Wavelet analysis residual kriging vs. neural network residual kriging

 This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method – wavelet analysis residual kriging (WARK) – is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.     

A multidimensional scaling approach to enforce reproduction of transition probabilities in truncated plurigaussian simulation

Truncated plurigaussian (TPG) simulation is a flexible method for simulating rock types in deposits with complicated ordering structures. The truncation of a multivariate Gaussian distribution controls the proportions and ordering of rock types in the simulation while the variogram for each Gaussian variable controls rock type continuity. The determination of a truncation procedure for complicated geological environments is not trivial. A method for determining the truncation and fitting variograms applicable to any number of rock types and multivariate Gaussian distribution is developed here to address this problem. Multidimensional scaling is applied to place dissimilar categories far apart and similar categories close together. The multivariate space is then mapped using a Voronoi decomposition and rotated to optimize variogram reproduction. A case study simulating geologic layers at a large mineral deposit demonstrates the potential of this method and compares the results with sequential indicator simulation (SIS). Input proportion and transition probability reproduction with TPG is demonstrated to be better than SIS. Variogram reproduction is comparable for both techniques.     

Geostatistical modeling of clay spatial distribution in siliciclastic rock samples using the plurigaussian simulation method

In order to implement secondary and enhanced oil recovery processes in complex terrigenous formations as is usual in turbidite deposits, a precise knowledge of the spatial distribution of shale grains is a crucial element for the fluid flow prediction. The reason of this is that the interaction of water with shale grains can significantly modify their size and/or shape, which in turn would cause porous space sealing with the subsequent impact in the flow. In this work, a methodology for stochastic simulations of spatial grains distributions obtained from scanning electron microscopy images of siliciclastic rock samples is proposed. The aim of the methodology is to obtain stochastic models would let us investigate the shale grain behavior under various physico-chemical interactions and flux regimes, which in turn, will help us get effective petrophysical properties (porosity and permeability) at core scale. For stochastic spatial grains simulations a plurigaussian method is applied, which is based on the truncation of several standard Gaussian random functions. This approach is very flexible, since it allows to simultaneously manage the proportions of each grain category in a very general manner and to rigorously handle their spatial dependency relationships in the case of two or more grain categories. The obtained results show that the stochastically simulated porous media using the plurigaussian method adequately reproduces the proportions, basic statistics and sizes of the pore structures present in the studied reference images.     

A class of non-stationary covariance functions with compact support

This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in \(\mathbb{R}^n\) followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains.     

Stochastic multi-site generation of daily weather data

Spatial autocorrelation is a correlation between the values of a single variable, considering their geographical locations. This concept has successfully been used for multi-site generation of daily precipitation data (Khalili et al. in J Hydrometeorol 8(3):396–412, 2007). This paper presents an extension of this approach. It aims firstly to obtain an accurate reproduction of the spatial intermittence property in synthetic precipitation amounts, and then to extend the multi-site approach to the generation of daily maximum temperature, minimum temperature and solar radiation data. Monthly spatial exponential functions have been developed for each weather station according to the spatial dependence of the occurrence processes over the watershed, in order to fulfill the spatial intermittence condition in the synthetic time series of precipitation amounts. As was the case for the precipitation processes, the multi-site generation of daily maximum temperature, minimum temperature and solar radiation data is realized using spatially autocorrelated random numbers. These random numbers are incorporated into the weakly stationary generating process, as with the Richardson weather generator, and with no modifications made. Suitable spatial autocorrelations of random numbers allow the reproduction of the observed daily spatial autocorrelations and monthly interstation correlations. The Peribonca River Basin watershed is used to test the performance of the proposed approaches. Results indicate that the spatial exponential functions succeeded in reproducing an accurate spatial intermittence in the synthetic precipitation amounts. The multi-site generation approach was successfully applied for the weather data, which were adequately generated, while maintaining efficient daily spatial autocorrelations and monthly interstation correlations.     

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.     

Geostatistical seismic inversion for non‐stationary patterns using direct sequential simulation and co‐simulation

Geostatistical seismic inversion methods are routinely used in reservoir characterisation studies because of their potential to infer the spatial distribution of the petro‐elastic properties of interest (e.g., density, elastic, and acoustic impedance) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and a global spatial continuity model as estimated from the available well‐log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous, and, in many cases, non‐stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, the application of a single distribution function and a spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a three‐dimensional geostatistical inversion technique that is able to incorporate the reservoir's heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi‐distribution functions and spatial continuity models under non‐stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non‐stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques.     

Truncated plurigaussian simulations to characterize aquifer heterogeneity

Integrating geological concepts, such as relative positions and proportions of the different lithofacies, is of highest importance in order to render realistic geological patterns. The truncated plurigaussian simulation method provides a way of using both local and conceptual geological information to infer the distributions of the facies and then those of hydraulic parameters. The method ( Le Loc'h and Galli 1994 ) is based on the idea of truncating at least two underlying multi-Gaussian simulations in order to create maps of categorical variable. In this article, we show how this technique can be used to assess contaminant migration in highly heterogeneous media. We illustrate its application on the biggest contaminated site of Switzerland. It consists of a contaminant plume located in the lower fresh water Molasse on the western Swiss Plateau. The highly heterogeneous character of this formation calls for efficient stochastic methods in order to characterize transport processes.     

基于弹性波CT与GPR的岩体综合病害识别及三维地质建模

本文以地铁深基坑岩体边坡为研究对象,采用弹性波CT初步判断基坑岩体病害的类型及空间分布并辅以地质雷达进行验证;进而用分水岭算法分析弹性波CT获得的波速分布,以提取病害处的细部声速变化,圈定病害范围;在此基础上,以弹性波CT三维空间波速数据库的坐标信息为基础,结合分水岭算法得到的空间坐标信息获得建模数据库,导入GOCAD...     

GOCE卫星监测的中国区域重力异常

介绍了利用最新一代重力卫星GOCE(Gravity field and steady-state Ocean Circulation Explorer)重力场模型数据计算重力异常的原理和方法,采用最新发布的GOCE重力场模型数据(2009年10月-2010年7月)计算了中国区域(70°～130°E,15°～55°N)的重力异常,为了进一步分析重力异常与区域地质构造及地震活动性的对应关系,将计算结果与中国区域地形、地震活动区域等资料进行了对比分析,结果表明利用GOCE重力场模型数据计算的重力异常能够较好的反映区域地质构造分布特征,而且强震震中通常位于重力异常变化剧烈的高梯度带上.     

地震波形反演技术在砂泥岩薄互层结构表征中的应用

基于传播矩阵理论开发砂泥岩薄互层地震合成记录算法,与褶积算法、基于界面模型的Zoeppritz方法以及波动方程等方法相比,该方法更适用于具有复杂结构的薄互层模型,能够在充分考虑地震反射波动力学因素的同时不受网格间距的限制.基于正演算法开发了基于波形对比的砂泥岩薄互层地震反演技术,由地震反射波形特征的变化反演薄地层单元中砂体含量与空间位置等参数,进而确定薄互层段砂泥岩组合结构以及砂体的空间展布.理论模型验证了反演方法的有效性.通过测井分析建立薄互层地震地质模型,并将该技术应用于研究区实际地震数据,反演的砂体空间分布与测井资料进行对比分析,验证了反演方法的实用性.

     

基于地质体空间位置优化约束的航空重力梯度数据三维物性反演

重力数据的物性反演面临着严重的多解性问题,降低多解性的有效手段是加入约束条件.而边界识别、深度估计及成像方法可获取地质体的水平位置、深度范围等几何参数信息,本文将基于数据本身挖掘的地质体几何参数信息约束到物性反演中,以降低反演的多解性.通过引入基于深度信息的深度加权函数及基于水平位置的水平梯度加权函数建立优化约束条件,有效地提高了反演结果的横向及纵向分辨率.重力梯度数据包含更多的地质体空间特征信息,将优化约束反演方法应用到全张量数据的反演中,模型试验表明本文方法反演结果与理论模型更加吻合.最后对美国路易斯安那州文顿盐丘实测航空重力梯度数据的应用表明,本文方法在其他地球物理、地质资料不足的情况下获得更可靠的反演结果.

     

基于阈值约束的协克里金法联合反演重力与重力梯度数据

常规协克里金方法反演重力或重力梯度数据具有抗噪性好、加入先验信息容易等优点,其反演的地下密度分布能够识别异常体中心位置,还原异常体基本形态,但反演图像光滑,分辨率低,这是由于常规方法估计的密度协方差矩阵全局发散、平稳.为了通过协克里金方法获得聚焦的密度分布需要改善密度协方差矩阵的性质.首先,本文推导了理论密度协方差公式,其性质表明,当理论模型聚焦分布时,其密度协方差矩阵是非平稳且聚焦分布的.为了打破常规协方差矩阵全局平稳、发散的特征,本文设置密度阈值处理协方差矩阵,通过不断更新协方差矩阵来迭代实现协克里金反演,最终得到相对聚焦的反演结果.用本文方法处理重力与重力梯度数据恢复两种密度模型,均得到了与正演模型匹配的反演结果;再将方法运用于文顿盐丘的实际测量重力与重力梯度数据,反演结果与已知的地质情况匹配较好.

     

The use of a spatially heterogeneous simulation model for studying biotransformation processes of nitrogen and phosphorus compounds and the dynamics of oxygen dissolved in water in the ecosystem of Neva Bay, the Gulf of Finland: 2. Input data for calculations, modeling results, and their analysis

The data collected for model calculations is systematized for natural and design conditions. The natural conditions did not take into account the effect of the complex of water-protection structures on the hydrological regime of Neva Bay and on the biogenic load onto this water area, while the design conditions, conversely, reflected the possible impact of those structures on the hydrology and ecology of the area. Numerical experiments were used to study the processes of transformation of N and P compounds and the dynamics of dissolved O₂ in Neva Bay water area. In the comparison of the calculated and observed concentrations of biogenic substances, Theil criterion was evaluated to assess the adequacy of the model in reproducing the concentration fields of the distribution of biogenic substances over Neva Bay water area. The major qualitative and quantitative features of the formation of the spatial heterogeneity and the time variations in the concentrations of biogenic element compounds over Neva Bay water area are identified. Possible improvements of the model in the reproduction of the complex of processes that are of particular importance for the development of substance transformations in shallow ecosystems are considered.     

Depth determination from a non-stationary magnetic profile for scaling geology

The conventional spectral analysis method for interpretation of magnetic data assumes stationary spatial series and a white‐noise source distribution. However, long magnetic profiles may not be stationary in nature and source distributions are not white. Long non‐stationary magnetic profiles can be divided into stationary subprofiles following Wiener filter theory. A least‐squares inverse method is used to calculate the scaling exponents and depth values of magnetic interfaces from the power spectrum. The applicability of this approach is demonstrated on non‐stationary synthetic and field magnetic data collected along the Nagaur–Jhalawar transect, western India. The stationarity of the whole profile and the subprofiles of the synthetic and field data is tested. The variation of the mean and standard deviations of the subprofiles is significantly reduced compared with the whole profile. The depth values found from the synthetic model are in close agreement with the assumed depth values, whereas for the field data these are in close agreement with estimates from seismic, magnetotelluric and gravity data.     

Time-domain forward and inverse modeling of lossy soils with frequency-independent Q for near-surface applications

In this paper, we are concerned with a full-waveform-based methodology that allows the simultaneous imaging of the soil's stiffness and attenuating properties, using solely the soil's surficial response to probing waves.To date, field observations of small-strain wave attenuation in geomaterials at moderate spatial scales suggest that a commonly used metric of intrinsic and apparent attenuation, the seismic quality factor Q, is frequency-independent for a wide part of the frequency spectrum, including the frequency range of interest to seismic applications. We discuss first the forward simulation of waves in near-surface soil deposits directly in the time-domain using simplified models that adequately approximate nearly frequency-independent Q. To this end, we first review various attenuation models that aim at reproducing the frequency-independent Q behavior, and conclude, supported by site analyses, that, even though a generalized Maxwell body with eight Maxwell elements in parallel (GMB8) provides the best fit to frequency-independent Q, we favor a version of it with fewer parameters (GMB2), in order to reduce modeling complexity, while still retaining good agreement with the GMB8 model.We report on forward site analyses that lend credence to the choice of the GMB2 simplified model. We, then, use the GMB2 constitutive relation in the context of full-waveform inversion, and report on numerical experiments that lead to the imaging of the soil's properties in heterogeneous semi-infinite domains.     

Simulation of intrinsic random fields of order <Emphasis Type="Italic">k</Emphasis> with a continuous spectral algorithm

Intrinsic random fields of order k, defined as random fields whose high-order increments (generalized increments of order k) are second-order stationary, are used in spatial statistics to model regionalized variables exhibiting spatial trends, a feature that is common in earth and environmental sciences applications. A continuous spectral algorithm is proposed to simulate such random fields in a d-dimensional Euclidean space, with given generalized covariance structure and with Gaussian generalized increments of order k. The only condition needed to run the algorithm is to know the spectral measure associated with the generalized covariance function (case of a scalar random field) or with the matrix of generalized direct and cross-covariances (case of a vector random field). The algorithm is applied to synthetic examples to simulate intrinsic random fields with power generalized direct and cross-covariances, as well as an intrinsic random field with power and spline generalized direct covariances and Matérn generalized cross-covariance.     

Estimation of extreme floods of the River Meuse using a stochastic weather generator and a rainfall–runoff model / Estimation des crues extrêmes de la Meuse à l'aide d'un générateur stochastique de variables météorologiques et d'un modèle pluie–débit

Abstract

A stochastic weather generator has been developed to simulate long daily sequences of areal rainfall and station temperature for the Belgian and French sub-basins of the River Meuse. The weather generator is based on the principle of nearest-neighbour resampling. In this method rainfall and temperature data are sampled simultaneously from multiple historical records with replacement such that the temporal and spatial correlations are well preserved. Particular emphasis is given to the use of a small number of long station records in the resampling algorithm. The distribution of the 10-day winter maxima of basin-average rainfall is quite well reproduced. The generated sequences were used as input for hydrological simulations with the semi-distributed HBV rainfall–runoff model. Though this model is capable of reproducing the flood peaks of December 1993 and January 1995, it tends to underestimate the less extreme daily peak discharges. This underestimation does not show up in the 10-day average discharges. The hydrological simulations with the generated daily rainfall and temperature data reproduce the distribution of the winter maxima of the 10-day average discharges well. Resampling based on long station records leads to lower rainfall and discharge extremes than resampling from the data over a shorter period for which areal rainfall was available.     

基于先验信息约束的重磁三维交互反演建模技术——以铜陵矿集区为例

三维地质建模是实现深部矿产勘查突破的重要途径,其通过控矿地质体的三维建模,直观刻画控矿要素之间的空间、成因和演化关系,帮助理解成矿系统,开展深部找矿预测.当前三维建模主要采用地质资料构建,在缺少钻孔等已知资料的情况下,难于构建出可靠的三维地质模型.为了克服常规三维地质建模方法可信度低、精度差的缺点,本文将重磁交互反演技术引入到三维地质建模中,提出了基于先验信息约束,通过二度半剖面交互反演、三维物性反演联合修正的三维地质模型方法.采用该方法建立了铜陵矿集区的三维地质模型,并开展了深部找矿预测,取得以下主要认识:1)基于先验信息约束的重磁交互反演建模技术能大幅提高三维地质模型的可信度,是实现地下地质体"透明化"的重要途径;2)铜陵地区重要控矿地层(C-P-T2)主要分布于向斜区和火山岩覆盖区,深部岩浆岩条件优越,深部找矿工作应从传统的背斜隆起区转向向斜区和火山岩覆盖区以及部分凹陷区,这将极大拓展铜陵地区找矿空间;3)铜陵地区传统的五大矿田的侵入岩均具有复合岩体特征,特别是与辉石闪长岩共生的矿产以铁铜矿为主,而与金矿密切相关的侵入岩则多为中酸性岩体,这一推断如果成立,将对铜陵地区找矿突破产生重大影响;4)铜陵地区的推覆构造十分发育,木镇凹陷区的早古生代基底和南陵盆地北西缘的戴公山背斜就是一套区域性推覆构造的产物,三维地质模型还揭示铜陵地区侵入岩具有深、中、浅三重结构,这为铜陵隆起的推覆成因提供了证据,也指示了在铜陵之外再寻找类似铜陵矿集区的良好前景.     

THE INFLUENCE OF TOPOGRAPHY ON TIME AND SPACE DISTRIBUTION OF SOIL SURFACE WATER CONTENT

The distribution of water content in time and space at the soil surface has been investigated on a small farmland catchment (1.3 km² ) from four field surveys corresponding to different moisture statuses. For each survey, about 400 samples were collected at the soil surface at a depth of 5 cm along ten axes parallel to the greatest slope. The relationship between the measurements and the topography has been analysed. The structure of the data is well explained by a topographic index referring to the downslope conditions and defined as the elevation difference between the sample point and the stream point corresponding to the outlet of the water pathway derived from the digital elevation model (DEM). This index can be considered as an hydraulic head, at least for saturated conditions. A threshold for this index allows two domains within the catchment to be distinguished; an upper domain where the water content is nearly constant and varies slowly, and a lower domain where moisture status increases and is highly variable. The spatial distribution of these two domains is well correlated to the spatial distribution of the soils. Thus, both topography and the spatial distribution of soil appear to control the spatial distribution of surface water content at the 1-km² scale. © 1997 by John Wiley & Sons Ltd.