基于PSO的地震盲反褶积方法

本文基于地层反射系数非高斯的统计特性,在反褶积输出单位方差约束下,将反褶积输出的负熵表示为非多项式函数,作为盲反褶积的目标函数,然后采用粒子群算法优化目标函数寻找最佳反褶积算子,实现地震信号的盲反褶积.数值模拟和实际资料处理结果表明,与传统反褶积方法相比,本文方法同时适应于最小相位子波及混合相位子波的反褶积,能够更好地从地震数据中估计反射系数,有效拓宽地震资料的频谱,得到高分辨率的地震资料.     

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.     

基于Gabor变换反褶积技术在渤海某工区的应用研究

使用常规的Wiener反褶积必须假设震源子波在地层旅行过程中是平稳的即一成不变的,这个前提条件与实际野外地震资料采集差别较大,而基于Gabor变换反褶积技术考虑到地震能量的衰减、子波的形变等非平稳性特征.地震道在Gabor域可因式分解成三项即震源子波、衰减函数和反射系数,该技术设计POU窗函数,并利用此函数在Gabor域对地震信号进行局部时频分解.Gabor域反褶积算法在Gabor域通过除以衰减函数和震源子波的乘积来估算地层反射系数,然后再做Gabor反变换可求得时间域的地层反射系数.理论模型的测试和实际地震资料的应用均表明,与Wiener反褶积相比较,基于Gabor变换反褶积可补偿中深层的能量衰减并因此拓宽有效频带和提高时间分辨率.     

一种非白噪反射系数序列的预测反褶积方法（英文）

常规预测反褶积方法需要假设反射系数是不相关的白噪声序列,利用维纳-霍夫(WH,Wiener-Hopf)方程求解滤波器,消除地震记录中的相关成分,从而实现衰减多次波和提高分辨率的目的。实际上,一次波反射系数序列存在一定的相关成分,不满足白噪声假设,处理后反射系数序列的相关成分也被消除掉,导致有效信号失真。针对这一问题,本文提出了一种改进方法。首先,利用谱模拟方法直接从地震记录中估计子波自相关;其次,利用估引计的子波自相关构建包含多次波相关信息并避免一次波反射系数相关信息的自相关函数;最后,将构建的自相关函数带入WH方程,计算预测滤波算子进行预测反褶积处理。文中对该方法进行了模型试算和实际资料处理,并于与传统预测反褶积进行对比,结果表明:本文方法能够适应非白噪的反射系数序列,处理后不改变反射系数序列的统计特性,与传统预测反褶积相比,本方法在不降低多次波衰减能力和数据分辨率提升水平的前提下,大大降低了处理噪声,提高了处理的保真性。     

用遗传算法实现地震信号反褶积

遗传算法作为寻优手段具有全局优化和很好的稳定性．本文将遗传算法用于地震信号反褶积处理，与已往方法相比它具有更好的分辨率和稳定性我们采用Bernoulli－Gaussian模型和ARMA模型分别描述地震反射系数序列和地震子波，用最大似然和最小预测误差准则分别构造用于估计反射系数序列和地震子波的目标函数，用遗传算法优化目标函数，以实现地震信号反褶积．     

一种改进的基于互信息率的盲反褶积方法

互信息率(MIR)作为随机序列统计独立性的一种度量,同时包含了序列的幅度信息与相位信息,特别适合作为盲反褶积的统计准则.但基于MIR的盲反褶积方法对噪声非常敏感,并且该算法的运算量很大.本文研究了随机噪声对反褶积的影响,通过在目标函数中加入噪声约束项,抑制了反褶积过程中高频噪声的干扰,加强了算法的抗噪性能.针对算法计算...     

随机稀疏脉冲非线性反褶积

常规的反褶积方法通过线性褶积压缩子波提高地震记录的分辨率,其能力受到有效信号频带的限制.随机稀疏脉冲非线性反褶积方法将传统的以子波压缩为核心理念的反褶积方法转移到反射系数位置和大小的检测上来,它直接从地震记录中通过非线性反演方法得到反射系数的位置和大小,突破了地震资料有效频带的限制,能够较大幅度提高地震记录的分辨率.同时通过对反射系数统计特征的有效约束,减小了反褶积结果的多解性.模型实验表明,随机稀疏脉冲反褶积对噪声和子波的敏感性较小,能够较好的保护弱反射信号.在模型实验的基础上,利用随机稀疏脉冲反褶积对实际地震资料进行了实验处理,有效的改善了地震资料的分辨率.     

非稳态地震稀疏约束反褶积研究（英文）

传统Robinson褶积模型主要受缚于三种不合理的假设,即白噪反射系数、最小相位地震子波与稳态假设,而现代反射系数反演方法（如稀疏约束反褶积等）均在前两个假设上寻求突破的同时却忽视了一个重要事实：实际地震信号具有典型的非稳态特征,这直接冲击着反射系数反演中地震子波不随时间变化的这一基础性假设。本文首先通过实际反射系数测试证实,非稳态效应造成重要信息无法得到有效展现,且对深层影响尤为严重。为校正非稳态影响,本文从描述非稳态方面具有普适性的非稳态褶积模型出发,借助对数域的衰减曲线指导检测非稳态影响并以此实现对非稳态均衡与校正。与常规不同,本文利用对数域Gabor反褶积仅移除非稳态影响,而将分离震源子波和反射系数的任务交给具有更符合实际条件的稀疏约束反褶积处理,因此结合两种反褶积技术即可有效解决非稳态特征影响,又能避免反射系数和地震子波理想化假设的不利影响。海上地震资料的应用实际表明,校正非稳态影响有助于恢复更丰富的反射系数信息,使得与地质沉积和构造相关的细节特征得到更加清晰的展现。     

基于α稳定分布的地震反演方法

本文介绍了α稳定分布的统计特征,并对比分析了实际地震信号与α稳定分布的动态样本方差特征,提出地震信号服从非高斯α稳定分布的假设.在此基础上,利用地震记录估计误差的p阶统计量作为代价函数,提出了基于非高斯α稳定分布的最小p范数地震反演方法.将该方法应用到单道反射系数理论模型及实际叠前弹性阻抗反演实例中,均取得了良好的反演效果.实际反演结果验证了本文提出的地震信号服从非高斯α稳定分布假设的合理性,以及最小p范数地震反演方法的可行性和有效性.     

叠前三参数非高斯反演方法研究

针对地球物理反演中广泛采用的"噪声高斯分布假设",本文研究了叠前地震资料中噪声的非高斯分布特征,提出了针对非高斯噪声的地震叠前非高斯反演概念和思想,构造了能同时压制高斯和非高斯噪声的混合范数作为反演目标函数,采用改进的Powell算法进行求解,有效地抑制了叠前地震资料中的高斯和非高斯混合噪声.模型试算和实际地震数据的反演结果验证了方法的正确性和算法的可靠性.     

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.     

Bayesian frequency-domain blind deconvolution of ground-penetrating radar data

Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.     

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.     

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.     

多分辨率地震信号反褶积

基于二进小波变换提出了一种新的反褶积方法─-多分辨率地震信号反褶积．在地震信号二进小波变换域中的各尺度上分别进行其分辨率随小波尺度变化的反褶积,利用不同分辨率反褶积结果之间的相关性,以及测量噪声随尺度的衰减特性,从低分辨率反褶积结果逼近高分辨率反褶积结果．理论分析和实验表明,该方法有较高的精度,并且在较低信噪比情况下有好的效果．     

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.