Fabrizio Donzelli

Fabrizio Donzelli, Martin J. Gander, Ronald D. Haynes

The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We propose a classical Schwarz method for solving this magnetotelluric approximation of the Maxwell equations, and prove its convergence using maximum principle techniques. This is not trivial, since solutions are complex valued, and we need a new result that the magnetotelluric approximations satisfy a maximum modulus principle for our proof. We illustrate our analysis with numerical experiments.

Fabrizio Donzelli, Alexander Bihlo, Mauricio Kischinhevsky et al.

In this paper, we report the advantages of using a stochastic algorithm in the context of mineral exploration based on gravity measurements. This approach has the advantage over deterministic methods in that it allows one to find the solution of the Poisson equation in specified, isolated points without the need of meshing the computational domain and solving the Poisson equation over the entire domain. Moreover, the stochastic approach is embarrassingly parallelizable and therefore suitable for an implementation on multi-core compute clusters with or without GPUs. Benchmark tests are carried out that show that the stochastic approach can yield accurate results for both the gravitational potential and the gravitational acceleration and could hence provide an alternative to existing deterministic methods used in mineral exploration.