Modeling of regional magnetic field applying spherical functions: practical aspect


  • Yu. P. Sumaruk Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine, Ukraine
  • L. M. Yankiv-Vitkovska Lviv Polytechnic National University, Ukraine
  • B. B. Dzuman Lviv Polytechnic National University, Ukraine



regional magnetic field, spherical functions, modeling


Modeling of geomagnetic field and creation of geomagnetic maps is one of the main directions of geomagnetic studies. For constructing global model the global spherical Lejeandre functions are used in most cases, though for constructing regional magnetic field it is impossible to use such an approach, because in this case spherical Lejeandre functions lose their orthogonality, and the solution becomes ambiguous. In this work we tested a method of constructing regional magnetic field applying spherical Lejeandre functions of effective order and integral power. Such functions generate a system of functions orthogonal by weight on an arbitrary spheric trapezium, though they lack recurrent correlations, that is why for their calculation we have to apply an expansion in hypergeometric series. An area of determination of such functions in spherical coordinate system is a spherical segment. As initial data measurements of geomagnetic field components Bx, By, Bz from nine geomagnetic observatories situated in the Central Europe by 2010-s were used. There are both regional and local components in this area, though anomalous field here is of weak intensity, therefore we may consider it in the first approximation as a regional one. Regional modeling of geomagnetic field was conducted within the limits of a procedure «Extraction-Calculation-Reconstruction». With this purpose we need first of all to calculate a systematic component of components using the global model. As a systematic component we used a global model International Geomagnetic Reference Field (IGRF) for this epoch. Abnormal values of geomagnetic field components ΔBx, ΔBy, ΔBz were calculated and unknown coefficients of the model were found by the method of the least squares. For stabilization of solution a regularization Tikhonov parameter was introduced. Dispersion of the model obtained was also calculated. Standard deviations of anomalous values of geomagnetic field components, their model values and difference between them have been given. Estimation of precision of the model obtained has been undertaken.


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How to Cite

Sumaruk, Y. P., Yankiv-Vitkovska, L. M., & Dzuman, B. B. (2019). Modeling of regional magnetic field applying spherical functions: practical aspect. Geofizicheskiy Zhurnal, 41(6), 165–172.