Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Zdeněk Martinec
Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin
The adjoint sensitivity method of global electromagnetic induction for CHAMP magnetic data
Martinec and McCreadie (2004) developed a time-domain spectral-finite element approach for the
forward modelling of electromagnetic induction vector data as measured by the CHAMP satellite. Here,
we present a new method of computing the sensitivity of the CHAMP electromagnetic induction data
on the Earth’s mantle electrical conductivity, which we term the adjoint sensitivity method. The forward
and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the
specification of prescribed boundary conditions. The respective boundary-value data at the satellite’s
altitude are the X magnetic component measured by the CHAMP vector magnetometer along satellite
tracks for the forward method and the difference between the measured and predicted Z magnetic
component for the adjoint method. The squares of these differences summed up over all CHAMP tracks
determine the misfit. The sensitivity of the CHAMP data, that is the partial derivatives of the misfit function
with respect to mantle conductivity parameters, are then determined by the scalar product of the forward
and adjoint solutions, multiplied by the gradient of the conductivity and integrated over all CHAMP tracks.
Such exactly determined sensitivities are checked against numerical differentiation of the misfit, and very
good agreement is obtained.
Literatur
Martinec, Z. and McCreadie, H. (2004). Electromagnetic induction modelling based on satellite magnetic
vector data. Geophys. J. Int., 157, 1045 - 1060.
Isabel Ostermann
Fraunhofer ITWM Kaiserslautern
Modeling Heat Transport in Deep Geothermal Systems by Radial Basis Functions
Geothermal power uses the intrinsic heat which is stored in the accessible part of the Earth’s crust. Its
importance among the renewable energy resources originates from the almost unlimited energy supply
of the Earth and its independence from external influences such as seasonal or even daily climatic
variability. Nevertheless, there are risks which have to be assessed. In particular, local depletion poses a
significant risk during the industrial utilization of deep geothermal reservoirs. In order to reduce this risk,
reliable techniques to predict the heat transport and the production temperature are required. To this end,
a 3D-model to simulate the heat transport in hydrothermal systems is developed which is based on a
transient advection-diffusion-equation for a 2-phase porous medium.
The existence, uniqueness, and continuity of the weak solution of the resulting initial boundary value
problem is verified. For the numerical realization, a linear Galerkin scheme is introduced on the basis of
scalar kernels. Exemplary applications of this method are investigated for the biharmonic kernel as well
as appropriate geometric representations of a hydrothermal reservoir. Moreover, numerical integration
methods on geoscientifically relevant bounded regions in 3D are introduced and tested for the considered
geometries.
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