# Processing Non-Gaussian Data Residuals in Geomagnetism

^{1}

^{2}

## Abstract

**:**

## Featured Application

**A possible application of the data processing method described below is to separate noise due to external effects from noise due to the limited accuracy of the sensor itself. Such a model may reveal the need for a calibration process and impose some statistical constraints on external effects.**

## Abstract

**2017**, 209, 1036–1047.

## 1. Introduction

## 2. Mixture Model

#### 2.1. The Unformal Interpretation

#### 2.2. Version of the General Formula

#### 2.3. Sequential Small Mixtures

## 3. Method: Real Data Analysis

- $S{T}_{1}$: Satellite A ${\sigma}_{1}=2.41$${s}_{1}=0.33$, Satellite B ${\sigma}_{1}=2.40$${s}_{1}=0.36$
- $S{T}_{0.75}$: Satellite A ${\sigma}_{0.75}=2.34$${s}_{0.75}=0.36$, Satellite B ${\sigma}_{0.75}=2.35$${s}_{0.75}=0.39$
- $S{T}_{0.5}$: Satellite A ${\sigma}_{0.5}=2.22$${s}_{0.5}=0.39$, Satellite B ${\sigma}_{0.5}=2.21$${s}_{0.5}=0.46$
- $S{T}_{0.25}$: Satellite A ${\sigma}_{0.25}=1.99$${s}_{0.25}=0.43$, Satellite B ${\sigma}_{0.25}=1.96$${s}_{0.25}=0.49$

## 4. Discussion

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Khokhlov, A.; Hulot, G. On the cause of the non-Gaussian distribution of residuals in geomagnetism. Geophys. J. Int.
**2017**, 209, 1036–1047. [Google Scholar] [CrossRef] - Jackson, A.; Jonkers, A.R.T.; Walker, M.R. Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. Lond. A
**2000**, 358, 957–990. [Google Scholar] [CrossRef] - Panovska, S.; Finlay, C.C.; Donadini, F.; Hirt, A. Spline analysis of Holocene sediment magnetic records: Uncertainty estimates for field modeling. JGR Solid Earth
**2012**, 117, B02101. [Google Scholar] [CrossRef] - Panovska, S.; Korte, M.; Finlay, C.C.; Constable, C.G. Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models. Geophys. J. Int.
**2015**, 202, 402–418. [Google Scholar] [CrossRef] - Walker, M.R.; Jackson, A. Robust modelling of the Earth’s magnetic field. Geophys. J. Int.
**2000**, 143, 799–808. [Google Scholar] [CrossRef][Green Version] - Feller, W. An Introduction to Probability Theory and Its Applications, 3rd ed.; Wiley: New York, NY, USA, 1971; Volume 2. [Google Scholar]
- Vigneron, P.; Hulot, G.; Olsen, N.; Léger, J.M.; Jager, T.; Brocco, L.; Sirol, O.; Coïsson, P.; Lalanne, X.; Chulliat, A.; et al. A 2015 International Geomagnetic Reference Field (IGRF) Candidate Model Based on Swarms Experimental Absolute Magnetometer Vector Mode Data. Earth Planets Space
**2015**, 67, 95. [Google Scholar] [CrossRef][Green Version] - Fratter, I.; Léger, J.M.; Bertrand, F.; Jager, T.; Hulot, G.; Brocco, L.; Vigneron, P. Swarm Absolute Scalar Magnetometers first in-orbit results. Acta Astronaut.
**2016**, 121, 76–87. [Google Scholar] [CrossRef] - Léger, J.M.; Jager, T.; Bertrand, F.; Hulot, G.; Brocco, L.; Vigneron, P.; Lalanne, X.; Chulliat, A.; Fratter, I. In-flight performances of the absolute scalar magnetometer vector mode on board the Swarm satellites. Earth Planets Space
**2015**, 67, 57. [Google Scholar] [CrossRef][Green Version] - Olsen, N.; Hulot, G.; Lesur, V.; Finlay, C.C.; Beggan, C.; Chulliat, A.; Sabaka, T.J.; Floberghagen, R.; Friis-Christensen, E.; Haagmans, R.; et al. The Swarm Initial Field Model for the 2014 geomagnetic field. Geophys. Res. Lett.
**2015**, 42, 1092–1098. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Standard deviations (in nT) computed every day for the mid-latitude residuals of the Swarm scalar data used to compute the VFM model of Vigneron et al. (2015). Blue large dots: data from the Swarm Alpha satellite and red dots: data from the Swarm Bravo satellite. Days are counted in Julian days, with 1 January 2000 taken as the reference.

**Figure 2.**Left: Histogram of the residuals (circles) of the Swarm Alpha scalar data used to compute the VFM model [7] together with histogram (triangles) of an identical number of simulated mixture of Gaussian distributions according to the parameters $s=0.41$, $\sigma =2.18$ recovered from the real data; right: the same plots but for the Swarm Bravo scalar data, parameters $s=0.47$ and $\sigma =2.10$.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Khokhlov, A. Processing Non-Gaussian Data Residuals in Geomagnetism. *Appl. Sci.* **2022**, *12*, 2097.
https://doi.org/10.3390/app12042097

**AMA Style**

Khokhlov A. Processing Non-Gaussian Data Residuals in Geomagnetism. *Applied Sciences*. 2022; 12(4):2097.
https://doi.org/10.3390/app12042097

**Chicago/Turabian Style**

Khokhlov, Andrey. 2022. "Processing Non-Gaussian Data Residuals in Geomagnetism" *Applied Sciences* 12, no. 4: 2097.
https://doi.org/10.3390/app12042097