Non-harmonic downward continuation method (NHDC)
Basing on geomagnetic model data sets given for the earth surface, the non-harmonic downward continuation method (NHDC) allows the calculation of the deep earth poloidal magnetic field (f. i. at the core-mantle boundary) which is diffusing up through the electrically conducting mantle (σ(r)≠0). Alternatively, the often used harmonic downward continuation assumes a nonconducting mantle (σ(r)=0).
NHDC procedure steps:
- Maxwell equations (quasi-stationary/pre-Maxwell form with conductivity)
- vectorial induction equation
- poloidal-toroidal decomposition (scalar functions)
- spherical surface harmonics decomposition
- one-side initial-boundary-value problems (parabolic differential equation, two boundary values, temporal instability)
- solution via an equivalent Volterra integral equation by a special regularization variant
... more details:
- Ballani, L.; Greiner-Mai, H; Stromeyer, D. (2002): Determining the magnetic field in the core-mantle-boundary zone by non-harmonic downward continuation. Geophys. J. Int., Vol. 149, 374-389, doi:10.1046/j.1365-246X.2002.01655.x .
- Greiner-Mai, H.; Ballani, L.; Stromeyer, D. (2004): The poloidal geomagnetic field in a differentially rotating upper core layer. Geophys. J. Int., Vol. 158, 864-873, doi:10.1111/j.1365-246X.2004.02343.x .
