# Interpretation of ground magnetic field

### Theory: Gauss (Chapman/Bartels):
Establish theoretical limitations
- Ground magnetic fields (curl(B) =0) can **not** be exactly modeled in terms of 2D currents at some radius below or above (*equivalent*) -- $B_r$ or $B_{horizontal}$ can be modeled independently as either completely internal or completely external
- With perfect coverage, and measurements of Br, external and internal sources can be separated
- This is regardless of the actual 3D structure of the currents below and above. And (I think!) ground magnetic fields are not sufficient to say anything about the 3D structures regardless of how perfect the coverage is
- Limitations
- Distribution of data (Thebault 2006)
- Maybe also something about structure: What are the limitations in resolving structures in the equivalent current with ground mags, given the distance (and realistic distribution)
- Hall and Pedersen currents != equivalent current. Fukushima theorem, effect of inclined field lines.
- Induction electric field

#### notes
- baseline subtraction
- ionosphere / magnetosphere separation

### Ideal example: Simulation of 3D current in space + 3D induced current in ground
- Model as 2D currents as discussed above
- Review of methods sfor internal/external separation
1. Ignore
2. Separation based on $B_r$ and horizontal
3. Mirror current approach
4. Nice transfer functions

- Demonstrate on the ideal example
- Hall / Pedersen

### Adding information beyond ground mags:
- 2D ionospheric conductance *and* wind -> Model the simulated current
- KRM / AMIE / ... (but this assumes internal / external separation is correct)
- Hall / Pedersen (**Michael**)
- ground conductivity
- ?
- 3D ionospheric conductivity - what are some examples where this is done?

## What kind of driver do we want in a simulation?
- What is the input in the inductino model that Alexander needs from the ionospheric simulation? 2D vector field on sphere ($R_0, \theta, \phi$)
- Simon's substorm current wedge varying in time as a Gaussian, since fourier transform of Gaussian is Gaussian
- The input should have also other scales present than the large-scale substorm current wedge. One of the questions we want to address is 2hat scales we can resolve
- Time resolution: 10 seconds?
- Jone will suggest some patterns for driving, and then we discuss

#### Other complications
- Satellite data:
- FACs
- Separate between magnetospheric and ionospheric sources not possible without satellite data

## Potential Relevant Publications

Thomson, A.W., McKay, A.J. & Viljanen, A. A review of progress in modelling of induced geoelectric and geomagnetic fields with special regard to induced currents. Acta Geophys. 57, 209–219 (2009). https://doi.org/10.2478/s11600-008-0061-7

Juusola, L., Vanhamäki, H., Viljanen, A., and Smirnov, M.: Induced currents due to 3D ground conductivity play a major role in the interpretation of geomagnetic variations, Ann. Geophys., 38, 983–998, https://doi.org/10.5194/angeo-38-983-2020, 2020.

Alekseev, D., Kuvshinov, A. & Palshin, N. Compilation of 3D global conductivity model of the Earth for space weather applications. Earth Planet Sp 67, 108 (2015). https://doi.org/10.1186/s40623-015-0272-5

Pulkkinen, Antti, Amm, Olaf, Viljanen, Ari: Separation of the geomagnetic variation field on the ground into external and internal parts using the spherical elementary current system method. (2003) doi: 10.1186/BF03351739

Sabaka, Hulot, Olsen - Mathematical Properties Relevant to Geomagnetic Field Modeling(2010)

Stavros Dimitrakoudis, David K. Milling, Andy Kale, Ian R. Mann: Sensitivity of Ground Magnetometer Array Elements for GIC Applications I: Resolving Spatial Scales With the BEAR and CARISMA Arrays. (2021) https://doi.org/10.1029/2021SW002919