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Spatial variability analysis of physical and mechanical indexes of loess
Published in Mohd Johari Mohd Yusof, Junwen Zhang, Advances in Civil Engineering: Structural Seismic Resistance, Monitoring and Detection, 2023
Xiqi Chen, Yanjie Zhang, Xu Wang, Daijun Jiang, Jiandong Li
For the solution of correlation distance, in addition to the recursive method of random field theory and correlation function method, another method for analyzing the randomness of soil parameters is the semi-variogram method of geostatistics. Geostatistics can be defined as the science of studying spatial natural phenomena with both structure and randomness on the basis of regionalized variable theory and with the help of semivariogram. It was originally used in the mining of mineral resources. With the development of understanding of engineering discipline, it is now widely used in all kinds of Engineering with the needs of spatial variability analysis and spatial prediction. Soulie first put forward the application of geostatistics theory to the study of spatial variability of soil parameters, and studied the spatial variability of undrained shear strength of soil by using semi-variogram (Soulie 1990). Zhang[12] quantitatively evaluated the variation law of rock and soil parameters by using semi variation function and comprehensive variation index of structural direction (Zhang 1996). Xue analyzed the influence of spatial variation characteristics on landslide deformation by using semi-variogram (Xue 2020). Tan[14] pointed out the theoretical relationship between the semi-variogram method and the correlation function method, and discussed the effects of whether the data is de trended, the initial value of fitting parameters and the number of participating curve fitting points on the correlation distance solved by the semi-variogram method (Tan 2020).
Characterization of geotechnical spatial variability in river embankments from spatially adjacent SCPT
Published in Guido Gottardi, Laura Tonni, Cone Penetration Testing 2022, 2022
F. Ceccato, M. Uzielli, P. Simonini
The spatial correlation structure of tip resistance is investigated using a geostatistical approach by means of semivariograms. Given the well-known anisotropy in geotechnical properties stemming from in-situ stress effects and other site-specific factors, horizontal and vertical variability are addressed separately. The adoption of specific geostatistical techniques and models relies heavily on the hypothesis of data stationarity, which denotes the invariance of a data set’s statistics to spatial location. Stationarity can be achieved through a number of data transformation techniques. Here, data decomposition is implemented, by which the “total” spatial variability of a spatially ordered measured geotechnical property [q(z1…zn)] in a sufficiently physically homogeneous soil unit is broken down into a trend function [t(z1…zn)] and a set of residuals about the trend [r(z1…zn)]. In the one-dimensional case, for instance, taking depth (z) as the single spatial coordinate, decomposition is expressed by the following additive relation qz=tz+rz
Stochastic characterization of a petroleum reservoir
Published in C. Guedes Soares, T.A. Santos, Trends in Maritime Technology and Engineering Volume 2, 2022
Geostatistical methods for reservoir characterization and modelling can be divided into deterministic and stochastic methods. In deterministic methods, all the conditions that can influence the predictions have to be completely known. Deterministic results can be unambiguously described by the completely known finite conditions, so deterministic analysis can only offer one solution. The true geological model in the subsurface is singular, but since the description of the subsurface is based on well data (point data), it is not possible to be certain that the solution obtained with geostatistical methods is the correct one. Therefore, all geostatistical models contain some uncertainty. They are a way of estimating the sub-surface conditions and they can provide only the most probable solution, in other words the closest to the real conditions (Zelenika et al., 2017).
Spatial interpolation of water quality index based on Ordinary kriging and Universal kriging
Published in Geomatics, Natural Hazards and Risk, 2023
Mohsin Khan, Mohammed M. A. Almazah, Asad EIlahi, Rizwan Niaz, A. Y. Al-Rezami, Baber Zaman
Ordinary Kriging and Universal kriging techniques were used to obtain the prediction maps of the water quality index (WQI). Kriging is a geostatistical approach that estimates a variable’s value over a continuous spatial field using a limited number of sampled data points. In kriging, the Variogram model has important for controlling kriging weights. In sample data, the gamma-values or semivariances for each pair of points are plotted against the distance between them. Mathematically variogram is defined as in Equation (4): where γ(h) is the semi-variance; N(h) the number of pairs separated by distance or lag h; Z() the measured sample at a point and Z( + h) the measured sample at point ( + h). The experimental variogram is the plot of observed values used to explore the spatial structure of the data. In contrast, the model that best fits the data is known as a theoretical or model variogram. In this study, Circular and Powered Exponential variograms were fitted to the experimental variogram.
Determination of most affected areas by earthquakes based on mobile signaling data: a case study of the 2022 Mw 6.6 Luding earthquake, China
Published in Geomatics, Natural Hazards and Risk, 2023
Xinxin Guo, Benyong Wei, Guiwu Su, Wenhua Qi, Tengfei Zhang
Spatial interpolation analysis is a geostatistical method that uses information from sampled points to forecast information about unknown points or regions. Spatial interpolation analysis includes several methods. Kriging interpolation uses the distance and spatial relationship between the unknown point and a range of sampled points to fit a model to determine the weights and provides a linear unbiased, optimal estimate of the attributes of the unknown region. Kriging is essentially a method of estimation by local weighted averaging: where is the estimate of point Z( is the measured value at point Z(), n is the total number of sample points and is the weights. The kriging interpolation method can represent the spatial variation in the attributes and is more accurate and realistic (Oliver and Webster 1990; Li et al. 2021).
A novel geostatistical index of uncertainty for short-term mining plan
Published in CIM Journal, 2023
G. M. C. Dias, M. M. Rocha, V. M. Silva
The use of geostatistical simulation methods to quantify uncertainties and classify mineral resources has significantly increased in recent decades and is becoming commonplace (Deutsch, 2018). Although simulation should be a standard method to quantify uncertainties, the industry still struggles with managing multiple realizations of a variable. The application of simulation methods to uncertainty assessment in medium- (quarterly, annual, biannual) and short-term (daily, weekly, monthly) mine planning is even more restricted. Concerns primarily center on high computational requirements for models that need to be frequently updated, the non-uniqueness of multiple realizations, and the high number of calculations, including mine planning algorithms, within a single block model (Deutsch, 2018). Another limit to widespread use of simulations is the availability of software to implement them. Different algorithms could be written to produce simulations from a given model, but they are not equally efficient. The implementation of certain algorithms may lead to inefficient programs, especially in terms of numerical precision, speed, and memory (Lantuéjoul, 2002).