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3D stochastic inversion of magnetic data 总被引：1，自引：0，他引：1
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Lateral bedrock erosion and valley formation in a heterogeneously layered landscape,Northeast Kansas
In this study, we present direct field measurements of modern lateral and vertical bedrock erosion during a 2-year study period, and optically stimulated luminescence (OSL) ages of fluvial material capping a flat bedrock surface at Kings Creek located in northeast Kansas, USA. These data provide insight into rates and mechanisms of bedrock erosion and valley-widening in a heterogeneously layered limestone-shale landscape. Lateral bedrock erosion outpaced vertical incision during our 2-year study period. Modern erosion rates, measured at erosion pins in limestone and shale bedrock reveal that shale erosion rate is a function of wetting and drying cycles, while limestone erosion rate is controlled by discharge and fracture spacing. Variability in fracture spacing amongst field sites controls the size of limestone block collapse into the stream, which either allowed continued lateral erosion following rapid detachment and transport of limestone blocks, or inhibited lateral erosion due to limestone blocks that protected the valley wall from further erosion. The OSL ages of fluvial material sourced from the strath terrace were older than any material previously dated at our study site and indicate that Kings Creek was actively aggrading and incising throughout the late Pleistocene. Coupling field measurements and observations with ages of fluvial terraces can be useful to investigate the timing and processes linked to how bedrock rivers erode laterally over time to form wide bedrock valleys. 相似文献
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A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers 总被引：2，自引：0，他引：2
The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation. 相似文献
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Min Liang Denis Marcotte 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(3):973-987
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. 相似文献
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In this paper, the effect on Kriging weights of non-bias conditions, when the same residual covariance model is used, has been studied by the l2 norm of the weights difference between Ordinary Kriging and Kriging with a trend model. Four covariance models, in 1-D and 2-D, and in interpolation and extrapolation conditions are examined. Situations in which both algorithms yield the same results are pointed out. 相似文献
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Denis Marcotte Keyvan Naraghi Claude Bellehumeur Erwan Gloaguen 《Mathematical Geology》2005,37(5):493-512
The profitability of a cement plant depends largely on its capacity to produce homogeneous cement with chemical composition close to specified targets for the cement type produced. One crucial step is the mixing of limestone with other raw materials in proportions calculated to meet these targets. Major design and operation decisions depend on the efficiency of this homogenizing step. The adequate modeling of the mixing process requires simulation of representative cross-correlated time series of chemical compositions of the raw materials involved. The chemical composition signals are obtained by multivariate geostatistical simulation using an LU (Cholesky) decomposition of the covariance matrix. Modifications to the usual LU method are presented. First, the effect on the raw covariance matrix of the closure property of chemical analysis is imposed. Second, the problem of memory space limitations in the LU method is tackled by using overlapping sliding neighbourhoods. The simulation algorithm is applied to the Joppa cement plant owned by Lafarge North America. The simulated raw material input streams are fed into the quality mix control (QMC), a proprietary software that models and controls the mixing operation to produce an output stream with cement characteristics as close as possible to desired targets. Two signal series are studied, one autocorrelated with a moderate temporal range and one with no autocorrelation. The QMC produces C3S output signals having comparable short scale periodic variograms except that the variance of the uncorrelated signal is four times greater than those of the autocorrelated signal and the real Joppa data. The raw material feeder variograms have the same sill for both the white noise and the autocorrelated signals. However, the autocorrelated signal feeder variogram presents lower short term dispersion variance, a characteristic feature of Joppa operations. Our results show the importance of simulating the right temporal structure of the raw materials to realistically forecast the behavior of the output signals. We also discuss some practical implications of these findings for the design and operation of a cement plant. 相似文献