Statistical simulation of random field on 2d area with Whittle-Matern typecorrelation function in the geophysical problem of environment monitoring

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.