利用基于子波估计的频谱校正方法提高Q值估计精度(英文)

用Q值刻画的地震衰减在地震信号处理和解释中具有很广泛的应用。利用反射地震资料进行Q值估计需要解决地震子波和反射系数序列耦合的问题。从反射地震资料中去除反射系数序列的影响,这个过程称为频谱校正。本文提出了一种基于子波估计的求取Q值的方法,进而设计了一个反Q滤波器。该方法利用反射地震资料的高阶统计量进行子波估计,并利用所估计子波实现频谱校正。我们利用合成数据实验给出了质心频移法与频谱比法这两种常用的Q值估计方法在不同参数设置下的性能。人工合成数据和实际数据处理表明,利用本文提出的方法进行频谱校正后,可以得到可靠的Q值估计。经过反Q滤波,地震数据的高频部分得到了有效地恢复。     

The attenuated Ricker wavelet basis for seismic trace decomposition and attenuation analysis

The widely used wavelets in the context of the matching pursuit are mostly focused on the time–frequency attributes of seismic traces. We propose a new type of wavelet basis based on the classic Ricker wavelet, where the quality factor Q is introduced. We develop a new scheme for seismic trace decomposition by applying the multi-channel orthogonal matching pursuit based on the proposed wavelet basis. Compared with the decomposition by the Ricker wavelets, the proposed method could use fewer wavelets to represent the seismic signal with fewer iterations. Besides, the quality factor of the subsurface media could be extracted from the decomposition results, and the seismic attenuation could be compensated expediently. We test the availability of the proposed methods on both synthetic seismic record and field post-stack data.     

Some remarks on Q-compensated sparse deconvolution without knowing the quality factor Q

The subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q-compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non-stationary sparse reflectivity inversion, we evaluate a series of methods for Q-compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q-compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two-phase Q-compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q-filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over-determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion-based Q estimation method handles the wave-interference effects better than conventional spectral-ratio-based methods. For Q-compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q-compensation without knowing Q but with wavelet given.     

Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivity

The attenuation of ground‐penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency‐independent‐Q or simply a constant‐Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency‐bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial‐and‐error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling.     

Q-LOG DETERMINATION ON DOWNGOING WAVELETS AND TUBE WAVE ANALYSIS IN VERTICAL SEISMIC PROFILES1

Seismic attenuation introduces modifications in the wavelet shape in vertical seismic profiles. These modifications can be quantified by measuring particular signal attributes such as rise-time, period and shape index. Use of signal attributes leads to estimations of a seismic-attenuation log (Q-log). To obtain accurate signal attributes it is important to minimize noise influence and eliminate local interference between upgoing and downgoing waves at each probe location. When tube waves are present it is necessary to eliminate them before performing separation of upgoing and downgoing events. We used a trace-by-trace Wiener filter to minimize the influence of tube waves. The separation of upgoing and downgoing waves was then performed in the frequency domain using a trace-pair filter. We used three possible methods based on signal attribute measurements to obtain g-log from the extracted downgoing wavefield. The first one uses a minimum phasing filter and the arrival time of the first extremum. The two other methods determine the Q-factor from simple relations between the amplitudes of the first extrema and the pseudo-periods of the down-going wavelet. The relations determined between a signal attribute and traveltime over quality factor were then calibrated using field source signature and constant-Q models computed by Ganley's method. Q-logs thus obtained from real data are discussed and compared with geological information, specifically at reservoir level. Analysis of the tube wave arrivals at the level of the reservoir showed a tube wave attenuation that could not be explained by simple transmission effects. There was also a loss of signal coherence. This could be interpreted as tube wave diffusion in the porous reservoir, followed by dispersion. If this interpretation can be verified, tube wave analysis could lead to further characterization of porous permeable zones.     

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.     

Nonstationary deconvolution using maximum kurtosis optimization

Deconvolution is an essential step for high-resolution imaging in seismic data processing. The frequency and phase of the seismic wavelet change through time during wave propagation as a consequence of seismic absorption. Therefore, wavelet estimation is the most vital step of deconvolution, which plays the main role in seismic processing and inversion. Gabor deconvolution is an effective method to eliminate attenuation effects. Since Gabor transform does not prepare the information about the phase, minimum-phase assumption is usually supposed to estimate the phase of the wavelet. This manner does not return the optimum response where the source wavelet would be dominantly a mixed phase. We used the kurtosis maximization algorithm to estimate the phase of the wavelet. First, we removed the attenuation effect in the Gabor domain and computed the amplitude spectrum of the source wavelet; then, we rotated the seismic trace with a constant phase to reach the maximum kurtosis. This procedure was repeated in moving windows to obtain the time-varying phase changes. After that, the propagating wavelet was generated to solve the inversion problem of the convolutional model. We showed that the assumption of minimum phase does not reflect a suitable response in the case of mixed-phase wavelets. Application of this algorithm on synthetic and real data shows that subtle reflectivity information could be recovered and vertical seismic resolution is significantly improved.     

基于改进的最佳匹配地震子波的地震资料衰减特性分析

简述了改进的最佳匹配地震子波的小波函数构造及参数的物理含义;根据地震波的高、低频分量在黏弹介质中传播时被地层吸收的差异,给出了一种在时-频域定性估计地震波衰减特性的方法;分别以改进的最佳匹配地震子波的小波及Morlet小波作为母小波分析地层吸收特性,并比较了两种小波函数刻画地层吸收特性的能力;测试了这种方法对噪声的敏感程度. 将文中提出的方法用于某油田的一段实测地震资料衰减分析,得到的吸收特性剖面能较好地反映油气的空间展布.     

Source/receiver array directivity effects on marine seismic attenuation measurements

Attenuation of seismic waves, quantified by the seismic quality factor Q, holds important information for seismic interpretation, due to its sensitivity to rock and fluid properties. A recently published study of Q, based on surface seismic reflection data, used a modified spectral ratio approach (QVO), but both source and receiver responses were treated as isotropic, based on simple raypath arguments. Here, this assumption has been tested by computing apparent attenuation generated by frequency-dependent directivity of typical marine source and receiver arrays and acquisition geometries. Synthetic wavelet spectra were computed for reflected rays, summed over the first Fresnel zone, from the base of a single interval, 50–3000 m thick and velocity 2000 m/s, overlying a 2200 m/s half-space, and for offsets of 71–2071 m. The source and receiver geometry were those of an actual survey. The modelled spectra are clearly affected by directivity, most strongly because of surface ghosts. In general, the strong high-frequency component, produced by the array design, leads to apparently negative attenuation in individual reflection events, though this is dependent on offset and target depth. For shallow targets (less than 400–500 ms two-way traveltime (TWT) depth), apparent Q-values as extreme as ?50 to ?100 were obtained. For deeper target depths, the directivity effect is far smaller. The implications of the model study were tested on real data. QVO was applied to 20 true-spectrum-processed CMPs, in a shallow (405–730 ms TWT) and a deeper (1000–1300 ms TWT) interval, firstly using a measured far-field source signature (effectively isotropic), and secondly using computed directivity effects instead. Mean interval Q^?1-values for the deeper interval, 0.029 ± 0.011 and 0.027 ± 0.018 for conventional and directional processing, respectively, suggested no directivity influence on attenuation estimation. For the shallow interval (despite poor spectral signal-to-noise ratios and hence scattered attenuation estimates), directional processing removed directivity-generated irregularities from the spectral ratios, resulting in an improvement from Q^?1_int = ?0.036 ± 0.130 to a realistic Q^?1_int = 0.012 ± 0.030: different at 94% confidence level. Equivalent Q-values are: for the deeper interval, 35 and 37 for conventional and directional processing, respectively, and ?28 and 86 for the shallow interval. These results support the conclusions of the model studies, i.e. that source/receiver directivity has a negligible effect except for shallow targets (e.g. TWT depth ≤ 500 ms) imaged with conventional acquisition geometry. In such cases directivity corrections to spectra are strongly recommended.     

利用EMD和子波振幅谱与相位谱关系的时变子波提取方法

本文首先分析了地震波在黏弹介质的传播规律,基于黏弹介质地震波动方程总结了时变子波振幅谱和相位谱的关系,从而得出结论,准确估计子波相位谱初值和不同时刻的子波振幅谱是实现时变子波准确提取的必要条件.在此基础上,针对传统方法限制子波振幅谱形态且受限于分段平稳假设的问题,提出了一种利用EMD(Empirical Mode Decomposition)和子波振幅谱与相位谱关系的时变子波提取方法,根据子波对数振幅谱光滑连续而反射系数对数振幅谱振荡剧烈的特点,采用EMD方法将不同时刻地震记录的对数振幅谱分解为一组具有不同振荡尺度的模态分量,通过滤除振荡剧烈分量、重构光滑连续分量提取时变子波振幅谱;再应用子波振幅谱和相位谱的关系提取时变子波相位谱,将分别提取的振幅谱和相位谱逐点进行合成,最终实现时变子波的准确提取.本文方法不需要求取Q值,适用于变Q值的情况,具有良好的抗噪性能.数值仿真和叠后实际资料处理结果表明,相比传统的分段提取方法,利用本文方法提取的时变子波准确度更高,研究成果对提高地震资料分辨率具有重要意义.     

Viscoacoustic least-squares reverse-time migration of different-order free-surface multiples

Multiples have longer propagation paths and smaller reflection angles than primaries for the same source–receiver combination, so they cover a larger illumination area. Therefore, multiples can be used to image shadow zones of primaries. Least-squares reverse-time migration of multiples can produce high-quality images with fewer artefacts, high resolution and balanced amplitudes. However, viscoelasticity exists widely in the earth, especially in the deep-sea environment, and the influence of Q attenuation on multiples is much more serious than primaries due to multiples have longer paths. To compensate for Q attenuation of multiples, Q-compensated least-squares reverse-time migration of different-order multiples is proposed by deriving viscoacoustic Born modelling operators, adjoint operators and demigration operators for different-order multiples. Based on inversion theory, this method compensates for Q attenuation along all the propagation paths of multiples. Examples of a simple four-layer model, a modified attenuating Sigsbee2B model and a field data set suggest that the proposed method can produce better imaging results than Q-compensated least-squares reverse-time migration of primaries and regular least-squares reverse-time migration of multiples.     

子波相位不准对反演结果的影响(英文)

本文重点讨论在振幅谱估计准确的情况下,采用不同相位谱子波作为实际估计子波进行线性最小二乘反演,并对结果进行分析。除子波相位外,所有其它影响反演结果的因素均忽略。稀疏反射系数模型(块状波阻抗模型)反演结果表明:(1)使用不同相位谱子波进行反演,其反演结果合成的记录与原始记录都非常匹配,但反演的反射系数和声波阻抗结果与真实模型有差异;(2)反演结果的可靠程度主要与不同相位子波z变换的根的分布有关,当估计子波与真实子波Z变换的根的分布仅在单位圆附近有差异时,反演的反射系数和声波阻抗与真实模型很接近;(3)尽管反演前后地震记录都匹配了,并且评价反演结果好坏的柯西准则或改进柯西准则(反演参数没有进行自适应处理)已经达到了最优(最小),但反演结果与真实模型仍存在较大差异。最后,针对子波相位估计不准可能导致反演效果较差这个问题,我们提出采用求L1范数、丰度、变分、柯西准则(反演参数进行了自适应处理)或/和改进柯西准则(反演参数进行了自适应处理)的最优值或次优值作为评价准则的一种解决办法,理论上得到了好的效果。     

地震复谱分解技术及其在烃类检测中的应用

谱分解技术在地震解释领域已得到广泛应用,但常用的谱分解方法存在两方面的不足.一是时间分辨率低,难以对薄层进行刻画;二是在烃类检测中多解性强,难以区分流体类型.为了改善该问题,本文提出一种基于地震复谱分解技术的烃类检测方法.复谱分解是指用一个包含多个不同频率Ricker子波的复子波库对地震道进行分解,从而得到时变子波频率和相位信息的过程.借助稀疏反演技术复谱分解可以获得高分辨率的时频能量谱和时频相位谱.本文首先通过拟合算例验证了复谱分解方法刻画薄层的能力以及求取子波频率和相位的准确性.然后利用基于Kelvin-Voigt模型的黏弹波动方程数值模拟对衰减引起子波相位改变的原因进行了分析.最后通过实际资料应用展示了本文方法在储层预测中的高时间分辨率优势,验证了利用子波相位信息识别气藏的有效性.     

Improved Gabor Deconvolution and Its Extended Applications

In log time-frequency spectra, the nonstationary convolution model is a linear equation and thus we improved the Gabor deconvolution by employing a log hyperbolic smoothing scheme which can be implemented as an iteration process. Numerical tests and practical applications demonstrate that improved Gabor deconvolution can further broaden frequency bandwidth with less computational expenses than the ordinary method. Moreover, we attempt to enlarge this method’s application value by addressing nonstationary and evaluating Q values. In fact, energy relationship of each hyperbolic bin (i.e., attenuation curve) can be taken as a quantitative indicator in balancing nonstationarity and conditioning seismic traces to the assumption of unchanging wavelet, which resultantly reveals more useful information for constrained reflectivity inversion. Meanwhile, a statistical method on Q-value estimation is also proposed by utilizing this linear model’s gradient. In practice, not only estimations well agree with geologic settings, but also applications on Q-compensation migration are favorable in characterizing deep geologic structures, such as the pinch-out boundary and water channel.     

L1 norm inversion method for deconvolution in attenuating media

In order to perform a good pulse compression, the conventional spike deconvolution method requires that the wavelet is stationary. However, this requirement is never reached since the seismic wave always suffers high‐frequency attenuation and dispersion as it propagates in real materials. Due to this issue, the data need to pass through some kind of inverse‐Q filter. Most methods attempt to correct the attenuation effect by applying greater gains for high‐frequency components of the signal. The problem with this procedure is that it generally boosts high‐frequency noise. In order to deal with this problem, we present a new inversion method designed to estimate the reflectivity function in attenuating media. The key feature of the proposed method is the use of the least absolute error (L1 norm) to define both the data and model error in the objective functional. The L1 norm is more immune to noise when compared to the usual L2 one, especially when the data are contaminated by discrepant sample values. It also favours sparse reflectivity when used to define the model error in regularization of the inverse problem and also increases the resolution, since an efficient pulse compression is attained. Tests on synthetic and real data demonstrate the efficacy of the method in raising the resolution of the seismic signal without boosting its noise component.     

P-wave complex-valued traveltimes in homogeneous attenuating transversely isotropic media

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.     

The simulation of far-field wavelets using frequency-domain air-gun array near-field wavelets

Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.     

零偏移距VSP资料层Q反演及其应用研究(英文)

地层品质因子Q的可用于地震资料高分辨率处理,而从VSP资料下行直达波更容易获取准确的地层品质因子。通过对零偏移距VSP资料的监控子波和下行初至波的频谱进行综合分析,仿照Ricker子波频谱的表达式,本文提出了震源子波频谱新的表达式。在震源子波频谱新的表达式基础上,我们介绍了改进的频谱拟合法和改进的谱比法的层Q值反演方法及相应的处理流程。基于本文提出的层Q值反演方法,利用实际的零偏移距VSP资料的下行直达波,反演稳定的层Q值,并用于零偏移距VSP资料及井旁地面地震资料的反Q滤波振幅补偿处理,提高了地震资料的分辨率。     

Improving the resolution of seismic traces based on the secondary time–frequency spectrum

The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time–frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform (ST) and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time–frequency spectrum. Second, using the secondary time–frequency spectrum, we design a twodimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time–frequency–space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio (SNR).     

The estimation of spectra from time‐frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.