地球物理勘探中几种二维插值方法的误差分析

为了研究采样和网格化方法对地球物理数据成图精度的影响,为野外数据采集布设提供一定的依据,采用数值模拟确定重力异常场场值,通过不同采样间距和不同插值方法计算重力异常绝对误差均方根值和节点处的绝对误差值,对比不同插值方法的误差,得到了如下认识：1）对于同一插值方法而言,存在小间距绝对误差均方根值小于大间距绝对误差均方根值的关系。2）对不同的插值方法而言:当采样间距小于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、反距离加权插值法、最近邻点法、最小曲率法,并且线性插值三角网法与自然邻点法具有几乎相同的数值;当采样间距大于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、最小曲率法、最近邻点法、反距离加权插值法,并且线性插值三角网法和自然邻点法具有几乎相同的数值。3）从绝对误差均方值看,径向基函数方法、改进的谢别德方法和克里金方法数值较小,其中径向基函数值绝对误差均方根值最小。4）从节点处绝对误差值来看,径向基函数方法、克里金方法、改进的谢别德方法相对其他插值方法具有更小的误差,不存在局部误差较小或较大的情况,是相对较好的插值方法,并且径向基函数方法是最好的。     

Predicting Threshold Exceedance by Local Block Means in Soil Pollution Surveys

Soil contamination by heavy metals and organic pollutants around industrial premises is a problem in many countries around the world. Delineating zones where pollutants exceed tolerable levels is a necessity for successfully mitigating related health risks. Predictions of pollutants are usually required for blocks because remediation or regulatory decisions are imposed for entire parcels. Parcel areas typically exceed the observation support, but are smaller than the survey domain. Mapping soil pollution therefore involves a local change of support. The goal of this work is to find a simple, robust, and precise method for predicting block means (linear predictions) and threshold exceedance by block means (nonlinear predictions) from data observed at points that show a spatial trend. By simulations, we compared the performance of universal block kriging (UK), Gaussian conditional simulations (CS), constrained (CK), and covariance-matching constrained kriging (CMCK), for linear and nonlinear local change of support prediction problems. We considered Gaussian and positively skewed spatial processes with a nonstationary mean function and various scenarios for the autocorrelated error. The linear predictions were assessed by bias and mean square prediction error and the nonlinear predictions by bias and Peirce skill scores.     

Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

以隶属度为权重的加权回归模型及在水文水资源中的应用

概率统计方法在水文水资源中的应用已有很长历史,常用的是线性回归模型。然而,等权线性回归模型的误差不仅与同步观测资料的长度及残差平方和有关,还随自变量与其均值的变幅加大而增大。因此,线性回归模型一般不应该用来外延。基于加权回归模型的基本理论,以隶属度为权重建立了加权回归模型,并证明了加权回归估计值的无偏性。通过实例分析计算,说明了方法的可行性。     

Model-based remote sensing algorithms for particulate organic carbon (POC) in the Northeastern Gulf of Mexico

Hydrographic data, including particulate organic carbon (POC) from the Northeastern Gulf of Mexico (NEGOM) study, were combined with remotely-sensed SeaWiFS data to estimate POC concentration using principal component analysis (PCA). The spectral radiance was extracted at each NEGOM station, digitized, and averaged. The mean value and spurious trends were removed from each spectrum. De-trended data included six wavelengths at 58 stations. The correlation between the weighting factors of the first six eigenvectors and POC concentration were applied using multiple linear regression. PCA algorithms based on the first three, four, and five modes accounted for 90, 95, and 98% of total variance and yielded significant correlations with POC with R ² = 0.89, 0.92, and 0.93. These full waveband approaches provided robust estimates of POC in various water types. Three different analyses (root mean square error, mean ratio and standard deviation) showed similar error estimates, and suggest that spectral variations in the modes defined by just the first four characteristic vectors are closely correlated with POC concentration, resulting in only negligible loss of spectral information from additional modes. The use of POC algorithms greatly increases the spatial and temporal resolution for interpreting POC cycling and can be extrapolated throughout and perhaps beyond the area of shipboard sampling.     

An application of the deterministic variogram to design-based variance estimation

When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators.     

岩土工程中位移监测方法及精度分析

在岩土工程位移监测中,选择哪种方法取决于监测时的条件;本文对监测中常用的测小角法、角度前方交会方法、距离前方交会方法、全站仪后方交会及极坐标综合方法等各种方法进行了研究。在目前各种文献中,一般都只是给出了监测点坐标的计算方法,充其量还给出监测点沿坐标轴方向的中误差以及点位中误差,而监测点其它方向的误差情况则无从计算。基于此,本文对以上各种监测方法的误差椭圆进行了推导,从而可以计算监测点沿各个方向误差并估算精度。     

基于神经网络模型的中国表层土壤有机质空间分布模拟方法

基于全国第二次土壤普查得到的6 241个典型土壤剖面数据,采用主成分分析方法和径向基函数神经网络模型建立不同植被类型—土纲单元内土壤有机质与气候、地形和植被等环境因子间的非线性关系,模拟全国表层土壤有机质的空间分析格局。结果表明,该模型具有较准确的预测能力,性能指数达到1.94。与普通克里格法、反比距离法和多元回归模型相比,神经网络模型对621个验证点模拟结果与实测值的相关系数为0.799,分别提高了0.265、0.181和0.120,平均绝对误差分别降低了4.25、4.43和2.34 g/kg,平均相对误差分别降低了30.16%、32.66%和5.93%,均方根误差则分别降低了8.61、8.24和6.24 g/kg;从模拟结果图来看,神经网络模型能够提供更多的细节信息。该方法为大尺度土壤性质空间分布模拟提供了有益的参考。     

Comparison of regression-based and combined versions of Inverse Distance Weighted methods for spatial interpolation of daily mean temperature data

This paper focuses on the performance of two regression-based and one Inverse Distance Weighted (IDW) and two combined versions of IDW methods for interpolation of daily mean temperature at the Black Sea Region of Turkey. Simple linear regression (SLR) and multiple linear regression (MLR) are used as regression-based methods. Combinations of IDW with TLR (temperature lapse rate) and gradient plus inverse distance squared (GIDS) are used as combined versions of IDW. This study targets to compare five spatial interpolation methods based on RMSE (root-mean-square error) statistics of interpolation errors for daily mean temperatures from 1981 to 2012. In order to compare the interpolation errors of the five methods, the leave-one-out cross-validation method was applied over long periods of 32 years on 52 different sites. The algorithms of the five interpolation methods’ codes were written in MATLAB by the authors of the paper.     

改进型粒子群算法及其在GPR全波形反演中的应用

探地雷达作为高精度的物探工作方法,其主要目的是反演解释地下结构的物性参数。笔者提出社会学习型粒子群优化反演方法,它以信号均方误差为目标函数,用时域有限差分方法作正演,并且针对反射波信号较弱、反演效果不佳的情况设计了对正演结果进行振幅补偿的方法,对反射波的振幅进行增益,以提高反演精度。通过与经典粒子群优化反演方法的结果对比,说明了该算法在准确度以及效率方面都有相当大的提高。经过分析多层介质仿真数据的一维反演结果,说明了该算法对多参数反演的有效性和良好的抗噪性。     

Efficiency of kriging estimation for square, triangular, and hexagonal grids

Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90 ² or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs.     

大定源回线全区视电阻率平移算法与核函数算法的对比

为了更快、更准确地进行瞬变电磁一维正、反演,研究了中心回线装置计算全区视电阻率的平移算法和核函数算法。研究表明,均匀半空间大定源回线的瞬变响应曲线具有平移伸缩特性和核函数特点,可以运用平移算法和核函数算法计算。推导出全区视电阻率的计算公式,通过三层K型、4层KH型地电模型理论计算,对比分析了平移算法和核函数算法的运算速度和误差,结果表明:平移算法的运算速度为0.140 6 s,均方根误差为1.824×10-2,核函数算法的运算速度为3.241 8 s,均方根误差为0.728×10-2,两种方法均能计算大定源回线的全区视电阻率,各有优缺点。      

EGM2008重力场模型在兴城物探测量中的应用

以吉林大学兴城物探教学实习测网为例,基于EGM2008重力场模型,采用二次曲面、移动曲线、最小二乘配置、三次样条和反距离加权改正插值法,计算了不同GPS水准点密度情况下的水准面模型,并利用二等水准测量方法验证了计算精度,分析了该模型的适定性。结果表明,三次样条插值法的精度和稳定性最高,其次是移动曲线法和最小二乘配置法;二次曲面拟合的精度最低,反距离加权改正法稳定性最差。所有算法都表明,在研究区,当GPS水准点间隔20 km时,基于EGM2008模型确定的大地水准面精度在0.1 m以内;而采用单独GPS水准点的区域大地水准面模型能达到14cm,完全满足各种比例尺情况下的石油物探测量要求。     

Normal and lognormal estimation

A comprehensive theoretical study of the problem of estimation of regionalized variables with normal or lognormal distribution is presented. Unbiased linear estimators are derived, under both assumptions that the population mean is known and unknown, and their error variance is calculated. The minimum variance kriging estimators are studied in more detail and are compared with the conditional expectations. The emphasis is on the study of lognormally distributed variates. The derived mathematical formulas are applicable to the optimal contouring of sample values with the appropriate distribution, as well as the optimal estimation of blocks of ore in mineral deposits.     

Gully erosion spatial modelling: Role of machine learning algorithms in selection of the best controlling factors and modelling process

This investigation assessed the efficacy of 10 widely used machine learning algorithms (MLA) comprising the least absolute shrinkage and selection operator (LASSO), generalized linear model (GLM), stepwise generalized linear model (SGLM), elastic net (ENET), partial least square (PLS), ridge regression, support vector machine (SVM), classification and regression trees (CART), bagged CART, and random forest (RF) for gully erosion susceptibility mapping (GESM) in Iran. The location of 462 previously existing gully erosion sites were mapped through widespread field investigations, of which 70% (323) and 30% (139) of observations were arbitrarily divided for algorithm calibration and validation. Twelve controlling factors for gully erosion, namely, soil texture, annual mean rainfall, digital elevation model (DEM), drainage density, slope, lithology, topographic wetness index (TWI), distance from rivers, aspect, distance from roads, plan curvature, and profile curvature were ranked in terms of their importance using each MLA. The MLA were compared using a training dataset for gully erosion and statistical measures such as RMSE (root mean square error), MAE (mean absolute error), and R-squared. Based on the comparisons among MLA, the RF algorithm exhibited the minimum RMSE and MAE and the maximum value of R-squared, and was therefore selected as the best model. The variable importance evaluation using the RF model revealed that distance from rivers had the highest significance in influencing the occurrence of gully erosion whereas plan curvature had the least importance. According to the GESM generated using RF, most of the study area is predicted to have a low (53.72%) or moderate (29.65%) susceptibility to gully erosion, whereas only a small area is identified to have a high (12.56%) or very high (4.07%) susceptibility. The outcome generated by RF model is validated using the ROC (Receiver Operating Characteristics) curve approach, which returned an area under the curve (AUC) of 0.985, proving the excellent forecasting ability of the model. The GESM prepared using the RF algorithm can aid decision-makers in targeting remedial actions for minimizing the damage caused by gully erosion.     

Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems

A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.     

面波基模式频散曲线提取解精度对比研究

针对不同方法提取面波基模式频散曲线精度问题,笔者分别采用τ-p变换、频率分解法、F-K变换、高分辨率线性拉东变换(High-Resolution Linear Radon Transform,简称HRLRT)对六层递增型地质模型合成瑞雷波记录进行频散能量成像,并按频散能量最大值拾取基模式频散曲线。为定量评价理论模型基模式频散曲线提取解与解析解的接近程度,引入了均方差与相关系数两种评价参数。评价结果表明,高分辨率线性拉东变换提取基模式频散曲线精度最高,均方差为11.167 8,相关系数为0.994 9;F-K变换提取基模式频散曲线精度最低,均方差为195.274,相关系数为0.515 2。     

Global Ocean Data Assimilation System Design and Algorithm Acceleration Based on Local Ensemble Transform Kalman Filter

An integrated analysis about computational time complexity of the Local Ensemble Transform Kalman Filter (LETKF) was performed. It is found that the calculation step of inverse matrix of the error covariance in ensemble space is the most computationally intensive and time consuming. In a parallel computing environment, the uneven distribution of CPU calculations in this step directly leads to low computational efficiency. To solve this problem, a new load balancing strategy was designed based on the "greedy algorithm". A high-performance parallel ocean data assimilation system based on the LETKF was developed and tested using this strategy. This system was based on the Parallel Ocean Program 2 (POP2) of the Community Earth System Model (CESM). The optimal interpolated sea surface temperature data (OISST) and Argo temperature profile data from January to February, 2004 were assimilated into the POP2. The results show that data assimilation effectively reduces the root mean square error of temperature and salinity. Using the new strategy, the exact same results are obtained but the computation time is reduced by half. At higher resolution (0.1°×0.1°),the computing performance is still doubled, indicating that this load balancing scheme is stable and reliable. In addition, the new method has high scalability and portability with great potential to be applied in operational forecasting.     

基于局地集合变换卡尔曼滤波的全球海洋资料同化系统设计及算法加速

通过对局地集合变换卡尔曼滤波(LETKF)算法的计算时间复杂度的完整分析,发现计算集合空间分析场误差协方差的逆矩阵这一过程计算量最大,耗时最长。且在并行计算环境下,该步骤CPU计算量分配不均是影响计算效率的直接原因。为解决这一问题,采用“贪心算法”设计了一套新的负载均衡策略,并使用该策略开发了一个基于LETKF和并行海洋模块2(POP2)的高性能并行海洋资料同化系统。将2004年1~2月日平均的最优插值海表温度资料(OISST)和同时期的Argo温盐剖面资料同化进入POP2。结果表明,同化有效降低了温度和盐度的均方根误差。同时,在不改变计算结果的前提下,相比原始同化系统,新系统计算性能提升1倍。在更高分辨率(0.1°×0.1°)下,该系统的计算性能仍然可以提升1倍,说明新设计的负载均衡方案稳定可靠。该方案具有很强的可扩展性和移植性,在业务预报中有广泛的应用前景。     

深拖平缆采集资料中鬼波衰减方法探讨

鬼波衰减是深拖平缆采集资料处理中非常重要的一步,也是实现宽频处理的关键步骤。为此,笔者分析了深拖平缆资料特点,推导了鬼波的时距曲线方程,在此基础上,介绍了线性Radon域最小平方反演方法衰减鬼波的基本原理,该方法首先通过最小平方方法求得无鬼波的Radon域数据,再应用反变换算子中的一次波算子进行反变换,从而实现了对鬼波的压制。采用该理论对模型数据与实际地震资料进行了试处理,结果表明,深拖平缆资料通过本文的鬼波衰减技术处理后,陷频点得到了补偿,有效频带得到了拓宽,达到了宽频处理的效果。