A tomographical method is presented that allows the reconstruction of the structure of soil layers between two boreholes. If the soil is water saturated, the transient field equation for pore water pressure S(x) delta tu(x,t)- Del .(k(x) Del u(x,t))=Q can be used to reconstruct the soil structure from its permeability k(x). The transient potential field u(x, t) is controlled by hydraulic dipoles (point source and point sink). The positions of source and sink are varied over both boreholes. Pore water pressure observations are used as data for the inverse problem. Uniqueness problems are discussed. The forward problem is discretized in a FE algorithm, the inverse problem solved by a standard output least-squares method.
We show the uniqueness of simultaneous determination of spatially dependent electric conductivity and permittivity for an inverse boundary value problem for the linearized Maxwell -Bloch system.
Proton resonance methods base on the analysis of magnetic fields, only. This may explain, why NMR data interpretations in geophysical field tests differ from those of time domain electromagnetic measurements for subsoils with high electrical conductivity. In this paper, a joint interpretation of transient electromagnetic and proton resonance surface data is discussed on the basis of the linearized MaxwellBloch system derived by the authors in earlier paper. Uniqueness of the simultaneous determination of spatially dependent electric conductivity and the initial magnetization is shown for a layered medium.
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