于二阶近似的方法提高了qP波R/T系数的精度,能得到一阶耦合近似无法表达的准确的qP-qS转换波的R/T系数解,且方法适用于较强的各向异性介质.  相似文献   

15.
Riemannian wavefield extrapolation is a technique for one‐way extrapolation of acoustic waves. Riemannian wavefield extrapolation generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian ones. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry. When coordinate systems conform with the propagated wavefield, extrapolation can be done accurately using low‐order kernels. However, in complex media or in cases where the coordinate systems do not conform with the propagating wavefields, low order kernels are not accurate enough and need to be replaced by more accurate, higher‐order kernels. Since Riemannian wavefield extrapolation is based on factorization of an acoustic wave‐equation, higher‐order kernels can be constructed using methods analogous to the one employed for factorization of the acoustic wave‐equation in Cartesian coordinates. Thus, we can construct space‐domain finite‐differences as well as mixed‐domain techniques for extrapolation. High‐order Riemannian wavefield extrapolation kernels improve the accuracy of extrapolation, particularly when the Riemannian coordinate systems does not closely match the general direction of wave propagation.  相似文献   

16.
Walkaway vertical seismic profile (VSP) data acquired in basalt‐covered areas can be used to improve knowledge of the sub‐basalt structure. A synthetic example and a case study from the North Atlantic (UK) show that elastic two‐way downward‐continuation migration combined with the stationary‐phase principle is well suited to the processing of VSP data. Vector data are processed using decoupled elastic migration algorithms in both isotropic and anisotropic media. To illustrate the value of decoupled imaging equations, conventional PP imaging is carried out on the enhanced VSP data and compared with the decoupled scheme. Decoupled vector migration operates directly on the displacement vector, and uses various wave modes. Downgoing waves are migrated to image basalt lava flows and measure their anisotropy. Upgoing waves are used for high‐resolution sub‐basalt imaging.  相似文献   

17.
Multiple scattering is usually ignored in migration algorithms, although it is a genuine part of the physical reflection response. When properly included, multiples can add to the illumination of the subsurface, although their crosstalk effects are removed. Therefore, we introduce full‐wavefield migration. It includes all multiples and transmission effects in deriving an image via an inversion approach. Since it tries to minimize the misfit between modeled and observed data, it may be considered a full waveform inversion process. However, full‐wavefield migration involves a forward modelling process that uses the estimated seismic image (i.e., the reflectivities) to generate the modelled full wavefield response, whereas a smooth migration velocity model can be used to describe the propagation effects. This separation of modelling in terms of scattering and propagation is not easily achievable when finite‐difference or finite‐element modelling is used. By this separation, a more linear inversion problem is obtained. Moreover, during the forward modelling, the wavefields are computed separately in the incident and scattered directions, which allows the implementation of various imaging conditions, such as imaging reflectors from below, and avoids low‐frequency image artefacts, such as typically observed during reverse‐time migration. The full wavefield modelling process also has the flexibility to image directly the total data (i.e., primaries and multiples together) or the primaries and the multiples separately. Based on various numerical data examples for the 2D and 3D cases, the advantages of this methodology are demonstrated.  相似文献   

18.
Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.  相似文献   

19.
Pure-mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo-acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure-mode equations for P- and S-waves resulting in an artefact-free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S-wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P- and S-waves in transversely isotropic media.  相似文献   

20.
We study the interaction of a seismic wavefield with a spherical acoustic gas‐ or fluid‐filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature that may help in detecting cavities in the subsurface. This is important for many applications, in particular the detection of underground nuclear explosions, which are to be prohibited by the Comprehensive Test Ban Treaty. To calculate the full seismic wavefield from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wavefield interaction consists of elastic scattering and the wavefield interaction between the acoustic and elastic media. Acoustic resonant modes caused by internal reflections in the acoustic cavity show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the un‐damped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas‐filled cavity, the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas‐filled cavities show up as persisting oscillations. However, due to the weak acoustic–elastic coupling in this case, the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid‐filled cavity has a stronger acoustic–elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid‐filled cavities, acoustic resonances show up as strong but fast decaying reverberations.  相似文献   

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