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.     

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．     

预条件共轭梯度法在地震数据重建方法中的应用

基于最小平方的Fourier地震数据重建方法最终转化为求解一个线性方程组, 其系数矩阵是Toeplitz矩阵,可以用共轭梯度法求解该线性方程组.共轭梯度法的迭代次数受系数矩阵病态程度的影响,地震数据的非规则采样程度越高,所形成的系数矩阵病态程度越高,就越难收敛和得到合理的计算结果.本文研究了基于Toeplitz矩阵的不同预条件的构造方法,以及对共轭梯度法收敛性的影响.通过预条件的使用,加快了共轭梯度法的迭代速度, 改进了共轭梯度算法的收敛性,提高了计算的效率.数值算例和实际地震数据重建试验证明了预条件共轭梯度法对计算效率有很大的提高.     

地表一致性反褶积在地震勘探中的应用及效果

地震资料的反褶积处理是通过改造地震激发子波,进而消除地震激发子波在传播过程中所受的虚反射、层间多次反射和大地滤波等影响的一种地震勘探资料处理方法.反褶积的方法很多,如:脉冲反褶积、预测反褶积、地表一致性反褶积.它们之间主要区别之一在于对地震子波的假设和估计地震子波的方法.所以在处理过程中应根据不同的区域资料特征采取不同的反褶积方法.本文以河南省某煤预查区地震勘探为实例,着重总结和比较地表一致性反褶积技术在地震资料处理中的应用效果.应用研究表明,适当选择时窗和自相关步长进行自相关分析,地表一致性反褶积能够展宽频谱,压缩地震子波,并能校正地震信号的相位谱,输出零相位子波,可以较大程度地提高地震资料的分辨率,提高勘探能力.     

倾子资料三维共轭梯度反演研究

在对倾子响应和共轭梯度算法深入分析的基础上,我们实现了倾子资料三维共轭梯度反演算法.基于倾子资料的三维共轭梯度反演研究,探讨了利用倾子资料进行三维反演定量解释的方法.通过对理论模型合成数据 进行反演试算,验证了所实现的倾子资料三维共轭梯度反演算法的有效性和稳定性.该反演算法可用于对大地电磁测深和地磁测深(地震地磁台站进...     

Toeplitz矩阵循环延拓后的特征值数值分析

本文采用数值分析的方法探讨Toeplitz矩阵延拓成ω循环矩阵时特征值的逼近程度.对于对称共轭型Toeplitz矩阵,采用ω=±i时对应的循环矩阵特征值的逼近程度较好;对于其它Toeplitz矩阵,采用共轭转置将其转化为对称共轭型矩阵后,才有利于特征值的逼近.可将本文方法广泛应用于地球物理中的数值计算(如位场计算、信号处理中的反褶积、地震资料的偏移处理等).     

基于二阶谱及多阶微分融合的频谱拓展方法

受地下介质吸收衰减及环境噪声的影响,地震反射波的频率主要集中在中低频,且频带较窄,信噪比较低.反褶积方法是解决此类问题的重要手段,而谱模拟反褶积方法因克服了传统反褶积的假设条件"反射系数为白噪声"而备受推崇,但子波振幅谱无法准确获取的缺陷限制了其应用.为此,在传统的谱模拟反褶积方法基础上进行改进,提出了一种基于二阶谱及多阶微分融合的频谱拓展方法.微分算子在频率域具有单调递增的线性特征,可提高信号的高频成分并压制低频成分,即具有分频属性,且反映频率的高低与微分阶数成正比.以期望子波振幅谱为约束条件,对不同阶微分信号的振幅谱进行融合,可获得精确的宽频地震资料,避免传统谱模拟反褶积方法在求取子波振幅谱过程中存在的误差.经过对薄互层模型及实际地震记录的试算,获得了比传统方法更好的效果,证明本文方法对提高地震资料分辨率比传统谱模拟反褶积方法更加有效.     

最小加权范数插值与调制升频结合的地震数据重建研究

提出一种新的反假频地震数据重建的两步算法,将最小加权范数插值(MWNI)方法与调制升频方法有效地结合起来.首先利用MWNI方法构建数据谱的低频部分,为了提高计算效率,在低频重建算法中,引入了预条件共轭梯度法求解反问题方程,并使用了与频率有关的变波数带宽技术;然后,基于重建的低频数据,采用调制升频方法重构数据的高频部分.调制升频方法灵活,简便,能有效地从低频资料中恢复出高频成分,克服了以往AR模型预测高频走不远的限制,当数据存在严重的空间假频时,亦能获得较好的重建效果.该两步算法不仅可用于规则地震数据的内插重建,也可用于含空道地震数据的重建.理论模型和实际地震数据重建试验表明,该方法效率高,精度高,反假频能力强,重建剖面波形连续、自然,与正确完整的地震剖面相似程度高,具有良好的实用价值和应用前景.     

基于S域谱模拟技术的时变子波提取方法研究

反褶积是叠前地震数据处理中的重要环节,反褶积效果的好坏很大程度上依赖于地震子波的准确性.早期的反褶积处理大多数都是基于Robinson提出的平稳褶积模型,即地震子波是时不变的,但实际上由于地下介质的吸收衰减作用,地震子波是随时间不断变化的,这说明要进一步改善反褶积,使用时变的地震子波是必要的,因此本文提出了一种从地震资料中直接提取时变子波的方法.具体地,首先对单道地震数据做S变换求出其时频谱,进而得到其时变振幅谱,然后利用谱模拟技术从求得的地震记录振幅谱中拟合出每一时刻的子波振幅谱,在子波是零相位假设的前提下,拟合出的时变子波振幅谱即是所求频率域的时变子波,本文最后利用正演的单道地震记录和实际资料分别验证了所求频率域时变子波的准确性.     

空间反射结构正则化多道反褶积（英文）

在高分辨率地震资料处理中通常采用稀疏脉冲反褶积方法来展宽地震数据的有效频带,增强地震数据刻画薄层结构的能力。但是,现有的稀疏脉冲反褶积方法采用逐道运行模式,未考虑地震信号在相邻道之间的空间约束关系。受高频噪声的影响,反褶积结果不仅具有较强的多解性,且降低了地震信号的空间连续性。为此,本文提出了一种空间反射结构正则化多道稀疏脉冲反褶积方法。该方法从地震数据本身提取空间反射结构表征算子,将表征算子引入到多道稀疏脉冲反演的正则化条件,增强了稀疏脉冲反褶积方法的抗噪性和稳定性。理论模型实验和实际资料处理证实了该方法的正确性和可行性。     

Preconditioned non‐linear conjugate gradient method for frequency domain full‐waveform seismic inversion

We present preconditioned non‐linear conjugate gradient algorithms as alternatives to the Gauss‐Newton method for frequency domain full‐waveform seismic inversion. We designed two preconditioning operators. For the first preconditioner, we introduce the inverse of an approximate sparse Hessian matrix. The approximate Hessian matrix, which is highly sparse, is constructed by judiciously truncating the Gauss‐Newton Hessian matrix based on examining the auto‐correlation and cross‐correlation of the Jacobian matrix. As the second preconditioner, we employ the approximation of the inverse of the Gauss‐Newton Hessian matrix. This preconditioner is constructed by terminating the iteration process of the conjugate gradient least‐squares method, which is used for inverting the Hessian matrix before it converges. In our preconditioned non‐linear conjugate gradient algorithms, the step‐length along the search direction, which is a crucial factor for the convergence, is carefully chosen to maximize the reduction of the cost function after each iteration. The numerical simulation results show that by including a very limited number of non‐zero elements in the approximate Hessian, the first preconditioned non‐linear conjugate gradient algorithm is able to yield comparable inversion results to the Gauss‐Newton method while maintaining the efficiency of the un‐preconditioned non‐linear conjugate gradient method. The only extra cost is the computation of the inverse of the approximate sparse Hessian matrix, which is less expensive than the computation of a forward simulation of one source at one frequency of operation. The second preconditioned non‐linear conjugate gradient algorithm also significantly saves the computational expense in comparison with the Gauss‐Newton method while maintaining the Gauss‐Newton reconstruction quality. However, this second preconditioned non‐linear conjugate gradient algorithm is more expensive than the first one.     

非稳态地震记录时变子波估计

地震子波估计是地震资料处理和解释中的一个关键问题,子波估计的可靠性会直接影响反褶积和反演的准确度.现有的子波估计方法分为确定型和统计型两种类型,本文通过结合这两类方法,利用确定型的谱分析法和统计型的偏度最大化方法,分别提取时变子波的振幅和相位信息,得到估计的时变子波.这种方法不需要对子波进行任何时不变或相位等的假设,具有对时变相位的估计能力.进而利用估计时变子波进行非稳态反褶积,提高地震记录的保真度,为精细储层预测和描述提供高质量的剖面.理论模型试算验证了方法的可行性,通过实际地震资料的处理应用,表明该方法能有效地提取出子波时变信息.     

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.     

多道瞬变电磁法(MTEM)虚拟波场提取技术

多道瞬变电磁法(MTEM)是近年来发展起来的一种新的地球物理勘查技术,其数据采集方式与地震法类似,因此,采用瞬变电磁拟地震解释方法对MTEM数据进行处理解释具有一定的优越性.研究MTEM虚拟波场有效提取方法具有重要意义.在以往奇异值分解法、预条件正则化共轭梯度法两种不同的常规提取方法研究基础上,本文提出采用相关叠加法提取MTEM虚拟波场信息.首先采用预条件正则化共轭梯度法对全时段MTEM数据进行虚拟波场提取,然后采用同种方法对划分的各时间段数据进行虚拟波场提取,最后对全时段提取结果与各个时间段提取结果进行相关性叠加,叠加结果作为最终的提取结果.实测MTEM数据虚拟波场提取结果表明,采用相关叠加法可以得到稳定、光滑的虚拟波场波形曲线,且抗干扰能力强.     

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.     

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.