The method of 3-D dataset statistical simulation with «cubic» correlation function on Rivne NPP example

Vyzhva, Z.; Demidov, V.; Vyzhva, A.

doi:10.3997/2214-4609.2020geo080

Geoinformatics: Theoretical and Applied Aspects 2020 2020

DOI: 10.3997/2214-4609.2020geo080

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The method of 3-D dataset statistical simulation with «cubic» correlation function on Rivne NPP example

Z. Vyzhva¹,

V. Demidov²,

A. Vyzhva³

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Cited by 3 publications

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“…Theoretical aspects of capacity use of statistical simulation to solving problems in the work of Geophysics considered in (Yadrenko, 1983;Grikh (Vyzhva) et al, 1993;Vyzhva, 2003;2011). Practical testing on real data density chalky strata on the territory of the Rivne NPP was carried out for the fields on the plane -in the (Vyzhva et al, 2004), by using only Bessel correlation function and Cauchy correlation function (Vyzhva et al, 2014;2017).…”

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confidence: 99%

“…Note, that methods of random fields statistical simulation used in geosciences problems were considered in such works as: (Chiles and Delfiner, 2012;Gneiting, 1997;Gneiting et al, 2010;Mantoglov and Wilson, 1981;Wackernagel, 2003;Prigarin, 2005;Vyzhva et al, 2010;2014;2017) and other.…”

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confidence: 99%

“…This problem was solved in works: (Vyzhva et al, 2004;2014;2017) by statistical simulation method that provides the ability to display values (random field on a plane) in any point of the monitoring area. The chalk strata averaged density at the industrial area was simulated using the built model and the involvement of the Bessel type correlation function (Vyzhva et al, 2004) and Cauchy correlation function (Vyzhva et al, 2004;2014;2017).…”

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Statistical Simulation of Random Field on 2d Area With Whittle-Matern Typecorrelation Function in the Geophysical Problem of Environment Monitoring

2019

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Due to the increasing number of natural and technogenic disasters the development of geological environment monitoring system is actual one using modern mathematical tools and information technology. The local monitoring of potentially dangerous objects is an important part of the overall environment monitoring system. The complex geophysical research was conducted on Rivne NPP area. The monitoring observations radioisotope study of soil density and humidity near the perimeter of buildings is of the greatest interest among these. In this case a problem occurred to supplement simulated data that were received at the control of chalky strata density changes at the research industrial area with use of radioisotope methods on a grid that included 29 wells. This problem was solved in this work by statistical simulation method that provides the ability to display values (the random field of a research object on a plane) in any point of the monitoring area. The chalk strata averaged density at the industrial area was simulated using the built model and the involvement optimal in the mean square sense Whittle-Matern type correlation function. In this paper the method is used and the model and procedure were developed with enough adequate data for Whittle-Matern type correlation function. The model and algorithm were developed and examples of karst-suffusion phenomena statistical simulation were given in the problem of density chalk strata monitoring at the Rivne NPP area. The statistical model of averaged density chalk strata distribution was built in the plane and statistical simulation algorithm was developed using Whittle-Matern type correlation function on the basis of spectral decomposition. The research subject realizations were obtained with required detail and regularity at the observation grid based on the developed software. Statistical analysis of the numerical simulation results was done and tested for its adequacy.

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Statistical Simulation of Random Field on 2d Area With Whittle-Matern Typecorrelation Function in the Geophysical Problem of Environment Monitoring

2019

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The Statistical Simulation of Random Fields With the Gaussian Type Correlation Function by the Investigation of the Magnetometry Data

VYZHVA,

DEMIDOV,

VYZHVA

2023

VKNUGEOL

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In the article, universal methods of statistical modeling (Monte Carlo methods) of geophysical data using the Gaussian correlation function have been developed, which make it possible to solve the problems of generating adequate realizations of random fields on a grid in three-dimensional space of required regularity and detail. Since in geophysics, most of the results of object research are presented in digital form, the accuracy of which depends on various random influences, the problem of the condition of the maps arises in the case when the data cannot be obtained with the specified detail in some observation areas. It is proposed to apply statistical simulation of random fields methods, to solve the problems of conditional maps, supplement the required detail of research results with additional data, to achieve the required accuracy of observations, and other similar problems in geophysics. An algorithm for numerical modeling of realizations of homogeneous isotropic random fields in three-dimensional space with a Gaussian correlation function is formulated on the basis of the theorem on estimation of the mean-square approximation of such random fields by the partial sum of the "spectral decomposition" series. Using the example of data from aeromagnetic surveying in the area of the Ovruch depression, the proposed algorithm for statistical modeling of random fields is implemented in solving the problems of map fitness by supplementing the data with simulated adequate implementations to the required level of detail. When analyzing data by profiles, they are divided into deterministic (trend) and random components. The trend is proposed to approximate by cubic splines and the homogeneous isotropic random component is proposed to modeling on the basis "spectral decomposition" of random fields on 3-D space in the Ovruch depression. According to the algorithm, authors received random component implementations on the study area with twice detail for each profile. When checking their adequacy, authors made the conclusions that the relevant random components histogram has Gaussian distribution. The built variogram of these implementations has the best approximation by theoretical variogram which is connected to the Gaussian type correlation function. As a result of superimposing the simulated array of the random component on the spline approximation of the real data, a more detailed implementation was obtained for the data of geomagnetic observations in the selected area. A comparative analysis of the results of modeling realizations random fields with the Gaussian correlation function with other correlation functions is carried out. Therefore, the method of statistical modeling of realizations of random fields in three-dimensional space with the Gaussian correlation function makes it possible to supplement the results of measurements of the full magnetic field intensity vector with data with a given detail as much as possible.

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The Statistical Simulation of Dataset in 3d Area With "Cubic" Соrrelation Function on Example Rivne NPP Geophysical Monitoring

VYZHVA,

DEMIDOV,

VYZHVA

2024

VKNUGEOL

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Background. The model and algorithm were developed by using optimal in the mean square sense "cubic" correlation function. An example of supplementing the results of geophysical studies of karst-suffuses phenomena with simulated data in the task of monitoring the density of the chalk stratum on the territory of the Rivne NPP is presented. The complex geophysical research was conducted on Rivne NPP area. The monitoring observations radioisotope study of soil density and humidity near the perimeter of buildings is of the greatest interest among these. In this case a problem was occurred to supplement simulated data that were received at the control of chalky strata density changes at the research industrial area with use of radioisotope methods on a grid that included 29 wells. This problem was solved in this work by statistical simulation method that provides the ability to display values (the random field of a research object in 3D area) in any point of the monitoring area. Methods. Based on the spectral decomposition of random fields in 3D space, a statistical model of the distribution of the average density of the chalk layer in the 3D observation area was built. Results. An algorithm for statistical simulation of random fields with a "cubic" correlation function is formulated. On the basis of the developed software, additional simulated realizations of the random component of the research subject on the grid of observations of the necessary detail and regularity were obtained. A statistical analysis of the results of the numerical simulation of the distribution of the average density of the chalk layer was carried out and their adequacy was tested. Conclusions. The method of statistical modeling of random fields with "cubic" correlation functions allows you to supplement data with a given accuracy.

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The method of 3-D dataset statistical simulation with «cubic» correlation function on Rivne NPP example

Cited by 3 publications

References 0 publications

Statistical Simulation of Random Field on 2d Area With Whittle-Matern Typecorrelation Function in the Geophysical Problem of Environment Monitoring

Statistical Simulation of Random Field on 2d Area With Whittle-Matern Typecorrelation Function in the Geophysical Problem of Environment Monitoring

The Statistical Simulation of Random Fields With the Gaussian Type Correlation Function by the Investigation of the Magnetometry Data

The Statistical Simulation of Dataset in 3d Area With "Cubic" Соrrelation Function on Example Rivne NPP Geophysical Monitoring

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