Increasing resolution of reverse‐time migration using time‐shift gathers

Reverse‐time migration has become an industry standard for imaging in complex geological areas. We present an approach for increasing its imaging resolution by employing time‐shift gathers. The method consists of two steps: (i) migrating seismic data with the extended imaging condition to get time‐shift gathers and (ii) accumulating the information from time‐shift gathers after they are transformed to zero‐lag time‐shift by a post‐stack depth migration on a finer grid. The final image is generated on a grid, which is denser than that of the original image, thus improving the resolution of the migrated images. Our method is based on the observation that non‐zero‐lag time‐shift images recorded on the regular computing grid contain the information of zero‐lag time‐shift image on a denser grid, and such information can be continued to zero‐lag time‐shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero‐offset migration and is almost negligible compared with the cost of pre‐stack shot‐record reverse‐time migration. Numerical tests on synthetic models demonstrate that the method can effectively improve reverse‐time migration resolution. It can also be regarded as an approach to improve the efficiency of reverse‐time migration by performing wavefield extrapolation on a coarse grid and by generating the final image on the desired fine grid.     

Mapping optimization based on sampling size in earth related and environmental phenomena

A critical sampling grid can be defined for an earth related natural variable distributed in space, according to established theoretical results and under certain mathematical conditions. Sampling above this critical limit does not substantially improve mapping results, while based on this limit the ideal process of reproducing the original phenomenon is theoretically defined. The aim of the present paper is, by using an innovative approach; to investigate the validity of commonly used interpolation algorithms, both stochastic and deterministic, below and above this critical sampling limit. When sampling is dense, application to a simulated spatial random field shows that the results are equally accurate with those derived with more sophisticated stochastic methods. On the other hand, when the sampling grid is sparse, deterministic methods produce less accurate results, therefore stochastic algorithms with minimum estimation error are a much better option. To further demonstrate these points, the interpolation algorithms were applied in three different sampling grid densities in a contaminated waste disposal site in Russia.     

Correlation functions of rainfall field and their application in network design in the tropics

The study examines the correlation function of tropical monsoon rainfall on monthly, seasonal and annual time scales and obtains the relationship between this function and the distance. The area selected for study is Vidarbha with a fairly dense network of rain gauges. Vidarbha is a meteorological sub-division of the state of Maharashtra in India. Utilizing the relationship between the correlation function of the rainfall field and the distance, the errors of optimum interpolation of rainfall at a point have been computed by applying the method of optimum interpolation byGandin (1970). Relationships between the errors of interpolation and distance have been evaluated and from this the maximum spacing allowed between rain gauges for a specified tolerable error in interpolation has been estimated for each of the periods.     

基于偏微分方程的定向插值在偏移成像中的应用

对于射线类偏移成像来说,求解射线追踪系统中所涉及的属性值不在网格节点上的插值计算问题是一个非常重要的环节,它影响到求解走时、路径和振幅信息的计算效率和精度,进而影响到整个偏移成像的质量和效率.本研究根据速度模型的空间梯度特点,考虑被插值点处速度的梯度在横向和纵向的分布特征,构建基于速度梯度空间变化的偏微分方程算法,将近几年发展起来的基于偏微分方程的定向插值算法引入到射线类偏移成像当中,实现射线追踪当中涉及的属性值不在网格节点上的插值计算.由于偏微分方程法本身固有的特性(局部特征不变性、解的唯一性和线性叠加性),因此,该算法可以实现不破坏原始速度模型空间梯度结构的非网格节点属性的插值计算.通过在常用的速度模型上的插值计算对比、不同速度模型上射线路径对比分析以及复杂介质模型上最后的偏移成像结果分析可以得出,应用基于速度梯度构建的偏微分方程插值算法在进行插值计算的过程当中可以实现不破坏原始速度模型空间速度梯度结构的属性计算,同时应用该算法可以最终提高射线类偏移成像的质量.

     

基于频率-结构双重加权阈值的地震数据插值

地震数据的插值是地震数据处理的关键环节,插值效果的优劣关系到后续反演、去噪、反褶积、偏移等工作的进行.基于稀疏反演的常规频率-波数（FK）域插值方法往往使用广义阈值,而由于缺失地震数据仅沿波数方向呈稀疏态,在沿频率方向呈类子波频谱形态分布的非稀疏态,直接应用基于Lp范数的广义阈值会难以补全缺失数据的高低频信息,不利于后续依赖低频信息的反演及依赖高频的高分辨率处理工作的开展;基于该问题,本文设计沿频率方向类子波频谱形态变化的频率加权阈值,同时考虑完整地震数据在波数域的聚集分布,引入沿波数方向的结构加权阈值,提出基于频率-结构的双重加权阈值,在补全缺失地震道的同时,保证其高低频信息的有效恢复.模型和实际数据表明,相比于广义阈值,基于频率-结构的双重加权阈值可以减少插值误差,最大限度保证缺失地震道位置插值结果高低频信息的完整性.

     

Non‐convex compressed sensing with frequency mask for seismic data reconstruction and denoising

Compressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity‐promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non‐convex regularizer instead of the conventional one‐norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency‐space () domain. The proposed non‐convex regularizer has better sparse recovery performance compared with one‐norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band‐limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal‐to‐noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low‐frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the domain compared with the domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.     

插值预报的一种新方法及其在降水预报中的应用

本文针对经典插值预报方法存在的不足,遵循插值预报的基本原理,提出了插值预报的一种新方法,此方法的实质是考虑了预报系统中不同预报因子对系统的最后演变结果的不同作用,将此方法应用于云南１８个测站五月雨量的预报中,结果表明,此方法无论在历史预报方面还是在外推预报方面均具有良好的稳定性和预报精度。     

一种边缘保持的地震数据插值方法

在地震数据处理中,地震数据插值方法常常用来解决地震数据空间采样率低和不规则的问题.本文提出了一种基于边缘保持滤波器的地震数据插值方法.在该方法中,对于一个1D信号,逐点滑动一个处理窗口,将信号分成多个信号片段.对于某一个待恢复的缺失采样点,存在多个包含(或邻近)该采样点的信号片段可以用来估计它.采用多项式来拟合这些信号片段,并选择拟合误差最小的信号片段估计此缺失采样点,达到边缘保持的目的.对于2D地震信号,先沿不同方向扫描抽取1D信号,然后采用上述1D边缘保持插值算法分别进行处理,得到沿不同方向的插值结果.对于任一待插值采样点,选取对应拟合误差最小的方向的插值结果作为最后输出的2D数据的插值结果.理论模型和实际资料的处理结果表明,所提方法具有保边缘、抗假频及能够进行不规则数据重建等特点,既能有效的实现不规则地震数据的重建,又能很好的保持原有数据的边缘特征.     

华北区年高温日数区域平均方法及趋势分析

利用华北地区33个代表站1961—2002年间的年高温日数序列,采用均生函数和最优子集回归法,设计出具有较强拟合能力和未来趋势预测的数理统计模型。该模型能较好地拟合历史实况,其信度达到了99%;也使用该模型做出华北地区2003—2005年3年的高温日数趋势预测,对2003年和2004年做出的趋势预测效果较好。     

1951-2016年秦巴山区霜期变化的时空特征分析

依据秦巴山区96个气象站点1951—2016年逐日最低气温数据,利用一元线性回归、M-K突变检验法和Cressman插值法分析了初、终霜日和霜期变化的时空特征,并对终霜日和霜期的变化趋势及其与海拔高度的关系进行了分析,结果表明:在时间变化上,秦巴山区平均初霜日呈现出推迟的趋势,且在1960年左右发生了显著突变,而平均终霜日则与之相反,表现出提前的趋势,平均霜期也呈现出显著的减少趋势,且在20世纪60年代中期至70年代末期间表现得十分明显;空间变化上,秦巴山区初霜日和霜期呈现出较大的南北差异,而终霜日则表现为较大的东西差异;在与海拔分布的关系上,秦巴山区部分地区终霜日和霜期的变化趋势有明显的海拔依赖性,表现为西部和中东部地区终霜日的变化趋势随海拔高度的增加而减少,北部地区霜期的变化趋势随着海拔高度的增加而减少。