A simple approach to the transformation of spherical harmonic models under coordinate system rotation

Santis, Angelo De; Torta, J. M.; Falcone, C.

doi:10.1111/j.1365-246x.1996.tb05284.x

Cited by 13 publications

(9 citation statements)

References 21 publications

(29 reference statements)

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“…Prior to being processed, all the data are rotated from the geocentric reference to the cone reference frame centered on the geocentric coordinates(Φ, Θ) (see Figure 1). Rotation formula are derived from standard spherical trigonometry and are given by De Santis et al [1996].…”

Section: Inverse Problemmentioning

confidence: 99%

Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R‐SCHA)

Thébault

Mandéa

Schott³

2006

J. Geophys. Res.

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[1] We have recently proposed the revised spherical cap harmonic analysis (R-SCHA) modeling technique. The new mathematical functions represent faithfully the spatial variations of potential fields in a restricted area. In this paper, we tackle the inverse problem and outline the efficiency of the new basis functions with respect to real magnetic data. Processing simultaneously repeat stations, observatory, aeromagnetic, and CHAMP satellite data provides our first vector lithospheric field model over France, which extends from surface to 500 km of altitude. The magnetic field is represented with a minimum horizontal spatial representation of 40 km at the mean Earth radius. The magnetic lithospheric map consistency is confirmed with a comparison to known geological features. The model variation with altitude also suggests that the major French magnetic anomaly, the Paris basin anomaly, is produced by a deep-rooted geological structure. These results demonstrate the superiority of regional modeling over global modeling for delineating small-scale details in the lithospheric field. In view of forthcoming satellite missions, like Swarm, the revised spherical cap harmonic analysis method will help to accurately represent the lithospheric field for more detailed geological interpretations.

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Section: Inverse Problemmentioning

confidence: 99%

Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R‐SCHA)

Thébault

Mandéa

Schott³

2006

J. Geophys. Res.

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“…To determine realistic a and d values a rotation of coordinates would be necessary (e.g. De Santis, Torta & Falcone 1996). All the above-mentioned inconveniences appear simultaneously when one applies SCHA with a specific rotation to the Sq field: spreading of the principal harmonic contribution, with the subsequent disappearance of harmonics significant enough to provide significant conductivity estimates; use of inherently rapidly varying spherical cap harmonics if the cap is small; and lack of complete (surface) knowledge of the variation field.…”

Section: Case With Rotation Of Coordinatesmentioning

confidence: 99%

On the derivation of the Earth's conductivity structure by means of spherical cap harmonic analysis

Torta

Santis

1996

Geophysical Journal International

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After Haines & Torta (1994) applied spherical cap harmonic analysis (SCHA) to deduce the formulation of equivalent currents in terms of spherical cap harmonic coefficients, it seemed appropriate to extend the same scheme that relates global spherical harmonics with the Earth's conductivity structure to regional modelling of geomagnetic-field variations. From the considerations made in this paper it seems difficult or even impossible to obtain either a conductivity-depth profile (by assuming a homogeneous mantle conductivity within the region) or a 3-D structure, from a regional analysis of global-scale phenomena such as the regular daily variation, by using the same formulations as employed in global analyses. There exist, in addition, some intrinsic limits of SCHA itself, which, although in general do not decrease its potential in regional geomagnetic modelling, can affect the derivation of a proper conductivity estimation.

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“…Before model inversion, the geographical coordinates

{false(φ, θ, r false)}_{S}

and geomagnetic component

{false(N, E, U false)}_{S}

of the observation data must be transformed from the spherical coordinate reference frame to the cone coordinate reference frame [45], as shown in Figure 1.…”

Section: Mathematical Model and Inversion Methodsmentioning

confidence: 99%

Combining CHAMP and Swarm Satellite Data to Invert the Lithospheric Magnetic Field in the Tibetan Plateau

Yaodong

Wang

Jiang

et al. 2017

Sensors

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CHAMP and Swarm satellite magnetic data are combined to establish the lithospheric magnetic field over the Tibetan Plateau at satellite altitude by using zonal revised spherical cap harmonic analysis (R-SCHA). These data are integrated with geological structures data to analyze the relationship between magnetic anomaly signals and large-scale geological tectonic over the Tibetan Plateau and to explore the active tectonic region based on the angle of the magnetic anomaly. Results show that the model fitting error is small for a layer 250-500 km high, and the RMSE of the horizontal and radial geomagnetic components is better than 0.3 nT. The proposed model can accurately describe medium-to long-scale lithospheric magnetic anomalies. Analysis indicates that a negative magnetic anomaly in the Tibetan Plateau significantly differs with a positive magnetic anomaly in the surrounding area, and the boundary of the positive and negative regions is generally consistent with the geological tectonic boundary in the plateau region. Significant differences exist between the basement structures of the hinterland of the plateau and the surrounding area. The magnetic anomaly in the Central and Western Tibetan Plateau shows an east-west trend, which is identical to the direction of the geological structures. The magnetic anomaly in the eastern part is arc-shaped and extends along the northeast direction. Its direction is significantly different from the trend of the geological structures. The strongest negative anomaly is located in the Himalaya block, with a central strength of up to −9 nT at a height of 300 km. The presence of a strong negative anomaly implies that the Curie isotherm in this area is relatively shallow and deep geological tectonic activity may exist.

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A simple approach to the transformation of spherical harmonic models under coordinate system rotation

Cited by 13 publications

References 21 publications

Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R‐SCHA)

Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R‐SCHA)

On the derivation of the Earth's conductivity structure by means of spherical cap harmonic analysis

Combining CHAMP and Swarm Satellite Data to Invert the Lithospheric Magnetic Field in the Tibetan Plateau

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