scholarly journals COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Loïc Huder ◽  
Nicolas Gillet ◽  
Christopher C. Finlay ◽  
Magnus D. Hammer ◽  
Hervé Tchoungui
Keyword(s):  
Geomagnetic Field ◽  
Field Model ◽  
Formal Model ◽  
A Priori ◽  
Magnetic Data ◽  
Core Field ◽  
The Core ◽  
Power Spectral ◽  
Ill Posed ◽  
Priori Information

Abstract We present the geomagnetic field model COV-OBS.x2 that covers the period 1840–2020. It is primarily constrained by observatory series, satellite data, plus older surveys. Over the past two decades, we consider annual differences of 4-monthly means at ground-based stations (since 1996), and virtual observatory series derived from magnetic data of the satellite missions CHAMP (over 2001–2010) and Swarm (since 2013). A priori information is needed to complement the constraints carried by geomagnetic records and solve the ill-posed geomagnetic inverse problem. We use for this purpose temporal cross-covariances associated with auto-regressive stochastic processes of order 2, whose parameters are chosen so as to mimic the temporal power spectral density observed in paleomagnetic and observatory series. We aim this way to obtain as far as possible realistic posterior model uncertainties. These can be used to infer for instance the core dynamics through data assimilation algorithms, or an envelope for short-term magnetic field forecasts. We show that because of the projection onto splines, one needs to inflate the formal model error variances at the most recent epochs, in order to account for unmodeled high frequency core field changes. As a by-product of the core field model, we co-estimate the external magnetospheric dipole evolution on periods longer than 2 years. It is efficiently summarized as the sum of a damped oscillator (of period 10.5 years and decay rate 55 years), plus a short-memory (6 years) damped random walk.

Sequential modelling of the Earth magnetic field

2020 ◽  
Author(s):  
Vincent Lesur ◽  
Guillaume Ropp
Keyword(s):  
Geomagnetic Field ◽  
Magnetic Data ◽  
Mathematical Representation ◽  
High Temporal Resolution ◽  
Core Field ◽  
The Core ◽  
Earth Magnetic Field ◽  
Geomagnetic Field Models ◽  
Modelling Techniques ◽  
Derived Series

<p>Geomagnetic field models derived from satellite data cover now more than twenty years and are obtained through the processing and analyses of a massive amount of vector magnetic data. As our understanding of the geomagnetic field progresses, these models have to describe contributions of more and more sources with rather complex mathematical representation. In order to handle this increasing complexity and amount of available data, we use a sequential modelling approach (a Kalman filter), combined with a correlation based modelling step (Holschneider et al; 2016). In order to reach high temporal resolution for the core field, a sequence of snapshot models, 3-months apart, has been built. The main characteristics of the derived series of Gauss coefficients are the same as those of recently released field models based on classic modelling techniques. The results we obtained show the importance of a careful calibration of the Kalman prediction steps as well as applying Kalman smoother at the end of the modelling. We identify also the induced fields as the main limitation for an increase resolution of the core field. We will present how these induced fields have been handle in a recent version of the model and future steps to progress further in the representation of the different sources of the geomagnetic field.</p>

scholarly journals Geomagnetic Virtual Observatories: monitoring geomagnetic secular variation with the Swarm satellites

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Magnus D. Hammer ◽  
Grace A. Cox ◽  
William J. Brown ◽  
Ciarán D. Beggan ◽  
Christopher C. Finlay
Keyword(s):  
Time Series ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Time Windows ◽  
Low Earth Orbit ◽  
Data Selection ◽  
Spherical Harmonic Analysis ◽  
Core Field ◽  
The Core ◽  
Swarm Satellites

AbstractWe present geomagnetic main field and secular variation time series, at 300 equal-area distributed locations and at 490 km altitude, derived from magnetic field measurements collected by the three Swarm satellites. These Geomagnetic Virtual Observatory (GVO) series provide a convenient means to globally monitor and analyze long-term variations of the geomagnetic field from low-Earth orbit. The series are obtained by robust fits of local Cartesian potential field models to along-track and East–West sums and differences of Swarm satellite data collected within a radius of 700 km of the GVO locations during either 1-monthly or 4-monthly time windows. We describe two GVO data products: (1) ‘Observed Field’ GVO time series, where all observed sources contribute to the estimated values, without any data selection or correction, and (2) ‘Core Field’ GVO time series, where additional data selection is carried out, then de-noising schemes and epoch-by-epoch spherical harmonic analysis are applied to reduce contamination by magnetospheric and ionospheric signals. Secular variation series are provided as annual differences of the Core Field GVOs. We present examples of the resulting Swarm GVO series, assessing their quality through comparisons with ground observatories and geomagnetic field models. In benchmark comparisons with six high-quality mid-to-low latitude ground observatories we find the secular variation of the Core Field GVO field intensities, calculated using annual differences, agrees to an rms of 1.8 nT/yr and 1.2 nT/yr for the 1-monthly and 4-monthly versions, respectively. Regular sampling in space and time, and the availability of data error estimates, makes the GVO series well suited for users wishing to perform data assimilation studies of core dynamics, or to study long-period magnetospheric and ionospheric signals and their induced counterparts. The Swarm GVO time series will be regularly updated, approximately every four months, allowing ready access to the latest secular variation data from the Swarm satellites.

scholarly journals Differences Amplitude Based Improvement of Minimum Variance Distortionless Response Filter

2020 ◽  
Vol 8 (5) ◽  
pp. 1635-1637
Keyword(s):  
A Priori ◽  
Minimum Variance ◽  
Coherent Noise ◽  
Noise Interference ◽  
Power Spectral ◽  
Minimum Variance Distortionless Response ◽  
Power Spectral Densities ◽  
Noisy Signals ◽  
A New Technique ◽  
Priori Information

In this work, the author introduces a new technique for improving the performance of minimum variance distortionless response filter in condition of coherent noise. The proposal algorithm exploits a priori information of differences amplitude to balance power spectral densities of observed noisy signals. The output signal of MVDR filter is then processed by an additional post-filtering, which based speech presence probability to suppress more noise interference and increase quality speech. In experiments using two noisy signal recordings in anechoeic room, the modified MVDR-filter results provides that the suggested algorithm increases speech quality compared to the conventional MVDR filter.

An optimal regularization method for convolution equations on the sourcewise represented set

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Ye Zhang ◽  
Dmitry V. Lukyanenko ◽  
Anatoly G. Yagola
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
A Priori ◽  
Noisy Data ◽  
Optimal Recovery ◽  
Multidimensional Case ◽  
A Priori Information ◽  
Ill Posed ◽  
Priori Information ◽  
Convolution Equations

AbstractIn this article, we consider an inverse problem for the integral equation of the convolution type in a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a priori information (sourcewise representation) based on optimal recovery theory we propose a new method. The regularization and optimization properties of this method are proved. An optimal minimal a priori error of the problem is found. Moreover, a so-called optimal regularized approximate solution and its corresponding error estimation are considered. Efficiency and applicability of this method are demonstrated in a numerical example of the image deblurring problem with noisy data.

scholarly journals Iterative Signal Detection Scheme Using Multilayer Perceptron for a Bit-Patterned Media Recording System

2020 ◽  
Vol 10 (24) ◽  
pp. 8819
Author(s):  
Seongkwon Jeong ◽  
Jaejin Lee
Keyword(s):  
Signal Detection ◽  
Data Storage ◽  
Multilayer Perceptron ◽  
A Priori ◽  
Magnetic Data ◽  
Bit Patterned Media ◽  
Detection Scheme ◽  
Patterned Media ◽  
Storage Density ◽  
Priori Information

Because of the physical and engineering problems of conventional magnetic data storage systems, bit-patterned media recording (BPMR) is expected to be a promising technology for extending the storage density to beyond 1 Tb /in2. To increase the storage density in BPMR systems, the separation between islands in both down- and cross-track directions must be reduced; this reduction results in two-dimensional interference from neighboring symbols in those directions, which is a major performance degradation factor in BPMR. Herein, we propose an iterative signal detection scheme between a Viterbi detector and a multilayer perceptron to improve the performance of a BPMR system. In the proposed signal detection scheme, we use the modified output of a multilayer perceptron as a priori information to improve equalization and extrinsic information to decrease the effect of intertrack interference.

Estimation of density, magnetization, and depth to source: A nonlinear and noniterative 3-D potential‐field method

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 814-830 ◽  
Author(s):  
Maurizio Fedi
Keyword(s):  
A Priori ◽  
Real Data ◽  
Field Method ◽  
Magnetic Data ◽  
System Of Equations ◽  
Source Depth ◽  
A Priori Information ◽  
Magnetization Direction ◽  
Priori Information ◽  
Magnetic Case

The depth to the top, or bottom, and the density of a 3-D homogeneous source can be estimated from its gravity or magnetic anomalies by using a priori information on the maximum and minimum source depths. For the magnetic case, the magnetization direction is assumed to be constant and known. The source is assumed to be within a layer of known depth to the top h and thickness t. A depth model, satisfying both the data and the a priori information is found, together with its associated density/magnetization contrast. The methodology first derives, from the measured data, a set of apparent densities [Formula: see text] (or magnetizations), which do not depend on the layer parameters h and t, but only on source thickness. A nonlinear system of equations based on [Formula: see text], with source thicknesses as unknowns, is constructed. To simplify the solution, a more practical system of equations is formed. Each equation depends on only one value of thickness. Solving for the thicknesses, taking into account the above a priori information, the source depth to the top (or to the bottom) is determined uniquely. Finally, the depth solutions allow a unit‐density gravity model to be computed, which is compared to the observed gravity to determine the density contrast. A similar procedure can be used for magnetic data. Tests on synthetic anomalies and on real data demonstrate the good performance of this method.

scholarly journals Retrieval of Canopy component temperatures through Bayesian inversion of directional thermal measurements

2009 ◽  
Vol 6 (2) ◽  
pp. 3007-3040 ◽  
Author(s):  
J. Timmermans ◽  
W. Verhoef ◽  
C. van der Tol ◽  
Z. Su
Keyword(s):  
Sensitivity Analysis ◽  
Surface Temperature ◽  
A Priori ◽  
Inversion Method ◽  
Success Rates ◽  
Brightness Temperatures ◽  
Ill Posed ◽  
Priori Information ◽  
The Individual ◽  
High Level

Abstract. In remote sensing evapotranspiration is estimated using a single surface temperature. This surface temperature is an aggregate over multiple canopy components. The temperature of the individual components can differ significantly, introducing errors in the evapotranspiration estimations. The temperature aggregate has a high level of directionality. An inversion method is presented in this paper to retrieve four canopy component temperatures from directional brightness temperatures. The Bayesian method uses both a priori information and sensor characteristics to solve the ill-posed inversion problem. The method is tested using two case studies: 1) a sensitivity analysis, using a large forward simulated dataset, and 2) in a reality study, using two datasets of two field campaigns. The results of the sensitivity analysis show that the Bayesian approach is able to retrieve the four component temperatures from directional brightness temperatures with good success rates using multi-directional sensors (ℜspectra≈0.3, ℜgonio≈0.3, and ℜAATSR≈0.5), and no improvement using mono-angular sensors (ℜ≈1). The results of the experimental study show that the approach gives good results for high LAI values (RMSEgrass=0.50 K, RMSEwheat=0.29 K, RMSEsugar beet=0.75 K, RMSEbarley=0.67 K), but for low LAI values the measurement setup provides extra disturbances in the directional brightness temperatures, RMSEyoung maize=2.85 K, RMSEmature maize=2.85 K. As these disturbances, were only present for two crops and can be eliminated using masked thermal images the method is considered successful.

scholarly journals A regional geomagnetic field model over Southern Africa derived with harmonic splines from Swarm satellite and ground-based data recorded between 2014 and 2019

2022 ◽  
Vol 74 (1) ◽  
Author(s):  
Emmanuel Nahayo ◽  
Monika Korte
Keyword(s):  
Field Intensity ◽  
Southern Africa ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Field Model ◽  
Radial Component ◽  
The South ◽  
Core Field ◽  
Swarm Satellite ◽  
Magnetic Observatories

AbstractA regional harmonic spline geomagnetic main field model, Southern Africa Core Field Model (SACFM-3), is derived from Swarm satellite and ground-based data for the southern African region, in the eastern part of the South Atlantic Anomaly (SAA) where the field intensity continues to decrease. Using SACFM-3 and the global CHAOS-6-×9 model, a detailed study was conducted to shed light on the high spatial and temporal geomagnetic field variations over Southern Africa between 2014 and 2019. The results show a steady decrease of the radial component Z in almost the entire region. In 2019, its rate of decrease in the western part of the region has reached high values, 76 nT/year and 78 nT/year at Tsumeb and Keetmanshoop magnetic observatories, respectively. For some areas in the western part of the region the radial component Z and field intensity F have decreased in strength, from 1.0 to 1.3% and from 0.9 to 1.2%, respectively, between the epochs 2014.5 and 2019.5. There is a noticeable decrease of the field intensity from the south-western coast of South Africa expanding towards the north and eastern regions. The results show that the SAA area is continuing to grow in the region. Abrupt changes in the linear secular variation in 2016 and 2017 are confirmed in the region using ground-based data, and the X component shows an abrupt change in the secular variation in 2018 at four magnetic observatories (Hermanus, Hartebeesthoek, Tsumeb and Keetmanshoop) that needs further investigation. The regional model SACFM-3 reflects to some extent these fast core field variations in the Z component at Hermanus, Hartebeesthoek and Keetmanshoop observatories. Graphical Abstract

scholarly journals Retrieval of canopy component temperatures through Bayesian inversion of directional thermal measurements

2009 ◽  
Vol 13 (7) ◽  
pp. 1249-1260 ◽  
Author(s):  
J. Timmermans ◽  
W. Verhoef ◽  
C. van der Tol ◽  
Z. Su
Keyword(s):  
Sensitivity Analysis ◽  
A Priori ◽  
Inversion Method ◽  
Success Rates ◽  
Brightness Temperatures ◽  
Single Temperature ◽  
Ill Posed ◽  
Priori Information ◽  
The Individual ◽  
High Level

Abstract. Evapotranspiration is usually estimated in remote sensing from single temperature value representing both soil and vegetation. This surface temperature is an aggregate over multiple canopy components. The temperature of the individual components can differ significantly, introducing errors in the evapotranspiration estimations. The temperature aggregate has a high level of directionality. An inversion method is presented in this paper to retrieve four canopy component temperatures from directional brightness temperatures. The Bayesian method uses both a priori information and sensor characteristics to solve the ill-posed inversion problem. The method is tested using two case studies: 1) a sensitivity analysis, using a large forward simulated dataset, and 2) in a reality study, using two datasets of two field campaigns. The results of the sensitivity analysis show that the Bayesian approach is able to retrieve the four component temperatures from directional brightness temperatures with good success rates using multi-directional sensors (Srspectra≈0.3, Srgonio≈0.3, and SrAATSR≈0.5), and no improvement using mono-angular sensors (Sr≈1). The results of the experimental study show that the approach gives good results for high LAI values (RMSEgrass=0.50 K, RMSEwheat=0.29 K, RMSEsugar beet=0.75 K, RMSEbarley=0.67 K); but for low LAI values the results were unsatisfactory (RMSEyoung maize=2.85 K). This discrepancy was found to originate from the presence of the metallic construction of the setup. As these disturbances, were only present for two crops and were not present in the sensitivity analysis, which had a low LAI, it is concluded that using masked thermal images will eliminate this discrepancy.

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