Inverse Problems

Constructing computational models of the Earth from noisy and incomplete data, and quantifying their associated uncertainty, is at the heart of modern geophysics.  Geomagnetism has long been a fruitful source of ideas in this regard, and this continues to be the case today with the challenge of exploiting huge satellite datasets using our ever increasing computational resources. I am working on a number of new inversion schemes in this area.

  • Together with PhD student Magnus Hammer (DTU Space) I have developed a modified Backus-Gilbert inversion scheme for constructing local averages of the core-mantle boundary (CMB) magnetic field, from satellite magnetic measurements.  This technique provides a useful alternative to global spherical harmonic models and directly provides information on the resolution and variances of the CMB field estimates.  We have studied the field, secular variation and accumulated secular acceleration over a variety of time windows using this method.

An example of a collection of localized estimates of the radial field acceleration at the core-mantle boundary in 2016, constructed using a two year time window:

Hammer, M. D., Finlay, C.C. (2019) Local averages of the core–mantle boundary magnetic field from satellite observations, Geophys. J. Int., Vol 216, 1901-1918

  • Together with Kathy Whaler (Edinburgh) I am working on core flow inversions from ground and satellite observations, seeking minimum norm solutions requiring minimal time-dependence and large-scale flow structures.  We are particularly interested in the resolution of the core flows and how this has improved using satellite data from the Swarm mission.

Whaler, K. A., Olsen, N., and Finlay, C.C. (2016) Decadal variability in core surface flows deduced from geomagnetic observatory monthly means,  Geophys. J. Int., Vol 207, 228-243, doi: 10.1093/gji/ggw268

  • In collaboration with Nils Olsen (DTU Space) and Andy Jackson (ETH Zurich), I am working on new methods of constructing maximum entropy regularized models of the lithospheric magnetic field, based spatial gradients of satellite magnetic field measurements.

Olsen, N., Ravat, D., Finlay, C.C., and Kother, L.K. (2017) LCS-1: a high-resolution global model of the lithospheric magnetic field derived from CHAMP and Swarm satellite observations, Geophys. J. Int., Vol 221, Pages 1461–1477, doi:10.1093/gji/ggx381.

Kother, L., Hammer, M.D., Finlay, C.C. and Olsen, N. (2015) An equivalent source method for modelling the global lithospheric magnetic field, Geophys. J., Int., Vol 203, 553-566,  doi: 10.1093/gji/ggv317

Stockmann, R., Finlay, C.C. and Jackson, A. (2009) Imaging Earth's crustal magnetic field with satellite data: a regularized spherical triangle tessellation approach, Geophys. J. Int. , 179, 929-944.