Generalized linear inversion, sometimes known as model perturbation, nonlinear regression, or inverse modeling, is applied to synthetic and real seismic data sets with the objective of obtaining an impedance profile as a function of time. The impedances solved for are parameterized in a manner that describes the unknown earth using fewer variables than previous seismic generalized linear inversion techniques. In this application only single traces of common‐midpoint (CMP) processed data will be inverted. The method of generalized linear inversion (GLI) presented here is designed to improve on the shortcomings of recursive inversion with respect to relative and absolute scale of the impedance results, resolution of impedance boundaries, and distortion from residual wavelet effects. In obtaining these goals other advantageous aspects of GLI were discovered. For example, it is insensitive to noise in many cases, and it will allow an interpreter to fix the impedance of any number of known lithologies in an interval being inverted. This last property is extremely useful when evaluating a prospect on an otherwise well‐understood seismic line. The GLI method is illustrated on a number of synthetic examples and one field data set from the Powder River basin of Wyoming.

Given a wavelet w and a noisy trace t + s * w + n, an approximation ŝ of the spike train s can be obtained using the [Formula: see text] norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train ŝ can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train ŝ may be qualitatively much different than those commonly extracted using the [Formula: see text] norm. The [Formula: see text] norm can also be used to extract a wavelet ŵ from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends. Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t. Although special algorithms have been developed to solve [Formula: see text] problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.

基于反射系数奇偶分解的基追踪反演方法,补充了地震资料中所缺失的低频与高频信息,较好地提高了反演结果对地层的分辨能力。但仅仅使用稀疏约束加入的低频信息缺乏合理性,可能与工区的实际地质情况不符,需要进一步改善反演结果的横向连续性。因此,提出在基追踪反演目标函数中加入模型约束,得到模型约束的基追踪反演目标函数,并使用梯度投影稀疏重构(Gradient Projection for Sparse Reconstruction,GPSR) 算法进行求解。模型约束的加入增强了反演的稳定性,使得反演结果中的低频信息更加符合工区实际地质背景信息,并且能够改善反演结果的横向连续性。楔形模型和实际数据测试结果表明,模型约束基追踪反演方法不仅保持了基追踪反演的稀疏性,地层阻抗呈现块化,反射界面刻画清晰,而且反演方法更为稳定,反演结果的横向连续性得到了改善,从而验证了该方法的可行性。

The basis pursuit inversion (BPI) method based on the dipole decomposition of reflection coefficients compensates the low-frequency and high-frequency information lacked in the seismic data,which can well improve the identification capability of inversion results on formations.However,it might not be reasonable to add the low frequency information just by the sparse constraint,and the information might not coincide with the true geological background.Therefore,we derived the model constrained BPI objective function by putting the model constraint to the origin objective function of BPI,and utilized the gradient projection for sparse reconstruction (GPSR) algorithm to solve the problem.It would not only enhance the inversion stability and make the low frequency information contained in inversion results more consistent with the actual work area,but also improve the lateral continuity of the inversion results.The results of the wedge model and real field data testing demonstrate that the model constrained BPI method not only keep the sparsity of the inversion results and shows the impedance in blocky,which characterizes the interface more clearly and improves the reliability of the inversion and the lateral continuity of the inversion results.

谱白化处理是提高地震勘探分辨能力的行之有效的方法。本文简述了谱白化处理的原理、实现过程及其参数的选择和使用。从实际处理中我们认识到该方法具有适应性广、可控性强、效果稳定的特点。文中给出的实例说明该方法既能提高分辨能力又不致将噪音放大得太厉害。最后还讨论了该方法的其它一些优点。

In seismic exploration, the spectral whitening is an effective measure for increasing the resolution. In this paper, the principle, the implementation procedure as well as the parameter selection and application of the spectral whitening were briefed to the point.We recognized by practice that this technique has the characteristics of wide adaptability, strong controllability as well as the stability in effects. Examples show that it could not only increase the resolution but it could also control the noise to some extent.

在以致密砂岩为储层的非常规致密油勘探开发中,由于靶区选择和水平井部署的需要,落实致密砂体的横向展布至关重要。松辽盆地北部白垩系扶余油层致密砂体整体薄层发育,特别是T₂强反射界面屏蔽问题的存在,一直制约着致密薄层砂体的识别精度。为此,开展了针对大庆长垣扶余油层致密薄砂体预测的谱反演方法应用研究。在简介谱反演方法原理的基础上,为了保证反演算法的计算精度,利用复数域快速匹配追踪算法提高时频转换的精度;通过提取时变子波提高反射系数时频谱的准确性。应用研究结果表明,将谱反演得到的地震反射系数体与宽频零相位子波进行褶积运算,获得的研究区宽频保幅地震数据有效削弱了T₂的屏蔽效应,改善了复合波的叠置问题,清晰地反映出了薄层砂体顶、底界面,并很好地保持了振幅与砂体的对应关系。

Due to the need of selecting target areas and deploying horizontal wells,it is very important to understand the lateral distribution of tight sand bodies in unconventional tight sandstone reservoir exploration and development.The tight sandstone is characterized by the development of Cretaceous thin-beds for Fuyu reservoir in the north of Songliao Basin.And the identification accuracy of the thin-bed sand bodies is restricted by the shielding effect from the strong reflection interface T2.Therefore,we study spectral inversion technique for the prediction of the tight thin-bed sand bodies in Fuyu formation,Daqing Placanticline.In order to ensure the accuracy of spectral inversion,fast matching pursuit algorithm in complex domain is used to improve the precision of the time-frequency conversion and the accuracy of time-frequency spectrum of reflection coefficient is increased by the time-varying wavelet extraction.The results of spectral inversion show that:the seismic reflection coefficient volumes from spectral inversion are convoluted with the broadband zero-phase wavelet,thus obtained broadband preserved amplitude seismic data effectively suppress the shielding effect from T2 in target area.The results also indicate the improvements of composite reflections overlay,the top and the bottom interface of the thin-bed sandstone detected clearly,and the favorable correspondence between amplitude attributes and sand bodies.

A principal limitation on seismic resolution is the earth attenuation, or [Formula: see text]-effect, including the energy dissipation of high-frequency wave components and the velocity dispersion that distorts seismic wavelets. An inverse [Formula: see text]-filtering procedure attempts to remove the [Formula: see text]-effect to produce high-resolution seismic data, but some existing methods either reduce the S/N ratio, which limits spatial resolution, or generate an illusory high-resolution wavelet that contains no more subsurface information than the original low-resolution data. In this paper, seismic inverse [Formula: see text]-filtering is implemented in a stabilized manner to produce high-quality data in terms of resolution and S/N ratio. Stabilization is applied to only the amplitude compensation operator of a full inverse [Formula: see text]-filter because its phase operator is unconditionally stable, but the scheme neither amplifies nor suppresses high frequencies at late times where the data contain mostly ambient noise. The latter property makes the process invertible, differentiating from some conventional stabilized inverse schemes that tend to suppress high frequencies at late times. The stabilized inverse [Formula: see text]-filter works for a general earth [Formula: see text]-model, variable with depth or traveltime, and is more accurate than a layered approach, which involves an approximation to the amplitude operator. Because the earth [Formula: see text]-model can now be defined accurately, instead of a constant-[Formula: see text] layered structure, the accuracy of the inverse [Formula: see text]-filter is much higher than for a layered approach, even when implemented in the Gabor transform domain. For the stabilization factor, an empirical relation is proposed to link it to a user-specified gain limit, as in an explicit gain-controlling scheme. Synthetic and real data exam-ples demonstrate that the stabilized inverse [Formula: see text]-filter corrects the wavelet distortion in terms of shape and timing, compensates for energy loss without boosting ambient noise, and produces desirable seismic images with high resolution and high S/N ratio.

Prestack inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is the estimation of elastic parameters in the thin layers and weak reflectors. To improve the resolution and the accuracy of the inversion results, we introduced the difference of L-1 and L-2 norms as a nearly unbiased approximation of the sparsity of a vector, denoted as the L1-2 norm, to the prestack inversion. The nonconvex penalty function of the L1-2 norm can be decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem can be solved efficiently by the alternating direction method of multipliers. Compared with the L-1 norm regularization, the L1-2 minimization can reconstruct reflectivities more accurately. In addition, the f-x predictive filtering was introduced to guarantee the lateral continuity of the location and the amplitude of the reflectivity series. The generalized linear inversion and f-x predictive filtering are combined for stable elastic impedance inversion results, and three parameters of P-wave velocity, S-wave velocity, and density can be inverted with the Bayesian linearized amplitude variation with offset inversion. The inversion results of synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and accuracy of the inversion results.