About approximation of 3-D random fields and statistical simulation

Vyzhva, Z.

doi:10.1515/156939703771378608

Cited by 7 publications

(7 citation statements)

References 3 publications

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“…We introduce the notation for input data on the profile as a random field By fields of such properties we can apply the method of statistical simulation of random fields on the sphere based on their spectral expansions (Vyzhva, 1997), which allows finding the perfect image of entire observations field for their certain implementation values. So we generate additional random component data in the points where geomagnetic measurements were not carried out, for example, with double precision intervals of 50 compare to 100 meters or between profiles.…”

Section: Fig 1 the Map Of Aeromagnetic Survey Data δT An In The Ovrmentioning

confidence: 99%

“…The built variogram of these implementations ( , , ), 7,..., 20 і r і     has the best approximation (the mean square deviation is 0, 195) by theoretical variogram which is connected to the Bessel type correlation function (Vyzhva, 1997), p. 214 for parameter a ≈4,2*10 -3 : These spectral coefficients we used in proposed above algorithm. The statistical simulation of realizations of the Gaussian isotropic random fields ( , , ), 7,..., 20 і r і     can be done by means of this algorithm.…”

Section: Fig 1 the Map Of Aeromagnetic Survey Data δT An In The Ovrmentioning

confidence: 99%

“…Methods of statistical simulation of random field on the sphere based on representation it by stochastic sums was considered in papers Chiles and Delfiner,1999;Prigarin, 2005;Vyzhva, 1997;Вижва та Ядренко, 2000) and other.…”

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confidence: 99%

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About Methods of Random Fields Statistical Simulation on the Sphere by the Aircraft Magnetometry Data

2018

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There have been developed universal methods of statistical simulation (Monte Carlo methods) of geophysical data for generating random fields on the sphere on grids of required detail and regularity. Most of the geophysical research results are submitted in digital form, which accuracy depends on various random effects (including equipment measurement error). The map accuracy problem occurs when the data cannot be obtained with a given detail in some areas. ²t is proposed to apply statistical simulation methods of random fields realizations, to solve the problems of conditional maps, adding of data to achieve the necessary precision, and other similar problems in geophysics. Theorems on the mean-square approximation of homogeneous and isotropic random fields on the sphere have been proved by special partial sums. A spectral coefficients method was used to formulate algorithms of statistical simulation by means of these theorems. A new effective statistical technique has been devised to simulate random fields on the sphere for geophysical problems. Statistical simulation of random fields on the sphere based on spectral decomposition has been introduced in order to enhance map accuracy by the example of aeromagnetic survey data in the Ovruch depression. It is divided into deterministic and random components for data analysis. The deterministic component is proposed to approximate by cubic splines and the random component is proposed to modeling on the basis of random fields on the sphere by spectral decomposition. Model example – the aircraft magnetometry data. According to the algorithm we received random component implementations on the study area with twice detail for each profile. When checking their adequacy we 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 Bessel type correlation function. The final stage was the imposing array of random components on the spline approximation of real data. As a result, we received more detailed implementation for the geomagnetic observation data in the selected area.

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Section: Fig 1 the Map Of Aeromagnetic Survey Data δT An In The Ovrmentioning

confidence: 99%

Section: Fig 1 the Map Of Aeromagnetic Survey Data δT An In The Ovrmentioning

confidence: 99%

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About Methods of Random Fields Statistical Simulation on the Sphere by the Aircraft Magnetometry Data

2018

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“…Theoretical aspects of capacity use of statistical simulation of solving problems in the work of Geophysics are considered in (Yadrenko, 1983;Grikh (Vyzhva) et al, 1993;Vyzhva, 2003Vyzhva, , 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), but using only Bessel correlation function and Cauchy functions (Vyzhva et al, 2014(Vyzhva et al, , 2017 and the Whittle-Matern type correlation function .…”

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confidence: 99%

“…Consider the same approach as in (Grikh 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.…”

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confidence: 99%

Statistical Simulation of Random Field on 2d Area With Generalized Gneiting Type Correlation Function in the Geophysical Problem of Environment Monitoring

Vyzhva¹,

Demidov²,

Vyzhva³

2022

VKNUGEOL

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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 averaged density at the industrial area was simulated using the built model and the involvement optimal in the mean square sense correlation function generalized Gneiting type. In this paper the method is used and the model and procedure were developed with enough adequate data for generalized Gneiting 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 generalized Gneiting type correlation function based on 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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2016

Simulation of Stochastic Processes With Given Accuracy and Reliability

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About approximation of 3-D random fields and statistical simulation

Cited by 7 publications

References 3 publications

About Methods of Random Fields Statistical Simulation on the Sphere by the Aircraft Magnetometry Data

About Methods of Random Fields Statistical Simulation on the Sphere by the Aircraft Magnetometry Data

Statistical Simulation of Random Field on 2d Area With Generalized Gneiting Type Correlation Function in the Geophysical Problem of Environment Monitoring

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