## 1 Introduction  
Observations of long-term natural processes, in particular magnetometry, at first sight, fully meet the initial requirements of mathematical statistics and, thus, the methods of this scientific discipline are widely used in data processing. At the same time, the characteristic of deviation (from mean values, baseline, mean scatter of instrument readings, etc. ), which is usually referred to as the residual term, is important enough for estimating the quality of observations. Corresponding statistics are related to the simplest statistical formula, which works fine in theory in the situation of fairness of the Gaussian hypothesis for the recorded data. The same hypothesis, at first sight, should be fulfilled in the situation of vector magnetic measurements because the observed value of the magnetic vector is always a sum of magnetic influences from many local and global sources, and the distribution law for sums of random variables is predicted by the Central Limit Theorem of Probability Theory, which states that under rather simple conditions, the sum of many independent random influences is very well approximated by the Gaussian law. Therefore, it is a common opinion that in processing observational data and calculating the characteristics of these data (for example, calculating the mean value of the residual), we can use Gaussian statistics without any restrictions and there is no reason to doubt the numerical value of the answer, which corresponds to the RMS deviation \(\sigma\) of a Gaussian random variable. However, the stationary nature of natural fluctuations can be assumed only with respect to specific time intervals: magnetic field measurements over a relatively short time can include significant nonstationarity of external factors--seasonal variations, magnetic storms, the presence of specific technological disturbances, etc. Thus, the idea that the observational series is just a sample of the general population corresponding to a fixed Gaussian random variable will generally give a very unrealistic picture. A more adequate model seems to be that of a mixture of random variables differing in parameters, and parameter variations are described by a separate random variable whose value distribution can be neglected only in a stationary situation. Earlier, the general approach was outlined in the article [1] for the example of real magnetic data, referring, however, not to ground-based magnetic observations, but to observations of magnetic satellites of the project Swarm, crossing different intensities of magnetic fields. In this case, in a relatively small time interval, it is possible to collect a lot of data that reflect random field variations, the corresponding data model was substantiated in detail in [1]. In the present article, we will consider the computations and, for the convenience of understanding the statistical model of variability, we will refer to exactly the same data as in [1]. The difference in the method of processing a large volume of SWARM magnetometer data and a large volume of observatory magnetometer data is insignificant for the explanation of the method as such. Recall that typical appropriate statistical assumptions are being made with respect to the distribution of the uncertainties \(\sigma_{i}\) affecting the data used. The statistical properties of these uncertainties, however, are not always well characterized. In such circumstances, assuming that uncertainties follow a Gaussian distribution would a priori make sense, since such a distribution often arises naturally as a consequence of the central limit theorem (i.e., when errors act in an additive manner). Relying on this assumption, and provided that \(s_{i}\) is an adequate measure of the error affecting the datum \(\gamma_{i}\), standard statistical estimations are then used to infer the model.