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Rocks, minerals and mineral inventory evaluation
Published in Ratan Raj Tatiya, Surface and Underground Excavations, 2013
Other types of kriging that are not widely used (Nobel, 1992) include universal kriging, co-kriging and soft kriging. Universal kriging is a method to incorporate trends (drifts) into the kriging equations. If the trends are defined according to a secondary variable, it is known as universal kriging with exogenic drift. Theoretically, the problem cannot be solved (Royle, 1990) as the nature of drift needs to be known in order to determine the underlying variogram and vice versa.
Spatial interpolation for real-time rainfall field estimation in areas with complex topography
Published in María Carolina Rogelis Prada, Operational Flood Forecasting, Warning and Response for Multi-Scale Flood Risks in Developing Cities, 2020
The geostatistical interpolation technique of Kriging groups different methods: Simple Kriging, Ordinary Kriging, Universal Kriging, Kriging with External Drift, Regression Kriging, Intrinsic Kriging etc, depending on the underlying model [Chiles and Delfiner, 1999]. The variogram is a key tool in Kriging methods to represent spatial structure by describing how the spatial continuity changes with distance and direction [Isaaks and Srivastava, 1989].
Tackling Heterogeneity in Groundwater Numerical Modeling: A Comparison of Linear and Inverse Geostatistical Approaches— Example of a Volcanic Aquifer in the East African Rift
Published in M. Thangarajan, Vijay P. Singh, Groundwater Assessment, Modeling, and Management, 2016
Kriging (Universal Kriging) is a linear geostatistical estimation method, which enables the estimation of a regionalized variable (Z) at any point in space, based on its measured values at other locations. A few noteworthy features regarding this interpolation method are highlighted hereunder. A detailed presentation can be found in basic geostatistics references (Isaaks and Srivastava, 1989; Journel and Huijbregts, 1978; Kitanidis, 2000).
Intelligent Computational Schemes for Designing more Seismic Damage-Tolerant Structures
Published in Journal of Earthquake Engineering, 2020
Hamoon Azizsoltani, Achintya Haldar
Universal Kriging predictor is a linear weighted sum of the observed values that can predict the value of the response at any unsampled point. Denoting to represent an IRS, the concept can be expressed as follows:
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 assumes a constant mean for a real-valued random function Z(si), but the mean value varies across the entire region, and the variable is said to be non-stationary. The non-stationary regionalized variable will have two components; the mean value of a regionalized variable and the residual. Universal kriging (UK) is one of the most frequently used methods for spatial mapping data when there is a trend in the data and the dependent variable does not fulfill the criterion of weak stationary. Weak stationery can be described as the mean of the response variable is constant over the region, and the spatial dependence of any two data points in space is a function of the distance between them. In Universal kriging, the mean is a function of coordinates in linear, quadratic, or higher form. The model of Universal kriging can be written as; where in Equation (9)μ(s) is the mean, and is the covariance matrix. In Universal kriging, the trend component μ(s) can be modeled as; where in Equation (10) is the coefficient, is th function that describes the trend, and represents the number of functions that are used to model the trend. The weights in Universal kriging is estimated in the same way as in Ordinary kriging. is the covariance matrix that can be written as (see Equation (11)); where R is a correlation matrix, and it depends on vector-valued parameter that is, = (). The values of the parameter are estimated using different methods of estimation, that is, Maximum likelihood Estimation (MLE), Restricted Maximum likelihood Estimation (REML), Ordinary Least Square (OLS) or Weighted Least Square (WLS).