A non-stationary geostatistical approach to multigaussian kriging for local reserve estimation

Multigaussian kriging technique has many applications in mining, soil science, environmental science and other fields. Particularly, in the local reserve estimation of a mineral deposit, multigaussian kriging is employed to derive panel-wise tonnages by predicting conditional probability of block grades. Additionally, integration of a suitable change of support model is also required to estimate the functions of the variables with larger support than that of the samples. However, under the assumption of strict stationarity, the grade distributions and important recovery functions are estimated by multigaussian kriging using samples within a supposedly spatial homogeneous domain. Conventionally, the underlying random function model is required to be stationary in order to carry out the inference on ore grade distribution and relevant statistics. In reality, conventional stationary model often fails to represent complicated geological structure. Traditionally, the simple stationary model neither considers the obvious changes in local means and variances, nor is it able to replicate spatial continuity of the deposit and hence produces unreliable outcomes. This study deals with the theoretical design of a non-stationary multigaussian kriging model allowing change of support and its application in the mineral reserve estimation scenario. Local multivariate distributions are assumed here to be strictly stationary in the neighborhood of the panels. The local cumulative distribution function and related statistics with respect to the panels are estimated using a distance kernel approach. A rigorous investigation through simulation experiments is performed to analyze the relevance of the developed model followed by a case study on a copper deposit.     

Multigaussian kriging for point-support estimation: incorporating constraints on the sum of the kriging weights

In the geostatistical analysis of regionalized data, the practitioner may not be interested in mapping the unsampled values of the variable that has been monitored, but in assessing the risk that these values exceed or fall short of a regulatory threshold. This kind of concern is part of the more general problem of estimating a transfer function of the variable under study. In this paper, we focus on the multigaussian model, for which the regionalized variable can be represented (up to a nonlinear transformation) by a Gaussian random field. Two cases are analyzed, depending on whether the mean of this Gaussian field is considered known or not, which lead to the simple and ordinary multigaussian kriging estimators respectively. Although both of these estimators are theoretically unbiased, the latter may be preferred to the former for practical applications since it is robust to a misspecification of the mean value over the domain of interest and also to local fluctuations around this mean value. An advantage of multigaussian kriging over other nonlinear geostatistical methods such as indicator and disjunctive kriging is that it makes use of the multivariate distribution of the available data and does not produce order relation violations. The use of expansions into Hermite polynomials provides three additional results: first, an expression of the multigaussian kriging estimators in terms of series that can be calculated without numerical integration; second, an expression of the associated estimation variances; third, the derivation of a disjunctive-type estimator that minimizes the variance of the error when the mean is unknown.     

A minimalistic approach for evapotranspiration estimation using the Prophet model

ABSTRACT

This study aimed to evaluate the potential of the recently introduced Prophet model for estimating reference evapotranspiration (ETo). A comparative study was conducted for benchmarking the model results with support vector regression (SVR) and temperature-based empirical models (Thornthwaite and Hargreaves) in southern Japan. The performance of the Prophet, SVR and temperature-based empirical models was evaluated by Nash–Sutcliffe efficiency (NSE) and coefficient of determination (R²). The results indicate that temperature-based Prophet and SVR models have greater accuracy than the empirical models. The Prophet model with sole input of relative humidity, sunshine hours or windspeed showed acceptable accuracy (NSE > 0.80; R² > 0.80), while SVR models with similar inputs showed greater errors. Accuracy improved with increasing number of input parameters, giving excellent performance (NSE > 0.95; R² > 0.95) with all input parameters. Hence, the Prophet model is a new promising approach for modelling ETo with limited input variables.     

利用支持向量分类(SVC)估算断层深度和特征选择(英文)

地下断层深度的估算是重力解释难题之一,我们试利用支持向量分类(SVC)法进行计算。使用正演和非线性反演技术,通过相关误错使检测地下断层深度成为可能。但必要有一个深度初始猜测值,而且这猜测值通常不是由重力资料得。本文我们介绍以SVC作为利用重力数据估算断层深度的一种手段。在这项研究中,我们假设一种地下断层深度可归为一种类型,SVC作为一个分类算法。为了有效地利用此SVC算法,我们基于一个正确的特征选择算法去选择正确的深度特征。本次研究中我们建立了一套基于不同深度地下断层的合成重力剖面训练集,用以训练用于计算实际的地下断层深度的SVC代码。然后用其它合成重力剖面训练集测试我们训练的SVC代码,同时也用实际资料验证了我们的训练SVC代码。     

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Abstract

Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

A kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers

We consider the problem of predicting the spatial field of particle-size curves (PSCs) from a sample observed at a finite set of locations within an alluvial aquifer near the city of Tübingen, Germany. We interpret PSCs as cumulative distribution functions and their derivatives as probability density functions. We thus (a) embed the available data into an infinite-dimensional Hilbert Space of compositional functions endowed with the Aitchison geometry and (b) develop new geostatistical methods for the analysis of spatially dependent functional compositional data. This approach enables one to provide predictions at unsampled locations for these types of data, which are commonly available in hydrogeological applications, together with a quantification of the associated uncertainty. The proposed functional compositional kriging (FCK) predictor is tested on a one-dimensional application relying on a set of 60 PSCs collected along a 5-m deep borehole at the test site. The quality of FCK predictions of PSCs is evaluated through leave-one-out cross-validation on the available data, smoothed by means of Bernstein Polynomials. A comparison of estimates of hydraulic conductivity obtained via our FCK approach against those rendered by classical kriging of effective particle diameters (i.e., quantiles of the PSCs) is provided. Unlike traditional approaches, our method fully exploits the functional form of PSCs and enables one to project the complete information content embedded in the PSC to unsampled locations in the system.     

Comparison between different techniques for evaluation of predominant periods using strong ground motion records and microtremors in Pereira Colombia

This paper presents a comparison between different techniques for evaluation of predominant periods in soft soil, for the urban area of Pereira city, Western Colombia. In this study we used microtremor and strong ground motion records obtained by a local array of seven accelerographs stations deployed in the city. Response spectra and spectral ratios have been calculated and compared with strong seismic events recorded in solid rock and soft soil stations. These observations allowed the determination of dominant response spectra for several sectors in the urban area. For the microtremor measurements and earthquake data, dominant periods were determined using interpretation of Fourier amplitude spectra and Nakamura's technique. A comparison between dominant periods obtained from strong ground motion records and those obtained from microtremor measurements show similarities, which is in the range 0.2–0.5 s. A preliminary version of a site response map for Pereira city was obtained from this analysis.     

Saltwater intrusion estimation in a karstified coastal system using density-dependent modelling and comparison with the sharp-interface approach

Abstract

Saltwater intrusion is a naturally occurring phenomenon that is exacerbated significantly by excessive groundwater exploitation in coastal aquifers. In order to determine the extent of saltwater intrusion in a karstified coastal aquifer in Crete, Greece, a three-dimensional, density-dependent groundwater flow and transport model was developed and compared to the more traditional sharp-interface approach. The karstified medium was modelled using a combination of the equivalent porous medium approach (for lower-order fractures) and a discrete fracture approach (for the main fractures/faults). The model takes into consideration the geomorphologic characteristics of the karstic system, such as the depth and orientation of the fault network, and the diffusion phenomena associated with the variable densities of freshwater and saltwater—parameters that create a complex system, inducing uncertainty in the model. The model results showed that the orientation of the fractures, the pumping activity and the fluid density effects drive the seawater intrusion front asymmetrically inland.

Editor Z.W. Kundzewicz

Citation Dokou, Z. and Karatzas, G.P., 2012. Saltwater intrusion estimation in a karstified coastal system using density-dependent modelling and comparison with the sharp-interface approach. Hydrological Sciences Journal, 57 (5), 985–999.     

Comparison of ordinary kriging and artificial neural network for spatial mapping of arsenic contamination of groundwater

In this technical note, we investigate the hypothesis that ‘non-linearity matters in the spatial mapping of complex patterns of groundwater arsenic contamination’. The spatial mapping pertained to data-driven techniques of spatial interpolation based on sampling data at finite locations. Using the well known example of extensive groundwater contamination by arsenic in Bangladesh, we find that the use of a highly non-linear pattern learning technique in the form of an artificial neural network (ANN) can yield more accurate results under the same set of constraints when compared to the ordinary kriging method. One ANN and a variogram model were used to represent the spatial structure of arsenic contamination for the whole country. The probability for successful detection of a well as safe or unsafe was found to be atleast 15% larger than that by kriging under the country-wide scenario. The probability of false hopes, which is a serious issue in public health monitoring was found to be significantly lower (by more than 10%) than that by kriging.     

Comparison between predictions using different simplified Newmarks' block-on-plane models and field values of earthquake induced displacements

The study is concerned with the assessment of simplified Newmarks' block-on-plane models available in the literature for evaluating the permanent earthquake induced displacements of cut slopes and embankments, and the recommendation of a well-verified model/procedure. For this purpose, incidents of earthquake induced displacements of geotechnical structures, were collected from worldwide literatures and used in the study. Actual values of displacements were compared with predictions using different models.Based on the analyses, interpretations and discussions in this study, it was concluded that the Nadim and Whitman method (Nadim F, Whitman RV. Journal of the Geotechnical Engineering Division, ASCE 1983;109(GT7):915–931) is the most accurate method for obtaining the earthquake induced displacement. The correlation coefficient between predicted values using the Nadim and Whitman method and the actual recorded ones for geotechnical structures was 0.770; the highest among correlation coefficients for other methods.     

利用动态时间规整方法实现不同时间长度地震观测资料的形态匹配

本文将动态时间规整方法引入到地震观测资料的形态匹配分析中,以解决因时间尺度不一致的两列观测数据无法定量比对的问题。基于动态时间规整技术方法原理,通过测试数据验证了动态时间规整方法的可行性,并利用云南西部地区的断层实际观测数据,分析了1996年丽江M_S7.0地震前的跨断层观测数据异常形态与当前数据异常形态的相似性问题。结果表明:① 动态时间规整方法可用于地震资料时间长度不一致时的相似性匹配;② 时间不一致的两列观测数据可用累积规整路径距离来定量表征,累积距离越短,曲线形态越一致;③ 动态时间规整方法可用于给定模板的前兆数据相似度的计算机自动提取,可提高当前仅依靠人工判别的工作效率;④ 从模式识别的角度考虑,当前下关跨断层水准观测数据变化形态与1996年丽江M_S7.0地震和2008年汶川M_S8.0地震前的水准数据变化形态较为一致。      

Least square approach to simulate wave propagation in irregular profiles using the indirect boundary element method

In earthquake engineering and seismology it is of interest to know the surface motion at a given site due to the incoming and scattered seismic waves by surface geology. This can be formulated in terms of diffraction of elastic waves and then the indirect boundary element method (IBEM) for dynamic elasticity is used. It is based on the explicit construction of diffracted waves at the boundaries from which they radiate. This provides the analyst with insight on the physics of diffraction. The IBEM has been applied to study the amplification of elastic waves in irregular soil profiles. From the strong or weak satisfaction of boundary conditions and a simple analytical discretization scheme a linear system of equations for the boundary sources is obtained. Here, we explore the use of a weak discretization strategy with more collocation points than force densities. The least squares enforcement of boundary conditions leads to a system with reduced number of unknowns. This approach naturally allows one to use both coarser and finer boundary discretizations for smooth and rapidly varying profiles, respectively. A well studied semicircular canyon under incident P or SV in-plane waves is used to calibrate this method. Several benefits are obtained using mixed meshing that leads to the least squares condensation of the IBEM.     

不同采样率数字石英水平摆记录资料对比

通过对采样率不同的两套数字石英水平摆倾斜仪观测曲线进行对比分析,结果显示：秒采样获得的倾斜记录的分钟值与分钟采样获得的倾斜记录的潮汐波一致。采用秒采样观测能够获得大量丰富的信息,在同震响应中,能清晰记录到P波、S波。秒采样提高了地震响应能力。     

不同采样率水位同震响应能力及其特征分析

分析同种仪器不同采样率水位资料同震响应记录情况,发现存在很大差异,不但形态上明显不同,响应能力及响应幅度上也差别很大.在此基础上认为,秒采样率数据能更好记录同震响应.指出,为了记录到真实完整可靠的同震响应,观测仪器应在采样率、数据存储容量、GPS授时、触发阈值、时值及分钟值取值方式等方面作改进.最后指出,同震响应分析可能是今后地震分析预报有所突破的一个研究方向.     

Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can reflect the reservoir attenuated features and can be used for inverse-Q filtering to compensate fo...     

Generation of runoff series at ungauged locations using empirical orthogonal functions in combination with kriging

The method of Empirical Orthogonal Functions (EOF method) is combined with an objective interpolation technique, kriging, to generate runoff series at ungauged locations. In a case study the results are compared to series interpolated by a combination of EOF analysis and regression using catchment characteristics as independent variables. The results are also compared to linear weighting of an existing runoff series, a commonly used method for spatial interpolation. The influence of altitude on the runoff is studied comparing kriging based on 2 and 3 coordinates. The study showed that the capacity of EOF analysis combined with kriging is as good as the traditionally used linear weighting. The results, when altitude is included in the kriging, are improved.     

日本仪器烈度计算3种方法对比

地震发生时的仪器烈度计算和震后的烈度速报对于地震预警系统以及震后救援具有重要的意义。仪器烈度计算速度的改善和计算结果的准确度对于整个预警过程都十分重要。日本仪器烈度计算方法的发展主要经过了3个阶段:1996年气象厅仪器烈度计算方法,2008年实时仪器烈度计算方法以及2013年实时仪器烈度计算方法。本文详细阐述了这3种烈度计算方法,并且采用2011年3月11日东日本9.0级地震的数据,对比分析了3种方法所得到的仪器烈度,发现2013年方法比1996年气象厅仪器烈度在计算速度上具有一定的优势;相比较于2008年的实时仪器烈度,2013年方法计算得到的实时仪器烈度更接近于1996年气象厅仪器烈度。      

CHAMP重力场恢复时域法和空域法比较研究

利用CHAMP数据恢复重力场的解算方法分为时域法和空域法.本文首先介绍了这两种方法恢复CHAMP重力场的基本原理和算法,分析了它们的优缺点.针对空域法中的延拓误差和格网化误差进行了讨论.计算表明:延拓误差中的截断误差部分影响量级约0.001 m2·s-2(均方误差意义下),最大误差仅为0.11 m2·s-2,可完全忽略;延拓误差中的参考重力场模型误差影响随参考场选取的不同而有所差异,整体而言小于0.1 m2·s-2,但最大误差可达1.3 m2·s-2,采用高精度的参考重力场模型能大大减小延拓误差影响.目前最常用的格网化方法包括加权平均方法和最小二乘配置方法,计算表明,利用30天的CHAMP数据进行2°×2°格网化处理,加权平均法的格网化误差在0.13 m2·s-2量级,最大误差可达1.58 m2·s-2,而最小二乘配置法的格网化误差在0.006 m2·s-2量级,最大误差仅为0.15 m2·s-2,明显优于加权平均法.文章最后对时域法和以快速最小二乘配置(FSC)为代表的空域法恢复60阶次的CHAMP重力场的精度进行了比较,结果表明:两种方法的得到的重力场模型精度相差不大,整体而言,时域法略优于空域法.