A stochastic model to quantify the steady-state crustal geotherms subject to uncertainties in thermal conductivity

In this communication the 1-D steady-state heat conduction problem is solved in a stochastic framework incorporating uncertainties in the depth-dependent thermal conductivity. For this purpose, a new approach to the perturbation method, an expansion series method, which allows for the incorporation of a large variance in the controlling parameters, has been used. This method helps in avoiding assumptions on the probability distribution of the parameter and instead uses information pertaining to the mean and spatial correlation structure. This information is easily available in most geological situations and hence the thermal conductivity is assumed to have a Gaussian coloured noise correlation structure. With this information the stochastic heat conduction equation in equilibrium is solved and analytical expressions for the first two moments, that is, the mean and variance of the temperature field, are obtained. The expression for variance shows that it is highly dependent on the coefficient of variability of thermal conductivity, on the correlation length scale and on the depth. The methodology developed has been applied to quantify the steady-state geotherms, along with their associated error bounds, on a standard crustal model.     

A model for temperature variations in sedimentary basins due to random radiogenic heat sources

The thermal structure of a sedimentary basin is controlled by its thermal conductivity, its boundary conditions, water flow, rate of sedimentation and erosion and radiogenic heat sources. The radiogenic heat production in the sediments is known to vary over several orders of magnitude, with the lowest values in evaporites and carbonates and the highest values in black shales. Due to a paucity of information available on the existing heat sources, this parameter can be represented with a known mean value and a Gaussian correlation structure rather than a deterministic function. In this paper, the 1-D steady-state thermal structure in a sedimentary basin has been modelled in a stochastic framework with a random radiogenic heat source, and analytical expressions for the first two moments of the temperature field have been obtained. A synthetic example has been examined to quantify the error bounds on the temperature field due to uncertainties in the radiogenic heat sources.     

Simultaneous determination of thermal conductivity, thermal diffusivity and specific heat in sI methane hydrate

Thermal conductivity, thermal diffusivity and specific heat of sI methane hydrate were measured as functions of temperature and pressure using a needle probe technique. The temperature dependence was measured between −20°C and 17°C at 31.5 MPa. The pressure dependence was measured between 31.5 and 102 MPa at 14.4°C. Only weak temperature and pressure dependencies were observed. Methane hydrate thermal conductivity differs from that of water by less than 10 per cent, too little to provide a sensitive measure of hydrate content in water-saturated systems. Thermal diffusivity of methane hydrate is more than twice that of water, however, and its specific heat is about half that of water. Thus, when drilling into or through hydrate-rich sediment, heat from the borehole can raise the formation temperature more than 20 per cent faster than if the formation's pore space contains only water. Thermal properties of methane hydrate should be considered in safety and economic assessments of hydrate-bearing sediment.     

Task-oriented information value measurement based on space-time prisms

Recent years have witnessed a large increase in the amount of information available from the Web and many other sources. Such an information deluge presents a challenge for individuals who have to identify useful information items to complete particular tasks in hand. Information value theory (IVT) from economics and artificial intelligence has provided some guidance on this issue. However, existing IVT studies often focus on monetary values, while ignoring the spatiotemporal properties which can play important roles in everyday tasks. In this paper, we propose a theoretical framework for task-oriented information value measurement. This framework integrates IVT with the space-time prism from time geography and measures the value of information based on its impact on an individual’s space-time prisms and its capability of improving task planning. We develop and formalize this framework by extending the utility function from space-time accessibility studies and elaborate it using a simplified example from time geography. We conduct a simulation on a real-world transportation network using the proposed framework. Our research could be applied to improving information display on small-screen mobile devices (e.g., smartwatches) by assigning priorities to different information items.     

Geothermal field interpretation in south-central Kansas for parts of the Nemaha Anticline and flanking Cherokee and Sedgwick basins

The first assessment of temperature conditions in Kansas was made by geothermal gradient computations from temperature measurements in shallow boreholes, and these conditions are related to structural patterns, sedimentary cover and underlying basement properties. The area of south-central Kansas was selected for detailed study of geothermal character in relation to the geology. The aim was to quantify the relations and to determine the relationship of different variables of the temperature field. Input parameters included geothermal variables of gradient and temperature, and structure and sediment thickness. Two approaches were used: (1) the numerical computation of theoretical temperature-depth models based on conductive heat transfer, and (2) a map-comparison technique based on algebraic methods. The temperature field information usable for the map comparison is different in response to different measurements (nonequilibrium BHTs and temperatures from logged measurements in equilibrium). Derived from modelled results (plotted isotherms on cross-sections), a close relation between gradients and thermal conductivity of the sediments was confirmed. The most noticeable effect on the geothermal field, as noted quantitatively from the map-comparison study, is the relation of thickness of outcropping Permo-Pennsylvanian units because of their different thermal conductivity. The eastward increase of mean gradients is inversely related to the total sediment thickness, but this is mostly recognizable using the shallow temperature gradients. This dissimilarity gives additional evidence for a close link between gradients and thermal conductivity of the sediments in which the temperature measurements were made. The effect caused by the structure in deeper (older) units is not important and seems not to be significant, nor is the influence of the basement rock composition as indicated by the temperature modelling.     

零通量面方法的应用研究

本文分析了零通量面方法的理论基础,总结了多年应用的效果指出研制相应的仪器,改进计算方法,建立零通量面与气象、地下水位等环境要素的关系模式是今后研究的主要方向。     

Quantifying soil variability in GIS applications: II Spatial distribution of soil properties

Abstract

Application of Geographical Information Systems (GIS) to environmental problems requires a spatial delineation of soil properties and some a priori knowledge of their variability. In the U.S.A. estimated soil properties are available from soil surveys published by the National Cooperative Soil Survey. However, information on the extent and nature of their variability is generally lacking. To remedy the situation, variability of selected soil properties measured at farm and watershed scales was compared with published values using geostatistical methods. Results showed that the variability of bulk density and hydraulic conductivity can be estimated by comparing regularized variograms of measured and published values. An overlay method was proposed that combines measured and published delineations of soil properties into an overlay with the properties of both. The technique makes it possible to incorporate variability into a GIS analysis using data available from published soil surveys.     

Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter 'electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between 'small' anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.     

“Krige”空间内插技术在地理学中的应用

称为“Krige”技术的内插稀疏观测资料的随机方法是Matheron(1970年)提出的,D.R.Krige首先将这一方法应用于找矿上,因而命名于“Krige”技术。本文首先定义和说明了空间协方差曲线,基于无偏估计和最优原理导出了“Krige”内插权重系数的代数方程组,最后给出实例说明该方法如何应用到地理学和水文学中。     

Spatial patterns of subsistence extraction of forest products – An indirect approach for estimation of forest degradation in dry forest

Successful implementation of a forest based climate change mitigation mechanism such as REDD + depends on robust and available methods for measurement and estimation of forest degradation. Currently available methods are for application in single-hit degradation incidents in high density humid forests. However, it has been suggested that gradual degradation, especially in dry forests, is more widespread and that methods are needed for measuring and estimating associated emissions. We assess the applicability of an indirect remote sensing approach for monitoring forest degradation: infrastructure and other indicators of human activities are mapped and used for spatial prediction of degradation activities. For proxy variables we tested distance to forest edge, distance to roads, and population pressure calculated as the sum of inhabitants per pixel in the Landscan 2010 population raster dataset multiplied by an inverse power distance decay function. Wood extraction incidents were counted in 160 plots in two dry forests in Tanzania with infrastructural entry from one side only. We analyzed the spatial pattern of forest degradation as a function of the chosen proxy variables using zero inflated count models which allows for an excess of zero counts. A jack-knife bootstrap using 10,000 runs was applied to optimize the population distance decay function. We found that the impact of forest degradation is highest near high population concentration, above 1000 individuals. Furthermore, distance to nearest forest edge or road was a significant proxy for estimation of the number of wood extraction incidents (p < 0.001), where degradation incidents decreased with increasing distance to forest edge or road. At 3000 m from the forest edge towards the forest core the probability of wood extraction is 20% and dropping. The population distance decay function was found to have a steep decline indicating a relative small impact on forest degradation. Further, and perhaps larger, studies are needed to be able to recommend a distance decay function for general application in Tanzania. However, the results are useful for understanding spatial patterns of wood harvesting as a function of distance to nearest forest edge or road in dry Miombo woodland areas with average population pressure at 1685 ± 101 persons within a radius of 4000 m from the wood extraction sites.     

TERRESTRIAL HEAT FLOW IN THE SWISS ALPS

i
Terrestrial heat flow has been measured in three Alpine railroad tunnels. The geothermal gradients were calculated from temperatures measured during the construction of the tunnels, and corrections for topographic irregularities were made. The thermal conductivity of 113 rock specimens from the vicinity of the tunnels was measured. The heat flow in the Gotthard tunnel was found to be 1.6 10^-6 cal/cm² sec, in the Simplon 2.2 10^-6 cal/cm² sec, and in the Loetschberg 1.9 10^-6 cal/cm² sec. Most of the flux at the surface can be attributed to radioactive decay in a thickened crust, but a non-uniform distribution of radioactive elements may be required to explain the relatively high heat flow in the Simplon and Loetschberg tunnels.     

Approximate depth averages of electrical conductivity from surface magnetotelluric data

This paper presents a simple non-linear method of magnetotelluric inversion that accounts for the computation of depth averages of the electrical conductivity profile of the Earth. The method is not exact but it still preserves the non-linear character of the magnetotelluric inverse problem. The basic formula for the averages is derived from the well-known conductance equation, but instead of following the tradition of solving directly for conductivity, a solution is sought in terras of spatial averages of the conductivity distribution. Formulas for the variance and the resolution are then readily derived. In terms of Backus-Gilbert theory for linear appraisal, it is possible to inspect the classical trade-off curves between variance and resolution, but instead of resorting to linearized iterative methods the curves can be computed analytically. The stability of the averages naturally depends on their variance but this can be controlled at will. In general, the better the resolution the worse the variance. For the case of optimal resolution and worst variance, the formula for the averages reduces to the well-known Niblett-Bostick transformation. This explains why the transformation is unstable for noisy data. In this respect, the computation of averages leads naturally to a stable version of the Niblett-Bostick transformation. The performance of the method is illustrated with numerical experiments and applications to field data. These validate the formula as an approximate but useful tool for making inferences about the deep conductivity profile of the Earth, using no information or assumption other than the surface geophysical measurements.     

Sudden Local Conductivity Changes in the Ionosphere

Summary. An attempt is made to describe the transient magnetic change caused by a sudden local change of conductivity in the ionosphere. In a rough illustrative model, electric current is taken to be flowing uniformly in a thin plane rigid sheet of uniform isotropic integrated conductivity, I/ϱO e.m.u. A particular type of perturbing current system is defined, and the type of conductivity anomaly which could produce it is derived. It is shown that the problem is equivalent to that of the free decay of the perturbing current system. For a very small change of conductivity, the current system is found to spread radially at a uniform rate, while decaying. The case of a large conductivity anomaly is analysed by a numerical method. It is concluded that effects at a distance would be similar to those produced by a very small change, and that near the anomaly there would be as well, a local decaying current vortex system. It is found in particular, that at a large distance L cm, the magnetic change would commence immediately and reach an extremum after time of order L × 10⁻⁶ s.     

The inverse problem for heat flow data in the presence of thermal conductivity variations

Summary. We demonstrate a method of performing linear programming optimizations of functionals of subsurface temperature, when thermal conductivity is a known piecewise-constant function. Data comprise heat flow measurements on the flat isothermal surface of this structure, within which heat transfer is by steady-state conduction. Two-dimensionality is assumed. The approach involves establishing constraints which demand the continuity of temperature and the normal component of heat flow across all internal boundaries. These unknown functions are expanded as truncated Fourier series whose coefficients become unknowns of the linear programming solution vector; linear relations are established between these coefficients which guarantee harmonicity of temperature in each region of uniform conductivity, as well as the continuity requirements. Variations of the formalism are detailed for three simple types of geometry. As an example the method is applied to a heat flow data set from Sass, Killeen & Mustonen over the Quirke Lake Syncline of Ontario, Canada.     

Convective and conductive heat transfer in sedimentary basins

In the Earth's crust the temperature is largely controlled by heat conduction. However, under some circumstances, the thermal state is disturbed by advection of heat associated with groundwater flow. The corresponding thermal disturbance depends on the water flow velocity (modulus and direction) and therefore thermal data may be used to constrain the pattern of natural fluid flow. In this paper, some models of thermal disturbance induced by convective heat transfer are presented. They are based on the assumption that the water flow is concentrated in thin permeable structures such as aquifer or fault zones. The steady-state and transient thermal effects associated with such scenarios are computed using a somewhat idealized model which depends on a small number of parameters: flow rate, time, aquifer geometry and thermal parameters of surrounding rocks. In order to extract the conductive and convective components of heat transfer from temperature data and to estimate the corresponding fluid flow rate, it is first necessary to estimate the thermal conductivity field. The problem of the estimation of thermal conductivity in clay-rich rocks, based on laboratory and in-situ measurements, is emphasized. Then a method is proposed for the inversion of temperature data in terms of fluid flow. Vertical and lateral variations of thermal conductivity are taken into account and the fluid flow is assumed to be concentrated on a specified surface (2-D quasi-horizontal pattern). Thermal effects of the flow are simulated by a distribution of surface heat production which can be calculated and then inverted in terms of horizontal fluid flow pattern.     

基于地理信息元组的分类预测理论及应用——以中亚矿集区预测为例

地理信息科学的迅速发展为矿集区预测提供了新的理论依据,使地理信息理论、相应的技术方法组合及应用的整体研究成为可能。在大量理论和实验研究的基础上提出了基于地理信息元组的分类预测理论体系,该理论体系由六个概念、一个空间信息本质、两个空间信息特性以及六个空间信息相关方法和约定的构成。并在该理论体系基础上结合空间数据分析方法和探索式空间数据分析方法,建立了基于地理信息元组的分类预测模型。应用该模型在中亚区域实现了Au矿集区预测目标。为中亚成矿域中其它区域(如新疆)的矿集区预测研究奠定了理论与方法论基础。     

DEM 点位地形信息量化模型研究

针对DEM 点位, 首先应用微分几何法对其所负载的语法信息量进行测度, 其次根据地形特征点类型及地形结构特征确定其语义信息量, 然后基于信息学理论构建了DEM 点位地形信息综合量化模型。在此基础上, 以黄土丘陵沟壑区作为实验样区, 对DEM 点位地形信息量提取方法及其在地形简化中的初步实例应用进行了探讨和验证。实验结果显示, 所提出的DEM 点位地形信息量化方案可行;基于DEM 地形信息量指数的多尺度DEM 构建方案, 具有机理明确、易于实现的特点, 并通过优先保留地形骨架特征点, 可以有效减少地形失真, 从而满足不同层次的多尺度数字地形建模和表达要求。对DEM 点位地形信息进行有效量化, 为认识DEM 地形信息特征提供了一个新的切入点, 同时为多尺度数字地形建模提供理论依据与方法支持。     

On the importance of rock thermal conductivity and heat flow density in basin and petroleum system modelling

Basin and petroleum systems are routinely modelled to provide qualitative and quantitative assessments of a hydrocarbon play. The importance of the rock thermal properties and heat flow density in thermal modelling the history of a basin are well-known, but little attention is paid to assumptions of the thermal conductivity, present-day heat flow density and thermal history of basins. Assumed values are often far from measured values when data are available to check parameters, and effective thermal conductivity models prescribed in many basin simulators require improvement. The reconstructed thermal history is often justified by a successful calibration to present-day temperature and vitrinite reflectance data. However, a successful calibration does not guarantee that the reconstruction history is correct. In this paper, we describe the pitfalls in setting the thermal conductivity and heat flow density in basin models and the typical uncertainties in these parameters, and we estimate the consequences by means of a one-dimensional model of the super-deep Tyumen SG-6 well area that benefits from large amounts of reliable input and calibration data. The results show that the entire approach to present-day heat flow evaluations needs to be reassessed. Unreliable heat flow density data along with a lack of measurements of rock thermal properties of cores can undermine the quality of basin and petroleum system modelling.     

Considering temperature dependence of thermo-physical properties of sandy soils in two scenarios of oil pollution

We analyzed the heat conductivity and volumetric heat capacity of sandy soil contaminated in two scenarios of oil pollution, and also determined the temperature dependencies of these changed thermophysical properties. In the first pollution scenario, the oil product was introduced into wet river sand, and in the second case, dry sand was contaminated by the oil product and was then moistened with water. By considering these two scenarios as multicomponent dispersion systems with varying degrees of contamination and humidity, and by using a polystructural granular model with pore spaces and closed inclusions, we calculated that the heat conductivity of the sandy soil increased under the first pollution scenario and decreased under the second, but the change in the volumetric heat capacity of the sandy soil was proportional only to the amount of oil pollution, not the manner in which it was introduced. We also determined the temperature dependencies of these two thermophysical properties of sandy soil when polluted by oil, of which information will be useful for future containment and remediation of oil-contaminated soil.     

Thermal properties of sediments in southern Israel: a comprehensive data set for heat flow and geothermal energy studies

To decipher the thermal structure of the sedimentary veneer in southern Israel, new values of thermal conductivity and porosity as well as of the radiogenic heat budget are provided. Thermal conductivity is measured for lithotypes and scaled up for geological formations. The new data are higher than most of the previously measured values, in particular for sandstones and siltstones, whose mean values are 5.0 and 2.9 W m^?1 K^?1. Mean values of the most abundant lithotypes, which are dolomites and limestones, are on the order of 4.1 and 2.7 W m^?1 K^?1, respectively. The total radiogenic heat production of the sedimentary cover varies slightly over southern Israel, due to variable lithology and total sediment thickness, yielding a maximum heat flow on the order of 4 mW m^?2 where the sedimentary section is thickest (ca. 7 km). A temperature prognosis was made by calculating temperature profiles to the top of the crystalline basement at five well locations applying the new thermal‐conductivity data set and three scenarios of surface heat flow (50, 55 and 60 mW m^?2). The calculated temperatures best match with measured drillstem‐test temperatures by using heat‐flow values close to the upper bound of range. Surface heat flow on the order of 55–60 mW m^?2 is supported by a reevaluation of an existing temperature log and the application of thermal conductivity from this study. The temperature prediction for southern Israel shows values of 100–120°C at 3500–4500 m depth, indicating a geothermal potential that can be used for heating as well as electricity production.