Statistical Simulation of 2d Random Field With Cauchy Correlation Function in the Geophysics Problem of Environment Monitoring

Abstract

(Рекомендовано членом редакційної колегії д-ром фіз.-мат. наук, проф. Б.П. Масловим) Due to the increasing number of natural and technogenic disasters the development of geological environment monitoring system is actual using modern mathematical tools and information technology.The local monitoring of potentially dangerous objects is an important part of the overall environment monitoring system. Complex geophysical research was conducted on Rivne NPP area. Among these monitoring observations radioisotope study of soil density and humidity near the perimeter of buildings is of the greatest interest.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 (random field on a plane) in any point of the monitoring area. The chalk strata average density at the industrial area was simulated using the built model and the involvement of the Cauchy type correlation function. This paper analyses the method and the model and procedure were developed with enough adequate data for Cauchy function. The method 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 average density chalk strata distribution was built in the plane and statistical simulation algorithm was developed using Cauchy 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 its adequacy.

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

“…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).…”

“…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).…”

“…We consider the same approach as in works: (Grikh (Vyzhva) et al, 1993;Vyzhva et al, 2004;Vyzhva, 2011). We use the method of statistical simulation of random fields, which are homogenous and isotropic, based on their spectral decomposition.…”

“…It is necessary to make the statistical analysis to build the model and procedure of statistical data simulation at observation area. If the verified data has distribution density with approximately Gaussian type, then procedure can be used, which is developed in (Grikh (Vyzhva) et al, 1993;Vyzhva et al, 2004;Vyzhva, 2011), to generate on the computer realizations of the simulated data by means of standard normal random variable sequences. The use of authors' techniques of statistical simulation implies preliminary statistical data processing to determine its statistical characteristics: the mathematical expectation and the correlation function.…”

“…The procedure of numerical simulation the realizations of the data field random component, by means of the abovementioned model (10), was conducted by using the Spectr 2.1 software, which is described in (Vyzhva et al, 2004).…”