Three‐term inversion of prestack seismic data using a weighted l2, 1 mixed norm

We present a new inversion method to estimate, from prestack seismic data, blocky P‐ and S‐wave velocity and density images and the associated sparse reflectivity levels. The method uses the three‐term Aki and Richards approximation to linearise the seismic inversion problem. To this end, we adopt a weighted mixed l_{2, 1}‐norm that promotes structured forms of sparsity, thus leading to blocky solutions in time. In addition, our algorithm incorporates a covariance or scale matrix to simultaneously constrain P‐ and S‐wave velocities and density. This a priori information is obtained by nearby well‐log data. We also include a term containing a low‐frequency background model. The l_{2, 1} mixed norm leads to a convex objective function that can be minimised using proximal algorithms. In particular, we use the fast iterative shrinkage‐thresholding algorithm. A key advantage of this algorithm is that it only requires matrix–vector multiplications and no direct matrix inversion. The latter makes our algorithm numerically stable, easy to apply, and economical in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l₂‐ or l₁‐norm regularised solutions, is able to provide consistent blocky and/or sparse estimators of P‐ and S‐wave velocities and density from a noisy and limited number of observations.     

Background velocity estimation using non-linear optimization for reflection tomography and migration misfit

We show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non-linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant-offset sections as input data for the inversion. A Kirchhoff summation scheme based on first-arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection-tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration-misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust. Our non-linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity-analysis method based on the reflection-tomography criterion, traveltimes do not have to be picked. Similarly, the migration-misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity-analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.     

Anisotropic velocity analysis1

Results from walkaway VSP and shale laboratory experiments show that shale anisotropy can be significantly anelliptic. Heterogeneity and anellipticity both lead to non-hyperbolic moveout curves and the resulting ambiguity in velocity analysis is investigated for the case of a factorizable anisotropic medium with a linear dependence of velocity on depth. More information can be obtained if there are several reflectors. The method of Dellinger et al. for anisotropic velocity analysis in layered transversely isotropic media is examined and is shown to be restricted to media having relatively small anellipticity. A new scheme, based on an expansion of the inverse-squared group velocity in spherical harmonics, is presented. This scheme can be used for larger anellipticity, and is applicable for horizontal layers having monoclinic symmetry with the symmetry plane parallel to the layers. The method is applied to invert the results of anisotropic ray tracing on a model Sand/shale sequence. For transversely isotropic media with small anisotropy, the scheme reduces to the method of Byun et al. and Byun and Corrigan. The expansion in spherical harmonics allows the P-phase slowness surface of each layer to be determined in analytic form from the layer parameters obtained by inversion without the need to assume that the anisotropy is weak.     

Converted-wave imaging in anisotropic media: theory and case studies

Common‐conversion‐point binning associated with converted‐wave (C‐wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted‐wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples. The converted‐wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point‐scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C‐wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C‐wave stacking velocity V_C2, the vertical and effective velocity ratios γ₀ and γ_eff, and the C‐wave anisotropic parameter χ_eff. These four parameters are referred to as the C‐wave stacking velocity model. In contrast, the C‐wave diffraction time from a point‐scatterer is determined by five parameters: γ₀, V_P2, V_S2, η_eff and ζ_eff, where η_eff and ζ_eff are, respectively, the P‐ and S‐wave anisotropic parameters, and V_P2 and V_S2 are the corresponding stacking velocities. V_P2, V_S2, η_eff and ζ_eff are referred to as the C‐wave PSTM velocity model. There is a one‐to‐one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C‐wave stacking velocities V_C2 and the migration velocity V_Cmig, which is in turn linked to V_P2 and V_S2. Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C‐wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C‐wave imaging compared with the dip‐moveout scheme, and these improvements have been confirmed by drilling.     

再论各向异性介质转换波地震学,第二部分:参数计算研究

在具有垂直对称轴横向各向同性介质中，利用四种参数来确定中间至远偏移距转换波（C-波）动校正。它们是C-波叠加速度Vc2，垂直速度比和有效速度比γ0和γeff以及各向异性参数χeff。我们将这四种参数作为C波叠加速度模型。C-波速度分析的目的就是确定这种叠加速度模型。C-波叠加速度模型Vc2，γ0，γeff，和χeff可以由P-波和C-波反射动校正资料获得。然而错误的传播是C-波反射动校正反演中的严重问题。当前短排列叠加速度由于是从双曲线动校正推算而得，因而其精度不足以为各向异性参数提供有意义的反演值。中间偏移非双曲线动校正不再被人们所勿略，而是可以用一个背景γ加以量化。非双曲线分析通过中间偏移距的γ校正量可以产生Vc2，若数据不含燥音，其误差小于1％。方法稳健，允许γ启始假定值的误差达20％。该方法也适用垂直非均匀各向异性介质。精度的提高使能够用4分量地震资料计算各向异性参数。为此提出了两种工作流程：双扫描和单扫描流程。理论数据和实际数据的应用表明这两种流程得出的结果其精度相似，但是单扫描流程比双扫描更有效。     

Converted-wave seismology in anisotropic media Revisited,Part II: Application to parameter estimation

In transversely isotropic media with a vertical symmetry axis (VTI), the converted-wave (C-wave) moveout over intermediate-to-far offsets is determined by four parameters. These are the C-wave stacking velocity V _C2, the vertical and effective velocity ratios γ ₀and γ _eff, and the anisotropic parameter X _eff. We refer to the four parameters as the C-wave stacking velocity model. The purpose of C-wave velocity analysis is to determine this stacking velocity model. The C-wave stacking velocity model V _C2, γ ₀, γ _geff, and X _eff can be determined from P- and C-wave reflection moveout data. However, error propagation is a severe problem in C-wave reflection-moveout inversion. The current short-spread stacking velocity as deduced from hyperbolic moveout does not provide sufficient accuracy to yield meaningful inverted values for the anisotropic parameters. The non-hyperbolic moveout over intermediate-offsets (x/z from 1.0 to 1.5) is no longer negligible and can be quantified using a background γ. Non-hyperbolic analysis with a γ correction over the intermediate offsets can yield V _C2 with errors less than 1% for noise free data. The procedure is very robust, allowing initial guesses of γ with up to 20% errors. It is also applicable for vertically inhomogeneous anisotropic media. This improved accuracy makes it possible to estimate anisotropic parameters using 4C seismic data. Two practical work flows are presented for this purpose: the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that the two flows yield results with similar accuracy but the single-scanning flow is more efficient than the double-scanning flow. This work is funded by the Edinburgh Anisotropy Project of the British Geological Survey. First Author Li Xiangyang, he is currently a professorial research seismologist (Grade 6) and technical director of the Edinburgh Anisotropy Project in the British Geological Survey. He also holds a honorary professorship multicomponent seismology at the School of Geosciences, University of Edinburgh. He received his BSc(1982) in Geophysics from Changchun Geological Institute, China, an MSc (1984) in applied geophysics from East China Petroleum Institute (now known as the China University of Petroleum), and a PhD (1992) in seismology from the University of Edinburgh. During 1984–1987, he worked as a lecturer with the East China Petroleum Institute. Since 1991, he has been employed by the British Geological Survey. His research interests include seismic anisotropy and multicomponent seismology.     

各向异性介质Low-rank有限差分法纯qP波叠前平面波最小二乘逆时偏移

拟声波最小二乘逆时偏移是一种极具潜力的地震波成像工具,但该方法遭受各向异性拟声波近似的限制,TTI介质正演模拟不稳定、反偏移记录中遭受伪横波二次扰动及数值频散假象,另外拟声波最小二乘逆时偏移还面临计算效率低、收敛速度慢、对速度等模型参数依赖性高等问题.为了克服各向异性拟声波最小二乘逆时偏移的缺陷,在反演框架下,本文借助Low-rank有限差分算法首次提出并实现了TTI介质纯qP波线性正演模拟及纯qP波最小二乘逆时偏移;为了进一步提升反演成像效率,同时改善反演成像方法对模型参数误差的依赖性及对地震数据噪声的适应性,通过引入叠前平面波优化策略,发展了TTI介质纯qP波叠前平面波最小二乘逆时偏移成像方法.在编程实现方法的基础上,通过开展模型成像测试,展示了本方法的优势和潜力：一方面加快了反演成像效率,另一方面也提升了方法的抗噪性,同时还降低了方法对模型参数的依赖性.     

First-Order Perturbation Theory for Seismic Isochrons

A first-order perturbation theory for seismic isochrons is presented in a model independent form. Two ray concepts are fundamental in this theory, the isochron ray and the velocity ray, for which I obtain first-order approximations to position vectors and slowness vectors. Furthermore, isochron points are connected to a shot and receiver by conventional ray fields. Based on independent perturbation of the shot and receiver ray I obtain first-order approximations to velocity rays. The theory is applicable for 3D inhomogeneous anisotropic media, given that the shot and receiver rays, as well as their perturbations, can be generated with such model generality. The theory has applications in sensitivity analysis of prestack depth migration and in velocity model updating. Numerical examples of isochron and velocity rays are shown for a 2D homogeneous VTI model. The general impression is that the first-order approximation is, with some exceptions, sufficiently accurate for practical applications using an anisotropic velocity model.     

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.     

Estimation of Thomsen＇s anisotropic parameters from walkaway VSP and applications

Estimation of Thomsen＇s anisotropic parameters is very important for accuratetime-to-depth conversion and depth migration data processing. Compared with othermethods, it is much easier and more reliable to estimate anisotropic parameters that arerequired for surface seismic depth imaging from vertical seismic profile （VSP） data, becausethe first arrivals of VSP data can be picked with much higher accuracy. In this study, wedeveloped a method for estimating Thomsen＇s P-wave anisotropic parameters in VTImedia using the first arrivals from walkaway VSP data. Model first-arrival travel times arecalculated on the basis of the near-offset normal moveout correction velocity in VTI mediaand ray tracing using Thomsen＇s P-wave velocity approximation. Then, the anisotropicparameters 0 and e are determined by minimizing the difference between the calculatedand observed travel times for the near and far offsets. Numerical forward modeling, usingthe proposed method indicates that errors between the estimated and measured anisotropicparameters are small. Using field data from an eight-azimuth walkaway VSP in TarimBasin, we estimated the parameters 0 and e and built an anisotropic depth-velocity modelfor prestack depth migration processing of surface 3D seismic data. The results showimprovement in imaging the carbonate reservoirs and minimizing the depth errors of thegeological targets.     

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant-Q (i.e. frequency-independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP-wave in the constant-Q viscoelastic anisotropic theory. For numerical simulations, the staggered-grid pseudo-spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional-order Laplacian approximation method is used to cope with spatial variable-order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant-Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional-order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.     

TI介质偏移速度建模研究

经过多年的研究发展,各向异性叠前深度偏移算法已经趋于完善.然而,在地震资料处理过程中导致成像结果不理想的主要原因还是由于建立的地层参数场不够精确.当地层参数接近其真实值时,基于波动方程的剩余曲率建模方法由于不受构造的影响,能够在各向异性和横向变速介质中进行速度分析,所以得到了广泛的研究.本文从偏移结果中抽取共成像道集,然后通过交互运用叠前深度偏移和参数更新实现各向异性偏移速度建模.对理论模型和实际资料进行的试算表明,该方法具有较强的适应性,能极大改善VTI介质反射界面成像效果和分辨率.     

3D description and inversion of reflection moveout of PS‐waves in anisotropic media

Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t²(x²) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (V_P0 and V_S0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (V_P0, V_S0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves.     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.     

苏北大陆科学钻探靶区深反射地震的叠前深度偏移

由于深反射地震数据具有信噪比低和记录长度长等特点,叠前深度偏移方法的应用有许多困难．为此,我们研究了一种适合于深反射地震的叠前深度偏移方法;包括：用逆风有限差分方法计算程函方程;在常规速度扫描的基础上,用协方差控制提高速度分析精度;用联合反演算法计算层速度,再插值后得到初始速度模型;用Ｋｉｒｃｈｈｏｆｆ法作为偏移速度分析工具,求得最终的速度模型;最终的速度模型作为有限差分深度偏移的输入,求得最终的偏移结果．用该方法对“中国大陆科学深钻工程”东海二维深反射地震数据ＤＨ－４线进行了叠前深度偏移,取得了良好的效果。     

Prestack migration velocity analysis based on simplified two-parameter moveout equation

Stacking velocity V _C2, vertical velocity ratio γ ₀, effective velocity ratio γ _eff, and anisotropic parameter χ _eff are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity V _C2 and anisotropic parameter k _eff) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocity V _C2, vertical velocity ratio γ ₀, effective velocity ratio γ _eff, and anisotropic parameter k _eff) PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratio γ ₀ of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratio γ _eff is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratio γ _eff is obtained by percentage scanning migration. This method simplifies the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice.     

Post‐stack stratigraphic inversion workflow applied to carbon dioxide storage: application to the saline aquifer of Sleipner field‡

In the Norwegian North Sea, the Sleipner field produces gas with a high CO₂ content. For environmental reasons, since 1996, more than 11 Mt of this carbon dioxide (CO₂) have been injected in the Utsira Sand saline aquifer located above the hydrocarbon reservoir. A series of seven 3D seismic surveys were recorded to monitor the CO₂ plume evolution. With this case study, time‐lapse seismics have been shown to be successful in mapping the spread of CO₂ over the past decade and to ensure the integrity of the overburden. Stratigraphic inversion of seismic data is currently used in the petroleum industry for quantitative reservoir characterization and enhanced oil recovery. Now it may also be used to evaluate the expansion of a CO₂ plume in an underground reservoir. The aim of this study is to estimate the P‐wave impedances via a Bayesian model‐based stratigraphic inversion. We have focused our study on the 1994 vintage before CO₂ injection and the 2006 vintage carried out after a CO₂ injection of 8.4 Mt. In spite of some difficulties due to the lack of time‐lapse well log data on the interest area, the full application of our inversion workflow allowed us to obtain, for the first time to our knowledge, 3D impedance cubes including the Utsira Sand. These results can be used to better characterize the spreading of CO₂ in a reservoir. With the post‐stack inversion workflow applied to CO₂ storage, we point out the importance of the a priori model and the issue to obtain coherent results between sequential inversions of different seismic vintages. The stacking velocity workflow that yields the migration model and the a priori model, specific to each vintage, can induce a slight inconsistency in the results.     

Inversion for elliptically anisotropic velocity using VSP reflection traveltimes

This paper presents a traveltime inversion approach, using the reflection traveltimes from offset VSP data, to reconstruct the horizontal and vertical velocities for stratified anisotropic media. The inverse problem is reduced to a set of linear equations, and solved by the singular value decomposition (SVD) technique. The validity of this inversion scheme is verified using two sets of synthetic data simulated using a finite‐difference method, one for an isotropic model and the other for an elliptically anisotropic model. The inversion result demonstrates that our anisotropic velocity inversion scheme may be applied to both isotropic and anisotropic media. The method is finally applied to a real offset VSP data set, acquired in an oilfield in northwestern China.     

Joint viscoacoustic waveform inversion with the separated upgoing and downgoing wavefields in zero-offset vertical seismic profile data

The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality-factor Q. The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality-factor is proposed based on the multi-objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the individual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the individual wavefields and improve the convergence of viscoacoustic full-waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality-factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical example validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.     

各向异性介质qP波传播描述I：伪纯模式波动方程

地球介质相对于地震波波长尺度的定向非均匀性会导致波速的各向异性,进而影响地震波场的运动学与动力学特征．各向异性弹性波动方程是描述该类介质波场传播的基本工具,在正演模拟、偏移成像与参数反演中起着关键作用．为了面向实际应用构建灵活、简便的各向异性波场传播算子,人们一直在寻求简化的各向异性波动方程．本文借鉴各向异性弹性波波型分离思想,通过对平面波形式的弹性波方程(即Christoffel方程)实施一种代表向波矢量方向投影的相似变换,推导出了一种适应任意各向异性介质、运动学上与原始弹性波方程完全等价,在动力学上突出qP波的新方程,即qP波伪纯模式波动方程．文中以横向各向同性(TI)介质为例,给出了相应的qP波伪纯模式波动方程及其声学与各向同性近似,并在此基础上开展了正演模拟和逆时偏移试验,展示了这种描述各向异性波场传播的新方程的特点与优势．