IMPULSE RESPONSE MODELS FOR NOISY VIBROSEIS† DATA*

A new method of Vibroseis deconvolution has been recently proposed by the authors. This discussion describes the effects of noise on the application of this method. The initial deconvolution step involves estimating the spectrum of the Vibroseis wavelet by homomorphic filtering. It is shown that noise causes problems with phase estimation. Hence, the Vibroseis wavelet is assumed to be zero phase. Examples demonstrate that zero phase cepstral filtering is a robust wavelet estimation approach for noisy data. The second step of the deconvolution method forms an impulse response model by a spectral extension method. Although this step can improve the resolution of seismic arrivals, it must be applied with caution in view of the deleterious effects of noise.     

Klauder wavelet removal before vibroseis deconvolution

The spiking deconvolution of a field seismic trace requires that the seismic wavelet on the trace be minimum phase. On a dynamite trace, the component wavelets due to the effects of recording instruments, coupling, attenuation, ghosts, reverberations and other types of multiple reflection are minimum phase. The seismic wavelet is the convolution of the component wavelets. As a result, the seismic wavelet on a dynamite trace is minimum phase and thus can be removed by spiking deconvolution. However, on a correlated vibroseis trace, the seismic wavelet is the convolution of the zero-phase Klauder wavelet with the component minimum-phase wavelets. Thus the seismic wavelet occurring on a correlated vibroseis trace does not meet the minimum-phase requirement necessary for spiking deconvolution, and the final result of deconvolution is less than optimal. Over the years, this problem has been investigated and various methods of correction have been introduced. In essence, the existing methods of vibroseis deconvolution make use of a correction that converts (on the correlated trace) the Klauder wavelet into its minimum-phase counterpart. The seismic wavelet, which is the convolution of the minimum-phase counterpart with the component minimum-phase wavelets, is then removed by spiking deconvolution. This means that spiking deconvolution removes both the constructed minimum-phase Klauder counterpart and the component minimum-phase wavelets. Here, a new method is proposed: instead of being converted to minimum phase, the Klauder wavelet is removed directly. The spiking deconvolution can then proceed unimpeded as in the case of a dynamite record. These results also hold for gap predictive deconvolution because gap deconvolution is a special case of spiking deconvolution in which the deconvolved trace is smoothed by the front part of the minimum-phase wavelet that was removed.     

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.     

Sparsity‐enhanced wavelet deconvolution

We propose a three‐step bandwidth enhancing wavelet deconvolution process, combining linear inverse filtering and non‐linear reflectivity construction based on a sparseness assumption. The first step is conventional Wiener deconvolution. The second step consists of further spectral whitening outside the spectral bandwidth of the residual wavelet after Wiener deconvolution, i.e., the wavelet resulting from application of the Wiener deconvolution filter to the original wavelet, which usually is not a perfect spike due to band limitations of the original wavelet. We specifically propose a zero‐phase filtered sparse‐spike deconvolution as the second step to recover the reflectivity dominantly outside of the bandwidth of the residual wavelet after Wiener deconvolution. The filter applied to the sparse‐spike deconvolution result is proportional to the deviation of the amplitude spectrum of the residual wavelet from unity, i.e., it is of higher amplitude; the closer the amplitude spectrum of the residual wavelet is to zero, but of very low amplitude, the closer it is to unity. The third step consists of summation of the data from the two first steps, basically adding gradually the contribution from the sparse‐spike deconvolution result at those frequencies at which the residual wavelet after Wiener deconvolution has small amplitudes. We propose to call this technique “sparsity‐enhanced wavelet deconvolution”. We demonstrate the technique on real data with the deconvolution of the (normal‐incidence) source side sea‐surface ghost of marine towed streamer data. We also present the extension of the proposed technique to time‐varying wavelet deconvolution.     

Signal-purity-spectrum-based colored deconvolution

Signal to noise ratio (SNR) and resolution are two important but contradictory characteristics used to evaluate the quality of seismic data. For relatively preserving SNR while enhancing resolution, the signal purity spectrum is introduced, estimated, and used to define the desired output amplitude spectrum after deconvolution. Since a real reflectivity series is blue rather than white, the effects of white reflectivity hypothesis on wavelets are experimentally analyzed and color compensation is applied after spectrum whitening. Experiments on real seismic data indicate that the cascade of the two processing stages can improve the ability of seismic data to delineate the geological details.     

SIGNAL ADJUSTMENT OF VIBROSEIS AND IMPULSIVE SOURCE DATA*

In certain areas continuous Vibroseis profiling is not possible due to varying terrain conditions. Impulsive sources can be used to maintain continuous coverage. While this technique keeps the coverage at the desired level, for the processing of the actual data there is the problem of using different sources resulting in different source wavelets. In addition, the effect of the free surface is different for these two energy sources. The approach to these problems consists of a minimum-phase transformation of the two-sided Vibroseis data by removal of the anticipation component of the autocorrelation of the filtered sweep and a minimum-phase transformation of the impulsive source data by replacement of the recording filter operator with its minimum-phase correspondent. Therefore, after this transformation, both datasets show causal wavelets and a conventional deconvolution (spike or predictive) may be used. After stacking, a zero-phase transformation can be performed resulting in traces well suited for computing pseudo-acoustic impedance logs or for application of complex seismic trace analysis. The solution is also applicable to pure Vibroseis data, thereby eliminating the need for a special Vibroseis deconvolution. The processing steps described above are demonstrated on synthetic and actual data. The transformation operators used are two-sided recursive (TSR) shaping filters. After application of the above adjustment procedure, remaining signal distortions can be removed by modifying only the phase spectrum or both the amplitude and phase spectra. It can be shown that an arbitrary distortion defined in the frequency domain, i.e., a distortion of the amplitude and phase spectrum, is noticeable in the time section as a two-sided signal.     

Spectral factorization technique for estimation of an ARMA operator for multichannel deconvolution of seismic data

A new spectral factorization method is presented for the estimation of a causal as well as a causally invertible ARMA operator from the correlation sequence of seismic traces. The method has been implemented for multichannel deconvolution of seismic traces with the aim of exploiting the trace-to-trace correlation that exists within seismograms. A layered earth model with a small reflectivity sequence has been considered, and the seismic traces have been considered as the output of a linear system driven by white noise reflection coefficient sequences. The present method is the concatenation of three algorithms, namely Kung's method for state variable ( F , G , H ) realization using a singular value decomposition (SVD) algorithm, Faurre's technique for computation of the strong spectral factor and Leverrier's algorithm for ARMA representation of the spectral factor. The inverted ARMA operator is used as a recursive filter for deconvolution of seismic traces. In the example shown, two traces with a covariance sequence of 160 ms length have been considered for multichannel deconvolution of stacked seismic traces. The results presented, when compared with those obtained from a conventional deconvolution algorithm, have shown encouraging prospects.     

Deconvolution of multicomponent seismic data by means of quaternions: Theory and preliminary results‡

Multicomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single components are not independent, the processing should be performed jointly for all the components. In this contribution, we use hypercomplex numbers, specifically quaternions, to implement the Wiener deconvolution for multicomponent seismic data. This new approach directly derives from the complex Wiener filter theory, but special care must be taken in the algorithm implementation due to the peculiar properties of quaternion algebra. Synthetic and real data examples show that quaternion deconvolution, either spiking or predictive, generally performs superiorly to the standard (scalar) deconvolution because it properly takes into account the vectorial nature of the wavefields. This provides a better wavelet estimation and thus an improved deconvolution performance, especially when noise affects differently the various components.     

An application of the autoregressive extrapolation technique to enhance deconvolution results: a 2D marine data example

Interpreting a post‐stack seismic section is difficult due to the band‐limited nature of the seismic data even post deconvolution. Deconvolution is a process that is universally applied to extend the bandwidth of seismic data. However, deconvolution falls short of this task as low and high frequencies of the deconvolved data are either still missing or contaminated by noise. In this paper we use the autoregressive extrapolation technique to recover these missing frequencies, using the high signal‐to‐noise ratio (S/N) portions of the spectrum of deconvolved data. I introduce here an algorithm to extend the bandwidth of deconvolved data. This is achieved via an autoregressive extrapolation technique, which has been widely used to replace missing or corrupted samples of data in signal processing. This method is performed in the spectral domain. The spectral band to be extrapolated using autoregressive prediction filters is first selected from the part of the spectrum that has a high signal‐to‐noise ratio (S/N) and is then extended. As there can be more than one zone of good S/N in the spectrum, the results of prediction filter design and extrapolation from three different bands are averaged. When the spectrum of deconvolved data is extended in this way, the results show higher vertical resolution to a degree that the final seismic data closely resemble what is considered to be a reflectivity sequence of the layered medium. This helps to obtain acoustic impedance with inversion by stable integration. The results show that autoregressive spectral extrapolation highly increases vertical resolution and improves horizon tracking to determine continuities and faults. This increase in coherence ultimately yields a more interpretable seismic section.     

基于VMD的随掘地震超前探测信号谱白化方法研究

随掘地震超前探测震源具有连续、非可控的特点,需要使用互相关技术将连续震源记录转换为等效脉冲震源记录以获取有效反射信号.但随掘地震超前探测信号往往包含一些能量较强且频带较窄的优势频率成分,使得互相关处理会引入较严重的干扰.为此,本文提出将基于变分模态分解(VMD)的希尔伯特谱白化方法应用于随掘地震超前探测信号.该方法首先...     

A COMPARISON OF STATISTICAL AND DETERMINISTIC WIENER DECONVOLUTION OF DEEP-TOW SEISMIC DATA*

Wiener ‘spiking’ deconvolution of seismic traces in the absence of a known source wavelet relies upon the use of digital filters, which are optimum in a least-squares error sense only if the wavelet to be deconvolved is minimum phase. In the marine environment in particular this condition is frequently violated, since bubble pulse oscillations result in source signatures which deviate significantly from minimum phase. The degree to which the deconvolution is impaired by such violation is generally difficult to assess, since without a measured source signature there is no optimally deconvolved trace with which the spiked trace may be compared. A recently developed near-bottom seismic profiler used in conjunction with a surface air gun source produces traces which contain the far-field source signature as the first arrival. Knowledge of this characteristic wavelet permits the design of two-sided Wiener spiking and shaping filters which can be used to accurately deconvolve the remainder of the trace. In this paper the performance of such optimum-lag filters is compared with that of the zero-lag (one-sided) operators which can be evaluated from the reflected arrival sequence alone by assuming a minimum phase source wavelet. Results indicate that the use of zero-lag operators on traces containing non-minimum phase wavelets introduces significant quantities of noise energy into the seismic record. Signal to noise ratios may however be preserved or even increased during deconvolution by the use of optimum-lag spiking or shaping filters. A debubbling technique involving matched filtering of the trace with the source wavelet followed by optimum-lag Wiener deconvolution did not give a higher quality result than can be obtained simply by the application of a suitably chosen Wiener shaping filter. However, cross correlation of an optimum-lag spike filtered trace with the known ‘actual output’ of the filter when presented with the source signature is found to enhance signal-to-noise ratio whilst maintaining improved resolution.     

反卷积在人工震源数据处理中的应用

震源到接收台站之间的地层响应函数能够反映地下介质信息。对地震波传播过程中的卷积模型进行推导:记录信号是众多震源子波经过时移加权叠加的结果;通过反卷积方法可去除震源子波信息,提取震源到接收台站之间的地层响应函数;地层响应函数中第一个突跳值对应的时间即为P波走时。在河北赤城—张北地区进行人工震源实验,通过反卷积计算得到该地区地层响应函数剖面图,得出P波波速约6 km/s。利用人工震源系统还可以对地下介质波速变化进行长期动态监测,对地震预测具有一定意义。     

Filtering vibroseis data in the precorrelation domain

Vibroseis data recorded at short source–receiver offsets can be swamped by direct waves from the source. The signal-to-noise ratio, where primary reflections are the signal and correlation side lobes are the noise, decreases with time and late reflection events are overwhelmed. This leads to low seismic resolution on the vibroseis correlogram. A new precorrelation filtering approach is proposed to suppress correlation noise. It is the ‘squeeze-filter-unsqueeze’ (SFU) process, a combination of ‘squeeze’ and ‘unsqueeze’ (S and U) transformations, together with the application of either an optimum least-squares filter or a linear recursive notch filter. SFU processing provides excellent direct wave removal if the onset time of the direct wave is known precisely, but when the correlation recognition method used to search for the first arrival fails, the SFU filtering will also fail. If the tapers of the source sweeps are badly distorted, a harmonic distortion will be introduced into the SFU-filtered trace. SFU appears to be more suitable for low-noise vibroseis data, and more effective when we know the sweep tapers exactly. SFU requires uncorrelated data, and is thus cpu intensive, but since it is automatic, it is not labour intensive. With non-linear sweeps, there are two approaches to the S,U transformations in SFU. The first requires the non-linear analytical sweep formula, and the second is to search and pick the zero nodes on the recorded pilot trace and then carry out the S,U transformations directly without requiring the algorithm or formula by which the sweep was generated. The latter method is also valid for vibroseis data with a linear sweep. SFU may be applied to the removal of any undesired signal, as long as the exact onset time of the unwanted signal in the precorrelation domain is known or determinable.     

一种改进的基于非高斯性最大化的预测反褶积算法

The predictive deconvolution algorithm （PD）, which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data （primaries and multiples） have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm （IPD） by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.     

基于信号子空间分解的三维地震资料高分辨率处理方法

提出了一种新的基于信号子空间分解技术的3 D地震资料高分辨率处理方法.利用信号子空间分解技术,不仅可以分离3 D地震资料中的信号和噪声,而且可以进一步根据地震同相轴的倾角不同,将混合信号进行分解得到单个同相轴信号.通过丢弃噪声子空间,只对不同信号子空间重构的信号利用谱白化技术进行高分辨率处理,然后累加所有处理结果,从而达到既提高地震资料的分辨率,又提高地震资料信噪比的目的.对合成资料和实际地震资料的处理结果表明,此法具有好的应用前景.     

地震子波处理的二步法反褶积方法研究

针对玛湖斜坡区三块三维地震资料和赛汉塔拉凹陷二块三维地震资料连片处理中的特点,结合地质任务和处理目标要求,提出了地震数据连片处理中的地震子波处理的方法.该方法主要体现了两次反褶积,一次是采用地表一致性反褶积,将不同震源的频带拓宽到一个标准上;再一次采用相位校正反褶积,将不同震源的数据校正到相同相位上.为了保证提取的相位校正反褶积算子稳定,采用叠后地震道提取（主要考虑到叠后地震道信噪比高,算子稳定性强）,然后将该算子应用到叠前地震道,进行相位校正.     

柯西约束盲反褶积技术在井间地震的应用

利用地面三维地震资料将二维井间地震资料推广到井间范围以外。对于提高井间地震的效益,加快其应用十分重要．为了将井间地震二维资料推广到井外三维,需要从地面地震低频信息提取层位、断面的几何信息,反褶积方法是重要的部分．本文给出了盲源反褶积方法的一种具体实现。并结合优化的预条件共轭梯度法以改善算法的稳定性,同时减少计算量．然后对经过高频恢复的地面地震数据与井间地震数据进行联合约束反演,有效地提高了地面地震的频带．并用实际资料的处理给予证实．     

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.     

PROCESSING SHEAR-WAVE VSP DATA*

Shear-wave arrivals in vertical seismic profiling recordings made with Vibroseis can be more accurately determined by wavelet processing and spectrum whitening. This method aids discrimination of shear-wave arrivals against P-wave disturbances. The data, thus improved, can be used to determine the main axis of shear-wave polarization for each sounding depth in order to maximize shear-wave amplitude by properly adding the two horizontal component signals vectorially.     

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.