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1.
Wavefield extrapolation and prestack depth migration in anelastic inhomogeneous media 总被引：6，自引：0，他引：6
Wavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively. 相似文献
2.
A depth migration method is presented that uses Radon-transformed common-source seismograms as input. It is shown that the Radon depth migration method can be extended to spatially varying velocity depth models by using asymptotic ray theory (ART) to construct wavefield continuation operators. These operators downward continue an incident receiver-array plane wave and an assumed point-source wavefield into the subsurface. The migration velocity model is constrained to have longer characteristic wavelengths than the dominant source wavelength such that the ART approximations for the continuation operators are valid. This method is used successfully to migrate two synthetic data examples:
- 1 a point diffractor, and
- 2 a dipping layer and syncline interface model.
3.
Iterative migration velocity analysis is computationally expensive, where most of the computation time is used for generating prestack depth images. By using a reduced form of Kirchhoff migration, denoted as wave path migration, we can significantly speed up the depth imaging process and reduce the entire velocity analysis expense accordingly. Our results with 2D synthetic and field data show that wave path migration velocity analysis can efficiently improve the velocity model and the wave path migration velocity analysis updated velocity correlates well with that from the Kirchhoff migration velocity analysis. The central processing unit comparison shows that, for a 2D synthetic and field data set, wave path migration velocity analysis is six times faster than Kirchhoff migration velocity analysis. This efficiency should be even greater for 3D data. 相似文献
4.
逆时偏移成像(RTM)常用来处理复杂速度模型,包括陡倾角及横向速度变化剧烈的模型.与常规偏移成像方法(如Kirchhoff偏移)相比,逆时偏移成像能提供更好的偏移成像结果,近些年逆时偏移成像越来越广泛地应用到勘探地震中,它逐渐成为石油地震勘探中的一种行业标准.电磁波和弹性波在动力学和运动学上存在相似性,故本文开发了基于麦克斯韦方程组的电磁波逆时偏移成像算法,并将其应用到探地雷达数据处理中.时间域有限差分(FDTD)用于模拟电磁波正向和逆向传播过程,互相关成像条件用于获得最终偏移结果.逆时偏移成像算法中,偏移成像结果受初始模型影响较大,而其中决定电磁波传播速度的介电常数的影响尤为重要.本文基于时间域全波形反演(FWI)算法反演获得了更为精确的地下介电常数模型,并将其反演结果作为逆时偏移成像的初始介电常数模型.为了验证此算法的有效性,首先构建了一个复杂地质结构模型,合成了共偏移距及共炮点探地雷达数据,分别应用常规Kirchhoff偏移算法及逆时偏移成像算法进行偏移处理,成像结果显示由逆时偏移成像算法得到的偏移结果与实际模型具有较高的一致性;此外本文在室内沙槽中进行了相关的物理模拟实验,采集了共偏移距及共炮点探地雷达数据,分别应用Kirchhoff和叠前逆时偏移成像算法进行处理,结果表明叠前逆时偏移成像在实际应用中能获得更好的成像效果. 相似文献
5.
An algorithm for modelling and migrating ground penetrating radar (GPR) data in moderately heterogeneous dispersive media is presented. The method is based on wavefield extrapolation in the frequency–wavenumber (f–k) domain, from the solution of the 2D Maxwell's equations. The wavefield is extrapolated by a phase-shift technique using a constant relative permittivity K and a quality factor Q. It is then modified by a correction term to handle the lateral K and Q variations. The spatial distribution of the K and Q-factor values, representing the given model parameters, is introduced into the algorithm by a regular grid parametrization. The radar wave dispersion and attenuation, induced by relaxation processes, are taken into account by a linear frequency-dependent Q model, and expressed by a complex wavenumber in the propagation equation. A synthetic case and a field data set illustrate the potential of the method for frequencies of 300, 500 and 900 MHz. In the first case, a typical civil engineering problem is considered. The frequency dependence of the wave velocity and attenuation is well illustrated. The synthetic data are afterwards migrated using the initial model parameters. The results show the importance of using spatially varying model parameters in the migration processes. The second case concerns an application of the method to a real data set. In order to adjust the model parameters, a forward modelling sequence is performed until the best match between the measured and the synthetic data is achieved. A depth migration is then applied to the data, and the result is compared with the initial model parameters. In conclusion, we assess the contributions of the method to industrial applications, by discussing the performance of the algorithm compared with its limitations. 相似文献
6.
Velocity model updating in prestack Kirchhoff time migration for PS converted waves: Part I – Theory
A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted‐wave velocity only, and the other factor depending on all parameters. The velocity‐dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non‐hyperbolic behaviour of the moveout. This non‐hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal‐moveout common‐image‐point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio (VP/VS) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration. 相似文献
7.
Conventional seismic data processing methods based on post‐stack time migration have been playing an important role in coal exploration for decades. However, post‐stack time migration processing often results in low‐quality images in complex geological environments. In order to obtain high‐quality images, we present a strategy that applies the Kirchhoff prestack time migration (PSTM) method to coal seismic data. In this paper, we describe the implementation of Kirchhoff PSTM to a 3D coal seam. Meanwhile we derive the workflow of 3D Kirchhoff PSTM processing based on coal seismic data. The processing sequence of 3D Kirchhoff PSTM includes two major steps: 1) the estimation of the 3D root‐mean‐square (RMS) velocity field; 2) Kirchhoff prestack time migration processing. During the construction of a 3D velocity model, dip moveout velocity is served as an initial migration velocity field. We combine 3D Kirchhoff PSTM with the continuous adjustment of a 3D RMS velocity field by the criteria of flattened common reflection point gathers. In comparison with post‐stack time migration, the application of 3D Kirchhoff PSTM to coal seismic data produces better images of the coal seam reflections. 相似文献
8.
单程波波场延拓算子在地震偏移成像中有重要应用.单程波波场延拓算子按其实现方式可分为Kirchhoff积分、空间隐式有限差分和Fourier变换方法,他们代表了算子的不同表示方法,当截断使用这些方法时会得到不同的精度.象征表示对这些方法的导出和精度分析有重要作用.算子作用于正弦波函数所得函数称为算子的象征.算子的象征是褶积算子Fourier变换的推广.Fourier变换方法则直接用象征函数的可分表示求出.空间隐式有限差分则可以用象征函数的Padè近似或部分分式导出.单程波算子在深度域的积分称为单程波算子积分解.本文推导了单程波算子积分解的象征表达式,给出了算子象征的代数运算的头几阶表达式,这些表达式还未在前人文献中发现.Kirchhoff积分所需格林函数可以通过象征函数和鞍点法导出.基于积分解的象征表达式给出了非对称走时公式,对改善Kirchhoff积分的聚焦性能有重要意义. 相似文献
9.
Introduction The calculation of seismic wave traveltimes is a basic and the most important step in tomo-graphy, seismic wave forward modeling and Kirchhoff prestack depth migration. Limitations withtraditional ray tracing fall into four categories. a) Analytical methods can only realize ray tracingfor simply varying velocity fields, so they have relative small applied-range; b) Shooting methodsof ray tracing can cause shadow zones. When the shadow zones exist the method will invalid; c)… 相似文献
10.
Computation of complex-valued traveltimes provides an efficient approach to describe the seismic wave attenuation for applications like attenuation tomography, inverse Q filtering and Kirchhoff migration with absorption compensation. Attenuating acoustic transverse isotropy can be used to describe the directional variation of velocity and attenuation of P-waves in thin-bedding geological structures. We present an approximate method to solve the acoustic eikonal equation for an attenuating transversely isotropic medium with a vertical symmetry axis. We take into account two similar parameterizations of an attenuating vertical symmetry axis medium. The first parameterization uses the normal moveout velocity, whereas the second parameterization uses the horizontal velocity. For each parameterization, we combine perturbation theory and the Shanks transform in different ways to derive analytic solutions. Numerical examples show that the analytic solutions derived from the second parameterization yield better accuracy. The Shanks transform solution with respect to only the anellipticity parameter from the second parameterization is demonstrated numerically to be the most accurate among all the analytic solutions. 相似文献
11.
A laboratory study of seismic velocity and attenuation anisotropy in near-surface sedimentary rocks 总被引：4，自引：0，他引：4
The laboratory ultrasonic pulse‐echo method was used to collect accurate P‐ and S‐wave velocity (±0.3%) and attenuation (±10%) data at differential pressures of 5–50 MPa on water‐saturated core samples of sandstone, limestone and siltstone that were cut parallel and perpendicular to the vertical borehole axis. The results, when expressed in terms of the P‐ and S‐wave velocity and attenuation anisotropy parameters for weakly transversely isotropic media (ɛ, γ, ɛQ, γQ) show complex variations with pressure and lithology. In general, attenuation anisotropy is stronger and more sensitive to pressure changes than velocity anisotropy, regardless of lithology. Anisotropy is greatest (over 20% for velocity, over 70% for attenuation) in rocks with visible clay/organic matter laminations in hand specimens. Pressure sensitivities are attributed to the opening of microcracks with decreasing pressure. Changes in magnitude of velocity and attenuation anisotropy with effective pressure show similar trends, although they can show different signs (positive or negative values of ɛ, ɛQ, γ, γQ). We conclude that attenuation anisotropy in particular could prove useful to seismic monitoring of reservoir pressure changes if frequency‐dependent effects can be quantified and modelled. 相似文献
12.
Analysis of quality factors for Rayleigh channel waves 总被引：3，自引：1，他引：2
To facilitate investigation of the effect of imperfect elastic dissipation on thepropagation of Rayleigh-type channel waves and use of their quality factors in investigationsof the properties of coal seams, a simple method for calculating the quality factor QR isproposed in this paper. Introduction of complex velocities into the dispersion function allowscalculation of the dispersion function of Rayleigh-type channel waves in coal seams. By thecontrol variable method, we analyzed changes in QR with changes in coal seam thickness andP- and S-wave Q-factors within the coal seam and adjacent rock layers. The numerical resultsshow that the trend of the QR curve is consistent with the group velocity curve. The minimumQR value occurs at the Airy phase frequency; the Airy phase frequency decreases as coal seamthickness increases. The value of QR increases with increasing Qs2 （quality factor for S wavein coal seam）. We can compensate for the absorption of Rayleigh-type channel waves usingthe computed QR curve. Inversion of the QR curve can also be used to predict the thicknessesand litholoeies of coal seams. 相似文献
13.
Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high‐frequency components, such as noise, and create undesirable imaging artefacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant‐Q wave equation with decoupled fractional Laplacians and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse‐time migration. A time‐dependent imaging condition is derived by applying Q‐compensation in the frequency domain, whereas a time‐independent imaging condition is formed in the image space by calculating image normalisation weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high‐frequency noise in the data. 相似文献
14.
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. 相似文献
15.
16.
S. Karato 《Pure and Applied Geophysics》1998,153(2-4):239-256
—A microphysical model of seismic wave attenuation is developed to provide a physical basis to interpret temperature and frequency dependence of seismic wave attenuation. The model is based on the dynamics of dislocation motion in minerals with a high Peierls stress. It is proposed that most of seismic wave attenuation occurs through the migration of geometrical kinks (micro-glide) and/or nucleation/migration of an isolated pair of kinks (Bordoni peak), whereas the long-term plastic deformation involves the continuing nucleation and migration of kinks (macro-glide). Kink migration is much easier than kink nucleation, and this provides a natural explanation for the vast difference in dislocation mobility between seismic and geological time scales. The frequency and temperature dependences of attenuation depend on the geometry and dynamics of dislocation motion both of which affect the distribution of relaxation times. The distribution of relaxation times is largely controlled by the distribution in distance between pinning points of dislocations, L, and the observed frequency dependence of Q, Q, Q∝ωα is shown to require a distribution function of P(L)∝L -m with m=4-2α The activation energy of Q ?1 in minerals with a high Peierls stress corresponds to that for kink nucleation and is similar to that of long-term creep. The observed large lateral variation in Q ?1 strongly suggests that the Q ?1 in the mantle is frequency dependent. Micro-deformation with high dislocation mobility will (temporarily) cease when all the geometrical kinks are exhausted. For a typical dislocation density of ～ 108 m?2, transient creep with small viscosity related to seismic wave attenuation will persist up to the strain of ～ 10?6, thus even a small strain (～ 10?6?10?4) process such as post-glacial rebound is only marginally affected by this type of anelastic relaxation. At longer time scales continuing nucleation of kinks becomes important and enables indefinitely large strain, steady-state creep, causing viscous behavior. 相似文献
17.
方位角度域共成像点道集能够客观反映地下介质的速度、各向异性参数异常以及振幅随角度变化（AVA）和裂缝信息。传统Kirchhoff PSTM通常输出偏移距域共成像点道集,对于速度分析、各向异性分析、AVA分析、裂缝识别等均存在诸多不便。本文提出了基于走时梯度的Kirchhoff叠前时间偏移全方位角度集输出方法并提出工业上切实可行的实现方案。通过走时场梯度计算波场传播方向矢量,形成能够反映观测系统参数和波场传播情况的全方位角度域共成像点道集。为了在大规模地震数据Kirchhoff积分叠前时间偏移中输出全方位角度道集,本文给出基于输入道方式的偏移实现方法,采用逐条inline线进行线偏移成像,从而大大降低了全方位角度道集输出对计算机内存的压力,显著提高了Kirchhoff积分时间偏移输出全方位角度道集的可行性。三维盐丘模型测试和海上某区块三维实际资料试验证明了本文方法的正确性。 相似文献
18.
Jiakang Xie 《Pure and Applied Geophysics》2010,167(10):1147-1162
Precise measurements of seismological Q are difficult because we lack detailed knowledge on how the Earth’s fine velocity structure affects the amplitude data. In a number of recent papers, Morozov (Geophys J Int 175:239–252, 2008; Seism Res Lett 80:5–7, 2009; Pure Appl Geophys, this volume, 2010) proposes a new procedure intended to improve Q determinations. The procedure relies on quantifying the structural effects using a new form of geometrical spreading (GS) model that has an exponentially decaying component with time, e ?γt·γ is a free parameter and is measured together with Q. Morozov has refit many previously published sets of amplitude attenuation data. In general, the new Q estimates are much higher than previous estimates, and all of the previously estimated frequency-dependence values for Q disappear in the new estimates. In this paper I show that (1) the traditional modeling of seismic amplitudes is physically based, whereas the new model lacks a physical basis; (2) the method of measuring Q using the new model is effectively just a curve fitting procedure using a first-order Taylor series expansion; (3) previous high-frequency data that were fit by a power-law frequency dependence for Q are expected to be also fit by the first-order expansion in the limited frequency bands involved, because of the long tails of power-law functions; (4) recent laboratory measurements of intrinsic Q of mantle materials at seismic frequencies provide independent evidence that intrinsic Q is often frequency-dependent, which should lead to frequency-dependent total Q; (5) published long-period surface wave data that were used to derive several recent Q models inherently contradict the new GS model; and (6) previous modeling has already included a special case that is mathematically identical to the new GS model, but with physical assumptions and measured Q values that differ from those with the new GS model. Therefore, while individually the previous Q measurements have limited precision, they cannot be improved by using the new GS model. The large number of Q measurements by seismologists are sufficient to show that Q values in the Earth are highly laterally variable and are often frequency dependent. 相似文献
19.
L. Fishman 《Pure and Applied Geophysics》2002,159(7-8):1637-1679
— Recently, de Hoop and coworkers developed an asymptotic, seismic inversion formula for application in complex environments supporting multi-pathed and multi-mode wave propagation (de Hoop et al., 1999; de Hoop and Brandsberg-Dahl, 2000; Stolk and de Hoop, 2000). This inversion is based on the Born/Kirchhoff approximation, and employs the global, uniform asymptotic extension of the geometrical method of “tracing rays” to account for caustic phenomena. While this approach has successfully inverted the multicomponent, ocean-bottom data from the Valhall field in Norway, accounting for severe focusing effects (de Hoop and Brandsberg-Dahl, 2000), it is not able to account properly for wave phenomena neglected in the “high-frequency” limit (i.e., diffraction effects) and strong scattering effects. To proceed further and incorporate wave effects in a nonlinear inversion scheme, the theory of directional wavefield decomposition and the construction of the generalized Bremmer coupling series are combined with the application of modern phase space and path (functional) integral methods to, ultimately, suggest an inversion algorithm which can be interpreted as a method of “tracing waves.” This paper is intended to provide the seismic community with an introduction to these approaches to direct and inverse wave propagation and scattering, intertwining some of the most recent new results with the basic outline of the theory, and culminating in an outline of the extended, asymptotic, seismic inversion algorithm. Modeling at the level of the fixed-frequency (elliptic), scalar Helmholtz equation, exact and uniform asymptotic constructions of the well-known, and fundamentally important, square-root Helmholtz operator (symbol) provide the most important results. 相似文献