Robust reconstruction of aliased data using autoregressive spectral estimates

Autoregressive modeling is used to estimate the spectrum of aliased data. A region of spectral support is determined by identifying the location of peaks in the estimated spatial spectrum of the data. This information is used to pose a Fourier reconstruction problem that inverts for a few dominant wavenumbers that are required to model the data. Synthetic and real data examples are used to illustrate the method. In particular, we show that the proposed method can accurately reconstruct aliased data and data with gaps.     

基于异构集群计算的地统计面插值并行算法

地统计面插值算法在空间统计分析中有广泛应用,其目的是通过一组面要素的某已知属性值估算另一组面要素的属性值。地统计面插值算法多是基于克里金（Kriging）插值及其衍生算法。克里金插值算法考虑属性在空间位置上的变异性,需计算要素之间的协方差,是典型的计算密集型算法。本文分析了基于克里金插值的地统计算法计算过程,该算法中面要素间协方差计算相互独立,可作为并行计算单元划分。另外,面要素间协方差计算可使用快速傅里叶变换（FFT）快速计算,而FFT是一种非常适合并行处理的计算密集型算法。本文根据算法特征设计了基于异构集群计算的并行算法,并使用MPI+CUDA实现了该算法。实验结果表明,本文实现的算法比使用MPI实现的CPU集群的算法有更好的性能,具备良好的可扩展性,并且随着插值精度提高表现出更好的性能。     

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.     

DEM-induced errors in developing a quasi-geoid model for Africa

Errors in digital elevation models (DEMs) will introduce errors in geoid and quasi-geoid models, via their use in interpolating free-air gravity anomalies and (in the case of the quasi-geoid) their use in computing the Molodensky G ₁ term. The effects of these errors and those of datum shifts are assessed using three independent DEMs for a test region in South Africa. It is shown that these effects are significant and that it is important to choose the best-possible DEM for use in geoid and quasi-geoid modelling. Acknowledgments.The land gravity data used for this research were provided by the South African Council for Geoscience. Marine gravity anomalies were provided by the Danish National Survey and Cadastre (Kort & Matrikelstyrelsen). The GLOBE DEM was provided by the US National Geophysical Data Centre, and the CDSM DEM was provided by the South African Chief Directorate for Surveying and Mapping. The constructive comments of the reviewers are gratefully acknowledged.     

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.     

数字地形模型的质量控制

本文在分析、研究现有解决DTM质量控制的各种方法的基础上,提出了利用实测断面数据的所谓“断面内插分析法”。其特点是全面考虑了各种因素的影响,完整而可靠地描述各种因素对最终DTM数据精度的影响。实验证明:该法是最稳定、最可靠的,它具有简便易行的特点,几乎不增加多少作业负担,易于作业人员所接受,为DTM数据获取提供了一套非常实用的质量控制方案。     

On selection of kernel parametes in relevance vector machines for hydrologic applications

Recent advances in statistical learning theory have yielded tools that are improving our capabilities for analyzing large and complex datasets. Among such tools, relevance vector machines (RVMs) are finding increasing applications in hydrology because of (1) their excellent generalization properties, and (2) the probabilistic interpretation associated with this technique that yields prediction uncertainty. RVMs combine the strengths of kernel-based methods and Bayesian theory to establish relationships between a set of input vectors and a desired output. However, a bias–variance analysis of RVM estimates revealed that a careful selection of kernel parameters is of paramount importance for achieving good performance from RVMs. In this study, several analytic methods are presented for selection of kernel parameters. These methods rely on structural properties of the data rather than expensive re-sampling approaches commonly used in RVM applications. An analytical expression for prediction risk in leave-one-out cross validation is derived. For brevity, the effectiveness of the proposed methods is assessed first by data generated from the benchmark sinc function, followed by an example involving estimation of hydraulic conductivity values over a field based on observations. It is shown that a straightforward maximization of likelihood function can lead to misleading results. The proposed methods are found to yield robust estimates of parameters for kernel functions.     

On unbiased backtransform of lognormal kriging estimates

Lognormal kriging is an estimation technique that was devised for handling highly skewed data distributions. This technique takes advantage of a logarithmic transformation that reduces the data variance. However, backtransformed lognormal kriging estimates are biased because the nonbias term is totally dependent on a semivariogram model. This paper proposes a new approach for backtransforming lognormal kriging estimates that not only presents none of the problems reported in the literature but also reproduces the sample histogram and, consequently, the sample mean.     

基于小波域高斯尺度混合模型的天气雷达图像高分辨率插值

采用可精确刻画雷达回波强度数据统计特征的小波域高斯尺度混合（GSM）模型作为雷达图像先验模型,进行天气雷达图像插值,在提高图像分辨率的同时有效重建降水回波中局部强回波值、小尺度变化细节等一些重要空间分布统计特征。分析和总结雷达回波强度数据小波频率域统计特点,建立小波域GSM模型;匹配天气雷达图像小波系数和GSM模型,利用贝叶斯理论估计更小尺度的小波系数,进行小波逆变换,完成高分辨率天气雷达图像插值。试验表明,该算法能从低分辨率图像中估计出高分辨率高频系数,且所利用的先验模型充分考虑降水数据本身的特点,可有效捕获降水回波结构的非高斯特征和局部相关特性,重建雷达图像中的局部变化细节。      

徐州市九里矿区土壤重金属插值分析及污染评价

通过对徐州市九里矿区的表层土壤进行采样测定,进而对该矿区土壤重金属富集与污染状况进行了分析与评价。结果表明,该矿区表层土壤中5种重金属(Cd、Cu、Zn、Pb、Cr)含量均略高于中国土壤元素背景值,土壤中Cd富集程度较高,污染较严重;Cu、Zn、Pb、Cr富集程度较低,污染程度较轻。在GIS环境下利用空间数据插值方法对重金属的空间分布特征研究发现,该城区土壤重金属含量与该区的工矿活动和交通活动等密切相关。