Modelling by Spherical Cap Harmonic Analysis: A Literature Review

Torta, J. M.

doi:10.1007/s10712-019-09576-2

Cited by 26 publications

(17 citation statements)

References 133 publications

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“…The SCHA method is selected as the sampling method from the mathematical method group (SCHA, R-SCHA, and R-SCHA2D). SCHA is chosen because it has been used often by researchers in recent decades (Torta, 2020). The potential field equation V in the SCHA is the following:…”

Section: Methodsmentioning

confidence: 99%

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How Accurate Geomagnetic Regional Modeling Using Ordinary Kriging For Clustered Distributed Data?: New Insight From Indonesian Archipelago

Syirojudin

Haryono

Ahadi

2021

Preprint

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Indonesia relies only on the limited number of repeat station networks due to the archipelago setting with the extensive sea with the clustery distributed pattern. This paper explored geostatistical modeling to overcome that typical data characteristic. The modeling used repeat station data from the 1985 to 2015 epoch. The research used ordinary kriging (OK) compared to the Spherical Cap Harmonic Analysis (SCHA) and Polynomial. The results show that the root means square error (RMSE) of each declination, inclination, and total intensity vary among epochs. OK method for declination component produces smaller average RMSE (7.67 minutes) than SCHA (9.26 minutes) and Polynomial (7.97minutes). For the inclination component, OK has an average RMSE of 9.55 minutes, smaller than SCHA (10.05) but slightly higher than Polynomial (9.36 minutes). For the total intensity component, OK produce an average RMSE of 63.58 nT, smaller than SCHA (82.24 nT) and Polynomial (68.97 nT). The finding shows that the kriging method can be a promising method to model the regional geomagnetic field, especially in the area of limited available data and clustered distributed data.

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Section: Methodsmentioning

confidence: 99%

“…The boundary effect of the existing method is also affected by the data configuration. Numerical instability due to wide data gaps resulting from sparse data patterns needs to be balanced with statistical or physical regulation to increase model reliability (Torta, 2020).…”

Section: Introductionmentioning

confidence: 99%

How Accurate Geomagnetic Regional Modeling Using Ordinary Kriging For Clustered Distributed Data?: New Insight From Indonesian Archipelago

Syirojudin

Haryono

Ahadi

2021

Preprint

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“…Regional geomagnetic modelling is principally used when measurements are restricted to a localised region or when high spatial frequency fields with much fewer parameters are required (Torta, 2019). Spherical Cap Harmonic Analysis (SCHA) was developed by Haines (1985a) to model the field over a small portion of the globe.…”

Section: Spherical Cap Harmonic Analysis (Scha)mentioning

confidence: 99%

“…In SCHA, the boundary conditions must be applied to the edge of the cap in order to solve Laplace's equation for the scalar magnetic potential. The boundary conditions require the continuity of the potential in longitude and regularity at the spherical cap pole (Torta, 2019). In the SCHA model, the scalar magnetic potential at 0 or at the edge of the spherical cap and its derivative in accordance with must be arbitrary…”

Section: Spherical Cap Harmonic Analysis (Scha)mentioning

confidence: 99%

“…This is because a high degree expansion is needed in order to include large wavelengths over a small-cap and can cause a problem if not enough data are available (Verbanac, 2007). As a rule, the cap region must be at least coincident with the spatial content of the features of the field being represented (Torta, 2019). This problem has been solved by Torta et al (1992) by increasing the cap half-angle to extend the wavelength content of the basis functions artificially.…”

Section: Spherical Cap Harmonic Analysis (Scha)mentioning

confidence: 99%

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Investigation of Regional Geomagnetic Field Modelling in Indonesia

Setiawan¹

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<p>This thesis deals with the application of the Spherical Cap Harmonic Analysis (SCHA) modelling technique to obtain geomagnetic field models for Indonesia, which have better resolution and accuracy than the International Geomagnetic Reference Field (IGRF). B-splines basis function and autoregressive forecasting are applied to improve estimates of secular variation and its forecast over the Indonesian region. The modelling technique is applied to geomagnetic observation data compiled from 68 geomagnetic repeat stations in Indonesia covering the period 1985 - 2015 from BMKG (Badan Meteorologi Klimatologi dan Geofisika / Agency for Meteorology, Climatology, and Geophysics) Indonesia, definitive data from five BMKG geomagnetic observatories and 13 INTERMAGNET (The International Real-Time Magnetic Observatory Network) observatories. Synthetic cartesian X, Y, and Z components at sea level at 17 fixed locations, calculated from IGRF-13, are also used. The area covered by the models in this thesis is the Indonesian region with a spherical cap half-angle of 30° and with the coordinate of the spherical cap pole at 122°E and 3°S. From statistical analysis and comparison with the IGRF, the SCHA model with index k = 7 is considered as the best SCHA model, both in resolution and accuracy. Compared with the root mean square deviation (RMSD) of the IGRF model, the RMSD of the SCHA model with index k = 7 is lower by 28 nT, 11 nT, and 34 nT for X, Y, and Z components, respectively. A model from interpolation of the SCHA with index k = 7 using the B-splines basis function for the year 1985.5 – 2015.5 shows that the SCHA model gives better results than the IGRF. The forecasting calculation for the year 2015.5 – 2020.5 suggests that the autoregressive order 3 of the SCHA with index k = 7 gives better results than the forecasting of the IGRF model, especially in the X, Z, and F components. However, in the Y component, the IGRF is still better than the SCHA model. The RMSD of the forecasted SCHA model is 154.92 nT, 200.87 nT, 104.39 nT, and 135.81 nT for X, Y, Z, and F components, respectively, while the RMSD of the IGRF model is 172.62 nT, 95.52 nT, 117.55 nT, and 162.38 nT for X, Y, Z, and F components. Thus, the forecasted SCHA model is suitable for data reduction of geomagnetic surveys in the Indonesian region but not preferable for navigation.</p>

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Mathematical Models of the EMF

Гвишиани

Soloviev

2020

Observations, Modeling and Systems Analysis in Geomagnetic Data Interpretation

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Modelling by Spherical Cap Harmonic Analysis: A Literature Review

Cited by 26 publications

References 133 publications

How Accurate Geomagnetic Regional Modeling Using Ordinary Kriging For Clustered Distributed Data?: New Insight From Indonesian Archipelago

How Accurate Geomagnetic Regional Modeling Using Ordinary Kriging For Clustered Distributed Data?: New Insight From Indonesian Archipelago

Investigation of Regional Geomagnetic Field Modelling in Indonesia

Mathematical Models of the EMF

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