Spherical harmonics expansion is then made in SM coordinates up to degree 2 for the ring current, in Geocentric Solar Magnetospheric (GSM) coordinates up to degree 2 and order 0 for magnetopause and magnetotail currents (Olsen et al. 2014).
Regarding the external field, we represent the near magnetospheric sources, e.g. magnetospheric ring current, by a spherical harmonic expansion in solar magnetic (SM) coordinates (up to n=2, with a special treatment of the n=1 terms).
Large-scale external (magnetospheric) sources are parameterized in a manner similar to the CHAOS-2 model, with an expansion of the remote magnetospheric sources (magnetotail and magnetopause) in Geocentric Solar Magnetospheric (GSM) coordinates (up to n = 2) and of near magnetospheric sources (magnetospheric ring current) in the Solar Magnetic (SM) coordinate system (also up to n = 2).
This involves expanding mapped BAC coordinates up to approximately 165kb, which is our observation of the median size of BACs where both end sequences have been mapped.
Assume that at some stage of the transmission Bob has received Cα coordinates up to an intermediate point p i, that is he has received coordinates (p1, p2,···, p i ) (i< n).
In the tests reported in Section 3, the ionospheric field was modelled in quasi-dipole coordinates up to degree Kmax = 45 and order Lmax = 5 (hence N q = 475 coefficients), with diurnal variations from p min = 0 to pmax = 4 (i.e., down to a period of 6 hours) and seasonal variations from s min = −2 to s max = 2 (i.e., constant, annual and semi-annual variation).
As the location of maximum activation may also vary between sessions (i.e. ON/OFF), a dispersion of coordinates up to 4 mm, equivalent to the radius of the extracted sphere, was allowed between sessions to ensure within-subject consistency of anatomical areas in patients.
The parameterization of external magnetic field contributions is also similar to that of our previous models, with an expansion of near magnetospheric sources in the Solar Magnetic (SM) coordinate system (up to (n=2), with special treatment of the (n=1) terms) and of remote magnetospheric sources in Geocentric Solar Magnetospheric (GSM) coordinates (also up to (n=2), but restricted to order (m=0)).
Hourly mean time series of external SHE coefficients in a geomagnetic dipole coordinate system (up to degree 3 and order 1) have been derived by analysis of 4.5 years of observatory data (July 1998-December 2002), details of the derivation are given in Olsen et al. (2005).
Hourly mean time series of external coefficients in a geomagnetic dipole coordinate system (up to degree n = 3 and order m = 1) have been obtained by analysis of 4.5 years of observatory data (July 1998 December 2002), details of the derivation are given in Olsen et al. (2006).
