Spherical Harmonic Series Solution for SLF/ELF Field in the Earth–Ionosphere Waveguide/Cavity

SUMMARY An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high-degree (>720) solid spherical harmonics at many scattered points in the space above the surface of the Earth. The algorithm is based on representation of the geomagnetic field elements in solid ellipsoidal harmonics and application of tensor product needlets. Open source FORTRAN and MATLAB realizations of this algorithm that rely on data from the Enhanced Magnetic Models 2015, 2017 (EMM2015, EMM2017) have been developed and extensively tested. The capabilities of the software are demonstrated on the example of the north, east and down components of the geomagnetic field as well as the derived horizontal intensity, total intensity, inclination and declination. For the range from −417 m under the Earth reference ellipsoid up to 1000 km above it the FORTRAN and MATLAB versions of the software run 465 and 189 times faster than the respective FORTRAN and MATLAB versions of the software using the standard spherical harmonic series method, while the accuracy is less than 1 nT and the memory (RAM) usage is 9 GB.

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A numerical study of the divergence of spherical harmonic series of the gravity and height anomalies at the earth's surface

Bulletin Géodésique ◽

10.1007/bf02520909 ◽

1983 ◽

Vol 57 (1-4) ◽

pp. 10-28 ◽

Cited By ~ 18

Author(s):

Christopher Jekeli

Keyword(s):

Spherical Harmonic ◽

Numerical Study ◽

Harmonic Series ◽

Spherical Harmonic Series

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Explicit Construction of the Modified Spherical Harmonic Series for the Gravity Gradients and Analysis of their Characteristics

Artificial Satellites ◽

10.2478/v10018-009-0001-z ◽

2007 ◽

Vol 42 (4) ◽

pp. 185-214

Author(s):

M. Petrovskaya ◽

A. Vershkov

Keyword(s):

Spherical Harmonic ◽

Orthogonal Series ◽

Explicit Construction ◽

Anomalous Behavior ◽

Harmonic Series ◽

Geopotential Model ◽

Orthogonal Expansion ◽

Gravity Gradients ◽

Spherical Harmonic Series ◽

Degree Variances

Explicit Construction of the Modified Spherical Harmonic Series for the Gravity Gradients and Analysis of their CharacteristicsThe present paper complements the research carried out in PV2008 (Petrovskaya and Vershkov, 2008), concerning the expansion of the gravity gradients in the local north-oriented reference frame in orthogonal series of modified spherical harmonics. In PV2008 procedures are developed for recovering the orthogonal bases of these series. Then an idea is briefly described how the spectral relations can be obtained between the gravity gradients and the geopotential. However no explicit procedures are demonstrated for their derivation. In the present paper successive transformations are described for each derivative which convert the initial non-orthogonal expansion into the orthogonal series. The resulting spectral relations are applied for evaluating the harmonic coefficients of these series at different altitudes, on the basis of the geopotential model EGM2008. The corresponding degree variances are estimated. The new simple expressions for the gravity gradients are convenient for various applications. In the present paper they are implemented for constructing digital colored maps for Fennoscandia region which attracts much attention of geophysicists. These maps visually demonstrate an anomalous behavior of the gravity gradients in this area.

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