ABOUT METHODS OF RANDOM FIELDS STATISTICAL SIMULATION ON THE SPHERE BY THE AIRCRAFT MAGNETOMETRY DATA - Vyzhva, Z.; Demidov, V.; Vyzhva, A. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
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. Іt 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.