METHODS OF STATISTICAL SIMULATION OF RANDOM FIELDS ON THE PLANE BY THE AIRCRAFT MAGNETOMETRY DATA - Vyzhva, Z.; Vyzhva, A. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
Universal methods of statistical simulation (Monte Carlo methods) of geophysical data for generating random processes and fields on 2-D grids of required detail and regularity have been developed. 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. Methods of statistical simulation of realizations of random processes and multi-dimensional random functions (random fields), to solve the problems of conditional maps, adding of data to achieve the necessary precision, and other such problems in geophysics are proposed to be applied. Theorems on the mean-square and another approximation of homogeneous and isotropic random 2-D fields by special partial sums have been proved. A randomization 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 in 2-D space (randomization method, spectral coefficients method and others) for geophysical problems. random fields in 2-D space statistical simulation based on spectral representation 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 stationary random component is proposed to model on the basis of spectral expansions of random fields. Model example is the aircraft magnetometry data 2-D field (on the plane). According to the algorithm we received noise implementations on the study area with double detalization for each profile. When checking their adequacy we came to 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 noise on the spline approximation of real data. As a result, we received more detailed implementation for the geomagnetic observation data in the selected area.
Keywords: Statistical simulation; randomizations method; spline-interpolation; conditional maps