Geomagnetic field value calculation in Gauss-Kruger projection associated coordinate system

Modern high-sensitive magnetometers that widely used now in geophysical investigations mainly measure absolute value of full vector of the geomagnetic field. It is the sum of a constant Earth’s magnetic field, the field variations and anomalous field, which is the subject of study. For the geomagnetic field mapping and the correct interpretation of the survey results, it is necessary to calculate the anomalous field. Reference value of the Earth's magnetic field at each point is assumed to be equal to the partial sum of the spherical functions series in the geocentric coordinate system. In computer modelling programs object’s coordinates conveniently represented in the generally accepted rectangular coordinates system, in Russia it is the Gauss-Kruger projection, abroad - Universal Transverse Mercator (UTM). There is a problem of the proper calculation of the Earth’s main magnetic field components in Cartesian coordinates in a given projection such as Gauss-Kruger. The initial data are the survey points coordinates that are determined in different reference ellipsoids, for example, in Krasovsky ellipsoid. We have analyzed and developed an algorithm and a computing program in MATLAB for solving this problem.