基于广义高斯分布的地震盲反褶积方法研究

Bussgang算法是针对褶积盲源分离问题提出的,本文将其用于地震盲反褶积处理.由于广义高斯概率密度函数具有逼近任意概率密度函数的能力,从反射系数序列的统计特征出发,引入广义高斯分布来体现反射系数序列超高斯分布特征.依据反射系数序列的统计特征和Bussgang算法原理,建立以Kullback-Leibler距离为非高斯性度量的目标函数,并导出算法中涉及到的无记忆非线性函数,最终实现了地震盲反褶积.模型试算和实际资料处理结果表明,该方法能较好地适应非最小相位系统,能够同时实现地震子波和反射系数估计,有效地提高地震资料分辨率.     

NON-LINEAR ESTIMATION OF REFLECTION COEFFICIENTS FROM SEISMIC DATA*

For years, reflection coefficients have been the main aim of traditional deconvolution methods for their significant informational content. A method to estimate seismic reflection coefficients has been derived by searching for their amplitude and their time positions without any other limitating assumption. The input data have to satisfy certain quality constraints like amplitude and almost zero phase noise—ghosts, reverberations, long period multiples, and diffracted waves should be rejected by traditional processing. The proposed algorithm minimizes a functional of the difference between the spectra of trace and reflectivity in the frequency domain. The estimation of reflection coefficients together with the consistent “wavelet’ is reached iteratively with a multidimensional Newton-Raphson technique. The residual error trace shows the behavior of the process. Several advantages are then obtainable from these reflection coefficients, like conversion to interval velocities with an optimum calibration either to the well logs or to the velocity analysis curves. The procedure can be applied for detailed stratigraphic interpretations or to improve the resolution of a conventional velocity analysis.     

Lp-NORM DECONVOLUTION1

The purpose of deconvolution is to retrieve the reflectivity from seismic data. To do this requires an estimate of the seismic wavelet, which in some techniques is estimated simultaneously with the reflectivity, and in others is assumed known. The most popular deconvolution technique is inverse filtering. It has the property that the deconvolved reflectivity is band-limited. Band-limitation implies that reflectors are not sharply resolved, which can lead to serious interpretation problems in detailed delineation. To overcome the adverse effects of band-limitation, various alternatives for inverse filtering have been proposed. One class of alternatives is L_p-norm deconvolution, L₁norm deconvolution being the best-known of this class. We show that for an exact convolutional forward model and statistically independent reflectivity and additive noise, the maximum likelihood estimate of the reflectivity can be obtained by L_p-norm deconvolution for a range of multivariate probability density functions of the reflectivity and the noise. The L_∞-norm corresponds to a uniform distribution, the L₂-norm to a Gaussian distribution, the L₁-norm to an exponential distribution and the L₀-norm to a variable that is sparsely distributed. For instance, if we assume sparse and spiky reflectivity and Gaussian noise with zero mean, the L_p-norm deconvolution problem is solved best by minimizing the L₀-norm of the reflectivity and the L₂-norm of the noise. However, the L₀-norm is difficult to implement in an algorithm. From a practical point of view, the frequency-domain mixed-norm method that minimizes the L₁norm of the reflectivity and the L₂-norm of the noise is the best alternative. L_p-norm deconvolution can be stated in both time and frequency-domain. We show that both approaches are only equivalent for the case when the noise is minimized with the L₂-norm. Finally, some L_p-norm deconvolution methods are compared on synthetic and field data. For the practical examples, the wide range of possible L_p-norm deconvolution methods is narrowed down to three methods with p= 1 and/or 2. Given the assumptions of sparsely distributed reflectivity and Gaussian noise, we conclude that the mixed L₁norm (reflectivity) L₂-norm (noise) performs best. However, the problems inherent to single-trace deconvolution techniques, for example the problem of generating spurious events, remain. For practical application, a greater problem is that only the main, well-separated events are properly resolved.     

ZERO MEMORY NON-LINEAR DECONVOLUTION*

A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions.     

Intermittence and peculiarities of a statistic characteristic of the geomagnetic field in geodynamo models

The analysis of the statistical characteristics of the geomagnetic field generated in the numerical geodynamo models has shown that the distribution of the spherical harmonic coefficients in some cases is not Gaussian but, instead, has much in common with the Laplace distribution. The shape of the corresponding histograms depends on the time scale, which allows interpreting the obtained data in terms of a mixture of Gaussian distributions. The similar effects associated with the intermittence were observed in the experiments in a turbulent fluid flow. Hence, the behavior of secular variations in the magnetic field of the Earth should perhaps be described in terms of a mixture of several Gaussian stationary processes corresponding to switching between the different regimes of geodynamo generation.     

AN INVESTIGATION OF THE SPECTRAL PROPERTIES OF PRIMARY REFLECTION COEFFICIENTS*

This paper investigates the form of the nonwhiteness found in the reflection coefficients from a wide variety of rock sequences around the world. In all but one case densities are taken as constant due to the paucity of suitable density data. The reflection sequences are pseudo-white only above a corner frequency, below which their power spectrum falls away according to a power law f^β, where β is between 0.5 and 1.5. This spectrum can be adequately modelled in practice very simply with an ARMA (1, 1) process which acts on a white innovation sequence. The corollary of this is that before wavelet estimation methods are applied (all of which-except those based on synthetic seismograms—presuppose white reflection sequences) or deconvolution filters estimated, seismic traces should be filtered with the inverse of this process. Interestingly, the estimated ARMA processes group themselves into two clearly differentiated categories, having very different indices of predictability (or, strictly, indices of linear determinism). The two categories apparently correlate precisely with two kinds of sedimentation: one which consists largely of sequences of rocks with repeating properties, called “repetitive” in this paper but perhaps loosely describable as “cyclic”, and the other which is randomly bedded with no apparent pattern of components. The former has indices of predictability which are two to four times as great as those of the latter. Another, probably related, property is that β for the repetitive sequences tends to be greater than that for non-repetitive rock columns. The observed power spectra are shown to be consistent with a simple model for the logarithm of acoustic impedance consisting of a mixture of processes where the distribution of (time) scale parameters is reciprocal. Detailed effects of block-averaging and sampling the logs are shown to depend on the type of sequence under examination.     

STABILIZATION OF NORMAL-INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE-INDUCED BIAS*

A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well-known inversion schemes for normal-incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half-spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two-stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson-recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large). In the non-linear terms of dynamic deconvolution and Levinson-recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson-recursion, which are set to zero if they are not significantly different from noise. The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.     

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

The purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.     

CORRECTING FOR COLOURED PRIMARY REFLECTIVITY IN DECONVOLUTION1

Statistical deconvolution, as it is usually applied on a routine basis, designs an operator from the trace autocorrelation to compress the wavelet which is convolved with the reflectivity sequence. Under the assumption of a white reflectivity sequence (and a minimum-delay wavelet) this simple approach is valid. However, if the reflectivity is distinctly non-white, then the deconvolution will confuse the contributions to the trace spectral shape of the wavelet and reflectivity. Given logs from a nearby well, a simple two-parameter model may be used to describe the power spectral shape of the reflection coefficients derived from the broadband synthetic. This modelling is attractive in that structure in the smoothed spectrum which is consistent with random effects is not built into the model. The two parameters are used to compute simple inverse- and forward-correcting filters, which can be applied before and after the design and implementation of the standard predictive deconvolution operators. For whitening deconvolution, application of the inverse filter prior to deconvolution is unnecessary, provided the minimum-delay version of the forward filter is used. Application of the technique to seismic data shows the correction procedure to be fast and cheap and case histories display subtle, but important, differences between the conventionally deconvolved sections and those produced by incorporating the correction procedure into the processing sequence. It is concluded that, even with a moderate amount of non-whiteness, the corrected section can show appreciably better resolution than the conventionally processed section.     

ESTIMATION OF ELASTIC PARAMETERS FROM AVO EFFECTS IN THE TAU-P DOMAIN1

A quantitative AVO algorithm suitable for media with slow lateral parameter variations is developed. The method is based on a target-oriented inversion scheme for estimation of elastic parameters in a locally horizontally stratified medium. The algorithm uses band-limited PP reflection coefficients in the τ-p domain to estimate P- and S-wave velocities, densities and layer thicknesses. To obtain these reflection coefficients, a pre-processing involving the Radon transform and multiple attenuation is necessary. Furthermore, a macromodel for the velocities above the target zone must be found prior to the inversion. Various inversion tests involving synthetic data with white Gaussian noise and modelling errors that are likely to occur in conjunction with real data have been performed. In general, the inversion algorithm is fairly robust, since it is able to reproduce the main features of the reference model: main interface locations and relative contrasts in the three unknown layer parameters are recovered. From a test combining the effect of source directivity, one thin layer and 20% white Gaussian noise, it was found that neglect of the source directivity in the inversion caused the largest errors in the estimates. This indicates that it is very important either to eliminate the source directivity in a preprocessing step, or to take the directivity into account in the present algorithm. Despite these problems it was concluded that the inversion algorithm was able to reproduce the main features of the reference model.     

薄互层条件下AVO技术的应用

本文结合实际资料在详细分析砂泥岩薄互层反射特征基础上,提出气层反射特征不仅有AVO正异常,还有AVO负异常及非正非负AVO异常.由于实际的砂泥岩薄互层组合的复杂变化,在解释中不能硬套通常的厚层反射或单个薄层的模式.针对不同地区不同层位,必须制作与实际地质情况相一致的CDP道集记录地震模型,才能得到正确的反射特征.应用本文提出的方法预测了宋站等地区的气藏分布,经钻探证实,获得了满意的结果.     

INVERSION METHOD IN THE SLANT STACK DOMAIN USING AMPLITUDES OF REFLECTION ARRIVALS*

Almost all ray-tracing methods ignore the analysis of the amplitudes of seismic arrivals and therefore utilize only half of the available information. We propose a method which is a combination of ray-tracing imaging and transformation of the amplitudes of wide-aperture data. Seismic data in the conventional X-T domain are first transformed to the domain of intercept time τ and ray parameter p to recover the plane wave response. The next step is the derivation of a series of plane wave reflection coefficients, which are mapped as a function of τ and p. The reflection coefficients R(τ, p) for two arbitrarily chosen traces can then be used in our inversion method to derive a slowness-depth and a density-depth profile. It is shown that the inclusion of amplitudes of seismic arrivals (in this method, we consider the acoustic case) makes the inverse method highly stable and accurate. In a horizontally stratified medium one can recover separate profiles of velocity and density. Since this method utilizes large-offset data, it can be used for separate recovery of velocity and density to a greater depth.     

基于带状混合矩阵ICA实现地震盲反褶积

基于对地震反褶积本质上是一个盲过程的认识,引入高阶统计学盲源分离技术——独立分量分析（ICA）实现地震盲反褶积.在无噪声假设条件下,利用地震记录时间延迟矩阵和地震子波带状褶积矩阵,将地震褶积模型转化为一般线性混合ICA模型,采用FastICA算法,将带状性质作为先验信息,实现所谓带状ICA算法（B\|ICA）,得到个数与子波算子长度相等的多个估计反射系数序列和估计子波序列,最后利用褶积模型提供的附加信息从中优选出最佳的反射系数序列及相应的地震子波.模型数据和实际二维地震道数值算例表明：对于统计性反褶积,在不对反射系数作高斯白噪假设,不对子波作最小相位假设的所谓“全盲”条件下,基于ICA方法（反射系数非高斯分布,地震子波非最小相位）可以较好解决地震盲反褶积问题,是基于二阶统计特性的地震信号统计性反褶积方法的提升,具有可行性和应用前景.     

EFFECTS OF SEDIMENT GRADATION ON THE GEOMETRY OF RIVER DELTAS

l INTRODUCTlONIn this study, formation of alluvial deltas was treated as a river-dominated type of topograPhy process,caused simply by sediment deposition from a channel into a wide basin. The influences of waves, tides,and density differences related to coastal effects were excluded. There have been numerous experimentalstUdies on river delta problems. For examPle, Shieh et al. (1988, 1997) used coarse sediment asexperimental material and revealed the development and the geometric simil…     

预条件共轭梯度反褶积的改进及其应用

预条件共轭梯度反褶积方法是结合盲反褶积的实现,运用基于Krylov子空间上优化的预条件共轭梯度法,完成反射系数的反演.用该方法处理地震资料时可提高资料频率,展宽有效频率宽度.但由于地震数据对不同频带的信噪比有差异,若直接运用该反褶积处理常伴随分辨率提高的同时出现信噪比显著降低的现象.对于此,本文采取如下方法的改进措施：①在时间域上,当地震数据的振幅较大时,对应的反褶积数据的振幅取值与原地震数据的振幅相等;②在频率域上,当地震数据的频谱幅值大于一定阀值时,对应的反褶积数据的频谱取做原地震数据的频谱.由本文所给的数值算例可以看出,此两项改进方法可取得较好的实用效果.     

电离层二次反射回波的分布规律和自相关系数

本文求得了当一次回波波场为高斯分布时,二次回波波场和振幅的分布律,一、二次回波振幅自相关系数间的关系,最后对与所得结果有关的问题进行了讨论。     

Perfect zerophase sections,fact or fiction?

The desired result of an optimum seismic data processing sequence, is a broad band zerophase section, i.e. a bandpassed version of the actual reflectivity function. However, a lot of socalled zerophase-sections still carry a significant phase-error, which is due to unrealistic assumptions in the processing stream in terms of the design of standard processes as for example deconvolution. The two major issues here are the color of the reflectivity series and the misuse of prewhitening. If not properly handled they lead to a phase- and amplitude spectrum bias in the final section, preventing it from being zerophase. Whereas the reflectivity bias leads to a phase error of 50 to 90 deg, the prewhitening bias results in a phase error, which is directly proportional to the logarithm of the actual prewhitening factor.Therefore, if the spike deconvolution process is applied in a time-variant manner, as a consequence a time-variant and usually frequency dependent phase error is introduced! In this article we have made an effort to include sufficient detail to facilitate a clear understanding of the problems involved.The standard processing flow should have a minimum-delay transform and spike deconvolution prestack, followed by a zerophase transform poststack, where the residual wavelet is assumed to be minimum phase.     

Experimental analysis and application of sparsity constrained deconvolution

Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchyconstrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.