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Standard cumulative semivariograms of stationary stochastic processes and regional correlation

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Abstract

The standard cumulative semivariograms (SCS), obtained analytically from the currently employed stationary stochastic processes, provide a basis for the model identification and its parameter as well as regional correlation estimations. The analytical solutions for different stationary stochastic processes such as independent (IP), moving average (MA), autoregressive (AR), and autoregressive integrated moving average ARIMA (1,0,1) processes give rise to different types of SCSs which can be expressed in terms of the autocorrelation structure parameters only. The SCSs of independent and MA processes appear as linear trends whereas other type of processes have SCSs which are nonlinear for short distances but become linear at large distances. Irrespective of the stationary stochastic process type the linear portions of SCSs have unit slopes. The vertical distance between these linear portions and that of the IP cumulative semivariogram (CS), provide an indicator for measuring the regional correlation. In the case of stationary processes, the straight line portions of any CS are parallel to each other. Hence, it is possible to identify the model from the sample CS. Finally, necessary procedures are provided for the model parameters estimation. The methodology developed, herein, is applied to some hydrochemical ions in the groundwater of the Wasia aquifer in central part of Kingdom of Saudi Arabia.

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Author notes

  1. Zekâi Sen

    Present address: Faculty of Aeronautics and Astronautics, Maslak, Technical University of Istanbul, 80626, Istanbul, Turkey

Authors and Affiliations

  1. Faculty of Earth Sciences, Hydrogeology Department, King Abdulaziz University, P. O. Box 1744, 21441, Jeddah, Kingdom of Saudi Arabia

    Zekâi Sen

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  1. Zekâi Sen
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Sen, Z. Standard cumulative semivariograms of stationary stochastic processes and regional correlation. Math Geol 24, 417–435 (1992). https://doi.org/10.1007/BF00891272

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  • DOI: https://doi.org/10.1007/BF00891272

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