S U M M A R Y This paper gives a new method for automatic calculation of K-indices by computer. The general philosophy of the method is the simulation of the hand-scaling procedure. The simple theory, based on the least-squares method with additional limitation of the second derivatives, is outlined. The method has two steps; in the second step the weighting factors are introduced to avoid errors connected with large variations. We call this method the Adaptive Smoothing (AS). The method was applied to data from three observatories, Belsk, Nurmijarvi and Sodankyla, for the period 1985 January 1 to 1986 February 28. The agreement with results from the hand-scaled method was 75-84 per cent. The percentage of the differences larger than one unit was less than 0.3 per cent.

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SUMMARY Infinite 2‐D splines of separated variables are a convenient tool to be used for approximation over a rectangle at the Earth’s surface of geomagnetic field components and transfer functions obtained from measurement data in unevenly distributed nodes. The spline approximation derived in this manner makes it possible to numerically calculate 2‐D Hilbert transforms and hence to reconstruct the magnetic tensor from tippers (induction vectors) by solving a large system of linear equations. The proposed method was tested on synthetic data and applied to the Carpathian region with the use of archival induction vectors collection.