2D地震数据规则化中随机稀疏采样方案

地震数据规则化是地震信号处理中一个重要步骤,近年来受到广泛关注的压缩感知技术已经被应用到地震数据规则化中。压缩感知技术突破了传统的Shannon-Nyqiust采样定理的限制,可以用采集的少量地震数据重构完整数据。基于压缩感知技术的地震数据规则化质量主要受三个因素影响,除了受地震信号在不同变换域的稀疏表达和11范数重构算法的影响外,极大地取决于地震道随机稀疏采样方式。尽管已有学者开展了2D地震数据离散均匀分布随机采样方式研究,但设计新的稀疏采样方案仍然很有必要。在本文中,我们提出满足Bernoulli分布规律的Bernoulli随机稀疏采样方式和它的抖动形式。对2D数值模拟数据进行四种随机稀疏采样方案和两种变换（Fourier变换和Curvelet变换）实验,对获取的不完整数据应用11范数谱投影梯度算法（SPGL1）进行重构。考虑到不同随机种子点产生不同约束矩阵R会有不同的规则化质量,对每种方案和每个稀疏采样因子进行10次规则化实验,并计算出相应信噪比（SNR）的平均值和标准偏差。实验结果表明,我们提出的新方案好于或等于已有的离散均匀分布采样方案。     

Generalized cross-covariances and their estimation

Generalized cross-covariances describe the linear relationships between spatial variables observed at different locations. They are invariant under translation of the locations for any intrinsic processes, they determine the cokriging predictors without additional assumptions and they are unique up to linear functions. If the model is stationary, that is if the variograms are bounded, they correspond to the stationary cross-covariances. Under some symmetry condition they are equal to minus the usual cross-variogram. We present a method to estimate these generalized cross-covariances from data observed at arbitrary sampling locations. In particular we do not require that all variables are observed at the same points. For fitting a linear coregionalization model we combine this new method with a standard algorithm which ensures positive definite coregionalization matrices. We study the behavior of the method both by computing variances exactly and by simulating from various models.     

Shearlet域稀疏约束地震数据重建

在地震数据处理流程中,通常对不规则的、稀疏的或者缺失的地震数据进行插值处理,通过插值方法来避免多次波的预测错误和成像假频等现象,使地震数据处理更加精准。Shearlet变换是一种多尺度变换,具有最佳的稀疏性、方向性以及局部化特性。将Shearlet变换与基于Landweber加速下降迭代方法结合起来对地震数据进行插值,在保证求解精度的同时提高了计算效率。信号和噪声在Shearlet域具有不同的分布特点,通过阈值法压制随机噪声,可提高算法的抗噪性。此外,采用jitter采样的方式,更好地压制了假频信息。理论和实际地震数据验证了该方法的有效性。     

On the pseudo cross-variogram

Normal cross-variograms cannot be estimated from data in the usual way when there are only a few points where both variables have been measured. But the experimental pseudo cross-variogram can be computed even where there are no matching sampling points, and this appears as its principal advantage. The pseudo cross-variogram may be unbounded, though for its existence the intrinsic hypothesis alone is not a sufficient stationarity condition. In addition the differences between the two random processes must be second order stationary. Modeling the function by linear coregionalization reflects the more restrictive stationarity condition: the pseudo cross-variogram can be unbounded only if the unbounded correlation structures are the same in all variograms. As an alternative to using the pseudo cross-variogram a new method is presented that allows estimating the normal cross variogram from data where only one variable has been measured at a point.